%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP276^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Feb 28 09:16:16 AM UTC 2026
% Result : ContradictoryAxioms 34.88s 9.15s
% Output : Refutation 34.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 33 ( 14 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 52 ( 5 ~; 0 |; 0 &; 47 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 212 ( 211 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4525 (4522 usr; 73 con; 0-8 aty)
% Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
real: $tType ).
thf(type_def_6,type,
int: $tType ).
thf(type_def_8,type,
set_nat: $tType ).
thf(type_def_9,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(type_def_10,type,
set_Pr4811707699266497531nteger: $tType ).
thf(type_def_11,type,
code_integer: $tType ).
thf(type_def_12,type,
nat: $tType ).
thf(type_def_13,type,
num: $tType ).
thf(type_def_14,type,
rat: $tType ).
thf(type_def_15,type,
set_Pr958786334691620121nt_int: $tType ).
thf(type_def_16,type,
product_prod_nat_nat: $tType ).
thf(type_def_17,type,
product_prod_int_int: $tType ).
thf(type_def_18,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(type_def_19,type,
complex: $tType ).
thf(type_def_20,type,
code_natural: $tType ).
thf(type_def_21,type,
option_num: $tType ).
thf(type_def_22,type,
produc8923325533196201883nteger: $tType ).
thf(type_def_23,type,
set_set_nat: $tType ).
thf(type_def_24,type,
filter_real: $tType ).
thf(type_def_25,type,
extended_enat: $tType ).
thf(type_def_26,type,
option_nat: $tType ).
thf(type_def_27,type,
filter_nat: $tType ).
thf(type_def_28,type,
filter1242075044329608583at_nat: $tType ).
thf(type_def_29,type,
set_o: $tType ).
thf(type_def_30,type,
set_complex: $tType ).
thf(type_def_31,type,
set_int: $tType ).
thf(type_def_32,type,
set_list_o: $tType ).
thf(type_def_33,type,
set_list_complex: $tType ).
thf(type_def_34,type,
set_list_int: $tType ).
thf(type_def_35,type,
set_list_list_nat: $tType ).
thf(type_def_36,type,
set_list_nat: $tType ).
thf(type_def_37,type,
set_list_set_nat: $tType ).
thf(type_def_38,type,
set_list_VEBT_VEBT: $tType ).
thf(type_def_39,type,
set_real: $tType ).
thf(type_def_40,type,
set_VEBT_VEBT: $tType ).
thf(type_def_41,type,
set_num: $tType ).
thf(type_def_42,type,
set_rat: $tType ).
thf(type_def_43,type,
list_nat: $tType ).
thf(type_def_44,type,
sum_sum_nat_nat: $tType ).
thf(type_def_45,type,
set_Sum_sum_nat_nat: $tType ).
thf(type_def_46,type,
char: $tType ).
thf(type_def_47,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(type_def_48,type,
vEBT_VEBT: $tType ).
thf(type_def_49,type,
list_o: $tType ).
thf(type_def_50,type,
list_list_o: $tType ).
thf(type_def_51,type,
list_list_int: $tType ).
thf(type_def_52,type,
list_int: $tType ).
thf(type_def_53,type,
list_list_nat: $tType ).
thf(type_def_54,type,
list_list_VEBT_VEBT: $tType ).
thf(type_def_55,type,
list_VEBT_VEBT: $tType ).
thf(type_def_56,type,
list_complex: $tType ).
thf(type_def_57,type,
list_real: $tType ).
thf(type_def_58,type,
list_set_nat: $tType ).
thf(type_def_59,type,
list_P6011104703257516679at_nat: $tType ).
thf(type_def_60,type,
list_P7333126701944960589_nat_o: $tType ).
thf(type_def_61,type,
list_P3521021558325789923at_int: $tType ).
thf(type_def_62,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(type_def_63,type,
option_o: $tType ).
thf(type_def_64,type,
option_int: $tType ).
thf(type_def_65,type,
list_num: $tType ).
thf(type_def_66,type,
option4927543243414619207at_nat: $tType ).
thf(type_def_67,type,
option_VEBT_VEBT: $tType ).
thf(type_def_68,type,
set_Product_prod_o_o: $tType ).
thf(type_def_69,type,
set_Pr6227168374412355847list_o: $tType ).
thf(type_def_70,type,
set_Pr7565137564259432987nteger: $tType ).
thf(type_def_71,type,
set_Pr765067013931698361st_int: $tType ).
thf(type_def_72,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(type_def_73,type,
set_Pr1542805901266377927at_nat: $tType ).
thf(type_def_74,type,
set_Pr4333006031979791559at_nat: $tType ).
thf(type_def_75,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(type_def_76,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(type_def_77,type,
list_C4705013386053401436er_nat: $tType ).
thf(type_def_78,type,
list_int_nat: $tType ).
thf(type_def_79,type,
list_nat_nat: $tType ).
thf(type_def_80,type,
list_P9162950289778280392at_nat: $tType ).
thf(type_def_81,type,
list_s9130966667114977576at_nat: $tType ).
thf(type_def_82,type,
list_Code_integer: $tType ).
thf(type_def_83,type,
list_P5578671422887162913nteger: $tType ).
thf(type_def_84,type,
list_P5707943133018811711nt_int: $tType ).
thf(type_def_85,type,
produc859450856879609959at_nat: $tType ).
thf(type_def_86,type,
list_P8469869581646625389at_nat: $tType ).
thf(type_def_87,type,
produc3843707927480180839at_nat: $tType ).
thf(type_def_88,type,
list_P5464809261938338413at_nat: $tType ).
thf(type_def_89,type,
list_s1210847774152347623at_nat: $tType ).
thf(type_def_90,type,
set_Code_integer: $tType ).
thf(type_def_91,type,
list_P3924974545808530565omplex: $tType ).
thf(type_def_92,type,
set_Pr5421754520313593387omplex: $tType ).
thf(type_def_93,type,
list_P5232166724548748803o_real: $tType ).
thf(type_def_94,type,
set_Pr6573716822653411497o_real: $tType ).
thf(type_def_95,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(type_def_96,type,
set_Pr7543698050874017315T_VEBT: $tType ).
thf(type_def_97,type,
list_P7942624414058669295plex_o: $tType ).
thf(type_def_98,type,
set_Pr216032351708956309plex_o: $tType ).
thf(type_def_99,type,
list_P7664491975274850627omplex: $tType ).
thf(type_def_100,type,
set_Pr5085853215250843933omplex: $tType ).
thf(type_def_101,type,
list_P2206113689347244737ex_int: $tType ).
thf(type_def_102,type,
set_Pr2254670189886740123ex_int: $tType ).
thf(type_def_103,type,
list_P4696196834278971493ex_nat: $tType ).
thf(type_def_104,type,
set_Pr4744753334818466879ex_nat: $tType ).
thf(type_def_105,type,
list_P7647014805210017729x_real: $tType ).
thf(type_def_106,type,
set_Pr1133549439701694107x_real: $tType ).
thf(type_def_107,type,
list_P7977503562704621835T_VEBT: $tType ).
thf(type_def_108,type,
set_Pr4085867452638698417T_VEBT: $tType ).
thf(type_def_109,type,
list_P1797514011394873281omplex: $tType ).
thf(type_def_110,type,
set_Pr1846070511934368667omplex: $tType ).
thf(type_def_111,type,
list_P6863124054624500543t_real: $tType ).
thf(type_def_112,type,
set_Pr3538720872664544793t_real: $tType ).
thf(type_def_113,type,
list_P3595434254542482545real_o: $tType ).
thf(type_def_114,type,
set_Pr4936984352647145239real_o: $tType ).
thf(type_def_115,type,
list_P3881527313128557121omplex: $tType ).
thf(type_def_116,type,
set_Pr6591433984475009307omplex: $tType ).
thf(type_def_117,type,
list_P4344331454722006975al_int: $tType ).
thf(type_def_118,type,
set_Pr1019928272762051225al_int: $tType ).
thf(type_def_119,type,
list_P6834414599653733731al_nat: $tType ).
thf(type_def_120,type,
set_Pr3510011417693777981al_nat: $tType ).
thf(type_def_121,type,
list_P8689742595348180415l_real: $tType ).
thf(type_def_122,type,
set_Pr6218003697084177305l_real: $tType ).
thf(type_def_123,type,
list_P877281246627933069T_VEBT: $tType ).
thf(type_def_124,type,
set_Pr6019664923565264691T_VEBT: $tType ).
thf(type_def_125,type,
list_P6254988961118846195et_nat: $tType ).
thf(type_def_126,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(type_def_127,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(type_def_128,type,
set_Pr3175402225741728619VEBT_o: $tType ).
thf(type_def_129,type,
list_P4108580160459392801omplex: $tType ).
thf(type_def_130,type,
set_Pr216944050393469383omplex: $tType ).
thf(type_def_131,type,
list_P4547456442757143711BT_int: $tType ).
thf(type_def_132,type,
set_Pr5066593544530342725BT_int: $tType ).
thf(type_def_133,type,
list_P7037539587688870467BT_nat: $tType ).
thf(type_def_134,type,
set_Pr7556676689462069481BT_nat: $tType ).
thf(type_def_135,type,
list_P2623026923184700063T_real: $tType ).
thf(type_def_136,type,
set_Pr7765410600122031685T_real: $tType ).
thf(type_def_137,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(type_def_138,type,
set_se7855581050983116737at_nat: $tType ).
thf(type_def_139,type,
typerep: $tType ).
thf(type_def_140,type,
list_typerep: $tType ).
thf(type_def_141,type,
produc8243902056947475879T_VEBT: $tType ).
thf(type_def_142,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(type_def_143,type,
set_Pr5001190662893202239st_int: $tType ).
thf(type_def_144,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(type_def_145,type,
set_Pr591367044826345187st_nat: $tType ).
thf(type_def_146,type,
set_Pr5170412164475753123T_VEBT: $tType ).
thf(type_def_147,type,
set_Pr3149072824959771635_nat_o: $tType ).
thf(type_def_148,type,
set_Pr1150278048023938153list_o: $tType ).
thf(type_def_149,type,
set_Pr6167073792073659919T_VEBT: $tType ).
thf(type_def_150,type,
set_Pr1262583345697558789T_VEBT: $tType ).
thf(type_def_151,type,
set_Pr7508168486584781291list_o: $tType ).
thf(type_def_152,type,
set_Pr4080907618048478043st_int: $tType ).
thf(type_def_153,type,
set_Pr8894456036836396799st_nat: $tType ).
thf(type_def_154,type,
list_P4002435161011370285od_o_o: $tType ).
thf(type_def_155,type,
product_prod_o_o: $tType ).
thf(type_def_156,type,
list_P3795440434834930179_o_int: $tType ).
thf(type_def_157,type,
product_prod_o_int: $tType ).
thf(type_def_158,type,
list_P6285523579766656935_o_nat: $tType ).
thf(type_def_159,type,
product_prod_o_nat: $tType ).
thf(type_def_160,type,
produc2504756804600209347T_VEBT: $tType ).
thf(type_def_161,type,
product_prod_nat_o: $tType ).
thf(type_def_162,type,
product_prod_nat_int: $tType ).
thf(type_def_163,type,
produc8025551001238799321T_VEBT: $tType ).
thf(type_def_164,type,
produc334124729049499915VEBT_o: $tType ).
thf(type_def_165,type,
produc4894624898956917775BT_int: $tType ).
thf(type_def_166,type,
produc9072475918466114483BT_nat: $tType ).
thf(type_def_167,type,
set_char: $tType ).
thf(type_def_168,type,
produc4953844613479565601on_nat: $tType ).
thf(type_def_169,type,
produc2233624965454879586on_nat: $tType ).
thf(type_def_170,type,
produc7248412053542808358at_nat: $tType ).
thf(type_def_171,type,
produc4471711990508489141at_nat: $tType ).
thf(type_def_172,type,
produc8306885398267862888on_nat: $tType ).
thf(type_def_173,type,
produc3447558737645232053on_num: $tType ).
thf(type_def_174,type,
produc7036089656553540234on_num: $tType ).
thf(type_def_175,type,
produc1193250871479095198on_num: $tType ).
thf(type_def_176,type,
produc6121120109295599847at_nat: $tType ).
thf(type_def_177,type,
produc5491161045314408544at_nat: $tType ).
thf(type_def_178,type,
produc5542196010084753463at_nat: $tType ).
thf(type_def_179,type,
produc648051720047351925omplex: $tType ).
thf(type_def_180,type,
product_prod_o_real: $tType ).
thf(type_def_181,type,
produc7822875418678951345atural: $tType ).
thf(type_def_182,type,
produc5835291356934675326atural: $tType ).
thf(type_def_183,type,
produc6088675342482847199plex_o: $tType ).
thf(type_def_184,type,
produc4411394909380815293omplex: $tType ).
thf(type_def_185,type,
produc6845221339535797307ex_int: $tType ).
thf(type_def_186,type,
produc1799700322190218207ex_nat: $tType ).
thf(type_def_187,type,
produc8892588492097263291x_real: $tType ).
thf(type_def_188,type,
produc7151440242714718331T_VEBT: $tType ).
thf(type_def_189,type,
produc5838698208256999739omplex: $tType ).
thf(type_def_190,type,
produc679980390762269497t_real: $tType ).
thf(type_def_191,type,
produc7102631898165422375list_o: $tType ).
thf(type_def_192,type,
produc1713839591385758857st_int: $tType ).
thf(type_def_193,type,
produc4203922736317485613st_nat: $tType ).
thf(type_def_194,type,
produc1922972420619397443T_VEBT: $tType ).
thf(type_def_195,type,
produc862207588354017979nteger: $tType ).
thf(type_def_196,type,
produc1186641810826059865st_int: $tType ).
thf(type_def_197,type,
produc149729814636038835list_o: $tType ).
thf(type_def_198,type,
produc1828647624359046049st_nat: $tType ).
thf(type_def_199,type,
produc872621073311890639T_VEBT: $tType ).
thf(type_def_200,type,
produc6392793444374437607at_nat: $tType ).
thf(type_def_201,type,
produc424102278133772007at_nat: $tType ).
thf(type_def_202,type,
produc3962069817607390347list_o: $tType ).
thf(type_def_203,type,
produc7831203938951381541st_int: $tType ).
thf(type_def_204,type,
produc1097915047028332489st_nat: $tType ).
thf(type_def_205,type,
produc9211091688327510695T_VEBT: $tType ).
thf(type_def_206,type,
product_prod_real_o: $tType ).
thf(type_def_207,type,
produc6979889472282505531omplex: $tType ).
thf(type_def_208,type,
produc8786904178792722361al_int: $tType ).
thf(type_def_209,type,
produc3741383161447143261al_nat: $tType ).
thf(type_def_210,type,
produc2422161461964618553l_real: $tType ).
thf(type_def_211,type,
produc3757001726724277373T_VEBT: $tType ).
thf(type_def_212,type,
produc7819656566062154093et_nat: $tType ).
thf(type_def_213,type,
produc8380087813684007313omplex: $tType ).
thf(type_def_214,type,
produc7272778201969148633d_enat: $tType ).
thf(type_def_215,type,
produc5170161368751668367T_real: $tType ).
thf(type_def_216,type,
literal: $tType ).
thf(func_def_0,type,
produc5542196010084753463at_nat: $tType ).
thf(func_def_1,type,
produc5491161045314408544at_nat: $tType ).
thf(func_def_2,type,
set_Pr4333006031979791559at_nat: $tType ).
thf(func_def_3,type,
produc424102278133772007at_nat: $tType ).
thf(func_def_4,type,
set_Pr1542805901266377927at_nat: $tType ).
thf(func_def_5,type,
list_P5464809261938338413at_nat: $tType ).
thf(func_def_6,type,
set_Pr4329608150637261639at_nat: $tType ).
thf(func_def_7,type,
produc1193250871479095198on_num: $tType ).
thf(func_def_8,type,
produc8306885398267862888on_nat: $tType ).
thf(func_def_9,type,
produc6121120109295599847at_nat: $tType ).
thf(func_def_10,type,
produc4471711990508489141at_nat: $tType ).
thf(func_def_11,type,
produc6392793444374437607at_nat: $tType ).
thf(func_def_12,type,
produc7036089656553540234on_num: $tType ).
thf(func_def_13,type,
produc2233624965454879586on_nat: $tType ).
thf(func_def_14,type,
produc3843707927480180839at_nat: $tType ).
thf(func_def_15,type,
list_P8469869581646625389at_nat: $tType ).
thf(func_def_16,type,
set_Pr8693737435421807431at_nat: $tType ).
thf(func_def_17,type,
produc5835291356934675326atural: $tType ).
thf(func_def_18,type,
set_Pr1916528119006554503T_VEBT: $tType ).
thf(func_def_19,type,
produc859450856879609959at_nat: $tType ).
thf(func_def_20,type,
set_Pr7565137564259432987nteger: $tType ).
thf(func_def_21,type,
produc9211091688327510695T_VEBT: $tType ).
thf(func_def_22,type,
set_Pr8894456036836396799st_nat: $tType ).
thf(func_def_23,type,
set_Pr4080907618048478043st_int: $tType ).
thf(func_def_24,type,
set_Pr1262583345697558789T_VEBT: $tType ).
thf(func_def_25,type,
produc862207588354017979nteger: $tType ).
thf(func_def_26,type,
set_Pr7508168486584781291list_o: $tType ).
thf(func_def_27,type,
set_Pr5170412164475753123T_VEBT: $tType ).
thf(func_def_28,type,
list_s9130966667114977576at_nat: $tType ).
thf(func_def_29,type,
produc1097915047028332489st_nat: $tType ).
thf(func_def_30,type,
produc7831203938951381541st_int: $tType ).
thf(func_def_31,type,
produc872621073311890639T_VEBT: $tType ).
thf(func_def_32,type,
set_Pr3451248702717554689st_nat: $tType ).
thf(func_def_33,type,
set_Pr765067013931698361st_int: $tType ).
thf(func_def_34,type,
list_P7413028617227757229T_VEBT: $tType ).
thf(func_def_35,type,
set_Pr6192946355708809607T_VEBT: $tType ).
thf(func_def_36,type,
list_P6254988961118846195et_nat: $tType ).
thf(func_def_37,type,
list_P5578671422887162913nteger: $tType ).
thf(func_def_38,type,
set_Pr5488025237498180813et_nat: $tType ).
thf(func_def_39,type,
set_Pr4811707699266497531nteger: $tType ).
thf(func_def_40,type,
produc3447558737645232053on_num: $tType ).
thf(func_def_41,type,
produc4953844613479565601on_nat: $tType ).
thf(func_def_42,type,
produc3962069817607390347list_o: $tType ).
thf(func_def_43,type,
produc1922972420619397443T_VEBT: $tType ).
thf(func_def_44,type,
set_Pr1150278048023938153list_o: $tType ).
thf(func_def_45,type,
set_Pr591367044826345187st_nat: $tType ).
thf(func_def_46,type,
set_Pr5001190662893202239st_int: $tType ).
thf(func_def_47,type,
produc7248412053542808358at_nat: $tType ).
thf(func_def_48,type,
list_P4108580160459392801omplex: $tType ).
thf(func_def_49,type,
list_P7977503562704621835T_VEBT: $tType ).
thf(func_def_50,type,
set_Pr216944050393469383omplex: $tType ).
thf(func_def_51,type,
set_Pr4085867452638698417T_VEBT: $tType ).
thf(func_def_52,type,
list_P9162950289778280392at_nat: $tType ).
thf(func_def_53,type,
list_P2623026923184700063T_real: $tType ).
thf(func_def_54,type,
list_P877281246627933069T_VEBT: $tType ).
thf(func_def_55,type,
produc1828647624359046049st_nat: $tType ).
thf(func_def_56,type,
produc1186641810826059865st_int: $tType ).
thf(func_def_57,type,
set_Pr7765410600122031685T_real: $tType ).
thf(func_def_58,type,
set_Pr6019664923565264691T_VEBT: $tType ).
thf(func_def_59,type,
list_P7037539587688870467BT_nat: $tType ).
thf(func_def_60,type,
list_P4547456442757143711BT_int: $tType ).
thf(func_def_61,type,
list_P5647936690300460905T_VEBT: $tType ).
thf(func_def_62,type,
set_Pr6227168374412355847list_o: $tType ).
thf(func_def_63,type,
produc8243902056947475879T_VEBT: $tType ).
thf(func_def_64,type,
list_s1210847774152347623at_nat: $tType ).
thf(func_def_65,type,
list_P7664491975274850627omplex: $tType ).
thf(func_def_66,type,
set_Pr7556676689462069481BT_nat: $tType ).
thf(func_def_67,type,
set_Pr5066593544530342725BT_int: $tType ).
thf(func_def_68,type,
set_Pr6167073792073659919T_VEBT: $tType ).
thf(func_def_69,type,
set_se7855581050983116737at_nat: $tType ).
thf(func_def_70,type,
set_Pr5085853215250843933omplex: $tType ).
thf(func_def_71,type,
produc7819656566062154093et_nat: $tType ).
thf(func_def_72,type,
produc7822875418678951345atural: $tType ).
thf(func_def_73,type,
produc8923325533196201883nteger: $tType ).
thf(func_def_74,type,
produc7272778201969148633d_enat: $tType ).
thf(func_def_75,type,
list_P3881527313128557121omplex: $tType ).
thf(func_def_76,type,
list_P7647014805210017729x_real: $tType ).
thf(func_def_77,type,
produc149729814636038835list_o: $tType ).
thf(func_def_78,type,
produc4203922736317485613st_nat: $tType ).
thf(func_def_79,type,
produc1713839591385758857st_int: $tType ).
thf(func_def_80,type,
set_Pr6591433984475009307omplex: $tType ).
thf(func_def_81,type,
set_Pr1133549439701694107x_real: $tType ).
thf(func_def_82,type,
list_P3126845725202233233VEBT_o: $tType ).
thf(func_def_83,type,
list_P1797514011394873281omplex: $tType ).
thf(func_def_84,type,
list_P4696196834278971493ex_nat: $tType ).
thf(func_def_85,type,
list_P2206113689347244737ex_int: $tType ).
thf(func_def_86,type,
list_P7495141550334521929T_VEBT: $tType ).
thf(func_def_87,type,
produc8380087813684007313omplex: $tType ).
thf(func_def_88,type,
produc7151440242714718331T_VEBT: $tType ).
thf(func_def_89,type,
set_Pr3175402225741728619VEBT_o: $tType ).
thf(func_def_90,type,
set_Pr1846070511934368667omplex: $tType ).
thf(func_def_91,type,
set_Pr4744753334818466879ex_nat: $tType ).
thf(func_def_92,type,
set_Pr2254670189886740123ex_int: $tType ).
thf(func_def_93,type,
set_Pr7543698050874017315T_VEBT: $tType ).
thf(func_def_94,type,
option4927543243414619207at_nat: $tType ).
thf(func_def_95,type,
list_P8689742595348180415l_real: $tType ).
thf(func_def_96,type,
filter1242075044329608583at_nat: $tType ).
thf(func_def_97,type,
set_Pr6218003697084177305l_real: $tType ).
thf(func_def_98,type,
list_P6834414599653733731al_nat: $tType ).
thf(func_def_99,type,
list_P4344331454722006975al_int: $tType ).
thf(func_def_100,type,
list_P6863124054624500543t_real: $tType ).
thf(func_def_101,type,
produc5170161368751668367T_real: $tType ).
thf(func_def_102,type,
produc3757001726724277373T_VEBT: $tType ).
thf(func_def_103,type,
set_Pr3510011417693777981al_nat: $tType ).
thf(func_def_104,type,
set_Pr1019928272762051225al_int: $tType ).
thf(func_def_105,type,
set_Pr3538720872664544793t_real: $tType ).
thf(func_def_106,type,
produc7102631898165422375list_o: $tType ).
thf(func_def_107,type,
list_P6011104703257516679at_nat: $tType ).
thf(func_def_108,type,
list_P3521021558325789923at_int: $tType ).
thf(func_def_109,type,
list_P5707943133018811711nt_int: $tType ).
thf(func_def_110,type,
produc9072475918466114483BT_nat: $tType ).
thf(func_def_111,type,
produc4894624898956917775BT_int: $tType ).
thf(func_def_112,type,
produc8025551001238799321T_VEBT: $tType ).
thf(func_def_113,type,
list_P7942624414058669295plex_o: $tType ).
thf(func_def_114,type,
list_P3924974545808530565omplex: $tType ).
thf(func_def_115,type,
set_Pr1261947904930325089at_nat: $tType ).
thf(func_def_116,type,
set_Pr958786334691620121nt_int: $tType ).
thf(func_def_117,type,
produc4411394909380815293omplex: $tType ).
thf(func_def_118,type,
set_Pr216032351708956309plex_o: $tType ).
thf(func_def_119,type,
set_Pr5421754520313593387omplex: $tType ).
thf(func_def_120,type,
list_C4705013386053401436er_nat: $tType ).
thf(func_def_121,type,
set_Sum_sum_nat_nat: $tType ).
thf(func_def_122,type,
list_P3595434254542482545real_o: $tType ).
thf(func_def_123,type,
list_P5232166724548748803o_real: $tType ).
thf(func_def_124,type,
produc6979889472282505531omplex: $tType ).
thf(func_def_125,type,
produc8892588492097263291x_real: $tType ).
thf(func_def_126,type,
list_list_VEBT_VEBT: $tType ).
thf(func_def_127,type,
set_Pr4936984352647145239real_o: $tType ).
thf(func_def_128,type,
set_Pr6573716822653411497o_real: $tType ).
thf(func_def_129,type,
set_list_list_nat: $tType ).
thf(func_def_130,type,
list_P7333126701944960589_nat_o: $tType ).
thf(func_def_131,type,
list_P6285523579766656935_o_nat: $tType ).
thf(func_def_132,type,
list_P3795440434834930179_o_int: $tType ).
thf(func_def_133,type,
set_list_VEBT_VEBT: $tType ).
thf(func_def_134,type,
produc334124729049499915VEBT_o: $tType ).
thf(func_def_135,type,
produc5838698208256999739omplex: $tType ).
thf(func_def_136,type,
produc1799700322190218207ex_nat: $tType ).
thf(func_def_137,type,
produc6845221339535797307ex_int: $tType ).
thf(func_def_138,type,
produc2504756804600209347T_VEBT: $tType ).
thf(func_def_139,type,
set_Pr3149072824959771635_nat_o: $tType ).
thf(func_def_140,type,
set_Pr2101469702781467981_o_nat: $tType ).
thf(func_def_141,type,
set_Pr8834758594704517033_o_int: $tType ).
thf(func_def_142,type,
set_list_set_nat: $tType ).
thf(func_def_143,type,
produc2422161461964618553l_real: $tType ).
thf(func_def_144,type,
produc3741383161447143261al_nat: $tType ).
thf(func_def_145,type,
produc8786904178792722361al_int: $tType ).
thf(func_def_146,type,
produc679980390762269497t_real: $tType ).
thf(func_def_147,type,
product_prod_nat_nat: $tType ).
thf(func_def_148,type,
product_prod_nat_int: $tType ).
thf(func_def_149,type,
product_prod_int_int: $tType ).
thf(func_def_150,type,
list_P4002435161011370285od_o_o: $tType ).
thf(func_def_151,type,
set_list_complex: $tType ).
thf(func_def_152,type,
produc6088675342482847199plex_o: $tType ).
thf(func_def_153,type,
produc648051720047351925omplex: $tType ).
thf(func_def_154,type,
set_Product_prod_o_o: $tType ).
thf(func_def_155,type,
list_nat_nat: $tType ).
thf(func_def_156,type,
list_int_nat: $tType ).
thf(func_def_157,type,
option_VEBT_VEBT: $tType ).
thf(func_def_158,type,
sum_sum_nat_nat: $tType ).
thf(func_def_159,type,
product_prod_real_o: $tType ).
thf(func_def_160,type,
product_prod_o_real: $tType ).
thf(func_def_161,type,
list_list_nat: $tType ).
thf(func_def_162,type,
list_list_int: $tType ).
thf(func_def_163,type,
list_VEBT_VEBT: $tType ).
thf(func_def_164,type,
set_list_nat: $tType ).
thf(func_def_165,type,
set_list_int: $tType ).
thf(func_def_166,type,
product_prod_nat_o: $tType ).
thf(func_def_167,type,
product_prod_o_nat: $tType ).
thf(func_def_168,type,
product_prod_o_int: $tType ).
thf(func_def_169,type,
list_set_nat: $tType ).
thf(func_def_170,type,
list_Code_integer: $tType ).
thf(func_def_171,type,
set_VEBT_VEBT: $tType ).
thf(func_def_172,type,
set_set_nat: $tType ).
thf(func_def_173,type,
set_Code_integer: $tType ).
thf(func_def_174,type,
list_list_o: $tType ).
thf(func_def_175,type,
list_typerep: $tType ).
thf(func_def_176,type,
list_complex: $tType ).
thf(func_def_177,type,
set_list_o: $tType ).
thf(func_def_178,type,
product_prod_o_o: $tType ).
thf(func_def_179,type,
set_complex: $tType ).
thf(func_def_180,type,
filter_real: $tType ).
thf(func_def_181,type,
option_num: $tType ).
thf(func_def_182,type,
option_nat: $tType ).
thf(func_def_183,type,
option_int: $tType ).
thf(func_def_184,type,
filter_nat: $tType ).
thf(func_def_185,type,
set_char: $tType ).
thf(func_def_186,type,
list_real: $tType ).
thf(func_def_187,type,
set_real: $tType ).
thf(func_def_188,type,
list_num: $tType ).
thf(func_def_189,type,
list_nat: $tType ).
thf(func_def_190,type,
list_int: $tType ).
thf(func_def_191,type,
vEBT_VEBT: $tType ).
thf(func_def_192,type,
set_rat: $tType ).
thf(func_def_193,type,
set_num: $tType ).
thf(func_def_194,type,
set_nat: $tType ).
thf(func_def_195,type,
set_int: $tType ).
thf(func_def_196,type,
code_natural: $tType ).
thf(func_def_197,type,
code_integer: $tType ).
thf(func_def_198,type,
option_o: $tType ).
thf(func_def_199,type,
extended_enat: $tType ).
thf(func_def_200,type,
list_o: $tType ).
thf(func_def_201,type,
typerep: $tType ).
thf(func_def_202,type,
complex: $tType ).
thf(func_def_203,type,
literal: $tType ).
thf(func_def_204,type,
set_o: $tType ).
thf(func_def_205,type,
char: $tType ).
thf(func_def_206,type,
real: $tType ).
thf(func_def_207,type,
rat: $tType ).
thf(func_def_208,type,
num: $tType ).
thf(func_def_209,type,
nat: $tType ).
thf(func_def_210,type,
int: $tType ).
thf(func_def_211,type,
archim7802044766580827645g_real: real > int ).
thf(func_def_212,type,
archim6058952711729229775r_real: real > int ).
thf(func_def_213,type,
bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_214,type,
bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_215,type,
bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
thf(func_def_216,type,
bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
thf(func_def_217,type,
bNF_Ca8987285221972644271er_int: set_Pr4811707699266497531nteger > ( code_integer > int ) > $o ).
thf(func_def_218,type,
bNF_Ca8989775692481694547er_nat: set_Pr4811707699266497531nteger > ( code_integer > nat ) > $o ).
thf(func_def_219,type,
bNF_Ca5547107478637473181er_num: set_Pr4811707699266497531nteger > ( code_integer > num ) > $o ).
thf(func_def_220,type,
bNF_Ca8354645632395198811er_rat: set_Pr4811707699266497531nteger > ( code_integer > rat ) > $o ).
thf(func_def_221,type,
bNF_Ca1968104039914474786nt_nat: set_Pr958786334691620121nt_int > ( int > nat ) > $o ).
thf(func_def_222,type,
bNF_Ca7748807862925029228nt_num: set_Pr958786334691620121nt_int > ( int > num ) > $o ).
thf(func_def_223,type,
bNF_Ca1332973979827979050nt_rat: set_Pr958786334691620121nt_int > ( int > rat ) > $o ).
thf(func_def_224,type,
bNF_Ca968750328013420230at_nat: set_Pr1261947904930325089at_nat > ( nat > nat ) > $o ).
thf(func_def_225,type,
bNF_Ca6749454151023974672at_num: set_Pr1261947904930325089at_nat > ( nat > num ) > $o ).
thf(func_def_226,type,
bNF_Ca333620267926924494at_rat: set_Pr1261947904930325089at_nat > ( nat > rat ) > $o ).
thf(func_def_227,type,
bNF_re1962705104956426057at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > $o ).
thf(func_def_228,type,
bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).
thf(func_def_229,type,
bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
thf(func_def_230,type,
bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
thf(func_def_231,type,
bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
thf(func_def_232,type,
bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
thf(func_def_233,type,
bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
thf(func_def_234,type,
bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
thf(func_def_235,type,
bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_236,type,
bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
thf(func_def_237,type,
bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
thf(func_def_238,type,
bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
thf(func_def_239,type,
bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
thf(func_def_240,type,
bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
thf(func_def_241,type,
bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
thf(func_def_242,type,
bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
thf(func_def_243,type,
bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
thf(func_def_244,type,
bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
thf(func_def_245,type,
bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
thf(func_def_246,type,
bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
thf(func_def_247,type,
bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
thf(func_def_248,type,
bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
thf(func_def_249,type,
bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
thf(func_def_250,type,
bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
thf(func_def_251,type,
bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
thf(func_def_252,type,
bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
thf(func_def_253,type,
bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
thf(func_def_254,type,
bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).
thf(func_def_255,type,
bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_256,type,
binomial: nat > nat > nat ).
thf(func_def_257,type,
gbinom8545251970709558553nteger: code_integer > nat > code_integer ).
thf(func_def_258,type,
gbinomial_complex: complex > nat > complex ).
thf(func_def_259,type,
gbinomial_int: int > nat > int ).
thf(func_def_260,type,
gbinomial_nat: nat > nat > nat ).
thf(func_def_261,type,
gbinomial_rat: rat > nat > rat ).
thf(func_def_262,type,
gbinomial_real: real > nat > real ).
thf(func_def_263,type,
bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
thf(func_def_264,type,
bit_concat_bit: nat > int > int > int ).
thf(func_def_265,type,
bit_ri7919022796975470100ot_int: int > int ).
thf(func_def_266,type,
bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
thf(func_def_267,type,
bit_ri631733984087533419it_int: nat > int > int ).
thf(func_def_268,type,
bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
thf(func_def_269,type,
bit_se725231765392027082nd_int: int > int > int ).
thf(func_def_270,type,
bit_se727722235901077358nd_nat: nat > nat > nat ).
thf(func_def_271,type,
bit_se8568078237143864401it_int: nat > int > int ).
thf(func_def_272,type,
bit_se8570568707652914677it_nat: nat > nat > nat ).
thf(func_def_273,type,
bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
thf(func_def_274,type,
bit_se168947363167071951atural: nat > code_natural > code_natural ).
thf(func_def_275,type,
bit_se2159334234014336723it_int: nat > int > int ).
thf(func_def_276,type,
bit_se2161824704523386999it_nat: nat > nat > nat ).
thf(func_def_277,type,
bit_se2002935070580805687sk_nat: nat > nat ).
thf(func_def_278,type,
bit_se1409905431419307370or_int: int > int > int ).
thf(func_def_279,type,
bit_se1412395901928357646or_nat: nat > nat > nat ).
thf(func_def_280,type,
bit_se545348938243370406it_int: nat > int > int ).
thf(func_def_281,type,
bit_se547839408752420682it_nat: nat > nat > nat ).
thf(func_def_282,type,
bit_se2793503036327961859nteger: nat > code_integer > code_integer ).
thf(func_def_283,type,
bit_se1617098188084679374atural: nat > code_natural > code_natural ).
thf(func_def_284,type,
bit_se7879613467334960850it_int: nat > int > int ).
thf(func_def_285,type,
bit_se7882103937844011126it_nat: nat > nat > nat ).
thf(func_def_286,type,
bit_se2923211474154528505it_int: nat > int > int ).
thf(func_def_287,type,
bit_se2925701944663578781it_nat: nat > nat > nat ).
thf(func_def_288,type,
bit_se7083795435491715335atural: nat > code_natural > code_natural ).
thf(func_def_289,type,
bit_se4203085406695923979it_int: nat > int > int ).
thf(func_def_290,type,
bit_se4205575877204974255it_nat: nat > nat > nat ).
thf(func_def_291,type,
bit_se6526347334894502574or_int: int > int > int ).
thf(func_def_292,type,
bit_se6528837805403552850or_nat: nat > nat > nat ).
thf(func_def_293,type,
bit_se1146084159140164899it_int: int > nat > $o ).
thf(func_def_294,type,
bit_se1148574629649215175it_nat: nat > nat > $o ).
thf(func_def_295,type,
bit_take_bit_num: nat > num > option_num ).
thf(func_def_296,type,
code_Suc: code_natural > code_natural ).
thf(func_def_297,type,
code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_298,type,
code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_299,type,
code_int_of_integer: code_integer > int ).
thf(func_def_300,type,
code_integer_of_int: int > code_integer ).
thf(func_def_301,type,
code_integer_of_nat: nat > code_integer ).
thf(func_def_302,type,
code_nat_of_integer: code_integer > nat ).
thf(func_def_303,type,
code_nat_of_natural: code_natural > nat ).
thf(func_def_304,type,
code_natural_of_nat: nat > code_natural ).
thf(func_def_305,type,
comple7806235888213564991et_nat: set_set_nat > set_nat ).
thf(func_def_306,type,
complete_Sup_Sup_nat: set_nat > nat ).
thf(func_def_307,type,
comple7399068483239264473et_nat: set_set_nat > set_nat ).
thf(func_def_308,type,
arg: complex > real ).
thf(func_def_309,type,
cis: real > complex ).
thf(func_def_310,type,
cnj: complex > complex ).
thf(func_def_311,type,
complex2: real > real > complex ).
thf(func_def_312,type,
im: complex > real ).
thf(func_def_313,type,
re: complex > real ).
thf(func_def_314,type,
csqrt: complex > complex ).
thf(func_def_315,type,
imaginary_unit: complex ).
thf(func_def_316,type,
rcis: real > real > complex ).
thf(func_def_317,type,
nat_to_rat_surj: nat > rat ).
thf(func_def_318,type,
nth_item_rel: nat > nat > $o ).
thf(func_def_319,type,
differ6690327859849518006l_real: ( real > real ) > filter_real > $o ).
thf(func_def_320,type,
has_fi5821293074295781190e_real: ( real > real ) > real > filter_real > $o ).
thf(func_def_321,type,
adjust_div: product_prod_int_int > int ).
thf(func_def_322,type,
adjust_mod: int > int > int ).
thf(func_def_323,type,
divmod_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_324,type,
eucl_rel_int: int > int > product_prod_int_int > $o ).
thf(func_def_325,type,
unique5706413561485394159nteger: produc8923325533196201883nteger > $o ).
thf(func_def_326,type,
unique6319869463603278526ux_int: product_prod_int_int > $o ).
thf(func_def_327,type,
unique6322359934112328802ux_nat: product_prod_nat_nat > $o ).
thf(func_def_328,type,
unique3479559517661332726nteger: num > num > produc8923325533196201883nteger ).
thf(func_def_329,type,
unique5052692396658037445od_int: num > num > product_prod_int_int ).
thf(func_def_330,type,
unique5055182867167087721od_nat: num > num > product_prod_nat_nat ).
thf(func_def_331,type,
unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_332,type,
unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
thf(func_def_333,type,
unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_334,type,
extended_eSuc: extended_enat > extended_enat ).
thf(func_def_335,type,
extended_enat2: nat > extended_enat ).
thf(func_def_336,type,
extended_Abs_enat: option_nat > extended_enat ).
thf(func_def_337,type,
extended_case_enat_o: ( nat > $o ) > $o > extended_enat > $o ).
thf(func_def_338,type,
extend3600170679010898289d_enat: ( nat > extended_enat ) > extended_enat > extended_enat > extended_enat ).
thf(func_def_339,type,
extend5688581933313929465d_enat: extended_enat ).
thf(func_def_340,type,
comm_s8582702949713902594nteger: code_integer > nat > code_integer ).
thf(func_def_341,type,
comm_s2602460028002588243omplex: complex > nat > complex ).
thf(func_def_342,type,
comm_s4660882817536571857er_int: int > nat > int ).
thf(func_def_343,type,
comm_s4663373288045622133er_nat: nat > nat > nat ).
thf(func_def_344,type,
comm_s4028243227959126397er_rat: rat > nat > rat ).
thf(func_def_345,type,
comm_s7457072308508201937r_real: real > nat > real ).
thf(func_def_346,type,
semiri3624122377584611663nteger: nat > code_integer ).
thf(func_def_347,type,
semiri2447717529341329178atural: nat > code_natural ).
thf(func_def_348,type,
semiri5044797733671781792omplex: nat > complex ).
thf(func_def_349,type,
semiri4449623510593786356d_enat: nat > extended_enat ).
thf(func_def_350,type,
semiri1406184849735516958ct_int: nat > int ).
thf(func_def_351,type,
semiri1408675320244567234ct_nat: nat > nat ).
thf(func_def_352,type,
semiri773545260158071498ct_rat: nat > rat ).
thf(func_def_353,type,
semiri2265585572941072030t_real: nat > real ).
thf(func_def_354,type,
invers8013647133539491842omplex: complex > complex ).
thf(func_def_355,type,
inverse_inverse_rat: rat > rat ).
thf(func_def_356,type,
inverse_inverse_real: real > real ).
thf(func_def_357,type,
at_bot_real: filter_real ).
thf(func_def_358,type,
at_top_nat: filter_nat ).
thf(func_def_359,type,
at_top_real: filter_real ).
thf(func_def_360,type,
eventually_nat: ( nat > $o ) > filter_nat > $o ).
thf(func_def_361,type,
eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
thf(func_def_362,type,
filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
thf(func_def_363,type,
filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
thf(func_def_364,type,
filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
thf(func_def_365,type,
prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
thf(func_def_366,type,
finite_card_o: set_o > nat ).
thf(func_def_367,type,
finite_card_complex: set_complex > nat ).
thf(func_def_368,type,
finite_card_int: set_int > nat ).
thf(func_def_369,type,
finite_card_list_o: set_list_o > nat ).
thf(func_def_370,type,
finite5120063068150530198omplex: set_list_complex > nat ).
thf(func_def_371,type,
finite_card_list_int: set_list_int > nat ).
thf(func_def_372,type,
finite7325466520557071688st_nat: set_list_list_nat > nat ).
thf(func_def_373,type,
finite_card_list_nat: set_list_nat > nat ).
thf(func_def_374,type,
finite5631907774883551598et_nat: set_list_set_nat > nat ).
thf(func_def_375,type,
finite5915292604075114978T_VEBT: set_list_VEBT_VEBT > nat ).
thf(func_def_376,type,
finite_card_nat: set_nat > nat ).
thf(func_def_377,type,
finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat ).
thf(func_def_378,type,
finite_card_real: set_real > nat ).
thf(func_def_379,type,
finite_card_set_nat: set_set_nat > nat ).
thf(func_def_380,type,
finite7802652506058667612T_VEBT: set_VEBT_VEBT > nat ).
thf(func_def_381,type,
finite_finite_o: set_o > $o ).
thf(func_def_382,type,
finite3207457112153483333omplex: set_complex > $o ).
thf(func_def_383,type,
finite_finite_int: set_int > $o ).
thf(func_def_384,type,
finite_finite_list_o: set_list_o > $o ).
thf(func_def_385,type,
finite8712137658972009173omplex: set_list_complex > $o ).
thf(func_def_386,type,
finite3922522038869484883st_int: set_list_int > $o ).
thf(func_def_387,type,
finite8100373058378681591st_nat: set_list_nat > $o ).
thf(func_def_388,type,
finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o ).
thf(func_def_389,type,
finite_finite_nat: set_nat > $o ).
thf(func_def_390,type,
finite_finite_num: set_num > $o ).
thf(func_def_391,type,
finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_392,type,
finite_finite_rat: set_rat > $o ).
thf(func_def_393,type,
finite_finite_real: set_real > $o ).
thf(func_def_394,type,
finite1152437895449049373et_nat: set_set_nat > $o ).
thf(func_def_395,type,
finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
thf(func_def_396,type,
bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
thf(func_def_397,type,
bij_betw_int_nat: ( int > nat ) > set_int > set_nat > $o ).
thf(func_def_398,type,
bij_be8532844293280997160at_nat: ( list_nat > nat ) > set_list_nat > set_nat > $o ).
thf(func_def_399,type,
bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
thf(func_def_400,type,
bij_betw_nat_int: ( nat > int ) > set_nat > set_int > $o ).
thf(func_def_401,type,
bij_be6293887246118711976st_nat: ( nat > list_nat ) > set_nat > set_list_nat > $o ).
thf(func_def_402,type,
bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
thf(func_def_403,type,
bij_be8693218025023041337at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_404,type,
bij_be4790990086886966983at_nat: ( nat > sum_sum_nat_nat ) > set_nat > set_Sum_sum_nat_nat > $o ).
thf(func_def_405,type,
bij_be5333170631980326235at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat > $o ).
thf(func_def_406,type,
bij_be5432664580149595207at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > set_nat > $o ).
thf(func_def_407,type,
comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_408,type,
comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_409,type,
comp_nat_nat_nat: ( nat > nat ) > ( nat > nat ) > nat > nat ).
thf(func_def_410,type,
id_o: $o > $o ).
thf(func_def_411,type,
id_nat: nat > nat ).
thf(func_def_412,type,
inj_on_int_nat: ( int > nat ) > set_int > $o ).
thf(func_def_413,type,
inj_on_list_nat_nat: ( list_nat > nat ) > set_list_nat > $o ).
thf(func_def_414,type,
inj_on_nat_int: ( nat > int ) > set_nat > $o ).
thf(func_def_415,type,
inj_on_nat_list_nat: ( nat > list_nat ) > set_nat > $o ).
thf(func_def_416,type,
inj_on_nat_nat: ( nat > nat ) > set_nat > $o ).
thf(func_def_417,type,
inj_on5538052773655684606at_nat: ( nat > product_prod_nat_nat ) > set_nat > $o ).
thf(func_def_418,type,
inj_on_nat_char: ( nat > char ) > set_nat > $o ).
thf(func_def_419,type,
inj_on5701776251185195458at_nat: ( nat > sum_sum_nat_nat ) > set_nat > $o ).
thf(func_def_420,type,
inj_on2178005380612969504at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_421,type,
inj_on_real_real: ( real > real ) > set_real > $o ).
thf(func_def_422,type,
inj_on_set_nat_nat: ( set_nat > nat ) > set_set_nat > $o ).
thf(func_def_423,type,
inj_on6343450744447823682at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > $o ).
thf(func_def_424,type,
map_fu6549440983881763648atural: ( code_natural > nat ) > ( ( nat > nat ) > code_natural > code_natural ) > ( nat > nat > nat ) > code_natural > code_natural > code_natural ).
thf(func_def_425,type,
map_fu1239815594074539274atural: ( code_natural > nat ) > ( nat > code_natural ) > ( nat > nat ) > code_natural > code_natural ).
thf(func_def_426,type,
map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
thf(func_def_427,type,
map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
thf(func_def_428,type,
map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
thf(func_def_429,type,
map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
thf(func_def_430,type,
map_fu4333342158222067775at_rat: ( rat > product_prod_int_int ) > ( ( product_prod_int_int > product_prod_int_int ) > rat > rat ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > rat > rat > rat ).
thf(func_def_431,type,
map_fu898904425404107465nt_o_o: ( rat > product_prod_int_int ) > ( $o > $o ) > ( product_prod_int_int > $o ) > rat > $o ).
thf(func_def_432,type,
map_fu5673905371560938248nt_rat: ( rat > product_prod_int_int ) > ( product_prod_int_int > rat ) > ( product_prod_int_int > product_prod_int_int ) > rat > rat ).
thf(func_def_433,type,
map_fu1856342031159181835at_o_o: ( real > nat > rat ) > ( $o > $o ) > ( ( nat > rat ) > $o ) > real > $o ).
thf(func_def_434,type,
the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
thf(func_def_435,type,
fun_pair_leq: set_Pr8693737435421807431at_nat ).
thf(func_def_436,type,
fun_pair_less: set_Pr8693737435421807431at_nat ).
thf(func_def_437,type,
gcd_Gcd_int: set_int > int ).
thf(func_def_438,type,
gcd_Gcd_nat: set_nat > nat ).
thf(func_def_439,type,
gcd_Lcm_nat: set_nat > nat ).
thf(func_def_440,type,
bezw: nat > nat > product_prod_int_int ).
thf(func_def_441,type,
bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_442,type,
gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
thf(func_def_443,type,
gcd_gcd_int: int > int > int ).
thf(func_def_444,type,
gcd_gcd_nat: nat > nat > nat ).
thf(func_def_445,type,
gcd_lcm_Code_integer: code_integer > code_integer > code_integer ).
thf(func_def_446,type,
gcd_lcm_int: int > int > int ).
thf(func_def_447,type,
gcd_lcm_nat: nat > nat > nat ).
thf(func_def_448,type,
gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_449,type,
semiri4256215615220890538in_int: set_int > int ).
thf(func_def_450,type,
semiri4258706085729940814in_nat: set_nat > nat ).
thf(func_def_451,type,
abs_abs_Code_integer: code_integer > code_integer ).
thf(func_def_452,type,
abs_abs_complex: complex > complex ).
thf(func_def_453,type,
abs_abs_int: int > int ).
thf(func_def_454,type,
abs_abs_rat: rat > rat ).
thf(func_def_455,type,
abs_abs_real: real > real ).
thf(func_def_456,type,
minus_8373710615458151222nteger: code_integer > code_integer > code_integer ).
thf(func_def_457,type,
minus_7197305767214868737atural: code_natural > code_natural > code_natural ).
thf(func_def_458,type,
minus_minus_complex: complex > complex > complex ).
thf(func_def_459,type,
minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat ).
thf(func_def_460,type,
minus_minus_int: int > int > int ).
thf(func_def_461,type,
minus_minus_nat: nat > nat > nat ).
thf(func_def_462,type,
minus_minus_rat: rat > rat > rat ).
thf(func_def_463,type,
minus_minus_real: real > real > real ).
thf(func_def_464,type,
minus_minus_set_o: set_o > set_o > set_o ).
thf(func_def_465,type,
minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
thf(func_def_466,type,
minus_minus_set_int: set_int > set_int > set_int ).
thf(func_def_467,type,
minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat ).
thf(func_def_468,type,
minus_minus_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_469,type,
minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_470,type,
minus_minus_set_real: set_real > set_real > set_real ).
thf(func_def_471,type,
minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat ).
thf(func_def_472,type,
minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_473,type,
monoid_nat: ( nat > nat > nat ) > nat > $o ).
thf(func_def_474,type,
one_one_Code_integer: code_integer ).
thf(func_def_475,type,
one_one_Code_natural: code_natural ).
thf(func_def_476,type,
one_one_complex: complex ).
thf(func_def_477,type,
one_on7984719198319812577d_enat: extended_enat ).
thf(func_def_478,type,
one_one_int: int ).
thf(func_def_479,type,
one_one_nat: nat ).
thf(func_def_480,type,
one_one_rat: rat ).
thf(func_def_481,type,
one_one_real: real ).
thf(func_def_482,type,
plus_p5714425477246183910nteger: code_integer > code_integer > code_integer ).
thf(func_def_483,type,
plus_p4538020629002901425atural: code_natural > code_natural > code_natural ).
thf(func_def_484,type,
plus_plus_complex: complex > complex > complex ).
thf(func_def_485,type,
plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat ).
thf(func_def_486,type,
plus_plus_int: int > int > int ).
thf(func_def_487,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_488,type,
plus_plus_num: num > num > num ).
thf(func_def_489,type,
plus_plus_rat: rat > rat > rat ).
thf(func_def_490,type,
plus_plus_real: real > real > real ).
thf(func_def_491,type,
sgn_sgn_Code_integer: code_integer > code_integer ).
thf(func_def_492,type,
sgn_sgn_int: int > int ).
thf(func_def_493,type,
sgn_sgn_rat: rat > rat ).
thf(func_def_494,type,
sgn_sgn_real: real > real ).
thf(func_def_495,type,
times_3573771949741848930nteger: code_integer > code_integer > code_integer ).
thf(func_def_496,type,
times_2397367101498566445atural: code_natural > code_natural > code_natural ).
thf(func_def_497,type,
times_times_complex: complex > complex > complex ).
thf(func_def_498,type,
times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat ).
thf(func_def_499,type,
times_times_int: int > int > int ).
thf(func_def_500,type,
times_times_nat: nat > nat > nat ).
thf(func_def_501,type,
times_times_num: num > num > num ).
thf(func_def_502,type,
times_times_rat: rat > rat > rat ).
thf(func_def_503,type,
times_times_real: real > real > real ).
thf(func_def_504,type,
uminus1351360451143612070nteger: code_integer > code_integer ).
thf(func_def_505,type,
uminus1482373934393186551omplex: complex > complex ).
thf(func_def_506,type,
uminus_uminus_int: int > int ).
thf(func_def_507,type,
uminus_uminus_rat: rat > rat ).
thf(func_def_508,type,
uminus_uminus_real: real > real ).
thf(func_def_509,type,
uminus8566677241136511917omplex: set_complex > set_complex ).
thf(func_def_510,type,
uminus1532241313380277803et_int: set_int > set_int ).
thf(func_def_511,type,
uminus5710092332889474511et_nat: set_nat > set_nat ).
thf(func_def_512,type,
uminus6524753893492686040at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_513,type,
uminus612125837232591019t_real: set_real > set_real ).
thf(func_def_514,type,
zero_z3403309356797280102nteger: code_integer ).
thf(func_def_515,type,
zero_z2226904508553997617atural: code_natural ).
thf(func_def_516,type,
zero_zero_complex: complex ).
thf(func_def_517,type,
zero_z5237406670263579293d_enat: extended_enat ).
thf(func_def_518,type,
zero_zero_int: int ).
thf(func_def_519,type,
zero_zero_nat: nat ).
thf(func_def_520,type,
zero_zero_rat: rat ).
thf(func_def_521,type,
zero_zero_real: real ).
thf(func_def_522,type,
groups8507830703676809646_o_nat: ( $o > nat ) > set_o > nat ).
thf(func_def_523,type,
groups6621422865394947399nteger: ( complex > code_integer ) > set_complex > code_integer ).
thf(func_def_524,type,
groups7754918857620584856omplex: ( complex > complex ) > set_complex > complex ).
thf(func_def_525,type,
groups5690904116761175830ex_int: ( complex > int ) > set_complex > int ).
thf(func_def_526,type,
groups5693394587270226106ex_nat: ( complex > nat ) > set_complex > nat ).
thf(func_def_527,type,
groups5058264527183730370ex_rat: ( complex > rat ) > set_complex > rat ).
thf(func_def_528,type,
groups5808333547571424918x_real: ( complex > real ) > set_complex > real ).
thf(func_def_529,type,
groups7873554091576472773nteger: ( int > code_integer ) > set_int > code_integer ).
thf(func_def_530,type,
groups3049146728041665814omplex: ( int > complex ) > set_int > complex ).
thf(func_def_531,type,
groups4538972089207619220nt_int: ( int > int ) > set_int > int ).
thf(func_def_532,type,
groups4541462559716669496nt_nat: ( int > nat ) > set_int > nat ).
thf(func_def_533,type,
groups3906332499630173760nt_rat: ( int > rat ) > set_int > rat ).
thf(func_def_534,type,
groups8778361861064173332t_real: ( int > real ) > set_int > real ).
thf(func_def_535,type,
groups6529277132148336714omplex: ( list_nat > complex ) > set_list_nat > complex ).
thf(func_def_536,type,
groups4396056296759096172at_nat: ( list_nat > nat ) > set_list_nat > nat ).
thf(func_def_537,type,
groups8399112307953289288t_real: ( list_nat > real ) > set_list_nat > real ).
thf(func_def_538,type,
groups7501900531339628137nteger: ( nat > code_integer ) > set_nat > code_integer ).
thf(func_def_539,type,
groups2073611262835488442omplex: ( nat > complex ) > set_nat > complex ).
thf(func_def_540,type,
groups7108830773950497114d_enat: ( nat > extended_enat ) > set_nat > extended_enat ).
thf(func_def_541,type,
groups3539618377306564664at_int: ( nat > int ) > set_nat > int ).
thf(func_def_542,type,
groups3542108847815614940at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_543,type,
groups2906978787729119204at_rat: ( nat > rat ) > set_nat > rat ).
thf(func_def_544,type,
groups6591440286371151544t_real: ( nat > real ) > set_nat > real ).
thf(func_def_545,type,
groups7713935264441627589nteger: ( real > code_integer ) > set_real > code_integer ).
thf(func_def_546,type,
groups5754745047067104278omplex: ( real > complex ) > set_real > complex ).
thf(func_def_547,type,
groups1932886352136224148al_int: ( real > int ) > set_real > int ).
thf(func_def_548,type,
groups1935376822645274424al_nat: ( real > nat ) > set_real > nat ).
thf(func_def_549,type,
groups1300246762558778688al_rat: ( real > rat ) > set_real > rat ).
thf(func_def_550,type,
groups8097168146408367636l_real: ( real > real ) > set_real > real ).
thf(func_def_551,type,
groups8255218700646806128omplex: ( set_nat > complex ) > set_set_nat > complex ).
thf(func_def_552,type,
groups8294997508430121362at_nat: ( set_nat > nat ) > set_set_nat > nat ).
thf(func_def_553,type,
groups5107569545109728110t_real: ( set_nat > real ) > set_set_nat > real ).
thf(func_def_554,type,
groups771621172384141258BT_nat: ( vEBT_VEBT > nat ) > set_VEBT_VEBT > nat ).
thf(func_def_555,type,
groups8682486955453173170nteger: ( complex > code_integer ) > set_complex > code_integer ).
thf(func_def_556,type,
groups3708469109370488835omplex: ( complex > complex ) > set_complex > complex ).
thf(func_def_557,type,
groups858564598930262913ex_int: ( complex > int ) > set_complex > int ).
thf(func_def_558,type,
groups861055069439313189ex_nat: ( complex > nat ) > set_complex > nat ).
thf(func_def_559,type,
groups225925009352817453ex_rat: ( complex > rat ) > set_complex > rat ).
thf(func_def_560,type,
groups766887009212190081x_real: ( complex > real ) > set_complex > real ).
thf(func_def_561,type,
groups3827104343326376752nteger: ( int > code_integer ) > set_int > code_integer ).
thf(func_def_562,type,
groups7440179247065528705omplex: ( int > complex ) > set_int > complex ).
thf(func_def_563,type,
groups1705073143266064639nt_int: ( int > int ) > set_int > int ).
thf(func_def_564,type,
groups1707563613775114915nt_nat: ( int > nat ) > set_int > nat ).
thf(func_def_565,type,
groups1072433553688619179nt_rat: ( int > rat ) > set_int > rat ).
thf(func_def_566,type,
groups2316167850115554303t_real: ( int > real ) > set_int > real ).
thf(func_def_567,type,
groups3455450783089532116nteger: ( nat > code_integer ) > set_nat > code_integer ).
thf(func_def_568,type,
groups6464643781859351333omplex: ( nat > complex ) > set_nat > complex ).
thf(func_def_569,type,
groups705719431365010083at_int: ( nat > int ) > set_nat > int ).
thf(func_def_570,type,
groups708209901874060359at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_571,type,
groups73079841787564623at_rat: ( nat > rat ) > set_nat > rat ).
thf(func_def_572,type,
groups129246275422532515t_real: ( nat > real ) > set_nat > real ).
thf(func_def_573,type,
groups8110221916422527690omplex: ( product_prod_nat_nat > complex ) > set_Pr1261947904930325089at_nat > complex ).
thf(func_def_574,type,
groups6225526099057966256nteger: ( real > code_integer ) > set_real > code_integer ).
thf(func_def_575,type,
groups713298508707869441omplex: ( real > complex ) > set_real > complex ).
thf(func_def_576,type,
groups4694064378042380927al_int: ( real > int ) > set_real > int ).
thf(func_def_577,type,
groups4696554848551431203al_nat: ( real > nat ) > set_real > nat ).
thf(func_def_578,type,
groups4061424788464935467al_rat: ( real > rat ) > set_real > rat ).
thf(func_def_579,type,
groups1681761925125756287l_real: ( real > real ) > set_real > real ).
thf(func_def_580,type,
groups9116527308978886569_o_int: ( $o > int ) > int > list_o > int ).
thf(func_def_581,type,
groups4561878855575611511st_nat: list_nat > nat ).
thf(func_def_582,type,
the_real: ( real > $o ) > real ).
thf(func_def_583,type,
if_Code_integer: $o > code_integer > code_integer > code_integer ).
thf(func_def_584,type,
if_complex: $o > complex > complex > complex ).
thf(func_def_585,type,
if_Extended_enat: $o > extended_enat > extended_enat > extended_enat ).
thf(func_def_586,type,
if_int: $o > int > int > int ).
thf(func_def_587,type,
if_list_nat: $o > list_nat > list_nat > list_nat ).
thf(func_def_588,type,
if_nat: $o > nat > nat > nat ).
thf(func_def_589,type,
if_num: $o > num > num > num ).
thf(func_def_590,type,
if_option_nat: $o > option_nat > option_nat > option_nat ).
thf(func_def_591,type,
if_option_num: $o > option_num > option_num > option_num ).
thf(func_def_592,type,
if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_593,type,
if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
thf(func_def_594,type,
if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_595,type,
if_rat: $o > rat > rat > rat ).
thf(func_def_596,type,
if_real: $o > real > real > real ).
thf(func_def_597,type,
if_set_nat: $o > set_nat > set_nat > set_nat ).
thf(func_def_598,type,
if_Sum_sum_nat_nat: $o > sum_sum_nat_nat > sum_sum_nat_nat > sum_sum_nat_nat ).
thf(func_def_599,type,
if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_600,type,
infini8530281810654367211te_nat: set_nat > nat > nat ).
thf(func_def_601,type,
abs_Integ: product_prod_nat_nat > int ).
thf(func_def_602,type,
rep_Integ: int > product_prod_nat_nat ).
thf(func_def_603,type,
intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_604,type,
nat2: int > nat ).
thf(func_def_605,type,
pcr_int: product_prod_nat_nat > int > $o ).
thf(func_def_606,type,
ring_1_Ints_real: set_real ).
thf(func_def_607,type,
ring_1_of_int_rat: int > rat ).
thf(func_def_608,type,
ring_1_of_int_real: int > real ).
thf(func_def_609,type,
inf_inf_int: int > int > int ).
thf(func_def_610,type,
inf_inf_nat: nat > nat > nat ).
thf(func_def_611,type,
inf_inf_rat: rat > rat > rat ).
thf(func_def_612,type,
inf_inf_set_complex: set_complex > set_complex > set_complex ).
thf(func_def_613,type,
inf_inf_set_int: set_int > set_int > set_int ).
thf(func_def_614,type,
inf_inf_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_615,type,
inf_inf_set_num: set_num > set_num > set_num ).
thf(func_def_616,type,
inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_617,type,
inf_inf_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_618,type,
inf_inf_set_real: set_real > set_real > set_real ).
thf(func_def_619,type,
semila9081495762789891438tr_nat: ( nat > nat > nat ) > nat > $o ).
thf(func_def_620,type,
semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
thf(func_def_621,type,
sup_sup_int: int > int > int ).
thf(func_def_622,type,
sup_sup_nat: nat > nat > nat ).
thf(func_def_623,type,
sup_sup_rat: rat > rat > rat ).
thf(func_def_624,type,
sup_sup_set_complex: set_complex > set_complex > set_complex ).
thf(func_def_625,type,
sup_sup_set_int: set_int > set_int > set_int ).
thf(func_def_626,type,
sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
thf(func_def_627,type,
sup_sup_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_628,type,
sup_sup_set_num: set_num > set_num > set_num ).
thf(func_def_629,type,
sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_630,type,
sup_sup_set_rat: set_rat > set_rat > set_rat ).
thf(func_def_631,type,
sup_sup_set_real: set_real > set_real > set_real ).
thf(func_def_632,type,
sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
thf(func_def_633,type,
lattic8265883725875713057ax_nat: set_nat > nat ).
thf(func_def_634,type,
lattic5364784637807008409ex_nat: ( complex > nat ) > set_complex > complex ).
thf(func_def_635,type,
lattic1922116423962787043ex_num: ( complex > num ) > set_complex > complex ).
thf(func_def_636,type,
lattic4729654577720512673ex_rat: ( complex > rat ) > set_complex > complex ).
thf(func_def_637,type,
lattic5003618458639192673nt_num: ( int > num ) > set_int > int ).
thf(func_def_638,type,
lattic7811156612396918303nt_rat: ( int > rat ) > set_int > int ).
thf(func_def_639,type,
lattic7446932960582359483at_nat: ( nat > nat ) > set_nat > nat ).
thf(func_def_640,type,
lattic4004264746738138117at_num: ( nat > num ) > set_nat > nat ).
thf(func_def_641,type,
lattic6811802900495863747at_rat: ( nat > rat ) > set_nat > nat ).
thf(func_def_642,type,
lattic1613168225601753569al_num: ( real > num ) > set_real > real ).
thf(func_def_643,type,
lattic4420706379359479199al_rat: ( real > rat ) > set_real > real ).
thf(func_def_644,type,
lattic7826324295020591184_F_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
thf(func_def_645,type,
bfun_nat_real: ( nat > real ) > filter_nat > $o ).
thf(func_def_646,type,
append_nat: list_nat > list_nat > list_nat ).
thf(func_def_647,type,
concat_o: list_list_o > list_o ).
thf(func_def_648,type,
concat_int: list_list_int > list_int ).
thf(func_def_649,type,
concat_nat: list_list_nat > list_nat ).
thf(func_def_650,type,
concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_651,type,
count_list_o: list_o > $o > nat ).
thf(func_def_652,type,
count_list_complex: list_complex > complex > nat ).
thf(func_def_653,type,
count_list_int: list_int > int > nat ).
thf(func_def_654,type,
count_list_nat: list_nat > nat > nat ).
thf(func_def_655,type,
count_list_real: list_real > real > nat ).
thf(func_def_656,type,
count_list_set_nat: list_set_nat > set_nat > nat ).
thf(func_def_657,type,
count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_658,type,
distinct_o: list_o > $o ).
thf(func_def_659,type,
distinct_complex: list_complex > $o ).
thf(func_def_660,type,
distinct_int: list_int > $o ).
thf(func_def_661,type,
distinct_list_nat: list_list_nat > $o ).
thf(func_def_662,type,
distinct_nat: list_nat > $o ).
thf(func_def_663,type,
distin6923225563576452346at_nat: list_P6011104703257516679at_nat > $o ).
thf(func_def_664,type,
distinct_real: list_real > $o ).
thf(func_def_665,type,
distinct_set_nat: list_set_nat > $o ).
thf(func_def_666,type,
distinct_VEBT_VEBT: list_VEBT_VEBT > $o ).
thf(func_def_667,type,
enumerate_o: nat > list_o > list_P7333126701944960589_nat_o ).
thf(func_def_668,type,
enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
thf(func_def_669,type,
enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
thf(func_def_670,type,
enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(func_def_671,type,
find_o: ( $o > $o ) > list_o > option_o ).
thf(func_def_672,type,
find_int: ( int > $o ) > list_int > option_int ).
thf(func_def_673,type,
find_nat: ( nat > $o ) > list_nat > option_nat ).
thf(func_def_674,type,
find_num: ( num > $o ) > list_num > option_num ).
thf(func_def_675,type,
find_P8199882355184865565at_nat: ( product_prod_nat_nat > $o ) > list_P6011104703257516679at_nat > option4927543243414619207at_nat ).
thf(func_def_676,type,
find_VEBT_VEBT: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > option_VEBT_VEBT ).
thf(func_def_677,type,
fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
thf(func_def_678,type,
lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
thf(func_def_679,type,
lenlex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
thf(func_def_680,type,
lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
thf(func_def_681,type,
lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
thf(func_def_682,type,
lenlex325483962726685836at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
thf(func_def_683,type,
lenlex1357538814655152620at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
thf(func_def_684,type,
lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
thf(func_def_685,type,
lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
thf(func_def_686,type,
lex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
thf(func_def_687,type,
lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
thf(func_def_688,type,
lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
thf(func_def_689,type,
lex_Pr8571645452597969515at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
thf(func_def_690,type,
lex_se2245640040323279819at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
thf(func_def_691,type,
lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
thf(func_def_692,type,
linord2614967742042102400et_nat: set_nat > list_nat ).
thf(func_def_693,type,
cons_C1897838848541180310er_nat: ( code_integer > nat ) > list_C4705013386053401436er_nat > list_C4705013386053401436er_nat ).
thf(func_def_694,type,
cons_int_nat: ( int > nat ) > list_int_nat > list_int_nat ).
thf(func_def_695,type,
cons_nat_nat: ( nat > nat ) > list_nat_nat > list_nat_nat ).
thf(func_def_696,type,
cons_P4861729644591583992at_nat: ( product_prod_nat_nat > nat ) > list_P9162950289778280392at_nat > list_P9162950289778280392at_nat ).
thf(func_def_697,type,
cons_s2538900923071588440at_nat: ( set_Pr1261947904930325089at_nat > nat ) > list_s9130966667114977576at_nat > list_s9130966667114977576at_nat ).
thf(func_def_698,type,
cons_o: $o > list_o > list_o ).
thf(func_def_699,type,
cons_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
thf(func_def_700,type,
cons_complex: complex > list_complex > list_complex ).
thf(func_def_701,type,
cons_int: int > list_int > list_int ).
thf(func_def_702,type,
cons_nat: nat > list_nat > list_nat ).
thf(func_def_703,type,
cons_num: num > list_num > list_num ).
thf(func_def_704,type,
cons_P9044669534377732177nteger: produc8923325533196201883nteger > list_P5578671422887162913nteger > list_P5578671422887162913nteger ).
thf(func_def_705,type,
cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
thf(func_def_706,type,
cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
thf(func_def_707,type,
cons_P8732206157123786781at_nat: produc859450856879609959at_nat > list_P8469869581646625389at_nat > list_P8469869581646625389at_nat ).
thf(func_def_708,type,
cons_P3940603068885512221at_nat: produc3843707927480180839at_nat > list_P5464809261938338413at_nat > list_P5464809261938338413at_nat ).
thf(func_def_709,type,
cons_real: real > list_real > list_real ).
thf(func_def_710,type,
cons_set_nat: set_nat > list_set_nat > list_set_nat ).
thf(func_def_711,type,
cons_s6881495754146722583at_nat: set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat ).
thf(func_def_712,type,
cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_713,type,
nil_nat: list_nat ).
thf(func_def_714,type,
map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
thf(func_def_715,type,
map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_716,type,
set_o2: list_o > set_o ).
thf(func_def_717,type,
set_Code_integer2: list_Code_integer > set_Code_integer ).
thf(func_def_718,type,
set_complex2: list_complex > set_complex ).
thf(func_def_719,type,
set_int2: list_int > set_int ).
thf(func_def_720,type,
set_list_o2: list_list_o > set_list_o ).
thf(func_def_721,type,
set_list_int2: list_list_int > set_list_int ).
thf(func_def_722,type,
set_list_nat2: list_list_nat > set_list_nat ).
thf(func_def_723,type,
set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
thf(func_def_724,type,
set_nat2: list_nat > set_nat ).
thf(func_def_725,type,
set_Pr1389080609085208608omplex: list_P3924974545808530565omplex > set_Pr5421754520313593387omplex ).
thf(func_def_726,type,
set_Pr2600826154070092190o_real: list_P5232166724548748803o_real > set_Pr6573716822653411497o_real ).
thf(func_def_727,type,
set_Pr655345902815428824T_VEBT: list_P7495141550334521929T_VEBT > set_Pr7543698050874017315T_VEBT ).
thf(func_def_728,type,
set_Pr920681315882439344nteger: list_P5578671422887162913nteger > set_Pr4811707699266497531nteger ).
thf(func_def_729,type,
set_Pr6829704231520703882plex_o: list_P7942624414058669295plex_o > set_Pr216032351708956309plex_o ).
thf(func_def_730,type,
set_Pr8199049879907524818omplex: list_P7664491975274850627omplex > set_Pr5085853215250843933omplex ).
thf(func_def_731,type,
set_Pr4995810437751016784ex_int: list_P2206113689347244737ex_int > set_Pr2254670189886740123ex_int ).
thf(func_def_732,type,
set_Pr9173661457260213492ex_nat: list_P4696196834278971493ex_nat > set_Pr4744753334818466879ex_nat ).
thf(func_def_733,type,
set_Pr1225976482156248400x_real: list_P7647014805210017729x_real > set_Pr1133549439701694107x_real ).
thf(func_def_734,type,
set_Pr5158653123227461798T_VEBT: list_P7977503562704621835T_VEBT > set_Pr4085867452638698417T_VEBT ).
thf(func_def_735,type,
set_Pr3989287306472219216omplex: list_P1797514011394873281omplex > set_Pr1846070511934368667omplex ).
thf(func_def_736,type,
set_Pr2470121279949933262nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int ).
thf(func_def_737,type,
set_Pr112895574167722958t_real: list_P6863124054624500543t_real > set_Pr3538720872664544793t_real ).
thf(func_def_738,type,
set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_739,type,
set_Pr5518436109238095868at_nat: list_P8469869581646625389at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_740,type,
set_Pr5196769464307566348real_o: list_P3595434254542482545real_o > set_Pr4936984352647145239real_o ).
thf(func_def_741,type,
set_Pr8536649499196266448omplex: list_P3881527313128557121omplex > set_Pr6591433984475009307omplex ).
thf(func_def_742,type,
set_Pr8219819362198175822al_int: list_P4344331454722006975al_int > set_Pr1019928272762051225al_int ).
thf(func_def_743,type,
set_Pr3174298344852596722al_nat: list_P6834414599653733731al_nat > set_Pr3510011417693777981al_nat ).
thf(func_def_744,type,
set_Pr5999470521830281550l_real: list_P8689742595348180415l_real > set_Pr6218003697084177305l_real ).
thf(func_def_745,type,
set_Pr8897343066327330088T_VEBT: list_P877281246627933069T_VEBT > set_Pr6019664923565264691T_VEBT ).
thf(func_def_746,type,
set_Pr9040384385603167362et_nat: list_P6254988961118846195et_nat > set_Pr5488025237498180813et_nat ).
thf(func_def_747,type,
set_Pr3765526544606949372at_nat: list_P5464809261938338413at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_748,type,
set_Pr7708085864119495200VEBT_o: list_P3126845725202233233VEBT_o > set_Pr3175402225741728619VEBT_o ).
thf(func_def_749,type,
set_Pr6387300694196750780omplex: list_P4108580160459392801omplex > set_Pr216944050393469383omplex ).
thf(func_def_750,type,
set_Pr2853735649769556538BT_int: list_P4547456442757143711BT_int > set_Pr5066593544530342725BT_int ).
thf(func_def_751,type,
set_Pr7031586669278753246BT_nat: list_P7037539587688870467BT_nat > set_Pr7556676689462069481BT_nat ).
thf(func_def_752,type,
set_Pr1087130671499945274T_real: list_P2623026923184700063T_real > set_Pr7765410600122031685T_real ).
thf(func_def_753,type,
set_Pr9182192707038809660T_VEBT: list_P7413028617227757229T_VEBT > set_Pr6192946355708809607T_VEBT ).
thf(func_def_754,type,
set_real2: list_real > set_real ).
thf(func_def_755,type,
set_set_nat2: list_set_nat > set_set_nat ).
thf(func_def_756,type,
set_se5049602875457034614at_nat: list_s1210847774152347623at_nat > set_se7855581050983116737at_nat ).
thf(func_def_757,type,
set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_758,type,
size_list_typerep: ( typerep > nat ) > list_typerep > nat ).
thf(func_def_759,type,
size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
thf(func_def_760,type,
tl_nat: list_nat > list_nat ).
thf(func_def_761,type,
list_update_o: list_o > nat > $o > list_o ).
thf(func_def_762,type,
list_u5447711078246177391nteger: list_Code_integer > nat > code_integer > list_Code_integer ).
thf(func_def_763,type,
list_update_complex: list_complex > nat > complex > list_complex ).
thf(func_def_764,type,
list_update_int: list_int > nat > int > list_int ).
thf(func_def_765,type,
list_update_nat: list_nat > nat > nat > list_nat ).
thf(func_def_766,type,
list_u2254550707601501961nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger > list_P5578671422887162913nteger ).
thf(func_def_767,type,
list_u3002344382305578791nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int > list_P5707943133018811711nt_int ).
thf(func_def_768,type,
list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
thf(func_def_769,type,
list_u5003261594476800725at_nat: list_P8469869581646625389at_nat > nat > produc859450856879609959at_nat > list_P8469869581646625389at_nat ).
thf(func_def_770,type,
list_u4696772448584712917at_nat: list_P5464809261938338413at_nat > nat > produc3843707927480180839at_nat > list_P5464809261938338413at_nat ).
thf(func_def_771,type,
list_u6961636818849549845T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT > list_P7413028617227757229T_VEBT ).
thf(func_def_772,type,
list_update_real: list_real > nat > real > list_real ).
thf(func_def_773,type,
list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
thf(func_def_774,type,
list_u8444657558853818831at_nat: list_s1210847774152347623at_nat > nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat ).
thf(func_def_775,type,
list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_776,type,
listrel_o_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
thf(func_def_777,type,
listrel_o_int: set_Pr8834758594704517033_o_int > set_Pr5001190662893202239st_int ).
thf(func_def_778,type,
listrel_o_nat: set_Pr2101469702781467981_o_nat > set_Pr591367044826345187st_nat ).
thf(func_def_779,type,
listrel_o_VEBT_VEBT: set_Pr7543698050874017315T_VEBT > set_Pr5170412164475753123T_VEBT ).
thf(func_def_780,type,
listre5734910445319291053nteger: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
thf(func_def_781,type,
listrel_int_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
thf(func_def_782,type,
listrel_nat_o: set_Pr3149072824959771635_nat_o > set_Pr1150278048023938153list_o ).
thf(func_def_783,type,
listrel_nat_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
thf(func_def_784,type,
listre5761932458788874033T_VEBT: set_Pr6167073792073659919T_VEBT > set_Pr1262583345697558789T_VEBT ).
thf(func_def_785,type,
listre818007680106770737at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
thf(func_def_786,type,
listre2047417242196832561at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
thf(func_def_787,type,
listrel_VEBT_VEBT_o: set_Pr3175402225741728619VEBT_o > set_Pr7508168486584781291list_o ).
thf(func_def_788,type,
listre5898179758603845167BT_int: set_Pr5066593544530342725BT_int > set_Pr4080907618048478043st_int ).
thf(func_def_789,type,
listre5900670229112895443BT_nat: set_Pr7556676689462069481BT_nat > set_Pr8894456036836396799st_nat ).
thf(func_def_790,type,
listre1230615542750757617T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
thf(func_def_791,type,
measur8870801148506250077nteger: list_C4705013386053401436er_nat > set_Pr4811707699266497531nteger ).
thf(func_def_792,type,
measures_int: list_int_nat > set_Pr958786334691620121nt_int ).
thf(func_def_793,type,
measures_nat: list_nat_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_794,type,
measur2679027848233739777at_nat: list_P9162950289778280392at_nat > set_Pr8693737435421807431at_nat ).
thf(func_def_795,type,
measur2694323259624372065at_nat: list_s9130966667114977576at_nat > set_Pr4329608150637261639at_nat ).
thf(func_def_796,type,
nth_o: list_o > nat > $o ).
thf(func_def_797,type,
nth_Code_integer: list_Code_integer > nat > code_integer ).
thf(func_def_798,type,
nth_complex: list_complex > nat > complex ).
thf(func_def_799,type,
nth_int: list_int > nat > int ).
thf(func_def_800,type,
nth_nat: list_nat > nat > nat ).
thf(func_def_801,type,
nth_num: list_num > nat > num ).
thf(func_def_802,type,
nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
thf(func_def_803,type,
nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
thf(func_def_804,type,
nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
thf(func_def_805,type,
nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
thf(func_def_806,type,
nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger ).
thf(func_def_807,type,
nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
thf(func_def_808,type,
nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
thf(func_def_809,type,
nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
thf(func_def_810,type,
nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
thf(func_def_811,type,
nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
thf(func_def_812,type,
nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
thf(func_def_813,type,
nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
thf(func_def_814,type,
nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
thf(func_def_815,type,
nth_real: list_real > nat > real ).
thf(func_def_816,type,
nth_set_nat: list_set_nat > nat > set_nat ).
thf(func_def_817,type,
nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_818,type,
product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
thf(func_def_819,type,
product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
thf(func_def_820,type,
product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
thf(func_def_821,type,
product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
thf(func_def_822,type,
produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
thf(func_def_823,type,
product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
thf(func_def_824,type,
produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(func_def_825,type,
product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
thf(func_def_826,type,
produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
thf(func_def_827,type,
produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
thf(func_def_828,type,
produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(func_def_829,type,
product_lists_o: list_list_o > list_list_o ).
thf(func_def_830,type,
product_lists_int: list_list_int > list_list_int ).
thf(func_def_831,type,
product_lists_nat: list_list_nat > list_list_nat ).
thf(func_def_832,type,
produc3021084454716106787T_VEBT: list_list_VEBT_VEBT > list_list_VEBT_VEBT ).
thf(func_def_833,type,
replicate_o: nat > $o > list_o ).
thf(func_def_834,type,
replicate_complex: nat > complex > list_complex ).
thf(func_def_835,type,
replicate_int: nat > int > list_int ).
thf(func_def_836,type,
replicate_nat: nat > nat > list_nat ).
thf(func_def_837,type,
replicate_real: nat > real > list_real ).
thf(func_def_838,type,
replicate_set_nat: nat > set_nat > list_set_nat ).
thf(func_def_839,type,
replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_840,type,
rotate1_o: list_o > list_o ).
thf(func_def_841,type,
rotate1_int: list_int > list_int ).
thf(func_def_842,type,
rotate1_nat: list_nat > list_nat ).
thf(func_def_843,type,
rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_844,type,
sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
thf(func_def_845,type,
take_nat: nat > list_nat > list_nat ).
thf(func_def_846,type,
take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_847,type,
upt: nat > nat > list_nat ).
thf(func_def_848,type,
upto: int > int > list_int ).
thf(func_def_849,type,
zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
thf(func_def_850,type,
zip_o_complex: list_o > list_complex > list_P3924974545808530565omplex ).
thf(func_def_851,type,
zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
thf(func_def_852,type,
zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
thf(func_def_853,type,
zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
thf(func_def_854,type,
zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
thf(func_def_855,type,
zip_Co3543743374963494515nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
thf(func_def_856,type,
zip_complex_o: list_complex > list_o > list_P7942624414058669295plex_o ).
thf(func_def_857,type,
zip_complex_complex: list_complex > list_complex > list_P7664491975274850627omplex ).
thf(func_def_858,type,
zip_complex_int: list_complex > list_int > list_P2206113689347244737ex_int ).
thf(func_def_859,type,
zip_complex_nat: list_complex > list_nat > list_P4696196834278971493ex_nat ).
thf(func_def_860,type,
zip_complex_real: list_complex > list_real > list_P7647014805210017729x_real ).
thf(func_def_861,type,
zip_co9157518722488180109T_VEBT: list_complex > list_VEBT_VEBT > list_P7977503562704621835T_VEBT ).
thf(func_def_862,type,
zip_int_complex: list_int > list_complex > list_P1797514011394873281omplex ).
thf(func_def_863,type,
zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
thf(func_def_864,type,
zip_int_real: list_int > list_real > list_P6863124054624500543t_real ).
thf(func_def_865,type,
zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
thf(func_def_866,type,
zip_nat_VEBT_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
thf(func_def_867,type,
zip_Pr4664179122662387191at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
thf(func_def_868,type,
zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
thf(func_def_869,type,
zip_real_complex: list_real > list_complex > list_P3881527313128557121omplex ).
thf(func_def_870,type,
zip_real_int: list_real > list_int > list_P4344331454722006975al_int ).
thf(func_def_871,type,
zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
thf(func_def_872,type,
zip_real_real: list_real > list_real > list_P8689742595348180415l_real ).
thf(func_def_873,type,
zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT ).
thf(func_def_874,type,
zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat ).
thf(func_def_875,type,
zip_se5600341670672612855at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > list_P5464809261938338413at_nat ).
thf(func_def_876,type,
zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
thf(func_def_877,type,
zip_VE2794733401258833515omplex: list_VEBT_VEBT > list_complex > list_P4108580160459392801omplex ).
thf(func_def_878,type,
zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
thf(func_def_879,type,
zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
thf(func_def_880,type,
zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real ).
thf(func_def_881,type,
zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
thf(func_def_882,type,
suc: nat > nat ).
thf(func_def_883,type,
compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
thf(func_def_884,type,
case_nat_o: $o > ( nat > $o ) > nat > $o ).
thf(func_def_885,type,
case_nat_nat: nat > ( nat > nat ) > nat > nat ).
thf(func_def_886,type,
pred: nat > nat ).
thf(func_def_887,type,
semiri4939895301339042750nteger: nat > code_integer ).
thf(func_def_888,type,
semiri3763490453095760265atural: nat > code_natural ).
thf(func_def_889,type,
semiri8010041392384452111omplex: nat > complex ).
thf(func_def_890,type,
semiri4216267220026989637d_enat: nat > extended_enat ).
thf(func_def_891,type,
semiri1314217659103216013at_int: nat > int ).
thf(func_def_892,type,
semiri1316708129612266289at_nat: nat > nat ).
thf(func_def_893,type,
semiri681578069525770553at_rat: nat > rat ).
thf(func_def_894,type,
semiri5074537144036343181t_real: nat > real ).
thf(func_def_895,type,
semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
thf(func_def_896,type,
semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
thf(func_def_897,type,
semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
thf(func_def_898,type,
semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
thf(func_def_899,type,
semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
thf(func_def_900,type,
semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
thf(func_def_901,type,
size_size_list_o: list_o > nat ).
thf(func_def_902,type,
size_s3445333598471063425nteger: list_Code_integer > nat ).
thf(func_def_903,type,
size_s3451745648224563538omplex: list_complex > nat ).
thf(func_def_904,type,
size_size_list_int: list_int > nat ).
thf(func_def_905,type,
size_s2710708370519433104list_o: list_list_o > nat ).
thf(func_def_906,type,
size_s533118279054570080st_int: list_list_int > nat ).
thf(func_def_907,type,
size_s3023201423986296836st_nat: list_list_nat > nat ).
thf(func_def_908,type,
size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
thf(func_def_909,type,
size_size_list_nat: list_nat > nat ).
thf(func_def_910,type,
size_size_list_num: list_num > nat ).
thf(func_def_911,type,
size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
thf(func_def_912,type,
size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
thf(func_def_913,type,
size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
thf(func_def_914,type,
size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
thf(func_def_915,type,
size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
thf(func_def_916,type,
size_s2970893825323803983at_int: list_P3521021558325789923at_int > nat ).
thf(func_def_917,type,
size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
thf(func_def_918,type,
size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
thf(func_def_919,type,
size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
thf(func_def_920,type,
size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
thf(func_def_921,type,
size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
thf(func_def_922,type,
size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
thf(func_def_923,type,
size_size_list_real: list_real > nat ).
thf(func_def_924,type,
size_s3254054031482475050et_nat: list_set_nat > nat ).
thf(func_def_925,type,
size_s8736152011456118867at_nat: list_s1210847774152347623at_nat > nat ).
thf(func_def_926,type,
size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
thf(func_def_927,type,
size_size_num: num > nat ).
thf(func_def_928,type,
size_size_option_nat: option_nat > nat ).
thf(func_def_929,type,
size_size_option_num: option_num > nat ).
thf(func_def_930,type,
size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
thf(func_def_931,type,
size_size_char: char > nat ).
thf(func_def_932,type,
size_size_typerep: typerep > nat ).
thf(func_def_933,type,
size_size_VEBT_VEBT: vEBT_VEBT > nat ).
thf(func_def_934,type,
nat_int_decode: nat > int ).
thf(func_def_935,type,
nat_int_encode: int > nat ).
thf(func_def_936,type,
nat_list_decode: nat > list_nat ).
thf(func_def_937,type,
nat_list_decode_rel: nat > nat > $o ).
thf(func_def_938,type,
nat_list_encode: list_nat > nat ).
thf(func_def_939,type,
nat_list_encode_rel: list_nat > list_nat > $o ).
thf(func_def_940,type,
nat_prod_decode: nat > product_prod_nat_nat ).
thf(func_def_941,type,
nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
thf(func_def_942,type,
nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_943,type,
nat_prod_encode: product_prod_nat_nat > nat ).
thf(func_def_944,type,
nat_set_decode: nat > set_nat ).
thf(func_def_945,type,
nat_set_encode: set_nat > nat ).
thf(func_def_946,type,
nat_sum_decode: nat > sum_sum_nat_nat ).
thf(func_def_947,type,
nat_sum_encode: sum_sum_nat_nat > nat ).
thf(func_def_948,type,
nat_triangle: nat > nat ).
thf(func_def_949,type,
root: nat > real > real ).
thf(func_def_950,type,
sqrt: real > real ).
thf(func_def_951,type,
bitM: num > num ).
thf(func_def_952,type,
inc: num > num ).
thf(func_def_953,type,
nat_of_num: num > nat ).
thf(func_def_954,type,
neg_nu8804712462038260780nteger: code_integer > code_integer ).
thf(func_def_955,type,
neg_nu7009210354673126013omplex: complex > complex ).
thf(func_def_956,type,
neg_numeral_dbl_int: int > int ).
thf(func_def_957,type,
neg_numeral_dbl_rat: rat > rat ).
thf(func_def_958,type,
neg_numeral_dbl_real: real > real ).
thf(func_def_959,type,
neg_nu7757733837767384882nteger: code_integer > code_integer ).
thf(func_def_960,type,
neg_nu6511756317524482435omplex: complex > complex ).
thf(func_def_961,type,
neg_nu3811975205180677377ec_int: int > int ).
thf(func_def_962,type,
neg_nu3179335615603231917ec_rat: rat > rat ).
thf(func_def_963,type,
neg_nu6075765906172075777c_real: real > real ).
thf(func_def_964,type,
neg_nu5831290666863070958nteger: code_integer > code_integer ).
thf(func_def_965,type,
neg_nu8557863876264182079omplex: complex > complex ).
thf(func_def_966,type,
neg_nu5851722552734809277nc_int: int > int ).
thf(func_def_967,type,
neg_nu5219082963157363817nc_rat: rat > rat ).
thf(func_def_968,type,
neg_nu8295874005876285629c_real: real > real ).
thf(func_def_969,type,
neg_numeral_sub_int: num > num > int ).
thf(func_def_970,type,
bit0: num > num ).
thf(func_def_971,type,
bit1: num > num ).
thf(func_def_972,type,
one: num ).
thf(func_def_973,type,
size_num: num > nat ).
thf(func_def_974,type,
num_of_nat: nat > num ).
thf(func_def_975,type,
numera6620942414471956472nteger: num > code_integer ).
thf(func_def_976,type,
numera5444537566228673987atural: num > code_natural ).
thf(func_def_977,type,
numera6690914467698888265omplex: num > complex ).
thf(func_def_978,type,
numera1916890842035813515d_enat: num > extended_enat ).
thf(func_def_979,type,
numeral_numeral_int: num > int ).
thf(func_def_980,type,
numeral_numeral_nat: num > nat ).
thf(func_def_981,type,
numeral_numeral_rat: num > rat ).
thf(func_def_982,type,
numeral_numeral_real: num > real ).
thf(func_def_983,type,
pow: num > num > num ).
thf(func_def_984,type,
pred_numeral: num > nat ).
thf(func_def_985,type,
sqr: num > num ).
thf(func_def_986,type,
none_nat: option_nat ).
thf(func_def_987,type,
none_num: option_num ).
thf(func_def_988,type,
none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
thf(func_def_989,type,
some_o: $o > option_o ).
thf(func_def_990,type,
some_int: int > option_int ).
thf(func_def_991,type,
some_nat: nat > option_nat ).
thf(func_def_992,type,
some_num: num > option_num ).
thf(func_def_993,type,
some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
thf(func_def_994,type,
some_VEBT_VEBT: vEBT_VEBT > option_VEBT_VEBT ).
thf(func_def_995,type,
case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
thf(func_def_996,type,
case_option_num_num: num > ( num > num ) > option_num > num ).
thf(func_def_997,type,
case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
thf(func_def_998,type,
size_option_nat: ( nat > nat ) > option_nat > nat ).
thf(func_def_999,type,
size_option_num: ( num > nat ) > option_num > nat ).
thf(func_def_1000,type,
size_o8335143837870341156at_nat: ( product_prod_nat_nat > nat ) > option4927543243414619207at_nat > nat ).
thf(func_def_1001,type,
the_nat: option_nat > nat ).
thf(func_def_1002,type,
the_num: option_num > num ).
thf(func_def_1003,type,
the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_1004,type,
order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1005,type,
order_5251275573222108571on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1006,type,
order_4861654808422542329on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1007,type,
order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat ).
thf(func_def_1008,type,
order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1009,type,
bot_bot_nat: nat ).
thf(func_def_1010,type,
bot_bot_set_o: set_o ).
thf(func_def_1011,type,
bot_bot_set_complex: set_complex ).
thf(func_def_1012,type,
bot_bot_set_int: set_int ).
thf(func_def_1013,type,
bot_bot_set_list_nat: set_list_nat ).
thf(func_def_1014,type,
bot_bot_set_nat: set_nat ).
thf(func_def_1015,type,
bot_bot_set_num: set_num ).
thf(func_def_1016,type,
bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1017,type,
bot_bot_set_rat: set_rat ).
thf(func_def_1018,type,
bot_bot_set_real: set_real ).
thf(func_def_1019,type,
bot_bot_set_set_nat: set_set_nat ).
thf(func_def_1020,type,
bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).
thf(func_def_1021,type,
ord_Least_nat: ( nat > $o ) > nat ).
thf(func_def_1022,type,
ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
thf(func_def_1023,type,
ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
thf(func_def_1024,type,
ord_less_int: int > int > $o ).
thf(func_def_1025,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_1026,type,
ord_less_num: num > num > $o ).
thf(func_def_1027,type,
ord_less_rat: rat > rat > $o ).
thf(func_def_1028,type,
ord_less_real: real > real > $o ).
thf(func_def_1029,type,
ord_less_set_complex: set_complex > set_complex > $o ).
thf(func_def_1030,type,
ord_less_set_int: set_int > set_int > $o ).
thf(func_def_1031,type,
ord_less_set_nat: set_nat > set_nat > $o ).
thf(func_def_1032,type,
ord_less_set_num: set_num > set_num > $o ).
thf(func_def_1033,type,
ord_less_set_rat: set_rat > set_rat > $o ).
thf(func_def_1034,type,
ord_less_set_real: set_real > set_real > $o ).
thf(func_def_1035,type,
ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
thf(func_def_1036,type,
ord_le3102999989581377725nteger: code_integer > code_integer > $o ).
thf(func_def_1037,type,
ord_le1926595141338095240atural: code_natural > code_natural > $o ).
thf(func_def_1038,type,
ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o ).
thf(func_def_1039,type,
ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o ).
thf(func_def_1040,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_1041,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_1042,type,
ord_less_eq_num: num > num > $o ).
thf(func_def_1043,type,
ord_less_eq_rat: rat > rat > $o ).
thf(func_def_1044,type,
ord_less_eq_real: real > real > $o ).
thf(func_def_1045,type,
ord_less_eq_set_o: set_o > set_o > $o ).
thf(func_def_1046,type,
ord_le211207098394363844omplex: set_complex > set_complex > $o ).
thf(func_def_1047,type,
ord_less_eq_set_int: set_int > set_int > $o ).
thf(func_def_1048,type,
ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o ).
thf(func_def_1049,type,
ord_less_eq_set_nat: set_nat > set_nat > $o ).
thf(func_def_1050,type,
ord_less_eq_set_num: set_num > set_num > $o ).
thf(func_def_1051,type,
ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1052,type,
ord_less_eq_set_rat: set_rat > set_rat > $o ).
thf(func_def_1053,type,
ord_less_eq_set_real: set_real > set_real > $o ).
thf(func_def_1054,type,
ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o ).
thf(func_def_1055,type,
ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o ).
thf(func_def_1056,type,
ord_max_Code_integer: code_integer > code_integer > code_integer ).
thf(func_def_1057,type,
ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat ).
thf(func_def_1058,type,
ord_max_int: int > int > int ).
thf(func_def_1059,type,
ord_max_nat: nat > nat > nat ).
thf(func_def_1060,type,
ord_max_num: num > num > num ).
thf(func_def_1061,type,
ord_max_rat: rat > rat > rat ).
thf(func_def_1062,type,
ord_max_real: real > real > real ).
thf(func_def_1063,type,
ord_max_set_int: set_int > set_int > set_int ).
thf(func_def_1064,type,
ord_max_set_nat: set_nat > set_nat > set_nat ).
thf(func_def_1065,type,
ord_max_set_real: set_real > set_real > set_real ).
thf(func_def_1066,type,
ord_min_nat: nat > nat > nat ).
thf(func_def_1067,type,
order_Greatest_nat: ( nat > $o ) > nat ).
thf(func_def_1068,type,
order_mono_nat_nat: ( nat > nat ) > $o ).
thf(func_def_1069,type,
order_5726023648592871131at_nat: ( nat > nat ) > $o ).
thf(func_def_1070,type,
ordering_top_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > $o ).
thf(func_def_1071,type,
top_top_set_int: set_int ).
thf(func_def_1072,type,
top_top_set_list_nat: set_list_nat ).
thf(func_def_1073,type,
top_top_set_nat: set_nat ).
thf(func_def_1074,type,
top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1075,type,
top_top_set_real: set_real ).
thf(func_def_1076,type,
top_top_set_char: set_char ).
thf(func_def_1077,type,
top_to6661820994512907621at_nat: set_Sum_sum_nat_nat ).
thf(func_def_1078,type,
power_8256067586552552935nteger: code_integer > nat > code_integer ).
thf(func_def_1079,type,
power_7079662738309270450atural: code_natural > nat > code_natural ).
thf(func_def_1080,type,
power_power_complex: complex > nat > complex ).
thf(func_def_1081,type,
power_8040749407984259932d_enat: extended_enat > nat > extended_enat ).
thf(func_def_1082,type,
power_power_int: int > nat > int ).
thf(func_def_1083,type,
power_power_nat: nat > nat > nat ).
thf(func_def_1084,type,
power_power_rat: rat > nat > rat ).
thf(func_def_1085,type,
power_power_real: real > nat > real ).
thf(func_def_1086,type,
produc4035269172776083154on_nat: ( nat > nat > $o ) > produc4953844613479565601on_nat > produc2233624965454879586on_nat ).
thf(func_def_1087,type,
produc3209952032786966637at_nat: ( nat > nat > nat ) > produc7248412053542808358at_nat > produc4471711990508489141at_nat ).
thf(func_def_1088,type,
produc8929957630744042906on_nat: ( nat > nat > nat ) > produc4953844613479565601on_nat > produc8306885398267862888on_nat ).
thf(func_def_1089,type,
produc3576312749637752826on_num: ( num > num > $o ) > produc3447558737645232053on_num > produc7036089656553540234on_num ).
thf(func_def_1090,type,
produc5778274026573060048on_num: ( num > num > num ) > produc3447558737645232053on_num > produc1193250871479095198on_num ).
thf(func_def_1091,type,
produc3994169339658061776at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > produc6121120109295599847at_nat > produc5491161045314408544at_nat ).
thf(func_def_1092,type,
produc2899441246263362727at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > produc6121120109295599847at_nat > produc5542196010084753463at_nat ).
thf(func_def_1093,type,
product_Pair_o_o: $o > $o > product_prod_o_o ).
thf(func_def_1094,type,
produc414345526774272751omplex: $o > complex > produc648051720047351925omplex ).
thf(func_def_1095,type,
product_Pair_o_int: $o > int > product_prod_o_int ).
thf(func_def_1096,type,
product_Pair_o_nat: $o > nat > product_prod_o_nat ).
thf(func_def_1097,type,
product_Pair_o_real: $o > real > product_prod_o_real ).
thf(func_def_1098,type,
produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT ).
thf(func_def_1099,type,
produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger ).
thf(func_def_1100,type,
produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural ).
thf(func_def_1101,type,
produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_1102,type,
produc2908979694703026321plex_o: complex > $o > produc6088675342482847199plex_o ).
thf(func_def_1103,type,
produc101793102246108661omplex: complex > complex > produc4411394909380815293omplex ).
thf(func_def_1104,type,
produc1367138851071493491ex_int: complex > int > produc6845221339535797307ex_int ).
thf(func_def_1105,type,
produc1369629321580543767ex_nat: complex > nat > produc1799700322190218207ex_nat ).
thf(func_def_1106,type,
produc1746590499379883635x_real: complex > real > produc8892588492097263291x_real ).
thf(func_def_1107,type,
produc2757191886755552429T_VEBT: complex > vEBT_VEBT > produc7151440242714718331T_VEBT ).
thf(func_def_1108,type,
produc7948753499206759283omplex: int > complex > produc5838698208256999739omplex ).
thf(func_def_1109,type,
product_Pair_int_int: int > int > product_prod_int_int ).
thf(func_def_1110,type,
produc801115645435158769t_real: int > real > produc679980390762269497t_real ).
thf(func_def_1111,type,
produc8435520187683070743list_o: list_o > list_o > produc7102631898165422375list_o ).
thf(func_def_1112,type,
produc2951025481305455875st_int: list_o > list_int > produc1713839591385758857st_int ).
thf(func_def_1113,type,
produc7128876500814652583st_nat: list_o > list_nat > produc4203922736317485613st_nat ).
thf(func_def_1114,type,
produc6043759678074843571T_VEBT: list_o > list_VEBT_VEBT > produc1922972420619397443T_VEBT ).
thf(func_def_1115,type,
produc750622340256944499nteger: list_Code_integer > list_Code_integer > produc862207588354017979nteger ).
thf(func_def_1116,type,
produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int ).
thf(func_def_1117,type,
produc699922362453767013list_o: list_nat > list_o > produc149729814636038835list_o ).
thf(func_def_1118,type,
produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat ).
thf(func_def_1119,type,
produc8335345208264861441T_VEBT: list_nat > list_VEBT_VEBT > produc872621073311890639T_VEBT ).
thf(func_def_1120,type,
produc5943733680697469783at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > produc6392793444374437607at_nat ).
thf(func_def_1121,type,
produc7536900900485677911at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > produc424102278133772007at_nat ).
thf(func_def_1122,type,
produc2717590391345394939list_o: list_VEBT_VEBT > list_o > produc3962069817607390347list_o ).
thf(func_def_1123,type,
produc1392282695434103839st_int: list_VEBT_VEBT > list_int > produc7831203938951381541st_int ).
thf(func_def_1124,type,
produc5570133714943300547st_nat: list_VEBT_VEBT > list_nat > produc1097915047028332489st_nat ).
thf(func_def_1125,type,
produc3897820843166775703T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > produc9211091688327510695T_VEBT ).
thf(func_def_1126,type,
product_Pair_nat_o: nat > $o > product_prod_nat_o ).
thf(func_def_1127,type,
product_Pair_nat_int: nat > int > product_prod_nat_int ).
thf(func_def_1128,type,
product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
thf(func_def_1129,type,
produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat ).
thf(func_def_1130,type,
produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
thf(func_def_1131,type,
produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
thf(func_def_1132,type,
produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
thf(func_def_1133,type,
produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
thf(func_def_1134,type,
produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat ).
thf(func_def_1135,type,
product_Pair_real_o: real > $o > product_prod_real_o ).
thf(func_def_1136,type,
produc1693001998875562995omplex: real > complex > produc6979889472282505531omplex ).
thf(func_def_1137,type,
produc3179012173361985393al_int: real > int > produc8786904178792722361al_int ).
thf(func_def_1138,type,
produc3181502643871035669al_nat: real > nat > produc3741383161447143261al_nat ).
thf(func_def_1139,type,
produc4511245868158468465l_real: real > real > produc2422161461964618553l_real ).
thf(func_def_1140,type,
produc6931449550656315951T_VEBT: real > vEBT_VEBT > produc3757001726724277373T_VEBT ).
thf(func_def_1141,type,
produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat ).
thf(func_def_1142,type,
produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat ).
thf(func_def_1143,type,
produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
thf(func_def_1144,type,
produc5617778602380981643omplex: vEBT_VEBT > complex > produc8380087813684007313omplex ).
thf(func_def_1145,type,
produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat ).
thf(func_def_1146,type,
produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
thf(func_def_1147,type,
produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
thf(func_def_1148,type,
produc8117437818029410057T_real: vEBT_VEBT > real > produc5170161368751668367T_real ).
thf(func_def_1149,type,
produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
thf(func_def_1150,type,
produc457027306803732586at_nat: set_nat > ( nat > set_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1151,type,
produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1152,type,
produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
thf(func_def_1153,type,
produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
thf(func_def_1154,type,
produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
thf(func_def_1155,type,
produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
thf(func_def_1156,type,
produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
thf(func_def_1157,type,
produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
thf(func_def_1158,type,
produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_1159,type,
produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1160,type,
produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_1161,type,
produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
thf(func_def_1162,type,
produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
thf(func_def_1163,type,
produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_1164,type,
produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
thf(func_def_1165,type,
product_fst_int_int: product_prod_int_int > int ).
thf(func_def_1166,type,
product_fst_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_1167,type,
product_snd_int_int: product_prod_int_int > int ).
thf(func_def_1168,type,
product_snd_nat_nat: product_prod_nat_nat > nat ).
thf(func_def_1169,type,
produc5538323210962509403atural: ( produc7822875418678951345atural > produc5835291356934675326atural ) > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_1170,type,
iterat8892046348760725948atural: code_natural > ( code_natural > produc7822875418678951345atural > produc5835291356934675326atural ) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_1171,type,
log: code_natural > code_natural > code_natural ).
thf(func_def_1172,type,
minus_shift: code_natural > code_natural > code_natural > code_natural ).
thf(func_def_1173,type,
next: produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_1174,type,
range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural ).
thf(func_def_1175,type,
abs_Rat: product_prod_int_int > rat ).
thf(func_def_1176,type,
fract: int > int > rat ).
thf(func_def_1177,type,
rep_Rat: rat > product_prod_int_int ).
thf(func_def_1178,type,
field_5140801741446780682s_real: set_real ).
thf(func_def_1179,type,
normalize: product_prod_int_int > product_prod_int_int ).
thf(func_def_1180,type,
pcr_rat: product_prod_int_int > rat > $o ).
thf(func_def_1181,type,
positive: rat > $o ).
thf(func_def_1182,type,
quotient_of: rat > product_prod_int_int ).
thf(func_def_1183,type,
ratrel: product_prod_int_int > product_prod_int_int > $o ).
thf(func_def_1184,type,
ratreal: rat > real ).
thf(func_def_1185,type,
real2: ( nat > rat ) > real ).
thf(func_def_1186,type,
cauchy: ( nat > rat ) > $o ).
thf(func_def_1187,type,
pcr_real: ( nat > rat ) > real > $o ).
thf(func_def_1188,type,
positive2: real > $o ).
thf(func_def_1189,type,
realrel: ( nat > rat ) > ( nat > rat ) > $o ).
thf(func_def_1190,type,
rep_real: real > nat > rat ).
thf(func_def_1191,type,
vanishes: ( nat > rat ) > $o ).
thf(func_def_1192,type,
real_V2521375963428798218omplex: set_complex ).
thf(func_def_1193,type,
real_V5970128139526366754l_real: ( real > real ) > $o ).
thf(func_def_1194,type,
real_V4572627801940501177l_real: ( real > real ) > $o ).
thf(func_def_1195,type,
real_V1022390504157884413omplex: complex > real ).
thf(func_def_1196,type,
real_V7735802525324610683m_real: real > real ).
thf(func_def_1197,type,
real_V4546457046886955230omplex: real > complex ).
thf(func_def_1198,type,
real_V2046097035970521341omplex: real > complex > complex ).
thf(func_def_1199,type,
real_V1485227260804924795R_real: real > real > real ).
thf(func_def_1200,type,
field_nat: set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_1201,type,
id_nat2: set_Pr1261947904930325089at_nat ).
thf(func_def_1202,type,
antisym_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1203,type,
refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1204,type,
total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1205,type,
trans_nat: set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1206,type,
algebr932160517623751201me_int: int > int > $o ).
thf(func_def_1207,type,
algebr934650988132801477me_nat: nat > nat > $o ).
thf(func_def_1208,type,
divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
thf(func_def_1209,type,
divide5121882707175180666atural: code_natural > code_natural > code_natural ).
thf(func_def_1210,type,
divide1717551699836669952omplex: complex > complex > complex ).
thf(func_def_1211,type,
divide_divide_int: int > int > int ).
thf(func_def_1212,type,
divide_divide_nat: nat > nat > nat ).
thf(func_def_1213,type,
divide_divide_rat: rat > rat > rat ).
thf(func_def_1214,type,
divide_divide_real: real > real > real ).
thf(func_def_1215,type,
dvd_dvd_Code_integer: code_integer > code_integer > $o ).
thf(func_def_1216,type,
dvd_dvd_Code_natural: code_natural > code_natural > $o ).
thf(func_def_1217,type,
dvd_dvd_complex: complex > complex > $o ).
thf(func_def_1218,type,
dvd_dvd_int: int > int > $o ).
thf(func_def_1219,type,
dvd_dvd_nat: nat > nat > $o ).
thf(func_def_1220,type,
dvd_dvd_rat: rat > rat > $o ).
thf(func_def_1221,type,
dvd_dvd_real: real > real > $o ).
thf(func_def_1222,type,
modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
thf(func_def_1223,type,
modulo8411746178871703098atural: code_natural > code_natural > code_natural ).
thf(func_def_1224,type,
modulo_modulo_int: int > int > int ).
thf(func_def_1225,type,
modulo_modulo_nat: nat > nat > nat ).
thf(func_def_1226,type,
unit_f2748546683901255202or_nat: nat > nat ).
thf(func_def_1227,type,
zero_n356916108424825756nteger: $o > code_integer ).
thf(func_def_1228,type,
zero_n8403883297036319079atural: $o > code_natural ).
thf(func_def_1229,type,
zero_n1201886186963655149omplex: $o > complex ).
thf(func_def_1230,type,
zero_n2684676970156552555ol_int: $o > int ).
thf(func_def_1231,type,
zero_n2687167440665602831ol_nat: $o > nat ).
thf(func_def_1232,type,
zero_n2052037380579107095ol_rat: $o > rat ).
thf(func_def_1233,type,
zero_n3304061248610475627l_real: $o > real ).
thf(func_def_1234,type,
suminf_real: ( nat > real ) > real ).
thf(func_def_1235,type,
summable_real: ( nat > real ) > $o ).
thf(func_def_1236,type,
sums_complex: ( nat > complex ) > complex > $o ).
thf(func_def_1237,type,
sums_int: ( nat > int ) > int > $o ).
thf(func_def_1238,type,
sums_nat: ( nat > nat ) > nat > $o ).
thf(func_def_1239,type,
sums_real: ( nat > real ) > real > $o ).
thf(func_def_1240,type,
collect_complex: ( complex > $o ) > set_complex ).
thf(func_def_1241,type,
collect_int: ( int > $o ) > set_int ).
thf(func_def_1242,type,
collect_list_o: ( list_o > $o ) > set_list_o ).
thf(func_def_1243,type,
collect_list_complex: ( list_complex > $o ) > set_list_complex ).
thf(func_def_1244,type,
collect_list_int: ( list_int > $o ) > set_list_int ).
thf(func_def_1245,type,
collec5989764272469232197st_nat: ( list_list_nat > $o ) > set_list_list_nat ).
thf(func_def_1246,type,
collect_list_nat: ( list_nat > $o ) > set_list_nat ).
thf(func_def_1247,type,
collect_list_set_nat: ( list_set_nat > $o ) > set_list_set_nat ).
thf(func_def_1248,type,
collec5608196760682091941T_VEBT: ( list_VEBT_VEBT > $o ) > set_list_VEBT_VEBT ).
thf(func_def_1249,type,
collect_nat: ( nat > $o ) > set_nat ).
thf(func_def_1250,type,
collect_num: ( num > $o ) > set_num ).
thf(func_def_1251,type,
collec3392354462482085612at_nat: ( product_prod_nat_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_1252,type,
collect_rat: ( rat > $o ) > set_rat ).
thf(func_def_1253,type,
collect_real: ( real > $o ) > set_real ).
thf(func_def_1254,type,
collect_set_nat: ( set_nat > $o ) > set_set_nat ).
thf(func_def_1255,type,
pow_nat: set_nat > set_set_nat ).
thf(func_def_1256,type,
image_int_int: ( int > int ) > set_int > set_int ).
thf(func_def_1257,type,
image_int_nat: ( int > nat ) > set_int > set_nat ).
thf(func_def_1258,type,
image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
thf(func_def_1259,type,
image_nat_int: ( nat > int ) > set_nat > set_int ).
thf(func_def_1260,type,
image_nat_list_nat: ( nat > list_nat ) > set_nat > set_list_nat ).
thf(func_def_1261,type,
image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_1262,type,
image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1263,type,
image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
thf(func_def_1264,type,
image_nat_char: ( nat > char ) > set_nat > set_char ).
thf(func_def_1265,type,
image_678696785212003926at_nat: ( nat > sum_sum_nat_nat ) > set_nat > set_Sum_sum_nat_nat ).
thf(func_def_1266,type,
image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).
thf(func_def_1267,type,
image_real_real: ( real > real ) > set_real > set_real ).
thf(func_def_1268,type,
image_char_nat: ( char > nat ) > set_char > set_nat ).
thf(func_def_1269,type,
image_1320371278474632150at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > set_nat ).
thf(func_def_1270,type,
insert_o: $o > set_o > set_o ).
thf(func_def_1271,type,
insert_complex: complex > set_complex > set_complex ).
thf(func_def_1272,type,
insert_int: int > set_int > set_int ).
thf(func_def_1273,type,
insert_list_nat: list_nat > set_list_nat > set_list_nat ).
thf(func_def_1274,type,
insert_nat: nat > set_nat > set_nat ).
thf(func_def_1275,type,
insert_num: num > set_num > set_num ).
thf(func_def_1276,type,
insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1277,type,
insert_rat: rat > set_rat > set_rat ).
thf(func_def_1278,type,
insert_real: real > set_real > set_real ).
thf(func_def_1279,type,
insert_set_nat: set_nat > set_set_nat > set_set_nat ).
thf(func_def_1280,type,
insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
thf(func_def_1281,type,
vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
thf(func_def_1282,type,
set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).
thf(func_def_1283,type,
set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
thf(func_def_1284,type,
set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
thf(func_def_1285,type,
set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
thf(func_def_1286,type,
set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
thf(func_def_1287,type,
set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
thf(func_def_1288,type,
set_or1266510415728281911st_int: int > int > set_int ).
thf(func_def_1289,type,
set_or1269000886237332187st_nat: nat > nat > set_nat ).
thf(func_def_1290,type,
set_or7049704709247886629st_num: num > num > set_num ).
thf(func_def_1291,type,
set_or633870826150836451st_rat: rat > rat > set_rat ).
thf(func_def_1292,type,
set_or1222579329274155063t_real: real > real > set_real ).
thf(func_def_1293,type,
set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
thf(func_def_1294,type,
set_or4662586982721622107an_int: int > int > set_int ).
thf(func_def_1295,type,
set_or4665077453230672383an_nat: nat > nat > set_nat ).
thf(func_def_1296,type,
set_ord_atLeast_nat: nat > set_nat ).
thf(func_def_1297,type,
set_ord_atMost_int: int > set_int ).
thf(func_def_1298,type,
set_ord_atMost_nat: nat > set_nat ).
thf(func_def_1299,type,
set_ord_atMost_num: num > set_num ).
thf(func_def_1300,type,
set_ord_atMost_rat: rat > set_rat ).
thf(func_def_1301,type,
set_ord_atMost_real: real > set_real ).
thf(func_def_1302,type,
set_or4236626031148496127et_nat: set_nat > set_set_nat ).
thf(func_def_1303,type,
set_or6656581121297822940st_int: int > int > set_int ).
thf(func_def_1304,type,
set_or6659071591806873216st_nat: nat > nat > set_nat ).
thf(func_def_1305,type,
set_or5832277885323065728an_int: int > int > set_int ).
thf(func_def_1306,type,
set_or5834768355832116004an_nat: nat > nat > set_nat ).
thf(func_def_1307,type,
set_or1633881224788618240n_real: real > real > set_real ).
thf(func_def_1308,type,
set_or1210151606488870762an_nat: nat > set_nat ).
thf(func_def_1309,type,
set_or5849166863359141190n_real: real > set_real ).
thf(func_def_1310,type,
set_ord_lessThan_int: int > set_int ).
thf(func_def_1311,type,
set_ord_lessThan_nat: nat > set_nat ).
thf(func_def_1312,type,
set_ord_lessThan_num: num > set_num ).
thf(func_def_1313,type,
set_ord_lessThan_rat: rat > set_rat ).
thf(func_def_1314,type,
set_or5984915006950818249n_real: real > set_real ).
thf(func_def_1315,type,
set_or890127255671739683et_nat: set_nat > set_set_nat ).
thf(func_def_1316,type,
char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
thf(func_def_1317,type,
size_char: char > nat ).
thf(func_def_1318,type,
comm_s629917340098488124ar_nat: char > nat ).
thf(func_def_1319,type,
integer_of_char: char > code_integer ).
thf(func_def_1320,type,
unique3096191561947761185of_nat: nat > char ).
thf(func_def_1321,type,
sum_Inl_nat_nat: nat > sum_sum_nat_nat ).
thf(func_def_1322,type,
sum_Inr_nat_nat: nat > sum_sum_nat_nat ).
thf(func_def_1323,type,
sum_ca7763040182479039464nt_nat: ( nat > int ) > ( nat > int ) > sum_sum_nat_nat > int ).
thf(func_def_1324,type,
sum_ca6763686470577984908at_nat: ( nat > nat ) > ( nat > nat ) > sum_sum_nat_nat > nat ).
thf(func_def_1325,type,
topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
thf(func_def_1326,type,
topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
thf(func_def_1327,type,
topolo6980174941875973593q_real: ( nat > real ) > $o ).
thf(func_def_1328,type,
topolo2177554685111907308n_real: real > set_real > filter_real ).
thf(func_def_1329,type,
topolo7531315842566124627t_real: ( nat > real ) > $o ).
thf(func_def_1330,type,
topolo2815343760600316023s_real: real > filter_real ).
thf(func_def_1331,type,
topolo4055970368930404560y_real: ( nat > real ) > $o ).
thf(func_def_1332,type,
arccos: real > real ).
thf(func_def_1333,type,
arcosh_real: real > real ).
thf(func_def_1334,type,
arctan: real > real ).
thf(func_def_1335,type,
arsinh_real: real > real ).
thf(func_def_1336,type,
artanh_real: real > real ).
thf(func_def_1337,type,
cos_complex: complex > complex ).
thf(func_def_1338,type,
cos_real: real > real ).
thf(func_def_1339,type,
cos_coeff: nat > real ).
thf(func_def_1340,type,
cot_real: real > real ).
thf(func_def_1341,type,
exp_complex: complex > complex ).
thf(func_def_1342,type,
exp_real: real > real ).
thf(func_def_1343,type,
ln_ln_real: real > real ).
thf(func_def_1344,type,
log2: real > real > real ).
thf(func_def_1345,type,
pi: real ).
thf(func_def_1346,type,
powr_real: real > real > real ).
thf(func_def_1347,type,
sin_complex: complex > complex ).
thf(func_def_1348,type,
sin_real: real > real ).
thf(func_def_1349,type,
sin_coeff: nat > real ).
thf(func_def_1350,type,
tan_real: real > real ).
thf(func_def_1351,type,
tanh_real: real > real ).
thf(func_def_1352,type,
transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1353,type,
transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1354,type,
transi2163837189807498211lp_nat: ( nat > nat > $o ) > nat > nat > $o ).
thf(func_def_1355,type,
typerep2: literal > list_typerep > typerep ).
thf(func_def_1356,type,
size_typerep: typerep > nat ).
thf(func_def_1357,type,
vEBT_Leaf: $o > $o > vEBT_VEBT ).
thf(func_def_1358,type,
vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1359,type,
vEBT_size_VEBT: vEBT_VEBT > nat ).
thf(func_def_1360,type,
vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
thf(func_def_1361,type,
vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(func_def_1362,type,
vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ).
thf(func_def_1363,type,
vEBT_VEBT_high: nat > nat > nat ).
thf(func_def_1364,type,
vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
thf(func_def_1365,type,
vEBT_VEBT_low: nat > nat > nat ).
thf(func_def_1366,type,
vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
thf(func_def_1367,type,
vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1368,type,
vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
thf(func_def_1369,type,
vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1370,type,
vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
thf(func_def_1371,type,
vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1372,type,
vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
thf(func_def_1373,type,
vEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(func_def_1374,type,
vEBT_vebt_buildup: nat > vEBT_VEBT ).
thf(func_def_1375,type,
vEBT_v4011308405150292612up_rel: nat > nat > $o ).
thf(func_def_1376,type,
vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1377,type,
vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1378,type,
vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1379,type,
vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1380,type,
vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1381,type,
vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1382,type,
vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
thf(func_def_1383,type,
vEBT_VEBT_minNull: vEBT_VEBT > $o ).
thf(func_def_1384,type,
vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1385,type,
vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
thf(func_def_1386,type,
vEBT_vebt_member: vEBT_VEBT > nat > $o ).
thf(func_def_1387,type,
vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1388,type,
vEBT_VEBT_add: option_nat > option_nat > option_nat ).
thf(func_def_1389,type,
vEBT_VEBT_greater: option_nat > option_nat > $o ).
thf(func_def_1390,type,
vEBT_VEBT_less: option_nat > option_nat > $o ).
thf(func_def_1391,type,
vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
thf(func_def_1392,type,
vEBT_VEBT_max_in_set: set_nat > nat > $o ).
thf(func_def_1393,type,
vEBT_VEBT_min_in_set: set_nat > nat > $o ).
thf(func_def_1394,type,
vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
thf(func_def_1395,type,
vEBT_V2881884560877996034ft_nat: ( nat > nat > $o ) > option_nat > option_nat > $o ).
thf(func_def_1396,type,
vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
thf(func_def_1397,type,
vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
thf(func_def_1398,type,
vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
thf(func_def_1399,type,
vEBT_VEBT_power: option_nat > option_nat > option_nat ).
thf(func_def_1400,type,
vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
thf(func_def_1401,type,
vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1402,type,
vEBT_vebt_mint: vEBT_VEBT > option_nat ).
thf(func_def_1403,type,
vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1404,type,
vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
thf(func_def_1405,type,
vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
thf(func_def_1406,type,
vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1407,type,
vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
thf(func_def_1408,type,
vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
thf(func_def_1409,type,
vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
thf(func_def_1410,type,
accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
thf(func_def_1411,type,
accp_nat: ( nat > nat > $o ) > nat > $o ).
thf(func_def_1412,type,
accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
thf(func_def_1413,type,
accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
thf(func_def_1414,type,
accp_P6183159247885693666d_enat: ( produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o ) > produc7272778201969148633d_enat > $o ).
thf(func_def_1415,type,
accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
thf(func_def_1416,type,
accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
thf(func_def_1417,type,
less_than: set_Pr1261947904930325089at_nat ).
thf(func_def_1418,type,
pred_nat: set_Pr1261947904930325089at_nat ).
thf(func_def_1419,type,
member_o: $o > set_o > $o ).
thf(func_def_1420,type,
member_Code_integer: code_integer > set_Code_integer > $o ).
thf(func_def_1421,type,
member_complex: complex > set_complex > $o ).
thf(func_def_1422,type,
member_int: int > set_int > $o ).
thf(func_def_1423,type,
member_list_o: list_o > set_list_o > $o ).
thf(func_def_1424,type,
member_list_int: list_int > set_list_int > $o ).
thf(func_def_1425,type,
member_list_nat: list_nat > set_list_nat > $o ).
thf(func_def_1426,type,
member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
thf(func_def_1427,type,
member_nat: nat > set_nat > $o ).
thf(func_def_1428,type,
member_num: num > set_num > $o ).
thf(func_def_1429,type,
member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o ).
thf(func_def_1430,type,
member1046615901120239500omplex: produc648051720047351925omplex > set_Pr5421754520313593387omplex > $o ).
thf(func_def_1431,type,
member7847949116333733898_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > $o ).
thf(func_def_1432,type,
member2802428098988154798_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > $o ).
thf(func_def_1433,type,
member7400031367953476362o_real: product_prod_o_real > set_Pr6573716822653411497o_real > $o ).
thf(func_def_1434,type,
member5477980866518848620T_VEBT: produc2504756804600209347T_VEBT > set_Pr7543698050874017315T_VEBT > $o ).
thf(func_def_1435,type,
member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o ).
thf(func_def_1436,type,
member6487239523555734774plex_o: produc6088675342482847199plex_o > set_Pr216032351708956309plex_o > $o ).
thf(func_def_1437,type,
member5793383173714906214omplex: produc4411394909380815293omplex > set_Pr5085853215250843933omplex > $o ).
thf(func_def_1438,type,
member595073364599660772ex_int: produc6845221339535797307ex_int > set_Pr2254670189886740123ex_int > $o ).
thf(func_def_1439,type,
member4772924384108857480ex_nat: produc1799700322190218207ex_nat > set_Pr4744753334818466879ex_nat > $o ).
thf(func_def_1440,type,
member47443559803733732x_real: produc8892588492097263291x_real > set_Pr1133549439701694107x_real > $o ).
thf(func_def_1441,type,
member1978952105866562066T_VEBT: produc7151440242714718331T_VEBT > set_Pr4085867452638698417T_VEBT > $o ).
thf(func_def_1442,type,
member8811922270175639012omplex: produc5838698208256999739omplex > set_Pr1846070511934368667omplex > $o ).
thf(func_def_1443,type,
member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
thf(func_def_1444,type,
member2744130022092475746t_real: produc679980390762269497t_real > set_Pr3538720872664544793t_real > $o ).
thf(func_def_1445,type,
member4159035015898711888list_o: produc7102631898165422375list_o > set_Pr6227168374412355847list_o > $o ).
thf(func_def_1446,type,
member8253032945758599840st_int: produc1713839591385758857st_int > set_Pr5001190662893202239st_int > $o ).
thf(func_def_1447,type,
member1519744053835550788st_nat: produc4203922736317485613st_nat > set_Pr591367044826345187st_nat > $o ).
thf(func_def_1448,type,
member1087064965665443052T_VEBT: produc1922972420619397443T_VEBT > set_Pr5170412164475753123T_VEBT > $o ).
thf(func_def_1449,type,
member749217712838834276nteger: produc862207588354017979nteger > set_Pr7565137564259432987nteger > $o ).
thf(func_def_1450,type,
member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o ).
thf(func_def_1451,type,
member6688923169008879818list_o: produc149729814636038835list_o > set_Pr1150278048023938153list_o > $o ).
thf(func_def_1452,type,
member7340969449405702474st_nat: produc1828647624359046049st_nat > set_Pr3451248702717554689st_nat > $o ).
thf(func_def_1453,type,
member5968030670617646438T_VEBT: produc872621073311890639T_VEBT > set_Pr1262583345697558789T_VEBT > $o ).
thf(func_def_1454,type,
member6693912407220327184at_nat: produc6392793444374437607at_nat > set_Pr1542805901266377927at_nat > $o ).
thf(func_def_1455,type,
member4080735728053443344at_nat: produc424102278133772007at_nat > set_Pr4333006031979791559at_nat > $o ).
thf(func_def_1456,type,
member3126162362653435956list_o: produc3962069817607390347list_o > set_Pr7508168486584781291list_o > $o ).
thf(func_def_1457,type,
member3703241499402361532st_int: produc7831203938951381541st_int > set_Pr4080907618048478043st_int > $o ).
thf(func_def_1458,type,
member6193324644334088288st_nat: produc1097915047028332489st_nat > set_Pr8894456036836396799st_nat > $o ).
thf(func_def_1459,type,
member4439316823752958928T_VEBT: produc9211091688327510695T_VEBT > set_Pr1916528119006554503T_VEBT > $o ).
thf(func_def_1460,type,
member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
thf(func_def_1461,type,
member8549952807677709168T_VEBT: produc8025551001238799321T_VEBT > set_Pr6167073792073659919T_VEBT > $o ).
thf(func_def_1462,type,
member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
thf(func_def_1463,type,
member772602641336174712real_o: product_prod_real_o > set_Pr4936984352647145239real_o > $o ).
thf(func_def_1464,type,
member7358116576843751780omplex: produc6979889472282505531omplex > set_Pr6591433984475009307omplex > $o ).
thf(func_def_1465,type,
member1627681773268152802al_int: produc8786904178792722361al_int > set_Pr1019928272762051225al_int > $o ).
thf(func_def_1466,type,
member5805532792777349510al_nat: produc3741383161447143261al_nat > set_Pr3510011417693777981al_nat > $o ).
thf(func_def_1467,type,
member7849222048561428706l_real: produc2422161461964618553l_real > set_Pr6218003697084177305l_real > $o ).
thf(func_def_1468,type,
member7262085504369356948T_VEBT: produc3757001726724277373T_VEBT > set_Pr6019664923565264691T_VEBT > $o ).
thf(func_def_1469,type,
member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
thf(func_def_1470,type,
member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
thf(func_def_1471,type,
member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o ).
thf(func_def_1472,type,
member3207599676835851048omplex: produc8380087813684007313omplex > set_Pr216944050393469383omplex > $o ).
thf(func_def_1473,type,
member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o ).
thf(func_def_1474,type,
member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
thf(func_def_1475,type,
member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o ).
thf(func_def_1476,type,
member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
thf(func_def_1477,type,
member_rat: rat > set_rat > $o ).
thf(func_def_1478,type,
member_real: real > set_real > $o ).
thf(func_def_1479,type,
member_set_nat: set_nat > set_set_nat > $o ).
thf(func_def_1480,type,
member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).
thf(func_def_1481,type,
member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
thf(func_def_1484,type,
deg: nat ).
thf(func_def_1485,type,
info: option4927543243414619207at_nat ).
thf(func_def_1486,type,
m: nat ).
thf(func_def_1487,type,
ma: nat ).
thf(func_def_1488,type,
mi: nat ).
thf(func_def_1489,type,
na: nat ).
thf(func_def_1490,type,
sa: vEBT_VEBT ).
thf(func_def_1491,type,
summary: vEBT_VEBT ).
thf(func_def_1492,type,
summary2: vEBT_VEBT ).
thf(func_def_1493,type,
treeList: list_VEBT_VEBT ).
thf(func_def_1494,type,
treeList2: list_VEBT_VEBT ).
thf(func_def_1513,type,
sP0: ( nat > $o ) > $o ).
thf(func_def_1514,type,
sP1: real > real > real > $o ).
thf(func_def_1515,type,
sP2: real > real > real > $o ).
thf(func_def_1516,type,
sP3: real > num > real > $o ).
thf(func_def_1517,type,
sP4: ( int > $o ) > $o ).
thf(func_def_1518,type,
sP5: list_VEBT_VEBT > nat > nat > nat > nat > $o ).
thf(func_def_1519,type,
sP6: nat > vEBT_VEBT > list_VEBT_VEBT > $o ).
thf(func_def_1520,type,
sP7: set_int > set_int > ( int > int ) > set_int > set_int > $o ).
thf(func_def_1521,type,
sP8: set_int > ( int > complex ) > $o ).
thf(func_def_1522,type,
sP9: set_int > set_int > ( int > int ) > ( int > int ) > $o ).
thf(func_def_1523,type,
sP10: set_int > ( int > complex ) > $o ).
thf(func_def_1524,type,
sP11: real > real > real > $o ).
thf(func_def_1525,type,
sP12: ( option4927543243414619207at_nat > option_num > $o ) > option4927543243414619207at_nat > option_num > $o ).
thf(func_def_1526,type,
sP13: set_nat > set_nat > ( nat > nat > $o ) > $o ).
thf(func_def_1527,type,
sP14: rat > num > rat > $o ).
thf(func_def_1528,type,
sP15: vEBT_VEBT > nat > vEBT_VEBT > $o ).
thf(func_def_1529,type,
sP16: rat > rat > rat > $o ).
thf(func_def_1530,type,
sP17: nat > nat > nat > $o ).
thf(func_def_1531,type,
sP18: nat > nat > nat > $o ).
thf(func_def_1532,type,
sP19: nat > nat > nat > $o ).
thf(func_def_1533,type,
sP20: real > ( real > real ) > ( real > real ) > real > $o ).
thf(func_def_1534,type,
sP21: num > num > num > $o ).
thf(func_def_1535,type,
sP22: num > num > num > $o ).
thf(func_def_1536,type,
sP23: num > num > num > $o ).
thf(func_def_1537,type,
sP24: real > num > real > $o ).
thf(func_def_1538,type,
sP25: $o > vEBT_VEBT > $o ).
thf(func_def_1539,type,
sP26: vEBT_VEBT > $o > $o ).
thf(func_def_1540,type,
sP27: nat > nat > list_VEBT_VEBT > nat > nat > $o ).
thf(func_def_1541,type,
sP28: nat > nat > list_VEBT_VEBT > nat > nat > $o > $o ).
thf(func_def_1542,type,
sP29: $o > $o > nat > $o ).
thf(func_def_1543,type,
sP30: $o > $o > nat > $o > $o ).
thf(func_def_1544,type,
sP31: $o > nat > vEBT_VEBT > $o ).
thf(func_def_1545,type,
sP32: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1546,type,
sP33: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1547,type,
sP34: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1548,type,
sP35: ( complex > complex ) > ( complex > complex ) > set_complex > set_complex > $o ).
thf(func_def_1549,type,
sP36: ( complex > complex ) > ( complex > complex ) > ( complex > complex ) > set_complex > $o ).
thf(func_def_1550,type,
sP37: set_complex > ( complex > complex ) > $o ).
thf(func_def_1551,type,
sP38: ( complex > complex ) > set_complex > $o ).
thf(func_def_1552,type,
sP39: rat > num > rat > $o ).
thf(func_def_1553,type,
sP40: vEBT_VEBT > nat > $o ).
thf(func_def_1554,type,
sP41: nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1555,type,
sP42: real > nat > real > $o ).
thf(func_def_1556,type,
sP43: real > num > real > $o ).
thf(func_def_1557,type,
sP44: $o > $o > nat > $o ).
thf(func_def_1558,type,
sP45: nat > ( nat > nat ) > $o ).
thf(func_def_1559,type,
sP46: $o > $o > nat > $o ).
thf(func_def_1560,type,
sP47: rat > rat > rat > $o ).
thf(func_def_1561,type,
sP48: vEBT_VEBT > option_nat > $o ).
thf(func_def_1562,type,
sP49: ( nat > int > $o ) > set_nat > set_int > $o ).
thf(func_def_1563,type,
sP50: num > real > real > $o ).
thf(func_def_1564,type,
sP51: option_nat > option_nat > option_nat > $o ).
thf(func_def_1565,type,
sP52: real > num > real > $o ).
thf(func_def_1566,type,
sP53: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o ).
thf(func_def_1567,type,
sP54: set_real > set_complex > ( complex > real > $o ) > $o ).
thf(func_def_1568,type,
sP55: vEBT_VEBT > $o > $o ).
thf(func_def_1569,type,
sP56: vEBT_VEBT > $o > $o ).
thf(func_def_1570,type,
sP57: $o > vEBT_VEBT > $o ).
thf(func_def_1571,type,
sP58: $o > vEBT_VEBT > $o ).
thf(func_def_1572,type,
sP59: rat > rat > rat > $o ).
thf(func_def_1573,type,
sP60: rat > rat > rat > $o ).
thf(func_def_1574,type,
sP61: rat > rat > rat > $o ).
thf(func_def_1575,type,
sP62: ( real > complex ) > ( complex > real ) > set_complex > set_complex > $o ).
thf(func_def_1576,type,
sP63: set_real > ( real > complex ) > $o ).
thf(func_def_1577,type,
sP64: ( complex > complex ) > set_complex > $o ).
thf(func_def_1578,type,
sP65: set_real > set_real > ( real > complex ) > set_complex > set_complex > $o ).
thf(func_def_1579,type,
sP66: ( int > $o ) > int > set_int > ( int > $o ) > $o ).
thf(func_def_1580,type,
sP67: set_real > ( int > real > $o ) > set_int > $o ).
thf(func_def_1581,type,
sP68: rat > num > rat > $o ).
thf(func_def_1582,type,
sP69: vEBT_VEBT > nat > $o ).
thf(func_def_1583,type,
sP70: nat > vEBT_VEBT > $o ).
thf(func_def_1584,type,
sP71: ( real > real ) > set_real > set_real > set_real > set_real > $o ).
thf(func_def_1585,type,
sP72: ( real > real ) > set_real > $o ).
thf(func_def_1586,type,
sP73: set_real > set_real > ( real > real ) > set_real > set_real > $o ).
thf(func_def_1587,type,
sP74: set_real > ( real > real ) > ( real > real ) > ( real > real ) > $o ).
thf(func_def_1588,type,
sP75: ( option_nat > option_num > $o ) > option_num > option_nat > $o ).
thf(func_def_1589,type,
sP76: nat > vEBT_VEBT > $o ).
thf(func_def_1590,type,
sP77: real > real > real > $o ).
thf(func_def_1591,type,
sP78: vEBT_VEBT > nat > $o ).
thf(func_def_1592,type,
sP79: vEBT_VEBT > nat > $o ).
thf(func_def_1593,type,
sP80: nat > vEBT_VEBT > $o ).
thf(func_def_1594,type,
sP81: option_num > option_num > option_num > $o ).
thf(func_def_1595,type,
sP82: vEBT_VEBT > nat > $o > $o ).
thf(func_def_1596,type,
sP83: list_nat > nat > $o ).
thf(func_def_1597,type,
sP84: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1598,type,
sP85: vEBT_VEBT > nat > $o > $o ).
thf(func_def_1599,type,
sP86: $o > vEBT_VEBT > nat > $o ).
thf(func_def_1600,type,
sP87: nat > $o > vEBT_VEBT > $o ).
thf(func_def_1601,type,
sP88: vEBT_VEBT > nat > vEBT_VEBT > $o ).
thf(func_def_1602,type,
sP89: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1603,type,
sP90: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1604,type,
sP91: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1605,type,
sP92: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1606,type,
sP93: vEBT_VEBT > nat > vEBT_VEBT > $o ).
thf(func_def_1607,type,
sP94: set_real > ( nat > real > $o ) > set_nat > $o ).
thf(func_def_1608,type,
sP95: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1609,type,
sP96: $o > nat > vEBT_VEBT > $o ).
thf(func_def_1610,type,
sP97: nat > $o > vEBT_VEBT > $o ).
thf(func_def_1611,type,
sP98: nat > vEBT_VEBT > $o ).
thf(func_def_1612,type,
sP99: vEBT_VEBT > nat > vEBT_VEBT > $o ).
thf(func_def_1613,type,
sP100: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1614,type,
sP101: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1615,type,
sP102: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1616,type,
sP103: vEBT_VEBT > nat > $o ).
thf(func_def_1617,type,
sP104: int > ( int > $o ) > int > $o ).
thf(func_def_1618,type,
sP105: int > ( int > $o ) > int > $o ).
thf(func_def_1619,type,
sP106: rat > rat > rat > $o ).
thf(func_def_1620,type,
sP107: rat > rat > rat > $o ).
thf(func_def_1621,type,
sP108: rat > num > rat > $o ).
thf(func_def_1622,type,
sP109: rat > rat > rat > $o ).
thf(func_def_1623,type,
sP110: vEBT_VEBT > nat > $o ).
thf(func_def_1624,type,
sP111: ( real > real > $o ) > set_real > set_real > $o ).
thf(func_def_1625,type,
sP112: rat > num > rat > $o ).
thf(func_def_1626,type,
sP113: nat > vEBT_VEBT > $o ).
thf(func_def_1627,type,
sP114: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1628,type,
sP115: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1629,type,
sP116: vEBT_VEBT > nat > $o ).
thf(func_def_1630,type,
sP117: nat > vEBT_VEBT > $o ).
thf(func_def_1631,type,
sP118: nat > vEBT_VEBT > $o ).
thf(func_def_1632,type,
sP119: ( option_num > option_num > $o ) > option_num > option_num > $o ).
thf(func_def_1633,type,
sP120: product_prod_int_int > int > int > $o ).
thf(func_def_1634,type,
sP121: int > int > int > $o ).
thf(func_def_1635,type,
sP122: int > int > int > $o ).
thf(func_def_1636,type,
sP123: int > int > int > $o ).
thf(func_def_1637,type,
sP124: real > num > real > $o ).
thf(func_def_1638,type,
sP125: set_nat > set_real > ( real > nat > $o ) > $o ).
thf(func_def_1639,type,
sP126: vEBT_VEBT > option_nat > $o ).
thf(func_def_1640,type,
sP127: vEBT_VEBT > option_nat > $o ).
thf(func_def_1641,type,
sP128: list_nat > nat > $o ).
thf(func_def_1642,type,
sP129: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_1643,type,
sP130: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_1644,type,
sP131: vEBT_VEBT > nat > option_nat > $o ).
thf(func_def_1645,type,
sP132: option_nat > nat > vEBT_VEBT > $o ).
thf(func_def_1646,type,
sP133: real > ( real > real ) > real > $o ).
thf(func_def_1647,type,
sP134: nat > vEBT_VEBT > $o ).
thf(func_def_1648,type,
sP135: nat > vEBT_VEBT > $o ).
thf(func_def_1649,type,
sP136: rat > num > rat > $o ).
thf(func_def_1650,type,
sP137: ( real > complex ) > set_real > $o ).
thf(func_def_1651,type,
sP138: set_real > set_real > ( real > real ) > set_real > set_real > $o ).
thf(func_def_1652,type,
sP139: set_real > ( real > complex ) > ( real > complex ) > ( real > real ) > $o ).
thf(func_def_1653,type,
sP140: ( real > real ) > ( real > real ) > set_real > set_real > $o ).
thf(func_def_1654,type,
sP141: rat > rat > rat > $o ).
thf(func_def_1655,type,
sP142: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_1656,type,
sP143: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_1657,type,
sP144: vEBT_VEBT > nat > option_nat > $o ).
thf(func_def_1658,type,
sP145: ( real > int ) > set_int > set_int > set_real > set_real > $o ).
thf(func_def_1659,type,
sP146: set_real > ( real > complex ) > ( int > complex ) > ( real > int ) > $o ).
thf(func_def_1660,type,
sP147: ( int > complex ) > set_int > $o ).
thf(func_def_1661,type,
sP148: set_int > set_int > ( real > int ) > ( int > real ) > $o ).
thf(func_def_1662,type,
sP149: ( option_nat > option_nat > $o ) > option_nat > option_nat > $o ).
thf(func_def_1663,type,
sP150: int > int > ( int > $o ) > $o ).
thf(func_def_1664,type,
sP151: ( int > $o ) > int > int > $o ).
thf(func_def_1665,type,
sP152: nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1666,type,
sP153: $o > nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1667,type,
sP154: $o > $o > nat > $o ).
thf(func_def_1668,type,
sP155: $o > $o > nat > $o > $o ).
thf(func_def_1669,type,
sP156: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1670,type,
sP157: vEBT_VEBT > nat > $o > $o ).
thf(func_def_1671,type,
sP158: real > num > real > $o ).
thf(func_def_1672,type,
sP159: ( option_num > option4927543243414619207at_nat > $o ) > option_num > option4927543243414619207at_nat > $o ).
thf(func_def_1673,type,
sP160: real > real > ( real > real ) > $o ).
thf(func_def_1674,type,
sP161: ( real > real ) > ( real > real ) > real > real > $o ).
thf(func_def_1675,type,
sP162: real > ( real > real ) > ( real > real ) > real > $o ).
thf(func_def_1676,type,
sP163: real > real > ( real > real ) > $o ).
thf(func_def_1677,type,
sP164: real > real > real > $o ).
thf(func_def_1678,type,
sP165: nat > real > ( nat > real > real ) > real > $o ).
thf(func_def_1679,type,
sP166: ( real > real ) > ( nat > real > real ) > real > real > nat > $o ).
thf(func_def_1680,type,
sP167: $o > nat > vEBT_VEBT > option4927543243414619207at_nat > nat > list_VEBT_VEBT > $o ).
thf(func_def_1681,type,
sP168: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1682,type,
sP169: nat > vEBT_VEBT > $o ).
thf(func_def_1683,type,
sP170: nat > real > ( nat > real > real ) > $o ).
thf(func_def_1684,type,
sP171: num > real > real > $o ).
thf(func_def_1685,type,
sP172: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1686,type,
sP173: vEBT_VEBT > nat > vEBT_VEBT > $o ).
thf(func_def_1687,type,
sP174: vEBT_VEBT > nat > vEBT_VEBT > $o ).
thf(func_def_1688,type,
sP175: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1689,type,
sP176: ( nat > real > real ) > real > nat > $o ).
thf(func_def_1690,type,
sP177: int > int > int > $o ).
thf(func_def_1691,type,
sP178: real > nat > ( nat > real > real ) > real > $o ).
thf(func_def_1692,type,
sP179: set_complex > set_complex > ( complex > int ) > set_int > set_int > $o ).
thf(func_def_1693,type,
sP180: ( complex > int ) > ( int > complex ) > set_int > set_int > $o ).
thf(func_def_1694,type,
sP181: set_complex > ( complex > complex ) > $o ).
thf(func_def_1695,type,
sP182: set_int > set_int > ( int > complex ) > set_complex > set_complex > $o ).
thf(func_def_1696,type,
sP183: vEBT_VEBT > nat > $o ).
thf(func_def_1697,type,
sP184: vEBT_VEBT > nat > $o ).
thf(func_def_1698,type,
sP185: real > real > real > $o ).
thf(func_def_1699,type,
sP186: set_int > set_real > ( real > int > $o ) > $o ).
thf(func_def_1700,type,
sP187: set_complex > ( complex > complex ) > ( int > complex ) > ( complex > int ) > $o ).
thf(func_def_1701,type,
sP188: ( complex > int ) > set_int > set_int > set_complex > set_complex > $o ).
thf(func_def_1702,type,
sP189: ( complex > int ) > ( int > complex ) > set_int > set_int > $o ).
thf(func_def_1703,type,
sP190: ( int > complex ) > set_int > $o ).
thf(func_def_1704,type,
sP191: ( complex > nat > $o ) > set_nat > set_complex > $o ).
thf(func_def_1705,type,
sP192: vEBT_VEBT > nat > $o ).
thf(func_def_1706,type,
sP193: set_real > set_real > ( int > real ) > ( real > int ) > $o ).
thf(func_def_1707,type,
sP194: ( int > complex ) > ( real > complex ) > ( int > real ) > set_int > $o ).
thf(func_def_1708,type,
sP195: ( int > real ) > set_real > set_real > set_int > set_int > $o ).
thf(func_def_1709,type,
sP196: set_real > set_real > ( real > int ) > set_int > set_int > $o ).
thf(func_def_1710,type,
sP197: nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1711,type,
sP198: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1712,type,
sP199: nat > nat > list_VEBT_VEBT > nat > nat > $o ).
thf(func_def_1713,type,
sP200: list_VEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1714,type,
sP201: nat > vEBT_VEBT > $o ).
thf(func_def_1715,type,
sP202: nat > vEBT_VEBT > $o ).
thf(func_def_1716,type,
sP203: nat > vEBT_VEBT > $o ).
thf(func_def_1717,type,
sP204: vEBT_VEBT > nat > $o ).
thf(func_def_1718,type,
sP205: real > real > real > $o ).
thf(func_def_1719,type,
sP206: ( real > real ) > ( real > real ) > real > real > $o ).
thf(func_def_1720,type,
sP207: real > real > ( real > real ) > $o ).
thf(func_def_1721,type,
sP208: real > ( real > real ) > real > $o ).
thf(func_def_1722,type,
sP209: real > ( real > real ) > real > $o ).
thf(func_def_1723,type,
sP210: real > real > real > $o ).
thf(func_def_1724,type,
sP211: ( option_num > option_nat > $o ) > option_nat > option_num > $o ).
thf(func_def_1725,type,
sP212: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > $o ).
thf(func_def_1726,type,
sP213: vEBT_VEBT > extended_enat > vEBT_VEBT > $o ).
thf(func_def_1727,type,
sP214: rat > rat > rat > $o ).
thf(func_def_1728,type,
sP215: ( int > $o ) > int > ( int > $o ) > set_int > $o ).
thf(func_def_1729,type,
sP216: vEBT_VEBT > nat > $o ).
thf(func_def_1730,type,
sP217: set_nat > ( int > nat > $o ) > set_int > $o ).
thf(func_def_1731,type,
sP218: ( option_nat > option4927543243414619207at_nat > $o ) > option_nat > option4927543243414619207at_nat > $o ).
thf(func_def_1732,type,
sP219: num > rat > rat > $o ).
thf(func_def_1733,type,
sP220: $o > $o > nat > $o ).
thf(func_def_1734,type,
sP221: $o > $o > nat > $o > $o ).
thf(func_def_1735,type,
sP222: $o > nat > vEBT_VEBT > $o ).
thf(func_def_1736,type,
sP223: rat > rat > rat > $o ).
thf(func_def_1737,type,
sP224: extended_enat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1738,type,
sP225: vEBT_VEBT > vEBT_VEBT > extended_enat > $o ).
thf(func_def_1739,type,
sP226: rat > num > rat > $o ).
thf(func_def_1740,type,
sP227: nat > vEBT_VEBT > $o ).
thf(func_def_1741,type,
sP228: nat > list_VEBT_VEBT > nat > nat > nat > $o ).
thf(func_def_1742,type,
sP229: nat > nat > list_VEBT_VEBT > $o ).
thf(func_def_1743,type,
sP230: ( option4927543243414619207at_nat > option_nat > $o ) > option4927543243414619207at_nat > option_nat > $o ).
thf(func_def_1744,type,
sP231: ( nat > $o ) > nat > nat > $o ).
thf(func_def_1745,type,
sP232: set_real > set_real > ( complex > real ) > ( real > complex ) > $o ).
thf(func_def_1746,type,
sP233: ( complex > complex ) > set_complex > $o ).
thf(func_def_1747,type,
sP234: set_real > ( real > complex ) > $o ).
thf(func_def_1748,type,
sP235: set_real > set_real > ( real > complex ) > set_complex > set_complex > $o ).
thf(func_def_1749,type,
sP236: vEBT_VEBT > option_nat > $o ).
thf(func_def_1750,type,
sP237: option_nat > vEBT_VEBT > nat > $o ).
thf(func_def_1751,type,
sP238: option_nat > nat > vEBT_VEBT > $o ).
thf(func_def_1752,type,
sP239: vEBT_VEBT > nat > option_nat > $o ).
thf(func_def_1753,type,
sP240: vEBT_VEBT > nat > option_nat > $o ).
thf(func_def_1754,type,
sP241: option_nat > vEBT_VEBT > nat > $o ).
thf(func_def_1755,type,
sP242: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_1756,type,
sP243: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_1757,type,
sP244: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_1758,type,
sP245: nat > vEBT_VEBT > option_nat > $o ).
thf(func_def_1759,type,
sP246: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_1760,type,
sP247: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_1761,type,
sP248: ( nat > $o ) > nat > nat > $o ).
thf(func_def_1762,type,
sP249: $o > $o > nat > $o ).
thf(func_def_1763,type,
sP250: $o > $o > $o > nat > $o ).
thf(func_def_1764,type,
sP251: $o > nat > vEBT_VEBT > $o ).
thf(func_def_1765,type,
sP252: vEBT_VEBT > $o > nat > $o ).
thf(func_def_1766,type,
sP253: vEBT_VEBT > nat > $o ).
thf(func_def_1767,type,
sP254: ( nat > real > real ) > real > nat > $o ).
thf(func_def_1768,type,
sP255: vEBT_VEBT > option_nat > $o ).
thf(func_def_1769,type,
sP256: vEBT_VEBT > option_nat > $o ).
thf(func_def_1770,type,
sP257: ( nat > int ) > int > nat > nat > $o ).
thf(func_def_1771,type,
sK258: set_set_nat > nat > set_set_nat ).
thf(func_def_1772,type,
sK259: nat > list_o ).
thf(func_def_1773,type,
sK260: nat > set_nat > nat ).
thf(func_def_1774,type,
sK261: int > int ).
thf(func_def_1775,type,
sK262: list_int > ( int > $o ) > int ).
thf(func_def_1776,type,
sK263: ( nat > rat ) > set_nat > ( nat > rat ) > nat ).
thf(func_def_1777,type,
sK264: option_nat > nat ).
thf(func_def_1778,type,
sK265: product_prod_int_int > int ).
thf(func_def_1779,type,
sK266: product_prod_int_int > int ).
thf(func_def_1780,type,
sK267: int > set_int > int ).
thf(func_def_1781,type,
sK268: ( nat > $o ) > nat ).
thf(func_def_1782,type,
sK269: nat > ( nat > real ) > nat ).
thf(func_def_1783,type,
sK270: nat > ( nat > real ) > nat ).
thf(func_def_1784,type,
sK271: ( int > rat ) > set_int > set_int > int ).
thf(func_def_1785,type,
sK272: ( int > rat ) > set_int > int ).
thf(func_def_1786,type,
sK273: ( nat > rat ) > nat ).
thf(func_def_1787,type,
sK274: set_nat > nat ).
thf(func_def_1788,type,
sK275: set_complex > ( complex > rat ) > complex ).
thf(func_def_1789,type,
sK276: set_complex > ( complex > rat ) > ( complex > rat ) > complex ).
thf(func_def_1790,type,
sK277: list_real > list_VEBT_VEBT > real > vEBT_VEBT ).
thf(func_def_1791,type,
sK278: ( nat > $o ) > nat > nat ).
thf(func_def_1792,type,
sK279: ( nat > $o ) > nat > nat ).
thf(func_def_1793,type,
sK280: ( num > rat ) > num ).
thf(func_def_1794,type,
sK281: ( num > rat ) > num ).
thf(func_def_1795,type,
sK282: ( nat > rat ) > ( nat > rat ) > rat ).
thf(func_def_1796,type,
sK283: nat > ( nat > rat ) > ( nat > rat ) > nat ).
thf(func_def_1797,type,
sK284: rat > ( nat > rat ) > ( nat > rat ) > nat ).
thf(func_def_1798,type,
sK285: ( real > nat ) > ( real > nat ) > set_real > real ).
thf(func_def_1799,type,
sK286: ( rat > rat > $o ) > rat ).
thf(func_def_1800,type,
sK287: ( rat > rat > $o ) > rat ).
thf(func_def_1801,type,
sK288: ( rat > rat > $o ) > rat ).
thf(func_def_1802,type,
sK289: ( rat > rat > $o ) > rat ).
thf(func_def_1803,type,
sK290: set_int > nat > set_int ).
thf(func_def_1804,type,
sK291: set_int > nat > int ).
thf(func_def_1805,type,
sK292: set_nat > ( nat > complex ) > set_nat > nat ).
thf(func_def_1806,type,
sK293: ( nat > code_integer ) > set_nat > nat ).
thf(func_def_1807,type,
sK294: ( set_nat > $o ) > list_set_nat > nat ).
thf(func_def_1808,type,
sK295: set_real > ( real > rat ) > real ).
thf(func_def_1809,type,
sK296: ( int > nat ) > ( int > nat ) > set_int > int ).
thf(func_def_1810,type,
sK297: set_real > ( real > code_integer ) > code_integer > real ).
thf(func_def_1811,type,
sK298: ( rat > rat > $o ) > rat ).
thf(func_def_1812,type,
sK299: ( rat > rat > $o ) > rat ).
thf(func_def_1813,type,
sK300: ( rat > rat > $o ) > rat ).
thf(func_def_1814,type,
sK301: ( rat > rat > $o ) > rat ).
thf(func_def_1815,type,
sK302: ( nat > rat ) > ( rat > rat > $o ) > ( nat > rat ) > set_nat > nat ).
thf(func_def_1816,type,
sK303: ( int > rat ) > set_int > int ).
thf(func_def_1817,type,
sK304: ( int > rat ) > ( int > nat ) > set_int > set_nat > ( nat > rat ) > nat ).
thf(func_def_1818,type,
sK305: set_real > set_real > nat > ( real > real > $o ) > real ).
thf(func_def_1819,type,
sK306: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_1820,type,
sK307: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_1821,type,
sK308: produc9072475918466114483BT_nat > nat ).
thf(func_def_1822,type,
sK309: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_1823,type,
sK310: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_1824,type,
sK311: produc9072475918466114483BT_nat > nat ).
thf(func_def_1825,type,
sK312: produc9072475918466114483BT_nat > nat ).
thf(func_def_1826,type,
sK313: produc9072475918466114483BT_nat > nat ).
thf(func_def_1827,type,
sK314: produc9072475918466114483BT_nat > nat ).
thf(func_def_1828,type,
sK315: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_1829,type,
sK316: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_1830,type,
sK317: produc9072475918466114483BT_nat > nat ).
thf(func_def_1831,type,
sK318: produc9072475918466114483BT_nat > nat ).
thf(func_def_1832,type,
sK319: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_1833,type,
sK320: produc9072475918466114483BT_nat > nat ).
thf(func_def_1834,type,
sK321: produc9072475918466114483BT_nat > nat ).
thf(func_def_1835,type,
sK322: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_1836,type,
sK323: produc9072475918466114483BT_nat > nat ).
thf(func_def_1837,type,
sK324: produc9072475918466114483BT_nat > nat ).
thf(func_def_1838,type,
sK325: produc9072475918466114483BT_nat > $o ).
thf(func_def_1839,type,
sK326: produc9072475918466114483BT_nat > $o ).
thf(func_def_1840,type,
sK327: ( real > real ) > ( real > real ) > set_real > real ).
thf(func_def_1841,type,
sK328: set_complex > ( complex > int ) > set_complex > complex ).
thf(func_def_1842,type,
sK329: ( int > $o ) > int ).
thf(func_def_1843,type,
sK330: ( int > $o ) > int ).
thf(func_def_1844,type,
sK331: nat > nat ).
thf(func_def_1845,type,
sK332: set_set_nat > ( set_nat > complex ) > real > set_nat ).
thf(func_def_1846,type,
sK333: nat > list_list_int > list_int ).
thf(func_def_1847,type,
sK334: ( int > rat ) > set_int > set_int > ( int > rat ) > int ).
thf(func_def_1848,type,
sK335: ( int > rat ) > set_int > set_int > int ).
thf(func_def_1849,type,
sK336: set_int > set_int > ( int > rat ) > int ).
thf(func_def_1850,type,
sK337: nat > vEBT_VEBT > list_VEBT_VEBT > nat ).
thf(func_def_1851,type,
sK338: nat > vEBT_VEBT > list_VEBT_VEBT > nat ).
thf(func_def_1852,type,
sK339: list_VEBT_VEBT > nat > nat > nat > nat > nat ).
thf(func_def_1853,type,
sK340: list_VEBT_VEBT > nat > nat > nat > nat > nat ).
thf(func_def_1854,type,
sK341: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_1855,type,
sK342: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_1856,type,
sK343: list_VEBT_VEBT > nat ).
thf(func_def_1857,type,
sK344: set_complex > ( complex > complex ) > ( complex > complex ) > complex ).
thf(func_def_1858,type,
sK345: set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_1859,type,
sK346: int > nat ).
thf(func_def_1860,type,
sK347: int > nat ).
thf(func_def_1861,type,
sK348: int > int ).
thf(func_def_1862,type,
sK349: nat > nat ).
thf(func_def_1863,type,
sK350: set_int > ( int > complex ) > int ).
thf(func_def_1864,type,
sK351: set_int > set_int > ( int > int ) > ( int > int ) > int ).
thf(func_def_1865,type,
sK352: set_int > ( int > complex ) > int ).
thf(func_def_1866,type,
sK353: set_int > set_int > ( int > int ) > set_int > set_int > int ).
thf(func_def_1867,type,
sK354: set_int > set_int > set_int > ( int > int ) > set_int > int ).
thf(func_def_1868,type,
sK355: ( int > complex ) > ( int > complex ) > set_int > ( int > int ) > int ).
thf(func_def_1869,type,
sK356: ( int > int ) > set_int > set_int > ( int > int ) > int ).
thf(func_def_1870,type,
sK357: ( real > rat ) > real ).
thf(func_def_1871,type,
sK358: ( real > rat ) > real ).
thf(func_def_1872,type,
sK359: set_complex > ( complex > nat ) > set_complex > complex ).
thf(func_def_1873,type,
sK360: set_real > ( real > int ) > ( real > int ) > real ).
thf(func_def_1874,type,
sK361: num > num ).
thf(func_def_1875,type,
sK362: num > num ).
thf(func_def_1876,type,
sK363: int > int ).
thf(func_def_1877,type,
sK364: set_complex > ( complex > nat ) > complex ).
thf(func_def_1878,type,
sK365: ( nat > rat ) > set_nat > nat ).
thf(func_def_1879,type,
sK366: set_int > ( int > real ) > int ).
thf(func_def_1880,type,
sK367: set_int > ( int > real ) > int ).
thf(func_def_1881,type,
sK368: complex > real ).
thf(func_def_1882,type,
sK369: ( nat > complex ) > nat > complex ).
thf(func_def_1883,type,
sK370: set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_1884,type,
sK371: set_real > ( real > nat ) > real ).
thf(func_def_1885,type,
sK372: ( int > real ) > set_int > int ).
thf(func_def_1886,type,
sK373: set_complex > ( complex > code_integer ) > code_integer > complex ).
thf(func_def_1887,type,
sK374: ( num > int ) > num ).
thf(func_def_1888,type,
sK375: ( num > int ) > num ).
thf(func_def_1889,type,
sK376: product_prod_int_int > int ).
thf(func_def_1890,type,
sK377: product_prod_int_int > int ).
thf(func_def_1891,type,
sK378: ( real > real ) > real > real ).
thf(func_def_1892,type,
sK379: ( rat > nat ) > rat ).
thf(func_def_1893,type,
sK380: ( rat > nat ) > rat ).
thf(func_def_1894,type,
sK381: ( set_nat > nat ) > set_set_nat > ( set_nat > nat ) > set_nat ).
thf(func_def_1895,type,
sK382: nat > real > nat ).
thf(func_def_1896,type,
sK383: list_o > list_o > set_Product_prod_o_o > nat ).
thf(func_def_1897,type,
sK384: ( nat > nat ) > nat ).
thf(func_def_1898,type,
sK385: ( nat > nat ) > nat ).
thf(func_def_1899,type,
sK386: set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_1900,type,
sK387: set_nat > ( nat > rat ) > rat > nat ).
thf(func_def_1901,type,
sK388: ( real > nat ) > real ).
thf(func_def_1902,type,
sK389: ( real > nat ) > real ).
thf(func_def_1903,type,
sK390: ( complex > int ) > ( complex > int ) > set_complex > complex ).
thf(func_def_1904,type,
sK391: ( nat > $o ) > nat > nat ).
thf(func_def_1905,type,
sK392: ( nat > $o ) > nat > nat ).
thf(func_def_1906,type,
sK393: nat > nat > nat ).
thf(func_def_1907,type,
sK394: nat > nat > nat ).
thf(func_def_1908,type,
sK395: nat > nat > nat ).
thf(func_def_1909,type,
sK396: ( int > rat ) > int ).
thf(func_def_1910,type,
sK397: ( int > rat ) > int ).
thf(func_def_1911,type,
sK398: nat > nat > nat ).
thf(func_def_1912,type,
sK399: ( int > rat ) > ( int > rat ) > ( rat > rat > $o ) > set_int > int ).
thf(func_def_1913,type,
sK400: ( rat > rat > $o ) > rat ).
thf(func_def_1914,type,
sK401: ( rat > rat > $o ) > rat ).
thf(func_def_1915,type,
sK402: ( rat > rat > $o ) > rat ).
thf(func_def_1916,type,
sK403: ( rat > rat > $o ) > rat ).
thf(func_def_1917,type,
sK404: int > int > int ).
thf(func_def_1918,type,
sK405: int > int > int ).
thf(func_def_1919,type,
sK406: ( nat > nat > $o ) > nat ).
thf(func_def_1920,type,
sK407: ( nat > nat > $o ) > nat ).
thf(func_def_1921,type,
sK408: ( nat > nat > $o ) > nat ).
thf(func_def_1922,type,
sK409: ( nat > nat > $o ) > nat ).
thf(func_def_1923,type,
sK410: ( nat > nat > $o ) > set_complex > ( complex > nat ) > ( complex > nat ) > complex ).
thf(func_def_1924,type,
sK411: ( option4927543243414619207at_nat > option_num > $o ) > option4927543243414619207at_nat > option_num > num ).
thf(func_def_1925,type,
sK412: ( option4927543243414619207at_nat > option_num > $o ) > option4927543243414619207at_nat > option_num > product_prod_nat_nat ).
thf(func_def_1926,type,
sK413: set_complex > ( complex > code_integer ) > complex ).
thf(func_def_1927,type,
sK414: code_integer > code_integer > code_integer ).
thf(func_def_1928,type,
sK415: rat > rat > rat ).
thf(func_def_1929,type,
sK416: set_nat > set_nat > ( nat > nat > $o ) > nat ).
thf(func_def_1930,type,
sK417: set_nat > set_nat > ( nat > nat > $o ) > nat ).
thf(func_def_1931,type,
sK418: set_nat > set_nat > ( nat > nat > $o ) > nat ).
thf(func_def_1932,type,
sK419: set_nat > ( nat > nat > $o ) > set_nat > nat ).
thf(func_def_1933,type,
sK420: set_int > int ).
thf(func_def_1934,type,
sK421: ( nat > $o ) > nat ).
thf(func_def_1935,type,
sK422: set_int > ( int > real ) > ( int > real ) > int ).
thf(func_def_1936,type,
sK423: set_int > set_int > ( int > real ) > int ).
thf(func_def_1937,type,
sK424: vEBT_VEBT > $o ).
thf(func_def_1938,type,
sK425: vEBT_VEBT > $o ).
thf(func_def_1939,type,
sK426: ( num > nat ) > num ).
thf(func_def_1940,type,
sK427: ( num > nat ) > num ).
thf(func_def_1941,type,
sK428: set_real > ( real > complex ) > set_real > real ).
thf(func_def_1942,type,
sK429: set_real > ( real > complex ) > ( real > complex ) > real ).
thf(func_def_1943,type,
sK430: set_real > ( real > rat ) > real ).
thf(func_def_1944,type,
sK431: ( nat > int ) > nat ).
thf(func_def_1945,type,
sK432: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1946,type,
sK433: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1947,type,
sK434: set_rat > rat ).
thf(func_def_1948,type,
sK435: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_1949,type,
sK436: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_1950,type,
sK437: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_1951,type,
sK438: vEBT_VEBT > nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_1952,type,
sK439: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1953,type,
sK440: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_1954,type,
sK441: list_o > list_VEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_1955,type,
sK442: ( real > nat ) > real ).
thf(func_def_1956,type,
sK443: ( real > nat ) > real ).
thf(func_def_1957,type,
sK444: set_complex > ( complex > real ) > complex ).
thf(func_def_1958,type,
sK445: ( int > num ) > int ).
thf(func_def_1959,type,
sK446: ( int > num ) > int ).
thf(func_def_1960,type,
sK447: ( real > real ) > set_real > real > real ).
thf(func_def_1961,type,
sK448: ( real > real ) > set_real > real > real ).
thf(func_def_1962,type,
sK449: num > num ).
thf(func_def_1963,type,
sK450: nat > list_VEBT_VEBT > ( vEBT_VEBT > $o ) > nat ).
thf(func_def_1964,type,
sK451: vEBT_VEBT > list_VEBT_VEBT > ( vEBT_VEBT > $o ) > nat ).
thf(func_def_1965,type,
sK452: ( int > int > int ) > int ).
thf(func_def_1966,type,
sK453: ( int > int > int ) > int ).
thf(func_def_1967,type,
sK454: ( int > int > int ) > int ).
thf(func_def_1968,type,
sK455: ( int > int > int ) > int ).
thf(func_def_1969,type,
sK456: ( int > int > int ) > int ).
thf(func_def_1970,type,
sK457: ( int > int > int ) > int ).
thf(func_def_1971,type,
sK458: ( int > int > int ) > int ).
thf(func_def_1972,type,
sK459: set_int > ( int > rat ) > int > int ).
thf(func_def_1973,type,
sK460: set_complex > complex ).
thf(func_def_1974,type,
sK461: set_complex > complex ).
thf(func_def_1975,type,
sK462: ( int > nat ) > set_int > int ).
thf(func_def_1976,type,
sK463: nat > ( nat > $o ) > nat ).
thf(func_def_1977,type,
sK464: set_list_o > nat ).
thf(func_def_1978,type,
sK465: set_int > ( int > rat ) > int ).
thf(func_def_1979,type,
sK466: set_real > ( real > real ) > real ).
thf(func_def_1980,type,
sK467: rat > rat ).
thf(func_def_1981,type,
sK468: ( nat > rat ) > set_nat > nat ).
thf(func_def_1982,type,
sK469: ( nat > rat ) > set_nat > ( int > rat ) > set_int > ( nat > int ) > int ).
thf(func_def_1983,type,
sK470: real > real > real ).
thf(func_def_1984,type,
sK471: ( real > code_integer ) > set_real > real ).
thf(func_def_1985,type,
sK472: code_integer > ( real > code_integer ) > code_integer > set_real > real ).
thf(func_def_1986,type,
sK473: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1987,type,
sK474: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat ).
thf(func_def_1988,type,
sK475: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat ).
thf(func_def_1989,type,
sK476: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_1990,type,
sK477: rat > rat ).
thf(func_def_1991,type,
sK478: ( complex > rat ) > set_complex > ( complex > rat ) > complex ).
thf(func_def_1992,type,
sK479: set_nat > set_nat > ( nat > rat ) > nat ).
thf(func_def_1993,type,
sK480: nat > real > ( nat > real ) > nat > real ).
thf(func_def_1994,type,
sK481: set_complex > ( complex > real ) > complex ).
thf(func_def_1995,type,
sK482: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_1996,type,
sK483: ( nat > $o ) > nat ).
thf(func_def_1997,type,
sK484: nat > nat > nat > nat ).
thf(func_def_1998,type,
sK485: ( produc859450856879609959at_nat > $o ) > nat ).
thf(func_def_1999,type,
sK486: ( produc859450856879609959at_nat > $o ) > nat ).
thf(func_def_2000,type,
sK487: ( produc859450856879609959at_nat > $o ) > product_prod_nat_nat ).
thf(func_def_2001,type,
sK488: complex > nat > nat ).
thf(func_def_2002,type,
sK489: set_complex > ( complex > real ) > ( complex > real ) > complex ).
thf(func_def_2003,type,
sK490: ( nat > nat > $o ) > nat ).
thf(func_def_2004,type,
sK491: ( nat > nat > $o ) > nat ).
thf(func_def_2005,type,
sK492: ( nat > nat > $o ) > nat ).
thf(func_def_2006,type,
sK493: ( nat > nat > $o ) > nat ).
thf(func_def_2007,type,
sK494: ( nat > rat ) > nat ).
thf(func_def_2008,type,
sK495: ( nat > rat ) > nat ).
thf(func_def_2009,type,
sK496: set_nat > nat ).
thf(func_def_2010,type,
sK497: ( nat > $o ) > list_nat > nat ).
thf(func_def_2011,type,
sK498: set_complex > ( complex > nat ) > set_complex > complex ).
thf(func_def_2012,type,
sK499: nat > list_nat ).
thf(func_def_2013,type,
sK500: int > int ).
thf(func_def_2014,type,
sK501: ( set_complex > $o ) > ( complex > rat ) > set_complex ).
thf(func_def_2015,type,
sK502: ( set_complex > $o ) > ( complex > rat ) > complex ).
thf(func_def_2016,type,
sK503: real > ( real > real ) > ( real > real ) > real > real ).
thf(func_def_2017,type,
sK504: real > real > ( real > real ) > ( real > real ) > real ).
thf(func_def_2018,type,
sK505: list_VEBT_VEBT > nat > list_nat > vEBT_VEBT ).
thf(func_def_2019,type,
sK506: ( nat > rat ) > nat ).
thf(func_def_2020,type,
sK507: ( int > rat ) > ( set_int > $o ) > set_int ).
thf(func_def_2021,type,
sK508: ( int > rat ) > ( set_int > $o ) > int ).
thf(func_def_2022,type,
sK509: nat > vEBT_VEBT > nat > nat ).
thf(func_def_2023,type,
sK510: ( real > real ) > real ).
thf(func_def_2024,type,
sK511: nat > nat ).
thf(func_def_2025,type,
sK512: int > int ).
thf(func_def_2026,type,
sK513: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_2027,type,
sK514: set_complex > set_complex > ( complex > complex ) > complex ).
thf(func_def_2028,type,
sK515: set_complex > set_complex > ( complex > complex ) > complex ).
thf(func_def_2029,type,
sK516: nat > set_nat > ( nat > nat ) > nat ).
thf(func_def_2030,type,
sK517: set_nat > ( nat > nat ) > nat ).
thf(func_def_2031,type,
sK518: nat > ( nat > $o ) > nat ).
thf(func_def_2032,type,
sK519: nat > ( nat > $o ) > nat ).
thf(func_def_2033,type,
sK520: ( rat > rat ) > rat ).
thf(func_def_2034,type,
sK521: ( rat > rat ) > rat ).
thf(func_def_2035,type,
sK522: set_int > ( int > real ) > int ).
thf(func_def_2036,type,
sK523: real > real > nat ).
thf(func_def_2037,type,
sK524: set_nat > nat > nat ).
thf(func_def_2038,type,
sK525: nat > nat > nat ).
thf(func_def_2039,type,
sK526: nat > ( nat > nat ) > nat > nat ).
thf(func_def_2040,type,
sK527: real > ( real > real ) > nat > ( nat > real ) > real ).
thf(func_def_2041,type,
sK528: ( real > rat ) > rat > set_real > real ).
thf(func_def_2042,type,
sK529: real > set_int > ( int > complex ) > int ).
thf(func_def_2043,type,
sK530: vEBT_VEBT > $o ).
thf(func_def_2044,type,
sK531: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2045,type,
sK532: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_2046,type,
sK533: vEBT_VEBT > nat ).
thf(func_def_2047,type,
sK534: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2048,type,
sK535: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2049,type,
sK536: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2050,type,
sK537: vEBT_VEBT > nat ).
thf(func_def_2051,type,
sK538: vEBT_VEBT > $o ).
thf(func_def_2052,type,
sK539: set_int > ( int > real ) > int > int ).
thf(func_def_2053,type,
sK540: ( complex > complex ) > set_complex > set_complex > complex ).
thf(func_def_2054,type,
sK541: complex > ( nat > complex ) > nat > nat > complex ).
thf(func_def_2055,type,
sK542: list_nat > list_nat > nat ).
thf(func_def_2056,type,
sK543: ( nat > real > real ) > nat ).
thf(func_def_2057,type,
sK544: ( nat > real > real ) > real ).
thf(func_def_2058,type,
sK545: real > ( nat > real > real ) > nat > ( real > real ) > real ).
thf(func_def_2059,type,
sK546: list_o > nat > list_o ).
thf(func_def_2060,type,
sK547: list_o > nat > $o ).
thf(func_def_2061,type,
sK548: vEBT_VEBT > $o > nat > vEBT_VEBT ).
thf(func_def_2062,type,
sK549: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2063,type,
sK550: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).
thf(func_def_2064,type,
sK551: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).
thf(func_def_2065,type,
sK552: vEBT_VEBT > $o > nat > vEBT_VEBT ).
thf(func_def_2066,type,
sK553: vEBT_VEBT > $o > nat > product_prod_nat_nat ).
thf(func_def_2067,type,
sK554: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2068,type,
sK555: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2069,type,
sK556: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2070,type,
sK557: vEBT_VEBT > $o > nat > vEBT_VEBT ).
thf(func_def_2071,type,
sK558: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).
thf(func_def_2072,type,
sK559: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2073,type,
sK560: $o > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2074,type,
sK561: $o > nat > vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_2075,type,
sK562: $o > vEBT_VEBT > nat > $o ).
thf(func_def_2076,type,
sK563: $o > vEBT_VEBT > nat > $o ).
thf(func_def_2077,type,
sK564: ( complex > complex ) > set_complex > complex ).
thf(func_def_2078,type,
sK565: set_complex > ( complex > complex ) > complex ).
thf(func_def_2079,type,
sK566: ( complex > complex ) > ( complex > complex ) > ( complex > complex ) > set_complex > complex ).
thf(func_def_2080,type,
sK567: ( complex > complex ) > ( complex > complex ) > set_complex > set_complex > complex ).
thf(func_def_2081,type,
sK568: set_complex > set_complex > set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_2082,type,
sK569: ( complex > complex ) > set_complex > set_complex > set_complex > set_complex > complex ).
thf(func_def_2083,type,
sK570: ( complex > complex ) > set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_2084,type,
sK571: list_o > list_complex > complex > $o ).
thf(func_def_2085,type,
sK572: list_nat > nat > nat ).
thf(func_def_2086,type,
sK573: ( nat > real ) > nat ).
thf(func_def_2087,type,
sK574: ( nat > real ) > nat ).
thf(func_def_2088,type,
sK575: nat > real > real ).
thf(func_def_2089,type,
sK576: ( complex > int ) > set_complex > ( complex > int ) > complex ).
thf(func_def_2090,type,
sK577: nat > nat ).
thf(func_def_2091,type,
sK578: set_int > set_int > ( int > rat ) > int ).
thf(func_def_2092,type,
sK579: ( real > real ) > ( real > real ) > set_real > real ).
thf(func_def_2093,type,
sK580: nat > nat > nat ).
thf(func_def_2094,type,
sK581: set_real > set_real > ( real > nat ) > real ).
thf(func_def_2095,type,
sK582: set_real > set_real > ( real > nat ) > real ).
thf(func_def_2096,type,
sK583: nat > nat ).
thf(func_def_2097,type,
sK584: nat > nat ).
thf(func_def_2098,type,
sK585: nat > nat ).
thf(func_def_2099,type,
sK586: ( rat > rat ) > rat ).
thf(func_def_2100,type,
sK587: ( rat > rat ) > rat ).
thf(func_def_2101,type,
sK588: real > nat ).
thf(func_def_2102,type,
sK589: set_list_nat > nat > list_nat ).
thf(func_def_2103,type,
sK590: set_list_nat > nat > set_list_nat ).
thf(func_def_2104,type,
sK591: set_num > num > num ).
thf(func_def_2105,type,
sK592: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat ).
thf(func_def_2106,type,
sK593: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > set_Pr8693737435421807431at_nat > list_P6011104703257516679at_nat ).
thf(func_def_2107,type,
sK594: nat > real > real ).
thf(func_def_2108,type,
sK595: int > int ).
thf(func_def_2109,type,
sK596: ( complex > nat ) > ( complex > nat ) > set_complex > complex ).
thf(func_def_2110,type,
sK597: real > real > real ).
thf(func_def_2111,type,
sK598: filter_nat > nat ).
thf(func_def_2112,type,
sK599: nat > nat > nat > nat ).
thf(func_def_2113,type,
sK600: complex > ( complex > nat ) > set_complex > complex ).
thf(func_def_2114,type,
sK601: ( complex > nat ) > set_complex > complex ).
thf(func_def_2115,type,
sK602: real > set_real > real ).
thf(func_def_2116,type,
sK603: nat > list_nat > nat ).
thf(func_def_2117,type,
sK604: nat > list_nat > list_nat ).
thf(func_def_2118,type,
sK605: ( nat > int ) > nat ).
thf(func_def_2119,type,
sK606: set_real > ( real > rat ) > real > real ).
thf(func_def_2120,type,
sK607: set_real > ( real > rat ) > ( real > rat ) > real ).
thf(func_def_2121,type,
sK608: vEBT_VEBT > nat > option4927543243414619207at_nat ).
thf(func_def_2122,type,
sK609: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2123,type,
sK610: vEBT_VEBT > nat > nat ).
thf(func_def_2124,type,
sK611: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2125,type,
sK612: vEBT_VEBT > $o ).
thf(func_def_2126,type,
sK613: vEBT_VEBT > $o ).
thf(func_def_2127,type,
sK614: ( complex > nat ) > set_complex > ( complex > nat ) > complex ).
thf(func_def_2128,type,
sK615: real > nat ).
thf(func_def_2129,type,
sK616: real > nat ).
thf(func_def_2130,type,
sK617: set_complex > ( complex > real ) > complex ).
thf(func_def_2131,type,
sK618: set_complex > ( complex > real ) > complex ).
thf(func_def_2132,type,
sK619: ( code_integer > $o ) > $o ).
thf(func_def_2133,type,
sK620: ( code_integer > $o ) > code_integer ).
thf(func_def_2134,type,
sK621: ( code_integer > $o ) > code_integer ).
thf(func_def_2135,type,
sK622: nat > ( nat > real > real ) > real > nat ).
thf(func_def_2136,type,
sK623: nat > ( nat > real > real ) > real > real ).
thf(func_def_2137,type,
sK624: ( real > real ) > real ).
thf(func_def_2138,type,
sK625: ( real > real ) > real ).
thf(func_def_2139,type,
sK626: set_int > ( int > nat ) > nat > int ).
thf(func_def_2140,type,
sK627: ( complex > nat ) > set_complex > complex ).
thf(func_def_2141,type,
sK628: set_nat > ( rat > rat > $o ) > ( nat > rat ) > ( nat > rat ) > nat ).
thf(func_def_2142,type,
sK629: ( rat > rat > $o ) > rat ).
thf(func_def_2143,type,
sK630: ( rat > rat > $o ) > rat ).
thf(func_def_2144,type,
sK631: ( rat > rat > $o ) > rat ).
thf(func_def_2145,type,
sK632: ( rat > rat > $o ) > rat ).
thf(func_def_2146,type,
sK633: set_complex > complex ).
thf(func_def_2147,type,
sK634: ( real > real ) > set_real > real ).
thf(func_def_2148,type,
sK635: set_Pr1261947904930325089at_nat > nat ).
thf(func_def_2149,type,
sK636: set_list_nat > nat > set_list_nat ).
thf(func_def_2150,type,
sK637: set_list_nat > nat > list_nat ).
thf(func_def_2151,type,
sK638: vEBT_VEBT > nat ).
thf(func_def_2152,type,
sK639: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_2153,type,
sK640: list_VEBT_VEBT > nat ).
thf(func_def_2154,type,
sK641: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_2155,type,
sK642: ( real > rat ) > set_real > ( real > rat ) > real ).
thf(func_def_2156,type,
sK643: ( complex > complex > $o ) > complex ).
thf(func_def_2157,type,
sK644: ( complex > complex > $o ) > complex ).
thf(func_def_2158,type,
sK645: ( complex > complex > $o ) > complex ).
thf(func_def_2159,type,
sK646: ( complex > complex > $o ) > complex ).
thf(func_def_2160,type,
sK647: ( nat > complex ) > ( complex > complex > $o ) > set_nat > ( nat > complex ) > nat ).
thf(func_def_2161,type,
sK648: ( int > rat ) > int ).
thf(func_def_2162,type,
sK649: ( int > rat ) > int ).
thf(func_def_2163,type,
sK650: set_int > ( int > nat ) > int ).
thf(func_def_2164,type,
sK651: set_nat > ( nat > rat ) > rat > nat ).
thf(func_def_2165,type,
sK652: product_prod_nat_nat > nat ).
thf(func_def_2166,type,
sK653: product_prod_nat_nat > nat ).
thf(func_def_2167,type,
sK654: ( nat > rat ) > nat ).
thf(func_def_2168,type,
sK655: ( nat > rat ) > nat ).
thf(func_def_2169,type,
sK656: ( real > real ) > set_real > real ).
thf(func_def_2170,type,
sK657: ( rat > nat ) > rat ).
thf(func_def_2171,type,
sK658: ( rat > nat ) > rat ).
thf(func_def_2172,type,
sK659: ( nat > complex ) > nat > nat ).
thf(func_def_2173,type,
sK660: set_nat > nat > nat ).
thf(func_def_2174,type,
sK661: set_nat > nat > set_nat ).
thf(func_def_2175,type,
sK662: nat > set_complex > set_complex ).
thf(func_def_2176,type,
sK663: ( complex > real ) > set_complex > ( complex > real ) > complex ).
thf(func_def_2177,type,
sK664: ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_2178,type,
sK665: list_VEBT_VEBT > ( vEBT_VEBT > $o ) > vEBT_VEBT ).
thf(func_def_2179,type,
sK666: ( complex > real ) > set_complex > complex ).
thf(func_def_2180,type,
sK667: ( int > int > $o ) > int ).
thf(func_def_2181,type,
sK668: ( int > int > $o ) > int ).
thf(func_def_2182,type,
sK669: ( int > int > $o ) > int ).
thf(func_def_2183,type,
sK670: ( int > int > $o ) > int ).
thf(func_def_2184,type,
sK671: ( int > int > $o ) > int ).
thf(func_def_2185,type,
sK672: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2186,type,
sK673: vEBT_VEBT > nat ).
thf(func_def_2187,type,
sK674: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2188,type,
sK675: extended_enat > nat > extended_enat > nat ).
thf(func_def_2189,type,
sK676: extended_enat > nat > extended_enat > nat ).
thf(func_def_2190,type,
sK677: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_2191,type,
sK678: nat > nat > nat ).
thf(func_def_2192,type,
sK679: nat > nat > nat ).
thf(func_def_2193,type,
sK680: nat > nat > nat ).
thf(func_def_2194,type,
sK681: nat > real > real ).
thf(func_def_2195,type,
sK682: nat > ( nat > nat ) > nat ).
thf(func_def_2196,type,
sK683: nat > ( nat > nat ) > nat ).
thf(func_def_2197,type,
sK684: ( nat > nat ) > nat > nat ).
thf(func_def_2198,type,
sK685: ( nat > nat ) > nat > nat ).
thf(func_def_2199,type,
sK686: option_num > num ).
thf(func_def_2200,type,
sK687: nat > ( nat > real ) > ( nat > real ) > nat ).
thf(func_def_2201,type,
sK688: ( nat > real ) > nat ).
thf(func_def_2202,type,
sK689: ( nat > real ) > ( nat > real ) > real ).
thf(func_def_2203,type,
sK690: ( nat > real ) > ( nat > real ) > nat ).
thf(func_def_2204,type,
sK691: ( nat > real ) > nat ).
thf(func_def_2205,type,
sK692: ( rat > nat ) > rat ).
thf(func_def_2206,type,
sK693: ( rat > nat ) > rat ).
thf(func_def_2207,type,
sK694: ( rat > real ) > rat ).
thf(func_def_2208,type,
sK695: ( rat > real ) > rat ).
thf(func_def_2209,type,
sK696: set_complex > ( complex > real ) > complex ).
thf(func_def_2210,type,
sK697: set_real > ( real > complex ) > set_real > real ).
thf(func_def_2211,type,
sK698: set_real > ( real > complex ) > ( real > complex ) > real ).
thf(func_def_2212,type,
sK699: nat > nat > nat ).
thf(func_def_2213,type,
sK700: ( real > nat ) > set_real > real ).
thf(func_def_2214,type,
sK701: vEBT_VEBT > $o ).
thf(func_def_2215,type,
sK702: vEBT_VEBT > $o ).
thf(func_def_2216,type,
sK703: ( real > int ) > real ).
thf(func_def_2217,type,
sK704: ( real > int ) > real ).
thf(func_def_2218,type,
sK705: set_int > ( int > real ) > set_int > int ).
thf(func_def_2219,type,
sK706: set_int > ( int > real ) > set_int > int ).
thf(func_def_2220,type,
sK707: vEBT_VEBT > option_nat > $o ).
thf(func_def_2221,type,
sK708: vEBT_VEBT > option_nat > $o ).
thf(func_def_2222,type,
sK709: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2223,type,
sK710: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2224,type,
sK711: vEBT_VEBT > nat ).
thf(func_def_2225,type,
sK712: vEBT_VEBT > option_nat > nat ).
thf(func_def_2226,type,
sK713: vEBT_VEBT > option_nat > nat ).
thf(func_def_2227,type,
sK714: vEBT_VEBT > option_nat > nat ).
thf(func_def_2228,type,
sK715: vEBT_VEBT > option_nat > vEBT_VEBT ).
thf(func_def_2229,type,
sK716: vEBT_VEBT > option_nat > list_VEBT_VEBT ).
thf(func_def_2230,type,
sK717: vEBT_VEBT > list_VEBT_VEBT > nat ).
thf(func_def_2231,type,
sK718: ( rat > rat > $o ) > rat ).
thf(func_def_2232,type,
sK719: set_complex > real > ( complex > real ) > complex ).
thf(func_def_2233,type,
sK720: ( nat > real ) > nat ).
thf(func_def_2234,type,
sK721: nat > nat > nat ).
thf(func_def_2235,type,
sK722: nat > nat > nat ).
thf(func_def_2236,type,
sK723: nat > nat > nat ).
thf(func_def_2237,type,
sK724: real > nat ).
thf(func_def_2238,type,
sK725: real > nat ).
thf(func_def_2239,type,
sK726: ( nat > real ) > nat ).
thf(func_def_2240,type,
sK727: real > ( nat > real ) > real ).
thf(func_def_2241,type,
sK728: real > ( nat > real ) > nat ).
thf(func_def_2242,type,
sK729: set_int > ( int > real ) > int ).
thf(func_def_2243,type,
sK730: ( rat > num ) > rat ).
thf(func_def_2244,type,
sK731: ( rat > num ) > rat ).
thf(func_def_2245,type,
sK732: real > real > real > real ).
thf(func_def_2246,type,
sK733: set_set_nat > set_nat ).
thf(func_def_2247,type,
sK734: nat > real > real ).
thf(func_def_2248,type,
sK735: set_list_nat > list_nat ).
thf(func_def_2249,type,
sK736: set_list_nat > list_nat ).
thf(func_def_2250,type,
sK737: list_nat > list_nat > set_list_nat > list_nat ).
thf(func_def_2251,type,
sK738: nat > list_list_o > list_o ).
thf(func_def_2252,type,
sK739: list_s1210847774152347623at_nat > set_Pr4329608150637261639at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2253,type,
sK740: list_s1210847774152347623at_nat > set_Pr4329608150637261639at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat ).
thf(func_def_2254,type,
sK741: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2255,type,
sK742: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2256,type,
sK743: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2257,type,
sK744: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2258,type,
sK745: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2259,type,
sK746: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2260,type,
sK747: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat ).
thf(func_def_2261,type,
sK748: ( rat > int ) > rat ).
thf(func_def_2262,type,
sK749: ( rat > int ) > rat ).
thf(func_def_2263,type,
sK750: set_nat > ( nat > nat ) > nat ).
thf(func_def_2264,type,
sK751: list_real > list_o > real > $o ).
thf(func_def_2265,type,
sK752: ( nat > real ) > set_nat > set_nat > nat ).
thf(func_def_2266,type,
sK753: ( nat > int > $o ) > set_nat > set_int > int ).
thf(func_def_2267,type,
sK754: ( nat > int > $o ) > set_nat > set_int > nat ).
thf(func_def_2268,type,
sK755: ( nat > int > $o ) > set_nat > set_int > nat ).
thf(func_def_2269,type,
sK756: set_int > set_nat > ( nat > int > $o ) > nat ).
thf(func_def_2270,type,
sK757: ( int > complex ) > set_int > int ).
thf(func_def_2271,type,
sK758: ( nat > nat ) > nat ).
thf(func_def_2272,type,
sK759: ( complex > $o ) > complex > complex ).
thf(func_def_2273,type,
sK760: ( complex > $o ) > complex > complex ).
thf(func_def_2274,type,
sK761: int > nat ).
thf(func_def_2275,type,
sK762: int > nat ).
thf(func_def_2276,type,
sK763: ( real > rat ) > set_real > real ).
thf(func_def_2277,type,
sK764: ( complex > real ) > real > set_complex > complex ).
thf(func_def_2278,type,
sK765: complex > list_complex > nat ).
thf(func_def_2279,type,
sK766: nat > list_VEBT_VEBT > ( vEBT_VEBT > $o ) > nat ).
thf(func_def_2280,type,
sK767: vEBT_VEBT > list_VEBT_VEBT > ( vEBT_VEBT > $o ) > nat ).
thf(func_def_2281,type,
sK768: set_rat > rat ).
thf(func_def_2282,type,
sK769: set_real > real > ( real > nat ) > real ).
thf(func_def_2283,type,
sK770: ( list_nat > real ) > real > set_list_nat > list_nat ).
thf(func_def_2284,type,
sK771: code_integer > code_integer ).
thf(func_def_2285,type,
sK772: ( nat > nat ) > nat ).
thf(func_def_2286,type,
sK773: ( real > rat ) > ( real > rat ) > set_real > real ).
thf(func_def_2287,type,
sK774: ( real > rat ) > set_real > set_real > real ).
thf(func_def_2288,type,
sK775: ( real > real ) > set_real > real ).
thf(func_def_2289,type,
sK776: ( real > nat ) > set_real > real ).
thf(func_def_2290,type,
sK777: ( real > nat ) > set_real > real ).
thf(func_def_2291,type,
sK778: rat > rat > rat ).
thf(func_def_2292,type,
sK779: ( int > complex ) > set_int > set_int > int ).
thf(func_def_2293,type,
sK780: set_real > set_real > ( real > real ) > real ).
thf(func_def_2294,type,
sK781: ( real > real ) > set_real > set_real > real ).
thf(func_def_2295,type,
sK782: ( int > rat ) > set_int > set_int > int ).
thf(func_def_2296,type,
sK783: ( int > rat ) > set_int > int ).
thf(func_def_2297,type,
sK784: ( int > rat ) > ( int > int ) > set_int > ( int > rat ) > set_int > int ).
thf(func_def_2298,type,
sK785: set_complex > ( complex > rat ) > set_complex > complex ).
thf(func_def_2299,type,
sK786: set_complex > ( complex > rat ) > set_complex > complex ).
thf(func_def_2300,type,
sK787: set_complex > ( complex > rat ) > ( complex > rat ) > set_complex > complex ).
thf(func_def_2301,type,
sK788: ( int > rat ) > ( int > rat ) > set_int > int ).
thf(func_def_2302,type,
sK789: ( real > real > $o ) > real ).
thf(func_def_2303,type,
sK790: ( real > real > $o ) > real ).
thf(func_def_2304,type,
sK791: ( real > real > $o ) > real ).
thf(func_def_2305,type,
sK792: ( real > real > $o ) > real ).
thf(func_def_2306,type,
sK793: ( real > real > $o ) > set_complex > ( complex > real ) > ( complex > real ) > complex ).
thf(func_def_2307,type,
sK794: ( real > nat ) > real ).
thf(func_def_2308,type,
sK795: ( real > nat ) > real ).
thf(func_def_2309,type,
sK796: option_nat > nat ).
thf(func_def_2310,type,
sK797: option_nat > ( nat > nat > nat ) > option_nat > option_nat > nat ).
thf(func_def_2311,type,
sK798: option_nat > ( nat > nat > nat ) > option_nat > option_nat > nat ).
thf(func_def_2312,type,
sK799: set_nat > ( nat > int ) > nat ).
thf(func_def_2313,type,
sK800: ( nat > code_integer ) > set_nat > code_integer > nat ).
thf(func_def_2314,type,
sK801: list_o > $o > ( $o > $o ) > nat ).
thf(func_def_2315,type,
sK802: nat > list_o > ( $o > $o ) > nat ).
thf(func_def_2316,type,
sK803: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_2317,type,
sK804: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat ).
thf(func_def_2318,type,
sK805: ( num > real ) > num ).
thf(func_def_2319,type,
sK806: ( num > real ) > num ).
thf(func_def_2320,type,
sK807: real > nat > real ).
thf(func_def_2321,type,
sK808: set_complex > ( complex > rat ) > complex ).
thf(func_def_2322,type,
sK809: ( rat > nat ) > rat ).
thf(func_def_2323,type,
sK810: ( rat > nat ) > rat ).
thf(func_def_2324,type,
sK811: set_int > ( int > code_integer ) > int ).
thf(func_def_2325,type,
sK812: nat > int > ( nat > int ) > nat > int ).
thf(func_def_2326,type,
sK813: real > real > real ).
thf(func_def_2327,type,
sK814: set_complex > ( complex > nat ) > complex ).
thf(func_def_2328,type,
sK815: ( set_nat > $o ) > ( nat > rat ) > nat ).
thf(func_def_2329,type,
sK816: ( set_nat > $o ) > ( nat > rat ) > set_nat ).
thf(func_def_2330,type,
sK817: set_int > ( int > nat ) > ( int > nat ) > int ).
thf(func_def_2331,type,
sK818: int > set_nat > ( nat > int ) > nat ).
thf(func_def_2332,type,
sK819: int > ( int > $o ) > int ).
thf(func_def_2333,type,
sK820: int > ( int > $o ) > int ).
thf(func_def_2334,type,
sK821: int > ( int > $o ) > int ).
thf(func_def_2335,type,
sK822: int > ( int > $o ) > int ).
thf(func_def_2336,type,
sK823: set_list_nat > nat > set_list_nat ).
thf(func_def_2337,type,
sK824: real > ( nat > real > real ) > nat > nat ).
thf(func_def_2338,type,
sK825: real > ( nat > real > real ) > nat > real ).
thf(func_def_2339,type,
sK826: real > ( real > real ) > ( nat > real > real ) > nat > real ).
thf(func_def_2340,type,
sK827: ( nat > nat > $o ) > nat ).
thf(func_def_2341,type,
sK828: ( nat > nat > $o ) > nat ).
thf(func_def_2342,type,
sK829: ( nat > nat > $o ) > nat ).
thf(func_def_2343,type,
sK830: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > code_integer ).
thf(func_def_2344,type,
sK831: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > list_Code_integer ).
thf(func_def_2345,type,
sK832: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > list_Code_integer ).
thf(func_def_2346,type,
sK833: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > code_integer ).
thf(func_def_2347,type,
sK834: set_nat > ( nat > code_integer ) > ( code_integer > code_integer > $o ) > ( nat > code_integer ) > nat ).
thf(func_def_2348,type,
sK835: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_2349,type,
sK836: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_2350,type,
sK837: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_2351,type,
sK838: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_2352,type,
sK839: ( rat > int ) > rat ).
thf(func_def_2353,type,
sK840: ( rat > int ) > rat ).
thf(func_def_2354,type,
sK841: real > int ).
thf(func_def_2355,type,
sK842: ( real > real > $o ) > real ).
thf(func_def_2356,type,
sK843: ( nat > $o ) > nat ).
thf(func_def_2357,type,
sK844: int > nat ).
thf(func_def_2358,type,
sK845: int > int ).
thf(func_def_2359,type,
sK846: set_int > ( int > real ) > int ).
thf(func_def_2360,type,
sK847: ( complex > nat ) > complex > set_complex > complex ).
thf(func_def_2361,type,
sK848: produc2233624965454879586on_nat > nat > nat > $o ).
thf(func_def_2362,type,
sK849: produc2233624965454879586on_nat > nat ).
thf(func_def_2363,type,
sK850: produc2233624965454879586on_nat > option_nat ).
thf(func_def_2364,type,
sK851: produc2233624965454879586on_nat > nat > nat > $o ).
thf(func_def_2365,type,
sK852: produc2233624965454879586on_nat > nat > nat > $o ).
thf(func_def_2366,type,
sK853: produc2233624965454879586on_nat > nat ).
thf(func_def_2367,type,
sK854: produc2233624965454879586on_nat > nat ).
thf(func_def_2368,type,
sK855: set_complex > ( complex > nat ) > complex ).
thf(func_def_2369,type,
sK856: set_nat > ( nat > code_integer ) > nat ).
thf(func_def_2370,type,
sK857: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_2371,type,
sK858: set_complex > ( complex > real ) > set_complex > complex ).
thf(func_def_2372,type,
sK859: ( nat > complex ) > nat > nat ).
thf(func_def_2373,type,
sK860: nat > ( nat > complex ) > nat ).
thf(func_def_2374,type,
sK861: nat > set_Pr1261947904930325089at_nat > list_nat > list_nat > list_nat ).
thf(func_def_2375,type,
sK862: nat > set_Pr1261947904930325089at_nat > list_nat > list_nat > nat ).
thf(func_def_2376,type,
sK863: list_complex > list_int > complex > int ).
thf(func_def_2377,type,
sK864: set_complex > set_complex > ( complex > rat ) > complex ).
thf(func_def_2378,type,
sK865: set_nat > ( nat > complex ) > set_nat > nat ).
thf(func_def_2379,type,
sK866: rat > rat ).
thf(func_def_2380,type,
sK867: set_list_nat > nat ).
thf(func_def_2381,type,
sK868: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2382,type,
sK869: produc5542196010084753463at_nat > product_prod_nat_nat ).
thf(func_def_2383,type,
sK870: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2384,type,
sK871: produc5542196010084753463at_nat > option4927543243414619207at_nat ).
thf(func_def_2385,type,
sK872: produc5542196010084753463at_nat > product_prod_nat_nat ).
thf(func_def_2386,type,
sK873: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
thf(func_def_2387,type,
sK874: produc5542196010084753463at_nat > product_prod_nat_nat ).
thf(func_def_2388,type,
sK875: set_nat > set_nat > ( nat > complex ) > nat ).
thf(func_def_2389,type,
sK876: set_num > num ).
thf(func_def_2390,type,
sK877: real > set_nat > ( nat > real ) > nat ).
thf(func_def_2391,type,
sK878: ( nat > $o ) > nat > nat > nat ).
thf(func_def_2392,type,
sK879: ( real > real ) > real ).
thf(func_def_2393,type,
sK880: ( real > real ) > real ).
thf(func_def_2394,type,
sK881: set_list_nat > list_nat ).
thf(func_def_2395,type,
sK882: set_list_nat > list_nat ).
thf(func_def_2396,type,
sK883: ( real > rat ) > set_real > real ).
thf(func_def_2397,type,
sK884: ( set_complex > $o ) > ( complex > num ) > complex ).
thf(func_def_2398,type,
sK885: ( set_complex > $o ) > ( complex > num ) > set_complex ).
thf(func_def_2399,type,
sK886: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_2400,type,
sK887: ( option4927543243414619207at_nat > option4927543243414619207at_nat > $o ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_2401,type,
sK888: ( complex > rat ) > set_complex > set_complex > complex ).
thf(func_def_2402,type,
sK889: ( complex > rat ) > set_complex > complex ).
thf(func_def_2403,type,
sK890: set_set_nat > set_nat > set_nat ).
thf(func_def_2404,type,
sK891: int > int > int > int ).
thf(func_def_2405,type,
sK892: int > int > int > int ).
thf(func_def_2406,type,
sK893: ( nat > int ) > ( nat > int ) > set_nat > nat ).
thf(func_def_2407,type,
sK894: ( complex > complex > $o ) > complex ).
thf(func_def_2408,type,
sK895: ( complex > complex > $o ) > complex ).
thf(func_def_2409,type,
sK896: ( complex > complex > $o ) > complex ).
thf(func_def_2410,type,
sK897: ( complex > complex > $o ) > complex ).
thf(func_def_2411,type,
sK898: set_nat > ( nat > complex ) > ( complex > complex > $o ) > ( nat > complex ) > nat ).
thf(func_def_2412,type,
sK899: ( real > nat ) > ( real > nat ) > set_real > real ).
thf(func_def_2413,type,
sK900: list_Code_integer > list_Code_integer > code_integer > code_integer ).
thf(func_def_2414,type,
sK901: rat > rat > rat > rat ).
thf(func_def_2415,type,
sK902: nat > ( nat > $o ) > nat ).
thf(func_def_2416,type,
sK903: nat > ( nat > $o ) > nat ).
thf(func_def_2417,type,
sK904: nat > nat > ( nat > $o ) > nat ).
thf(func_def_2418,type,
sK905: nat > nat > ( nat > $o ) > nat ).
thf(func_def_2419,type,
sK906: rat > set_int > ( int > rat ) > int ).
thf(func_def_2420,type,
sK907: ( nat > $o ) > nat > nat > nat ).
thf(func_def_2421,type,
sK908: ( real > real ) > set_real > real ).
thf(func_def_2422,type,
sK909: set_complex > ( complex > rat ) > set_complex > complex ).
thf(func_def_2423,type,
sK910: set_complex > complex ).
thf(func_def_2424,type,
sK911: set_complex > complex ).
thf(func_def_2425,type,
sK912: complex > complex > set_complex > complex ).
thf(func_def_2426,type,
sK913: list_int > nat > list_int ).
thf(func_def_2427,type,
sK914: list_int > nat > int ).
thf(func_def_2428,type,
sK915: ( nat > real ) > ( nat > real ) > nat ).
thf(func_def_2429,type,
sK916: ( num > rat ) > num ).
thf(func_def_2430,type,
sK917: ( num > rat ) > num ).
thf(func_def_2431,type,
sK918: ( int > rat ) > set_int > set_int > int ).
thf(func_def_2432,type,
sK919: set_real > set_complex > ( complex > real > $o ) > complex ).
thf(func_def_2433,type,
sK920: set_real > set_complex > ( complex > real > $o ) > real ).
thf(func_def_2434,type,
sK921: set_real > set_complex > ( complex > real > $o ) > complex ).
thf(func_def_2435,type,
sK922: ( complex > real > $o ) > set_complex > set_real > complex ).
thf(func_def_2436,type,
sK923: list_nat > nat > nat ).
thf(func_def_2437,type,
sK924: real > set_real > ( real > real ) > real > real ).
thf(func_def_2438,type,
sK925: set_real > ( real > real ) > real ).
thf(func_def_2439,type,
sK926: ( real > int ) > set_real > ( real > int ) > real ).
thf(func_def_2440,type,
sK927: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_2441,type,
sK928: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_2442,type,
sK929: set_complex > set_complex > ( complex > real ) > ( complex > real ) > complex ).
thf(func_def_2443,type,
sK930: ( int > rat ) > set_int > int ).
thf(func_def_2444,type,
sK931: ( num > nat ) > num ).
thf(func_def_2445,type,
sK932: ( num > nat ) > num ).
thf(func_def_2446,type,
sK933: ( rat > num ) > rat ).
thf(func_def_2447,type,
sK934: ( rat > num ) > rat ).
thf(func_def_2448,type,
sK935: ( rat > rat > $o ) > rat ).
thf(func_def_2449,type,
sK936: ( rat > rat > $o ) > rat ).
thf(func_def_2450,type,
sK937: ( rat > rat > $o ) > rat ).
thf(func_def_2451,type,
sK938: ( rat > rat > $o ) > rat ).
thf(func_def_2452,type,
sK939: ( rat > rat > $o ) > rat ).
thf(func_def_2453,type,
sK940: ( num > real ) > num ).
thf(func_def_2454,type,
sK941: ( num > real ) > num ).
thf(func_def_2455,type,
sK942: ( int > complex ) > set_int > set_int > int ).
thf(func_def_2456,type,
sK943: ( rat > num ) > rat ).
thf(func_def_2457,type,
sK944: ( rat > num ) > rat ).
thf(func_def_2458,type,
sK945: real > real > real ).
thf(func_def_2459,type,
sK946: nat > extended_enat > nat ).
thf(func_def_2460,type,
sK947: set_Pr4811707699266497531nteger > list_Code_integer > list_Code_integer > nat ).
thf(func_def_2461,type,
sK948: real > int ).
thf(func_def_2462,type,
sK949: ( nat > real ) > nat ).
thf(func_def_2463,type,
sK950: ( nat > real ) > nat ).
thf(func_def_2464,type,
sK951: $o > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2465,type,
sK952: $o > vEBT_VEBT > nat ).
thf(func_def_2466,type,
sK953: $o > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2467,type,
sK954: vEBT_VEBT > $o > vEBT_VEBT ).
thf(func_def_2468,type,
sK955: vEBT_VEBT > $o > list_VEBT_VEBT ).
thf(func_def_2469,type,
sK956: vEBT_VEBT > $o > nat ).
thf(func_def_2470,type,
sK957: vEBT_VEBT > $o > product_prod_nat_nat ).
thf(func_def_2471,type,
sK958: vEBT_VEBT > $o > $o ).
thf(func_def_2472,type,
sK959: vEBT_VEBT > $o > $o ).
thf(func_def_2473,type,
sK960: set_real > set_real > ( real > complex ) > set_complex > set_complex > real ).
thf(func_def_2474,type,
sK961: ( complex > complex ) > set_complex > complex ).
thf(func_def_2475,type,
sK962: set_real > ( real > complex ) > real ).
thf(func_def_2476,type,
sK963: ( real > complex ) > ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_2477,type,
sK964: set_complex > ( complex > complex ) > ( real > complex ) > ( complex > real ) > complex ).
thf(func_def_2478,type,
sK965: set_real > ( real > complex ) > set_real > ( complex > real ) > real ).
thf(func_def_2479,type,
sK966: set_complex > set_complex > set_real > set_real > ( complex > real ) > complex ).
thf(func_def_2480,type,
sK967: ( rat > real ) > rat ).
thf(func_def_2481,type,
sK968: ( rat > real ) > rat ).
thf(func_def_2482,type,
sK969: set_complex > ( complex > rat ) > complex ).
thf(func_def_2483,type,
sK970: ( real > rat ) > real ).
thf(func_def_2484,type,
sK971: ( real > rat ) > real ).
thf(func_def_2485,type,
sK972: ( rat > int ) > rat ).
thf(func_def_2486,type,
sK973: ( rat > int ) > rat ).
thf(func_def_2487,type,
sK974: ( nat > complex ) > nat ).
thf(func_def_2488,type,
sK975: set_complex > ( complex > real ) > complex ).
thf(func_def_2489,type,
sK976: ( list_nat > $o ) > list_nat ).
thf(func_def_2490,type,
sK977: num > num ).
thf(func_def_2491,type,
sK978: int > ( int > $o ) > int ).
thf(func_def_2492,type,
sK979: int > ( int > $o ) > int ).
thf(func_def_2493,type,
sK980: ( int > $o ) > int > int ).
thf(func_def_2494,type,
sK981: ( int > $o ) > int > int ).
thf(func_def_2495,type,
sK982: set_real > ( real > nat ) > set_real > real ).
thf(func_def_2496,type,
sK983: set_real > set_real > ( real > nat ) > real ).
thf(func_def_2497,type,
sK984: set_real > ( real > nat ) > set_real > ( real > nat ) > real ).
thf(func_def_2498,type,
sK985: set_nat > nat ).
thf(func_def_2499,type,
sK986: nat > set_nat > nat ).
thf(func_def_2500,type,
sK987: set_Pr2101469702781467981_o_nat > list_o > list_nat > nat ).
thf(func_def_2501,type,
sK988: produc9072475918466114483BT_nat > $o ).
thf(func_def_2502,type,
sK989: produc9072475918466114483BT_nat > $o ).
thf(func_def_2503,type,
sK990: produc9072475918466114483BT_nat > nat ).
thf(func_def_2504,type,
sK991: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_2505,type,
sK992: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_2506,type,
sK993: produc9072475918466114483BT_nat > nat ).
thf(func_def_2507,type,
sK994: produc9072475918466114483BT_nat > product_prod_nat_nat ).
thf(func_def_2508,type,
sK995: produc9072475918466114483BT_nat > nat ).
thf(func_def_2509,type,
sK996: produc9072475918466114483BT_nat > nat ).
thf(func_def_2510,type,
sK997: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_2511,type,
sK998: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_2512,type,
sK999: produc9072475918466114483BT_nat > nat ).
thf(func_def_2513,type,
sK1000: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_2514,type,
sK1001: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_2515,type,
sK1002: produc9072475918466114483BT_nat > nat ).
thf(func_def_2516,type,
sK1003: produc9072475918466114483BT_nat > nat ).
thf(func_def_2517,type,
sK1004: produc9072475918466114483BT_nat > nat ).
thf(func_def_2518,type,
sK1005: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_2519,type,
sK1006: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_2520,type,
sK1007: produc9072475918466114483BT_nat > nat ).
thf(func_def_2521,type,
sK1008: produc9072475918466114483BT_nat > product_prod_nat_nat ).
thf(func_def_2522,type,
sK1009: nat > nat > nat > nat ).
thf(func_def_2523,type,
sK1010: nat > nat > nat > nat ).
thf(func_def_2524,type,
sK1011: int > set_int > ( int > $o ) > int ).
thf(func_def_2525,type,
sK1012: int > set_int > ( int > $o ) > int ).
thf(func_def_2526,type,
sK1013: ( int > $o ) > int > int ).
thf(func_def_2527,type,
sK1014: ( int > $o ) > int ).
thf(func_def_2528,type,
sK1015: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_2529,type,
sK1016: set_int > int > ( int > $o ) > int ).
thf(func_def_2530,type,
sK1017: int > ( int > $o ) > int ).
thf(func_def_2531,type,
sK1018: int > ( int > $o ) > int ).
thf(func_def_2532,type,
sK1019: ( int > nat ) > set_int > set_int > int ).
thf(func_def_2533,type,
sK1020: set_complex > rat > ( complex > rat ) > complex ).
thf(func_def_2534,type,
sK1021: set_real > ( int > real > $o ) > set_int > int ).
thf(func_def_2535,type,
sK1022: set_real > ( int > real > $o ) > set_int > real ).
thf(func_def_2536,type,
sK1023: set_real > ( int > real > $o ) > set_int > int ).
thf(func_def_2537,type,
sK1024: set_real > set_int > ( int > real > $o ) > int ).
thf(func_def_2538,type,
sK1025: set_nat > nat ).
thf(func_def_2539,type,
sK1026: set_nat > nat ).
thf(func_def_2540,type,
sK1027: set_list_nat > list_nat ).
thf(func_def_2541,type,
sK1028: set_list_nat > list_nat ).
thf(func_def_2542,type,
sK1029: nat > vEBT_VEBT > nat ).
thf(func_def_2543,type,
sK1030: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2544,type,
sK1031: nat > vEBT_VEBT > nat ).
thf(func_def_2545,type,
sK1032: nat > vEBT_VEBT > nat ).
thf(func_def_2546,type,
sK1033: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2547,type,
sK1034: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2548,type,
sK1035: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2549,type,
sK1036: vEBT_VEBT > nat > nat ).
thf(func_def_2550,type,
sK1037: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2551,type,
sK1038: nat > vEBT_VEBT > nat ).
thf(func_def_2552,type,
sK1039: nat > vEBT_VEBT > nat ).
thf(func_def_2553,type,
sK1040: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2554,type,
sK1041: set_complex > ( complex > rat ) > complex > complex ).
thf(func_def_2555,type,
sK1042: ( int > real ) > set_int > set_int > int ).
thf(func_def_2556,type,
sK1043: ( nat > real ) > nat ).
thf(func_def_2557,type,
sK1044: ( nat > real ) > nat ).
thf(func_def_2558,type,
sK1045: ( nat > real ) > real ).
thf(func_def_2559,type,
sK1046: real > real ).
thf(func_def_2560,type,
sK1047: real > set_real > real ).
thf(func_def_2561,type,
sK1048: set_real > ( real > real ) > ( real > real ) > ( real > real ) > real ).
thf(func_def_2562,type,
sK1049: set_real > set_real > ( real > real ) > set_real > set_real > real ).
thf(func_def_2563,type,
sK1050: ( real > real ) > set_real > real ).
thf(func_def_2564,type,
sK1051: ( real > real ) > set_real > set_real > set_real > set_real > real ).
thf(func_def_2565,type,
sK1052: set_real > ( real > real ) > ( real > real ) > set_real > real ).
thf(func_def_2566,type,
sK1053: ( real > real ) > ( real > real ) > set_real > set_real > real ).
thf(func_def_2567,type,
sK1054: set_real > ( real > real ) > real ).
thf(func_def_2568,type,
sK1055: int > list_int > nat ).
thf(func_def_2569,type,
sK1056: ( option_nat > option_num > $o ) > option_num > option_nat > nat ).
thf(func_def_2570,type,
sK1057: ( option_nat > option_num > $o ) > option_num > option_nat > num ).
thf(func_def_2571,type,
sK1058: code_integer > code_integer > set_int > ( int > code_integer ) > int ).
thf(func_def_2572,type,
sK1059: set_int > ( int > code_integer ) > int ).
thf(func_def_2573,type,
sK1060: option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_2574,type,
sK1061: nat > ( nat > $o ) > nat ).
thf(func_def_2575,type,
sK1062: nat > ( nat > $o ) > nat ).
thf(func_def_2576,type,
sK1063: ( nat > real ) > ( nat > real ) > set_nat > nat ).
thf(func_def_2577,type,
sK1064: real > ( nat > real ) > nat > int ).
thf(func_def_2578,type,
sK1065: list_int > list_int > nat ).
thf(func_def_2579,type,
sK1066: nat > rat > nat ).
thf(func_def_2580,type,
sK1067: nat > nat > nat ).
thf(func_def_2581,type,
sK1068: ( rat > real ) > rat ).
thf(func_def_2582,type,
sK1069: ( rat > real ) > rat ).
thf(func_def_2583,type,
sK1070: ( nat > nat ) > set_nat > ( nat > nat ) > nat ).
thf(func_def_2584,type,
sK1071: ( real > real > $o ) > real ).
thf(func_def_2585,type,
sK1072: ( real > real > $o ) > real ).
thf(func_def_2586,type,
sK1073: ( real > real > $o ) > real ).
thf(func_def_2587,type,
sK1074: ( real > real > $o ) > real ).
thf(func_def_2588,type,
sK1075: ( real > real > $o ) > real ).
thf(func_def_2589,type,
sK1076: set_int > ( int > nat ) > set_int > int ).
thf(func_def_2590,type,
sK1077: set_Pr6167073792073659919T_VEBT > list_nat > list_VEBT_VEBT > nat ).
thf(func_def_2591,type,
sK1078: nat > ( product_prod_nat_nat > $o ) > list_P6011104703257516679at_nat > nat ).
thf(func_def_2592,type,
sK1079: product_prod_nat_nat > ( product_prod_nat_nat > $o ) > list_P6011104703257516679at_nat > nat ).
thf(func_def_2593,type,
sK1080: ( complex > real ) > set_complex > complex ).
thf(func_def_2594,type,
sK1081: $o > list_o > $o ).
thf(func_def_2595,type,
sK1082: int > int > int > int ).
thf(func_def_2596,type,
sK1083: set_nat > list_set_nat > set_nat ).
thf(func_def_2597,type,
sK1084: ( rat > nat ) > rat ).
thf(func_def_2598,type,
sK1085: ( rat > nat ) > rat ).
thf(func_def_2599,type,
sK1086: real > nat > real ).
thf(func_def_2600,type,
sK1087: set_int > ( int > nat ) > int ).
thf(func_def_2601,type,
sK1088: int > set_int > ( int > nat ) > int ).
thf(func_def_2602,type,
sK1089: nat > nat ).
thf(func_def_2603,type,
sK1090: ( num > int ) > num ).
thf(func_def_2604,type,
sK1091: ( num > int ) > num ).
thf(func_def_2605,type,
sK1092: rat > set_rat > rat ).
thf(func_def_2606,type,
sK1093: real > ( real > $o ) > real ).
thf(func_def_2607,type,
sK1094: real > ( real > $o ) > real ).
thf(func_def_2608,type,
sK1095: real > ( real > $o ) > real ).
thf(func_def_2609,type,
sK1096: real > ( real > $o ) > real ).
thf(func_def_2610,type,
sK1097: ( real > num ) > real ).
thf(func_def_2611,type,
sK1098: ( real > num ) > real ).
thf(func_def_2612,type,
sK1099: ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_2613,type,
sK1100: nat > ( num > $o ) > list_num > nat ).
thf(func_def_2614,type,
sK1101: num > ( num > $o ) > list_num > nat ).
thf(func_def_2615,type,
sK1102: ( nat > rat ) > set_nat > rat > nat ).
thf(func_def_2616,type,
sK1103: set_complex > ( complex > rat ) > set_complex > complex ).
thf(func_def_2617,type,
sK1104: set_complex > ( complex > rat ) > set_complex > complex ).
thf(func_def_2618,type,
sK1105: nat > ( nat > int ) > nat ).
thf(func_def_2619,type,
sK1106: nat > ( nat > int ) > int > nat ).
thf(func_def_2620,type,
sK1107: int > nat ).
thf(func_def_2621,type,
sK1108: int > nat ).
thf(func_def_2622,type,
sK1109: real > real ).
thf(func_def_2623,type,
sK1110: set_real > real ).
thf(func_def_2624,type,
sK1111: ( int > rat ) > ( int > rat ) > set_int > int ).
thf(func_def_2625,type,
sK1112: ( product_prod_int_int > $o ) > int ).
thf(func_def_2626,type,
sK1113: ( product_prod_int_int > $o ) > int ).
thf(func_def_2627,type,
sK1114: set_complex > complex ).
thf(func_def_2628,type,
sK1115: set_complex > complex ).
thf(func_def_2629,type,
sK1116: set_complex > complex ).
thf(func_def_2630,type,
sK1117: real > real > real ).
thf(func_def_2631,type,
sK1118: vEBT_VEBT > $o ).
thf(func_def_2632,type,
sK1119: vEBT_VEBT > $o ).
thf(func_def_2633,type,
sK1120: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2634,type,
sK1121: vEBT_VEBT > nat ).
thf(func_def_2635,type,
sK1122: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_2636,type,
sK1123: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2637,type,
sK1124: vEBT_VEBT > nat ).
thf(func_def_2638,type,
sK1125: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2639,type,
sK1126: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2640,type,
sK1127: ( nat > rat ) > set_nat > nat ).
thf(func_def_2641,type,
sK1128: set_real > ( real > nat ) > nat > real ).
thf(func_def_2642,type,
sK1129: real > real > real > real ).
thf(func_def_2643,type,
sK1130: vEBT_VEBT > nat ).
thf(func_def_2644,type,
sK1131: nat > vEBT_VEBT > $o ).
thf(func_def_2645,type,
sK1132: nat > vEBT_VEBT > $o ).
thf(func_def_2646,type,
sK1133: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2647,type,
sK1134: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2648,type,
sK1135: nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_2649,type,
sK1136: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2650,type,
sK1137: nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_2651,type,
sK1138: nat > vEBT_VEBT > nat ).
thf(func_def_2652,type,
sK1139: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2653,type,
sK1140: ( rat > rat ) > rat ).
thf(func_def_2654,type,
sK1141: ( rat > rat ) > rat ).
thf(func_def_2655,type,
sK1142: ( nat > complex ) > set_nat > nat ).
thf(func_def_2656,type,
sK1143: list_nat > ( nat > $o ) > nat ).
thf(func_def_2657,type,
sK1144: list_nat > ( nat > $o ) > nat ).
thf(func_def_2658,type,
sK1145: ( rat > rat ) > rat ).
thf(func_def_2659,type,
sK1146: ( rat > rat ) > rat ).
thf(func_def_2660,type,
sK1147: set_int > int ).
thf(func_def_2661,type,
sK1148: set_int > int ).
thf(func_def_2662,type,
sK1149: ( complex > complex > $o ) > complex ).
thf(func_def_2663,type,
sK1150: ( complex > complex > $o ) > complex ).
thf(func_def_2664,type,
sK1151: ( complex > complex > $o ) > complex ).
thf(func_def_2665,type,
sK1152: ( complex > complex > $o ) > complex ).
thf(func_def_2666,type,
sK1153: ( complex > complex ) > ( complex > complex ) > ( complex > complex > $o ) > set_complex > complex ).
thf(func_def_2667,type,
sK1154: ( real > nat ) > set_real > set_real > real ).
thf(func_def_2668,type,
sK1155: ( real > nat ) > ( real > nat ) > set_real > real ).
thf(func_def_2669,type,
sK1156: set_nat > list_set_nat > nat ).
thf(func_def_2670,type,
sK1157: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2671,type,
sK1158: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2672,type,
sK1159: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2673,type,
sK1160: nat > vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_2674,type,
sK1161: nat > vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_2675,type,
sK1162: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2676,type,
sK1163: set_complex > set_complex > ( complex > rat ) > complex ).
thf(func_def_2677,type,
sK1164: set_complex > set_complex > ( complex > int ) > complex ).
thf(func_def_2678,type,
sK1165: ( real > real ) > real ).
thf(func_def_2679,type,
sK1166: ( real > real ) > real ).
thf(func_def_2680,type,
sK1167: rat > ( nat > rat ) > nat ).
thf(func_def_2681,type,
sK1168: set_num > num > num ).
thf(func_def_2682,type,
sK1169: set_real > ( real > real ) > set_real > real ).
thf(func_def_2683,type,
sK1170: ( real > real ) > ( real > real ) > set_real > real ).
thf(func_def_2684,type,
sK1171: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2685,type,
sK1172: real > nat ).
thf(func_def_2686,type,
sK1173: ( complex > rat ) > set_complex > complex ).
thf(func_def_2687,type,
sK1174: nat > vEBT_VEBT > nat ).
thf(func_def_2688,type,
sK1175: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2689,type,
sK1176: nat > vEBT_VEBT > nat ).
thf(func_def_2690,type,
sK1177: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2691,type,
sK1178: vEBT_VEBT > nat > nat ).
thf(func_def_2692,type,
sK1179: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2693,type,
sK1180: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2694,type,
sK1181: vEBT_VEBT > nat > nat ).
thf(func_def_2695,type,
sK1182: vEBT_VEBT > nat > nat ).
thf(func_def_2696,type,
sK1183: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2697,type,
sK1184: vEBT_VEBT > nat > nat ).
thf(func_def_2698,type,
sK1185: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2699,type,
sK1186: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2700,type,
sK1187: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2701,type,
sK1188: nat > vEBT_VEBT > $o ).
thf(func_def_2702,type,
sK1189: nat > vEBT_VEBT > $o ).
thf(func_def_2703,type,
sK1190: ( nat > nat ) > set_nat > nat ).
thf(func_def_2704,type,
sK1191: ( int > real ) > set_int > real > int ).
thf(func_def_2705,type,
sK1192: nat > list_P6011104703257516679at_nat > ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_2706,type,
sK1193: product_prod_nat_nat > list_P6011104703257516679at_nat > ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_2707,type,
sK1194: int > int > set_int > int ).
thf(func_def_2708,type,
sK1195: set_int > int ).
thf(func_def_2709,type,
sK1196: set_int > int ).
thf(func_def_2710,type,
sK1197: ( int > nat ) > int > set_int > int ).
thf(func_def_2711,type,
sK1198: real > real > real ).
thf(func_def_2712,type,
sK1199: set_Pr5066593544530342725BT_int > list_int > list_VEBT_VEBT > nat ).
thf(func_def_2713,type,
sK1200: option_num > num ).
thf(func_def_2714,type,
sK1201: ( num > num > num ) > option_num > option_num > option_num > num ).
thf(func_def_2715,type,
sK1202: ( num > num > num ) > option_num > option_num > option_num > num ).
thf(func_def_2716,type,
sK1203: set_nat > nat > nat ).
thf(func_def_2717,type,
sK1204: ( int > real ) > set_int > int ).
thf(func_def_2718,type,
sK1205: int > ( nat > int ) > nat > nat ).
thf(func_def_2719,type,
sK1206: ( int > nat ) > set_int > nat > int ).
thf(func_def_2720,type,
sK1207: rat > rat > rat ).
thf(func_def_2721,type,
sK1208: set_nat > nat ).
thf(func_def_2722,type,
sK1209: nat > real > real ).
thf(func_def_2723,type,
sK1210: ( nat > nat ) > nat ).
thf(func_def_2724,type,
sK1211: option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_2725,type,
sK1212: ( real > rat ) > real ).
thf(func_def_2726,type,
sK1213: ( real > rat ) > real ).
thf(func_def_2727,type,
sK1214: vEBT_VEBT > nat > $o > vEBT_VEBT ).
thf(func_def_2728,type,
sK1215: vEBT_VEBT > nat > $o > nat ).
thf(func_def_2729,type,
sK1216: vEBT_VEBT > nat > $o > list_VEBT_VEBT ).
thf(func_def_2730,type,
sK1217: vEBT_VEBT > nat > $o > option4927543243414619207at_nat ).
thf(func_def_2731,type,
sK1218: vEBT_VEBT > nat > $o > vEBT_VEBT ).
thf(func_def_2732,type,
sK1219: vEBT_VEBT > $o ).
thf(func_def_2733,type,
sK1220: vEBT_VEBT > $o ).
thf(func_def_2734,type,
sK1221: ( real > rat ) > set_real > real ).
thf(func_def_2735,type,
sK1222: ( real > real ) > set_real > real ).
thf(func_def_2736,type,
sK1223: ( real > nat > $o ) > set_real > set_nat > nat > nat ).
thf(func_def_2737,type,
sK1224: set_complex > ( int > rat ) > ( complex > int ) > set_int > ( complex > rat ) > int ).
thf(func_def_2738,type,
sK1225: set_complex > ( complex > rat ) > complex ).
thf(func_def_2739,type,
sK1226: set_set_nat > set_nat ).
thf(func_def_2740,type,
sK1227: ( int > int > $o ) > set_int > set_int > nat > int ).
thf(func_def_2741,type,
sK1228: nat > list_num > ( num > $o ) > nat ).
thf(func_def_2742,type,
sK1229: list_num > ( num > $o ) > num > nat ).
thf(func_def_2743,type,
sK1230: ( num > real ) > num ).
thf(func_def_2744,type,
sK1231: ( num > real ) > num ).
thf(func_def_2745,type,
sK1232: ( nat > set_nat ) > nat ).
thf(func_def_2746,type,
sK1233: ( real > real > $o ) > real ).
thf(func_def_2747,type,
sK1234: ( real > real > $o ) > real ).
thf(func_def_2748,type,
sK1235: ( real > real > $o ) > real ).
thf(func_def_2749,type,
sK1236: ( real > real > $o ) > real ).
thf(func_def_2750,type,
sK1237: ( nat > real ) > set_nat > ( nat > real ) > ( real > real > $o ) > nat ).
thf(func_def_2751,type,
sK1238: ( int > code_integer ) > set_int > code_integer > int ).
thf(func_def_2752,type,
sK1239: set_complex > set_complex > ( complex > complex ) > complex ).
thf(func_def_2753,type,
sK1240: ( int > real ) > int ).
thf(func_def_2754,type,
sK1241: ( int > real ) > int ).
thf(func_def_2755,type,
sK1242: set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_2756,type,
sK1243: nat > ( nat > real ) > real > nat ).
thf(func_def_2757,type,
sK1244: ( real > code_integer ) > set_real > real ).
thf(func_def_2758,type,
sK1245: nat > nat ).
thf(func_def_2759,type,
sK1246: set_list_nat > nat > set_list_nat ).
thf(func_def_2760,type,
sK1247: set_list_nat > nat > list_nat ).
thf(func_def_2761,type,
sK1248: ( complex > rat ) > set_complex > complex ).
thf(func_def_2762,type,
sK1249: set_real > real ).
thf(func_def_2763,type,
sK1250: set_real > real ).
thf(func_def_2764,type,
sK1251: ( real > $o ) > list_real > nat ).
thf(func_def_2765,type,
sK1252: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_2766,type,
sK1253: nat > ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_2767,type,
sK1254: nat > ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_2768,type,
sK1255: set_int > ( int > rat ) > ( int > rat ) > int ).
thf(func_def_2769,type,
sK1256: set_complex > complex ).
thf(func_def_2770,type,
sK1257: set_complex > complex ).
thf(func_def_2771,type,
sK1258: nat > list_nat > nat ).
thf(func_def_2772,type,
sK1259: ( int > real ) > int ).
thf(func_def_2773,type,
sK1260: ( int > real ) > int ).
thf(func_def_2774,type,
sK1261: ( nat > nat ) > set_nat > nat ).
thf(func_def_2775,type,
sK1262: real > nat ).
thf(func_def_2776,type,
sK1263: real > int ).
thf(func_def_2777,type,
sK1264: ( int > real ) > set_int > ( int > real ) > int ).
thf(func_def_2778,type,
sK1265: ( nat > rat ) > nat ).
thf(func_def_2779,type,
sK1266: ( nat > rat ) > nat ).
thf(func_def_2780,type,
sK1267: ( produc859450856879609959at_nat > $o ) > product_prod_nat_nat ).
thf(func_def_2781,type,
sK1268: ( produc859450856879609959at_nat > $o ) > product_prod_nat_nat ).
thf(func_def_2782,type,
sK1269: set_int > ( int > int ) > int ).
thf(func_def_2783,type,
sK1270: ( nat > real ) > nat > ( nat > real ) > nat ).
thf(func_def_2784,type,
sK1271: ( nat > real ) > nat > ( nat > real ) > real ).
thf(func_def_2785,type,
sK1272: set_complex > ( complex > complex ) > complex ).
thf(func_def_2786,type,
sK1273: int > int ).
thf(func_def_2787,type,
sK1274: set_int > set_int > ( int > real ) > int ).
thf(func_def_2788,type,
sK1275: int > int > int ).
thf(func_def_2789,type,
sK1276: nat > nat ).
thf(func_def_2790,type,
sK1277: set_nat > nat > set_nat ).
thf(func_def_2791,type,
sK1278: set_nat > nat > nat ).
thf(func_def_2792,type,
sK1279: real > set_list_nat > ( list_nat > complex ) > list_nat ).
thf(func_def_2793,type,
sK1280: nat > $o > vEBT_VEBT > $o ).
thf(func_def_2794,type,
sK1281: nat > $o > vEBT_VEBT > $o ).
thf(func_def_2795,type,
sK1282: $o > vEBT_VEBT > nat > nat ).
thf(func_def_2796,type,
sK1283: $o > vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2797,type,
sK1284: $o > vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2798,type,
sK1285: $o > vEBT_VEBT > nat > nat ).
thf(func_def_2799,type,
sK1286: vEBT_VEBT > nat > $o > nat ).
thf(func_def_2800,type,
sK1287: vEBT_VEBT > nat > $o > vEBT_VEBT ).
thf(func_def_2801,type,
sK1288: vEBT_VEBT > nat > $o > list_VEBT_VEBT ).
thf(func_def_2802,type,
sK1289: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).
thf(func_def_2803,type,
sK1290: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2804,type,
sK1291: vEBT_VEBT > $o > nat > vEBT_VEBT ).
thf(func_def_2805,type,
sK1292: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2806,type,
sK1293: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2807,type,
sK1294: nat > $o > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2808,type,
sK1295: nat > $o > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2809,type,
sK1296: vEBT_VEBT > nat > ( vEBT_VEBT > $o ) > vEBT_VEBT ).
thf(func_def_2810,type,
sK1297: nat > ( nat > $o ) > nat ).
thf(func_def_2811,type,
sK1298: list_nat > nat > nat ).
thf(func_def_2812,type,
sK1299: list_nat > nat > list_nat ).
thf(func_def_2813,type,
sK1300: set_int > real > ( int > real ) > int ).
thf(func_def_2814,type,
sK1301: ( int > num ) > ( set_int > $o ) > set_int ).
thf(func_def_2815,type,
sK1302: ( int > num ) > ( set_int > $o ) > int ).
thf(func_def_2816,type,
sK1303: int > ( nat > $o ) > nat ).
thf(func_def_2817,type,
sK1304: ( real > complex ) > set_real > set_real > real ).
thf(func_def_2818,type,
sK1305: set_real > set_real > ( real > complex ) > real ).
thf(func_def_2819,type,
sK1306: ( nat > real ) > nat ).
thf(func_def_2820,type,
sK1307: ( nat > real ) > nat ).
thf(func_def_2821,type,
sK1308: set_int > ( int > rat ) > rat > int ).
thf(func_def_2822,type,
sK1309: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2823,type,
sK1310: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2824,type,
sK1311: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2825,type,
sK1312: vEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_2826,type,
sK1313: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2827,type,
sK1314: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2828,type,
sK1315: vEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_2829,type,
sK1316: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2830,type,
sK1317: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2831,type,
sK1318: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2832,type,
sK1319: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2833,type,
sK1320: nat > vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_2834,type,
sK1321: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_2835,type,
sK1322: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_2836,type,
sK1323: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2837,type,
sK1324: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2838,type,
sK1325: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2839,type,
sK1326: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2840,type,
sK1327: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2841,type,
sK1328: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2842,type,
sK1329: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2843,type,
sK1330: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2844,type,
sK1331: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2845,type,
sK1332: set_real > ( nat > real > $o ) > set_nat > nat ).
thf(func_def_2846,type,
sK1333: set_real > ( nat > real > $o ) > set_nat > nat ).
thf(func_def_2847,type,
sK1334: set_real > ( nat > real > $o ) > set_nat > real ).
thf(func_def_2848,type,
sK1335: set_nat > set_real > ( nat > real > $o ) > nat ).
thf(func_def_2849,type,
sK1336: ( int > real ) > set_int > int ).
thf(func_def_2850,type,
sK1337: ( int > real ) > set_int > int ).
thf(func_def_2851,type,
sK1338: real > ( int > real ) > real > set_int > int ).
thf(func_def_2852,type,
sK1339: ( nat > $o ) > nat ).
thf(func_def_2853,type,
sK1340: set_set_nat > nat > set_nat ).
thf(func_def_2854,type,
sK1341: set_set_nat > nat > set_set_nat ).
thf(func_def_2855,type,
sK1342: ( rat > real ) > rat ).
thf(func_def_2856,type,
sK1343: ( rat > real ) > rat ).
thf(func_def_2857,type,
sK1344: ( nat > rat ) > nat ).
thf(func_def_2858,type,
sK1345: ( nat > rat ) > nat ).
thf(func_def_2859,type,
sK1346: ( int > $o ) > int > int ).
thf(func_def_2860,type,
sK1347: set_nat > set_nat > ( nat > complex ) > nat ).
thf(func_def_2861,type,
sK1348: nat > $o > vEBT_VEBT > nat ).
thf(func_def_2862,type,
sK1349: nat > $o > vEBT_VEBT > nat ).
thf(func_def_2863,type,
sK1350: nat > $o > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2864,type,
sK1351: nat > $o > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2865,type,
sK1352: $o > nat > vEBT_VEBT > nat ).
thf(func_def_2866,type,
sK1353: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2867,type,
sK1354: $o > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2868,type,
sK1355: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2869,type,
sK1356: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).
thf(func_def_2870,type,
sK1357: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2871,type,
sK1358: vEBT_VEBT > $o > nat > nat ).
thf(func_def_2872,type,
sK1359: vEBT_VEBT > $o > nat > vEBT_VEBT ).
thf(func_def_2873,type,
sK1360: vEBT_VEBT > $o ).
thf(func_def_2874,type,
sK1361: vEBT_VEBT > $o ).
thf(func_def_2875,type,
sK1362: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2876,type,
sK1363: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2877,type,
sK1364: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_2878,type,
sK1365: set_complex > ( complex > nat ) > ( complex > nat ) > complex ).
thf(func_def_2879,type,
sK1366: nat > vEBT_VEBT > $o ).
thf(func_def_2880,type,
sK1367: nat > vEBT_VEBT > $o ).
thf(func_def_2881,type,
sK1368: vEBT_VEBT > nat > nat ).
thf(func_def_2882,type,
sK1369: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2883,type,
sK1370: vEBT_VEBT > nat > option4927543243414619207at_nat ).
thf(func_def_2884,type,
sK1371: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2885,type,
sK1372: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2886,type,
sK1373: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2887,type,
sK1374: vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_2888,type,
sK1375: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2889,type,
sK1376: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2890,type,
sK1377: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2891,type,
sK1378: nat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_2892,type,
sK1379: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_2893,type,
sK1380: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_2894,type,
sK1381: nat > nat ).
thf(func_def_2895,type,
sK1382: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2896,type,
sK1383: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2897,type,
sK1384: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2898,type,
sK1385: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_2899,type,
sK1386: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2900,type,
sK1387: vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_2901,type,
sK1388: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2902,type,
sK1389: vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_2903,type,
sK1390: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2904,type,
sK1391: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2905,type,
sK1392: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2906,type,
sK1393: vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_2907,type,
sK1394: vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_2908,type,
sK1395: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_2909,type,
sK1396: vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_2910,type,
sK1397: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_2911,type,
sK1398: ( list_VEBT_VEBT > $o ) > list_VEBT_VEBT ).
thf(func_def_2912,type,
sK1399: list_list_nat > nat > list_nat ).
thf(func_def_2913,type,
sK1400: ( set_nat > $o ) > ( set_nat > $o ) > set_nat ).
thf(func_def_2914,type,
sK1401: vEBT_VEBT > nat > nat ).
thf(func_def_2915,type,
sK1402: vEBT_VEBT > nat > nat ).
thf(func_def_2916,type,
sK1403: vEBT_VEBT > nat > nat ).
thf(func_def_2917,type,
sK1404: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_2918,type,
sK1405: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_2919,type,
sK1406: nat > vEBT_VEBT > $o ).
thf(func_def_2920,type,
sK1407: nat > vEBT_VEBT > $o ).
thf(func_def_2921,type,
sK1408: real > ( nat > real ) > real ).
thf(func_def_2922,type,
sK1409: ( real > rat ) > set_real > real ).
thf(func_def_2923,type,
sK1410: ( real > rat ) > set_real > real ).
thf(func_def_2924,type,
sK1411: ( nat > $o ) > nat ).
thf(func_def_2925,type,
sK1412: set_complex > ( complex > rat ) > set_complex > complex ).
thf(func_def_2926,type,
sK1413: ( complex > rat ) > set_complex > set_complex > complex ).
thf(func_def_2927,type,
sK1414: int > ( int > $o ) > int > int ).
thf(func_def_2928,type,
sK1415: int > ( int > $o ) > int > int ).
thf(func_def_2929,type,
sK1416: int > ( int > $o ) > int > int ).
thf(func_def_2930,type,
sK1417: int > ( int > $o ) > int > int ).
thf(func_def_2931,type,
sK1418: ( nat > num ) > nat ).
thf(func_def_2932,type,
sK1419: ( nat > num ) > nat ).
thf(func_def_2933,type,
sK1420: ( real > nat ) > nat > set_real > real ).
thf(func_def_2934,type,
sK1421: ( int > rat ) > int ).
thf(func_def_2935,type,
sK1422: ( int > rat ) > int ).
thf(func_def_2936,type,
sK1423: ( nat > nat ) > set_nat > nat ).
thf(func_def_2937,type,
sK1424: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_2938,type,
sK1425: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_2939,type,
sK1426: nat > ( nat > int ) > nat ).
thf(func_def_2940,type,
sK1427: nat > int > ( nat > int ) > nat ).
thf(func_def_2941,type,
sK1428: set_real > ( real > real ) > real > real ).
thf(func_def_2942,type,
sK1429: ( nat > num ) > nat ).
thf(func_def_2943,type,
sK1430: ( nat > num ) > nat ).
thf(func_def_2944,type,
sK1431: set_int > ( int > real ) > ( int > real ) > int ).
thf(func_def_2945,type,
sK1432: produc9072475918466114483BT_nat > $o ).
thf(func_def_2946,type,
sK1433: produc9072475918466114483BT_nat > nat ).
thf(func_def_2947,type,
sK1434: produc9072475918466114483BT_nat > $o ).
thf(func_def_2948,type,
sK1435: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).
thf(func_def_2949,type,
sK1436: produc9072475918466114483BT_nat > nat ).
thf(func_def_2950,type,
sK1437: produc9072475918466114483BT_nat > nat ).
thf(func_def_2951,type,
sK1438: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_2952,type,
sK1439: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_2953,type,
sK1440: ( nat > $o ) > nat ).
thf(func_def_2954,type,
sK1441: rat > nat ).
thf(func_def_2955,type,
sK1442: ( nat > real ) > set_nat > nat ).
thf(func_def_2956,type,
sK1443: ( nat > $o ) > nat > list_nat > nat ).
thf(func_def_2957,type,
sK1444: nat > ( nat > $o ) > list_nat > nat ).
thf(func_def_2958,type,
sK1445: ( nat > rat ) > nat ).
thf(func_def_2959,type,
sK1446: ( nat > rat ) > nat ).
thf(func_def_2960,type,
sK1447: ( nat > complex ) > nat > nat ).
thf(func_def_2961,type,
sK1448: ( nat > complex ) > nat > complex > complex ).
thf(func_def_2962,type,
sK1449: set_nat > nat ).
thf(func_def_2963,type,
sK1450: set_nat > nat ).
thf(func_def_2964,type,
sK1451: set_nat > nat ).
thf(func_def_2965,type,
sK1452: set_complex > ( complex > nat ) > set_complex > complex ).
thf(func_def_2966,type,
sK1453: ( real > rat ) > set_real > ( real > rat ) > real ).
thf(func_def_2967,type,
sK1454: ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_2968,type,
sK1455: nat > list_int ).
thf(func_def_2969,type,
sK1456: list_VEBT_VEBT > list_VEBT_VEBT > nat ).
thf(func_def_2970,type,
sK1457: nat > nat ).
thf(func_def_2971,type,
sK1458: real > set_complex > ( complex > real ) > complex ).
thf(func_def_2972,type,
sK1459: ( nat > complex ) > nat > ( nat > complex ) > nat ).
thf(func_def_2973,type,
sK1460: ( nat > complex ) > nat > ( nat > complex ) > complex ).
thf(func_def_2974,type,
sK1461: produc8923325533196201883nteger > code_integer ).
thf(func_def_2975,type,
sK1462: produc8923325533196201883nteger > code_integer ).
thf(func_def_2976,type,
sK1463: ( nat > rat ) > set_nat > nat ).
thf(func_def_2977,type,
sK1464: set_real > real ).
thf(func_def_2978,type,
sK1465: produc4471711990508489141at_nat > nat > nat > nat ).
thf(func_def_2979,type,
sK1466: produc4471711990508489141at_nat > nat ).
thf(func_def_2980,type,
sK1467: produc4471711990508489141at_nat > nat ).
thf(func_def_2981,type,
sK1468: produc4471711990508489141at_nat > nat ).
thf(func_def_2982,type,
sK1469: nat > ( nat > $o ) > nat > nat ).
thf(func_def_2983,type,
sK1470: ( nat > real ) > ( nat > real ) > set_nat > nat ).
thf(func_def_2984,type,
sK1471: int > int > int ).
thf(func_def_2985,type,
sK1472: ( real > complex ) > set_real > real > real ).
thf(func_def_2986,type,
sK1473: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_2987,type,
sK1474: int > int ).
thf(func_def_2988,type,
sK1475: real > real > nat ).
thf(func_def_2989,type,
sK1476: ( real > nat ) > set_real > real ).
thf(func_def_2990,type,
sK1477: rat > rat ).
thf(func_def_2991,type,
sK1478: set_nat > ( nat > complex ) > set_nat > nat ).
thf(func_def_2992,type,
sK1479: list_o > list_complex > complex > $o ).
thf(func_def_2993,type,
sK1480: set_int > ( int > complex ) > set_int > int ).
thf(func_def_2994,type,
sK1481: nat > vEBT_VEBT > ( vEBT_VEBT > $o ) > vEBT_VEBT ).
thf(func_def_2995,type,
sK1482: ( real > real ) > set_real > real ).
thf(func_def_2996,type,
sK1483: ( nat > num ) > nat ).
thf(func_def_2997,type,
sK1484: ( nat > num ) > nat ).
thf(func_def_2998,type,
sK1485: ( int > $o ) > int > int > int ).
thf(func_def_2999,type,
sK1486: int > ( int > $o ) > int > int ).
thf(func_def_3000,type,
sK1487: produc9072475918466114483BT_nat > $o ).
thf(func_def_3001,type,
sK1488: produc9072475918466114483BT_nat > nat ).
thf(func_def_3002,type,
sK1489: produc9072475918466114483BT_nat > $o ).
thf(func_def_3003,type,
sK1490: produc9072475918466114483BT_nat > nat ).
thf(func_def_3004,type,
sK1491: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3005,type,
sK1492: produc9072475918466114483BT_nat > product_prod_nat_nat ).
thf(func_def_3006,type,
sK1493: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3007,type,
sK1494: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3008,type,
sK1495: produc9072475918466114483BT_nat > nat ).
thf(func_def_3009,type,
sK1496: produc9072475918466114483BT_nat > product_prod_nat_nat ).
thf(func_def_3010,type,
sK1497: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3011,type,
sK1498: produc9072475918466114483BT_nat > nat ).
thf(func_def_3012,type,
sK1499: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3013,type,
sK1500: produc9072475918466114483BT_nat > nat ).
thf(func_def_3014,type,
sK1501: produc9072475918466114483BT_nat > nat ).
thf(func_def_3015,type,
sK1502: produc9072475918466114483BT_nat > nat ).
thf(func_def_3016,type,
sK1503: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3017,type,
sK1504: produc9072475918466114483BT_nat > nat ).
thf(func_def_3018,type,
sK1505: produc9072475918466114483BT_nat > nat ).
thf(func_def_3019,type,
sK1506: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3020,type,
sK1507: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3021,type,
sK1508: produc9072475918466114483BT_nat > $o ).
thf(func_def_3022,type,
sK1509: produc9072475918466114483BT_nat > $o ).
thf(func_def_3023,type,
sK1510: set_int > set_int > ( int > rat ) > int ).
thf(func_def_3024,type,
sK1511: ( int > rat ) > set_int > set_int > int ).
thf(func_def_3025,type,
sK1512: set_int > ( int > real ) > set_int > int ).
thf(func_def_3026,type,
sK1513: set_int > ( int > real ) > ( int > real ) > set_int > int ).
thf(func_def_3027,type,
sK1514: set_int > ( int > real ) > set_int > int ).
thf(func_def_3028,type,
sK1515: ( nat > nat > $o ) > nat ).
thf(func_def_3029,type,
sK1516: ( nat > nat > $o ) > nat ).
thf(func_def_3030,type,
sK1517: ( nat > nat > $o ) > nat ).
thf(func_def_3031,type,
sK1518: ( nat > nat > $o ) > nat ).
thf(func_def_3032,type,
sK1519: ( nat > nat > $o ) > nat ).
thf(func_def_3033,type,
sK1520: ( nat > $o ) > nat ).
thf(func_def_3034,type,
sK1521: ( nat > $o ) > $o ).
thf(func_def_3035,type,
sK1522: ( nat > $o ) > nat ).
thf(func_def_3036,type,
sK1523: ( nat > rat ) > rat ).
thf(func_def_3037,type,
sK1524: ( nat > rat ) > nat ).
thf(func_def_3038,type,
sK1525: set_int > ( int > real ) > ( int > real ) > int ).
thf(func_def_3039,type,
sK1526: set_nat > ( nat > code_integer ) > set_nat > nat ).
thf(func_def_3040,type,
sK1527: produc7036089656553540234on_num > num ).
thf(func_def_3041,type,
sK1528: produc7036089656553540234on_num > num ).
thf(func_def_3042,type,
sK1529: produc7036089656553540234on_num > num > num > $o ).
thf(func_def_3043,type,
sK1530: produc7036089656553540234on_num > num > num > $o ).
thf(func_def_3044,type,
sK1531: produc7036089656553540234on_num > num ).
thf(func_def_3045,type,
sK1532: produc7036089656553540234on_num > num > num > $o ).
thf(func_def_3046,type,
sK1533: produc7036089656553540234on_num > option_num ).
thf(func_def_3047,type,
sK1534: set_Pr4811707699266497531nteger > code_integer ).
thf(func_def_3048,type,
sK1535: ( int > nat ) > set_int > int ).
thf(func_def_3049,type,
sK1536: rat > rat > rat ).
thf(func_def_3050,type,
sK1537: ( int > nat ) > set_int > int ).
thf(func_def_3051,type,
sK1538: real > nat ).
thf(func_def_3052,type,
sK1539: real > nat ).
thf(func_def_3053,type,
sK1540: set_set_nat > set_nat ).
thf(func_def_3054,type,
sK1541: set_set_nat > set_nat ).
thf(func_def_3055,type,
sK1542: set_nat > set_nat > set_set_nat > set_nat ).
thf(func_def_3056,type,
sK1543: ( nat > int ) > ( nat > int ) > nat ).
thf(func_def_3057,type,
sK1544: num > num ).
thf(func_def_3058,type,
sK1545: nat > ( nat > $o ) > nat ).
thf(func_def_3059,type,
sK1546: vEBT_VEBT > nat > nat ).
thf(func_def_3060,type,
sK1547: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_3061,type,
sK1548: vEBT_VEBT > nat > nat ).
thf(func_def_3062,type,
sK1549: vEBT_VEBT > nat > nat ).
thf(func_def_3063,type,
sK1550: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_3064,type,
sK1551: nat > vEBT_VEBT > $o ).
thf(func_def_3065,type,
sK1552: nat > vEBT_VEBT > $o ).
thf(func_def_3066,type,
sK1553: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3067,type,
sK1554: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3068,type,
sK1555: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3069,type,
sK1556: vEBT_VEBT > nat ).
thf(func_def_3070,type,
sK1557: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3071,type,
sK1558: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3072,type,
sK1559: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3073,type,
sK1560: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3074,type,
sK1561: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3075,type,
sK1562: ( real > real > $o ) > set_real > set_real > real ).
thf(func_def_3076,type,
sK1563: ( real > real > $o ) > set_real > set_real > real ).
thf(func_def_3077,type,
sK1564: ( real > real > $o ) > set_real > set_real > real ).
thf(func_def_3078,type,
sK1565: set_real > set_real > ( real > real > $o ) > real ).
thf(func_def_3079,type,
sK1566: ( rat > real ) > rat ).
thf(func_def_3080,type,
sK1567: ( rat > real ) > rat ).
thf(func_def_3081,type,
sK1568: vEBT_VEBT > nat ).
thf(func_def_3082,type,
sK1569: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3083,type,
sK1570: vEBT_VEBT > nat ).
thf(func_def_3084,type,
sK1571: vEBT_VEBT > nat ).
thf(func_def_3085,type,
sK1572: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3086,type,
sK1573: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3087,type,
sK1574: vEBT_VEBT > nat ).
thf(func_def_3088,type,
sK1575: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3089,type,
sK1576: vEBT_VEBT > $o ).
thf(func_def_3090,type,
sK1577: vEBT_VEBT > $o ).
thf(func_def_3091,type,
sK1578: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3092,type,
sK1579: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_3093,type,
sK1580: real > nat ).
thf(func_def_3094,type,
sK1581: complex > list_complex > nat ).
thf(func_def_3095,type,
sK1582: ( nat > real ) > set_nat > real > nat ).
thf(func_def_3096,type,
sK1583: ( nat > $o ) > ( nat > $o ) > nat ).
thf(func_def_3097,type,
sK1584: real > real > ( real > $o ) > real ).
thf(func_def_3098,type,
sK1585: real > real > ( real > $o ) > real ).
thf(func_def_3099,type,
sK1586: real > int ).
thf(func_def_3100,type,
sK1587: ( nat > int ) > nat ).
thf(func_def_3101,type,
sK1588: set_nat > ( nat > code_integer ) > nat ).
thf(func_def_3102,type,
sK1589: ( rat > num ) > rat ).
thf(func_def_3103,type,
sK1590: ( rat > num ) > rat ).
thf(func_def_3104,type,
sK1591: ( real > $o ) > list_real > real ).
thf(func_def_3105,type,
sK1592: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3106,type,
sK1593: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3107,type,
sK1594: nat > vEBT_VEBT > nat ).
thf(func_def_3108,type,
sK1595: nat > vEBT_VEBT > nat ).
thf(func_def_3109,type,
sK1596: nat > vEBT_VEBT > nat ).
thf(func_def_3110,type,
sK1597: nat > vEBT_VEBT > $o ).
thf(func_def_3111,type,
sK1598: nat > vEBT_VEBT > $o ).
thf(func_def_3112,type,
sK1599: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3113,type,
sK1600: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_3114,type,
sK1601: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3115,type,
sK1602: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_3116,type,
sK1603: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_3117,type,
sK1604: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_3118,type,
sK1605: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3119,type,
sK1606: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3120,type,
sK1607: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_3121,type,
sK1608: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_3122,type,
sK1609: vEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_3123,type,
sK1610: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_3124,type,
sK1611: vEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_3125,type,
sK1612: vEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_3126,type,
sK1613: vEBT_VEBT > vEBT_VEBT > nat > nat ).
thf(func_def_3127,type,
sK1614: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_3128,type,
sK1615: list_nat > nat > list_nat > set_Pr1261947904930325089at_nat > list_nat ).
thf(func_def_3129,type,
sK1616: list_nat > nat > list_nat > set_Pr1261947904930325089at_nat > nat ).
thf(func_def_3130,type,
sK1617: nat > nat > nat ).
thf(func_def_3131,type,
sK1618: vEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_3132,type,
sK1619: ( nat > real ) > nat ).
thf(func_def_3133,type,
sK1620: ( nat > real ) > nat ).
thf(func_def_3134,type,
sK1621: list_o > set_Pr8834758594704517033_o_int > list_int > nat ).
thf(func_def_3135,type,
sK1622: int > nat ).
thf(func_def_3136,type,
sK1623: ( nat > real ) > nat > int ).
thf(func_def_3137,type,
sK1624: set_real > ( real > real ) > set_real > real ).
thf(func_def_3138,type,
sK1625: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3139,type,
sK1626: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3140,type,
sK1627: nat > vEBT_VEBT > nat ).
thf(func_def_3141,type,
sK1628: nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_3142,type,
sK1629: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3143,type,
sK1630: vEBT_VEBT > $o ).
thf(func_def_3144,type,
sK1631: vEBT_VEBT > $o ).
thf(func_def_3145,type,
sK1632: ( nat > rat ) > set_nat > ( nat > rat ) > nat ).
thf(func_def_3146,type,
sK1633: list_VEBT_VEBT > ( vEBT_VEBT > $o ) > nat ).
thf(func_def_3147,type,
sK1634: list_VEBT_VEBT > ( vEBT_VEBT > $o ) > vEBT_VEBT ).
thf(func_def_3148,type,
sK1635: ( complex > rat ) > set_complex > complex ).
thf(func_def_3149,type,
sK1636: ( rat > nat ) > rat ).
thf(func_def_3150,type,
sK1637: ( rat > nat ) > rat ).
thf(func_def_3151,type,
sK1638: nat > list_nat > ( nat > $o ) > nat ).
thf(func_def_3152,type,
sK1639: nat > list_nat > ( nat > $o ) > nat ).
thf(func_def_3153,type,
sK1640: ( complex > real ) > set_complex > complex ).
thf(func_def_3154,type,
sK1641: nat > ( nat > real ) > nat ).
thf(func_def_3155,type,
sK1642: ( real > $o ) > ( real > $o ) > real ).
thf(func_def_3156,type,
sK1643: ( nat > int ) > set_nat > nat ).
thf(func_def_3157,type,
sK1644: ( rat > int ) > rat ).
thf(func_def_3158,type,
sK1645: ( rat > int ) > rat ).
thf(func_def_3159,type,
sK1646: ( rat > int ) > rat ).
thf(func_def_3160,type,
sK1647: ( rat > int ) > rat ).
thf(func_def_3161,type,
sK1648: set_int > set_int > ( int > rat ) > int ).
thf(func_def_3162,type,
sK1649: set_int > ( int > rat ) > set_int > int ).
thf(func_def_3163,type,
sK1650: ( nat > $o ) > list_nat > nat ).
thf(func_def_3164,type,
sK1651: ( int > real ) > set_int > int ).
thf(func_def_3165,type,
sK1652: nat > ( nat > int > $o ) > int ).
thf(func_def_3166,type,
sK1653: list_int > nat > ( nat > int > $o ) > nat ).
thf(func_def_3167,type,
sK1654: nat > ( nat > int > $o ) > list_int ).
thf(func_def_3168,type,
sK1655: nat > ( nat > int > $o ) > nat ).
thf(func_def_3169,type,
sK1656: ( complex > complex > $o ) > complex ).
thf(func_def_3170,type,
sK1657: ( complex > complex > $o ) > complex ).
thf(func_def_3171,type,
sK1658: ( complex > complex > $o ) > complex ).
thf(func_def_3172,type,
sK1659: ( complex > complex > $o ) > complex ).
thf(func_def_3173,type,
sK1660: ( complex > complex ) > set_complex > ( complex > complex ) > ( complex > complex > $o ) > complex ).
thf(func_def_3174,type,
sK1661: nat > vEBT_VEBT > nat ).
thf(func_def_3175,type,
sK1662: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3176,type,
sK1663: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3177,type,
sK1664: vEBT_VEBT > nat > nat ).
thf(func_def_3178,type,
sK1665: vEBT_VEBT > nat > nat ).
thf(func_def_3179,type,
sK1666: vEBT_VEBT > nat > nat ).
thf(func_def_3180,type,
sK1667: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_3181,type,
sK1668: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_3182,type,
sK1669: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3183,type,
sK1670: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3184,type,
sK1671: vEBT_VEBT > nat > nat ).
thf(func_def_3185,type,
sK1672: vEBT_VEBT > nat > nat ).
thf(func_def_3186,type,
sK1673: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_3187,type,
sK1674: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_3188,type,
sK1675: vEBT_VEBT > $o ).
thf(func_def_3189,type,
sK1676: vEBT_VEBT > $o ).
thf(func_def_3190,type,
sK1677: nat > set_list_nat > set_list_nat ).
thf(func_def_3191,type,
sK1678: nat > set_list_nat > list_nat ).
thf(func_def_3192,type,
sK1679: set_nat > ( nat > real ) > nat ).
thf(func_def_3193,type,
sK1680: ( real > nat ) > set_real > set_real > real ).
thf(func_def_3194,type,
sK1681: ( real > nat ) > set_real > ( real > nat ) > real ).
thf(func_def_3195,type,
sK1682: ( int > $o ) > nat ).
thf(func_def_3196,type,
sK1683: ( int > $o ) > nat ).
thf(func_def_3197,type,
sK1684: set_int > ( int > real ) > int ).
thf(func_def_3198,type,
sK1685: nat > nat > nat > nat ).
thf(func_def_3199,type,
sK1686: nat > nat > nat > nat ).
thf(func_def_3200,type,
sK1687: set_list_nat > list_nat ).
thf(func_def_3201,type,
sK1688: ( real > num ) > ( set_real > $o ) > real ).
thf(func_def_3202,type,
sK1689: ( real > num ) > ( set_real > $o ) > set_real ).
thf(func_def_3203,type,
sK1690: set_real > ( real > nat ) > real ).
thf(func_def_3204,type,
sK1691: ( real > rat ) > real ).
thf(func_def_3205,type,
sK1692: ( real > rat ) > real ).
thf(func_def_3206,type,
sK1693: ( real > code_integer ) > set_real > real ).
thf(func_def_3207,type,
sK1694: list_real > list_VEBT_VEBT > real > vEBT_VEBT ).
thf(func_def_3208,type,
sK1695: ( nat > num ) > ( set_nat > $o ) > nat ).
thf(func_def_3209,type,
sK1696: ( nat > num ) > ( set_nat > $o ) > set_nat ).
thf(func_def_3210,type,
sK1697: ( rat > rat ) > rat ).
thf(func_def_3211,type,
sK1698: ( rat > rat ) > rat ).
thf(func_def_3212,type,
sK1699: set_complex > ( complex > code_integer ) > complex ).
thf(func_def_3213,type,
sK1700: num > num ).
thf(func_def_3214,type,
sK1701: real > nat ).
thf(func_def_3215,type,
sK1702: set_nat > ( nat > real ) > nat ).
thf(func_def_3216,type,
sK1703: ( complex > rat ) > set_complex > set_complex > complex ).
thf(func_def_3217,type,
sK1704: real > real ).
thf(func_def_3218,type,
sK1705: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3219,type,
sK1706: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).
thf(func_def_3220,type,
sK1707: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3221,type,
sK1708: produc9072475918466114483BT_nat > nat ).
thf(func_def_3222,type,
sK1709: produc9072475918466114483BT_nat > nat ).
thf(func_def_3223,type,
sK1710: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).
thf(func_def_3224,type,
sK1711: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3225,type,
sK1712: produc9072475918466114483BT_nat > nat ).
thf(func_def_3226,type,
sK1713: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3227,type,
sK1714: produc9072475918466114483BT_nat > $o ).
thf(func_def_3228,type,
sK1715: produc9072475918466114483BT_nat > $o ).
thf(func_def_3229,type,
sK1716: produc9072475918466114483BT_nat > nat ).
thf(func_def_3230,type,
sK1717: nat > set_nat > nat ).
thf(func_def_3231,type,
sK1718: ( nat > real ) > real ).
thf(func_def_3232,type,
sK1719: nat > ( nat > real ) > nat ).
thf(func_def_3233,type,
sK1720: ( nat > $o ) > nat > nat > nat ).
thf(func_def_3234,type,
sK1721: nat > vEBT_VEBT > nat ).
thf(func_def_3235,type,
sK1722: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3236,type,
sK1723: nat > vEBT_VEBT > nat ).
thf(func_def_3237,type,
sK1724: nat > vEBT_VEBT > nat ).
thf(func_def_3238,type,
sK1725: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3239,type,
sK1726: nat > vEBT_VEBT > nat ).
thf(func_def_3240,type,
sK1727: nat > vEBT_VEBT > nat ).
thf(func_def_3241,type,
sK1728: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3242,type,
sK1729: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3243,type,
sK1730: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3244,type,
sK1731: nat > vEBT_VEBT > nat ).
thf(func_def_3245,type,
sK1732: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3246,type,
sK1733: ( option_num > option_num > $o ) > option_num > option_num > num ).
thf(func_def_3247,type,
sK1734: ( option_num > option_num > $o ) > option_num > option_num > num ).
thf(func_def_3248,type,
sK1735: nat > nat > nat ).
thf(func_def_3249,type,
sK1736: ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_3250,type,
sK1737: set_real > nat > ( real > int > $o ) > set_int > int ).
thf(func_def_3251,type,
sK1738: list_nat > set_Pr7556676689462069481BT_nat > list_VEBT_VEBT > nat ).
thf(func_def_3252,type,
sK1739: ( int > rat ) > int ).
thf(func_def_3253,type,
sK1740: ( int > rat ) > int ).
thf(func_def_3254,type,
sK1741: product_prod_int_int > int > int > int ).
thf(func_def_3255,type,
sK1742: product_prod_int_int > int > int > int ).
thf(func_def_3256,type,
sK1743: int > int > product_prod_int_int > int ).
thf(func_def_3257,type,
sK1744: complex > real ).
thf(func_def_3258,type,
sK1745: complex > real ).
thf(func_def_3259,type,
sK1746: ( int > real ) > set_int > int ).
thf(func_def_3260,type,
sK1747: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3261,type,
sK1748: produc9072475918466114483BT_nat > nat ).
thf(func_def_3262,type,
sK1749: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3263,type,
sK1750: produc9072475918466114483BT_nat > nat ).
thf(func_def_3264,type,
sK1751: produc9072475918466114483BT_nat > nat ).
thf(func_def_3265,type,
sK1752: produc9072475918466114483BT_nat > $o ).
thf(func_def_3266,type,
sK1753: produc9072475918466114483BT_nat > $o ).
thf(func_def_3267,type,
sK1754: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3268,type,
sK1755: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).
thf(func_def_3269,type,
sK1756: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3270,type,
sK1757: produc9072475918466114483BT_nat > nat ).
thf(func_def_3271,type,
sK1758: produc9072475918466114483BT_nat > nat ).
thf(func_def_3272,type,
sK1759: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3273,type,
sK1760: produc9072475918466114483BT_nat > option4927543243414619207at_nat ).
thf(func_def_3274,type,
sK1761: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3275,type,
sK1762: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3276,type,
sK1763: produc9072475918466114483BT_nat > nat ).
thf(func_def_3277,type,
sK1764: produc9072475918466114483BT_nat > nat ).
thf(func_def_3278,type,
sK1765: produc9072475918466114483BT_nat > nat ).
thf(func_def_3279,type,
sK1766: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3280,type,
sK1767: produc9072475918466114483BT_nat > nat ).
thf(func_def_3281,type,
sK1768: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_3282,type,
sK1769: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3283,type,
sK1770: produc9072475918466114483BT_nat > $o ).
thf(func_def_3284,type,
sK1771: produc9072475918466114483BT_nat > $o ).
thf(func_def_3285,type,
sK1772: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3286,type,
sK1773: produc9072475918466114483BT_nat > product_prod_nat_nat ).
thf(func_def_3287,type,
sK1774: produc9072475918466114483BT_nat > nat ).
thf(func_def_3288,type,
sK1775: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3289,type,
sK1776: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3290,type,
sK1777: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3291,type,
sK1778: produc9072475918466114483BT_nat > nat ).
thf(func_def_3292,type,
sK1779: produc9072475918466114483BT_nat > nat ).
thf(func_def_3293,type,
sK1780: produc9072475918466114483BT_nat > nat ).
thf(func_def_3294,type,
sK1781: produc9072475918466114483BT_nat > nat ).
thf(func_def_3295,type,
sK1782: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3296,type,
sK1783: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3297,type,
sK1784: produc9072475918466114483BT_nat > nat ).
thf(func_def_3298,type,
sK1785: produc9072475918466114483BT_nat > nat ).
thf(func_def_3299,type,
sK1786: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_3300,type,
sK1787: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_3301,type,
sK1788: produc9072475918466114483BT_nat > product_prod_nat_nat ).
thf(func_def_3302,type,
sK1789: produc9072475918466114483BT_nat > nat ).
thf(func_def_3303,type,
sK1790: produc9072475918466114483BT_nat > $o ).
thf(func_def_3304,type,
sK1791: produc9072475918466114483BT_nat > $o ).
thf(func_def_3305,type,
sK1792: produc9072475918466114483BT_nat > nat ).
thf(func_def_3306,type,
sK1793: produc9072475918466114483BT_nat > $o ).
thf(func_def_3307,type,
sK1794: produc9072475918466114483BT_nat > $o ).
thf(func_def_3308,type,
sK1795: set_nat > nat > nat ).
thf(func_def_3309,type,
sK1796: set_int > real > ( int > real ) > int ).
thf(func_def_3310,type,
sK1797: ( nat > rat ) > rat ).
thf(func_def_3311,type,
sK1798: nat > ( nat > rat ) > nat ).
thf(func_def_3312,type,
sK1799: rat > ( nat > rat ) > nat ).
thf(func_def_3313,type,
sK1800: ( nat > rat ) > nat ).
thf(func_def_3314,type,
sK1801: list_o > ( $o > $o ) > $o ).
thf(func_def_3315,type,
sK1802: ( real > rat ) > set_real > rat > rat > real ).
thf(func_def_3316,type,
sK1803: ( real > rat ) > set_real > real ).
thf(func_def_3317,type,
sK1804: nat > ( $o > $o ) > list_o > nat ).
thf(func_def_3318,type,
sK1805: ( $o > $o ) > list_o > $o > nat ).
thf(func_def_3319,type,
sK1806: nat > real > ( real > $o ) > real ).
thf(func_def_3320,type,
sK1807: list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3321,type,
sK1808: set_int > ( int > rat ) > ( int > rat ) > int ).
thf(func_def_3322,type,
sK1809: rat > set_int > ( int > rat ) > int ).
thf(func_def_3323,type,
sK1810: ( rat > int ) > rat ).
thf(func_def_3324,type,
sK1811: ( rat > int ) > rat ).
thf(func_def_3325,type,
sK1812: ( complex > complex > $o ) > complex ).
thf(func_def_3326,type,
sK1813: ( complex > complex > $o ) > complex ).
thf(func_def_3327,type,
sK1814: ( complex > complex > $o ) > complex ).
thf(func_def_3328,type,
sK1815: ( complex > complex > $o ) > complex ).
thf(func_def_3329,type,
sK1816: ( complex > complex > $o ) > ( int > complex ) > ( int > complex ) > set_int > int ).
thf(func_def_3330,type,
sK1817: ( int > nat ) > set_int > set_int > int ).
thf(func_def_3331,type,
sK1818: real > nat ).
thf(func_def_3332,type,
sK1819: ( int > real ) > ( real > real > $o ) > ( int > real ) > set_int > int ).
thf(func_def_3333,type,
sK1820: ( real > real > $o ) > real ).
thf(func_def_3334,type,
sK1821: ( real > real > $o ) > real ).
thf(func_def_3335,type,
sK1822: ( real > real > $o ) > real ).
thf(func_def_3336,type,
sK1823: ( real > real > $o ) > real ).
thf(func_def_3337,type,
sK1824: nat > nat ).
thf(func_def_3338,type,
sK1825: nat > ( nat > $o ) > nat ).
thf(func_def_3339,type,
sK1826: set_real > nat > ( complex > real > $o ) > set_complex > real ).
thf(func_def_3340,type,
sK1827: $o > list_o > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_3341,type,
sK1828: list_int > list_VEBT_VEBT > int > vEBT_VEBT ).
thf(func_def_3342,type,
sK1829: vEBT_VEBT > nat > nat > nat ).
thf(func_def_3343,type,
sK1830: ( int > complex ) > set_int > set_int > int ).
thf(func_def_3344,type,
sK1831: ( int > complex ) > ( int > complex ) > set_int > set_int > int ).
thf(func_def_3345,type,
sK1832: ( int > complex ) > set_int > set_int > int ).
thf(func_def_3346,type,
sK1833: nat > real > real ).
thf(func_def_3347,type,
sK1834: ( real > complex > $o ) > set_complex > set_real > nat > complex ).
thf(func_def_3348,type,
sK1835: ( real > rat ) > set_real > rat > real ).
thf(func_def_3349,type,
sK1836: ( real > real ) > real ).
thf(func_def_3350,type,
sK1837: ( real > real ) > real ).
thf(func_def_3351,type,
sK1838: set_nat > set_real > ( real > nat > $o ) > nat ).
thf(func_def_3352,type,
sK1839: set_nat > set_real > ( real > nat > $o ) > real ).
thf(func_def_3353,type,
sK1840: set_nat > set_real > ( real > nat > $o ) > real ).
thf(func_def_3354,type,
sK1841: set_real > set_nat > ( real > nat > $o ) > real ).
thf(func_def_3355,type,
sK1842: ( nat > rat ) > set_nat > nat ).
thf(func_def_3356,type,
sK1843: set_nat > ( nat > rat ) > ( nat > nat ) > ( nat > rat ) > set_nat > nat ).
thf(func_def_3357,type,
sK1844: rat > rat > rat ).
thf(func_def_3358,type,
sK1845: ( $o > $o ) > list_o > nat ).
thf(func_def_3359,type,
sK1846: ( $o > $o ) > list_o > $o ).
thf(func_def_3360,type,
sK1847: set_nat > ( nat > rat ) > nat ).
thf(func_def_3361,type,
sK1848: set_complex > ( complex > real ) > complex ).
thf(func_def_3362,type,
sK1849: list_o > ( $o > $o ) > nat ).
thf(func_def_3363,type,
sK1850: ( complex > rat ) > set_complex > complex ).
thf(func_def_3364,type,
sK1851: ( nat > vEBT_VEBT > $o ) > nat > list_VEBT_VEBT ).
thf(func_def_3365,type,
sK1852: ( nat > vEBT_VEBT > $o ) > nat > nat ).
thf(func_def_3366,type,
sK1853: nat > ( nat > vEBT_VEBT > $o ) > vEBT_VEBT ).
thf(func_def_3367,type,
sK1854: list_VEBT_VEBT > ( nat > vEBT_VEBT > $o ) > nat > nat ).
thf(func_def_3368,type,
sK1855: vEBT_VEBT > option_nat > nat ).
thf(func_def_3369,type,
sK1856: vEBT_VEBT > option_nat > vEBT_VEBT ).
thf(func_def_3370,type,
sK1857: vEBT_VEBT > option_nat > nat ).
thf(func_def_3371,type,
sK1858: vEBT_VEBT > option_nat > nat ).
thf(func_def_3372,type,
sK1859: vEBT_VEBT > option_nat > list_VEBT_VEBT ).
thf(func_def_3373,type,
sK1860: vEBT_VEBT > option_nat > $o ).
thf(func_def_3374,type,
sK1861: vEBT_VEBT > option_nat > $o ).
thf(func_def_3375,type,
sK1862: vEBT_VEBT > option_nat > vEBT_VEBT ).
thf(func_def_3376,type,
sK1863: vEBT_VEBT > option_nat > list_VEBT_VEBT ).
thf(func_def_3377,type,
sK1864: vEBT_VEBT > option_nat > nat ).
thf(func_def_3378,type,
sK1865: ( int > $o ) > list_int > int ).
thf(func_def_3379,type,
sK1866: set_complex > ( complex > nat ) > complex ).
thf(func_def_3380,type,
sK1867: nat > rat > ( nat > rat ) > nat > rat ).
thf(func_def_3381,type,
sK1868: ( num > rat ) > num ).
thf(func_def_3382,type,
sK1869: ( num > rat ) > num ).
thf(func_def_3383,type,
sK1870: set_complex > ( complex > real ) > complex > complex ).
thf(func_def_3384,type,
sK1871: ( real > real ) > ( real > real ) > set_real > set_real > real ).
thf(func_def_3385,type,
sK1872: ( real > real ) > set_real > set_real > real ).
thf(func_def_3386,type,
sK1873: ( real > real ) > set_real > set_real > real ).
thf(func_def_3387,type,
sK1874: ( set_real > $o ) > ( real > rat ) > real ).
thf(func_def_3388,type,
sK1875: ( set_real > $o ) > ( real > rat ) > set_real ).
thf(func_def_3389,type,
sK1876: nat > set_real > real ).
thf(func_def_3390,type,
sK1877: nat > set_real > set_real ).
thf(func_def_3391,type,
sK1878: list_o > $o > nat ).
thf(func_def_3392,type,
sK1879: list_nat > nat > nat ).
thf(func_def_3393,type,
sK1880: list_nat > nat > list_nat ).
thf(func_def_3394,type,
sK1881: ( nat > real ) > ( nat > real ) > set_nat > nat ).
thf(func_def_3395,type,
sK1882: ( complex > rat ) > set_complex > ( complex > rat ) > complex ).
thf(func_def_3396,type,
sK1883: set_complex > set_complex > ( complex > rat ) > complex ).
thf(func_def_3397,type,
sK1884: ( complex > nat ) > set_complex > ( complex > nat ) > complex ).
thf(func_def_3398,type,
sK1885: set_real > set_real > ( real > complex ) > real ).
thf(func_def_3399,type,
sK1886: ( real > complex ) > set_real > set_real > real ).
thf(func_def_3400,type,
sK1887: produc1193250871479095198on_num > num > num > num ).
thf(func_def_3401,type,
sK1888: produc1193250871479095198on_num > num ).
thf(func_def_3402,type,
sK1889: produc1193250871479095198on_num > num ).
thf(func_def_3403,type,
sK1890: produc1193250871479095198on_num > num > num > num ).
thf(func_def_3404,type,
sK1891: produc1193250871479095198on_num > num ).
thf(func_def_3405,type,
sK1892: produc1193250871479095198on_num > option_num ).
thf(func_def_3406,type,
sK1893: produc1193250871479095198on_num > num > num > num ).
thf(func_def_3407,type,
sK1894: set_nat > nat ).
thf(func_def_3408,type,
sK1895: set_nat > nat ).
thf(func_def_3409,type,
sK1896: ( nat > rat ) > set_nat > nat ).
thf(func_def_3410,type,
sK1897: rat > rat ).
thf(func_def_3411,type,
sK1898: option4927543243414619207at_nat ).
thf(func_def_3412,type,
sK1899: vEBT_VEBT ).
thf(func_def_3413,type,
sK1900: list_VEBT_VEBT ).
thf(func_def_3414,type,
sK1901: ( nat > int ) > nat > nat ).
thf(func_def_3415,type,
sK1902: ( nat > int ) > nat > nat ).
thf(func_def_3416,type,
sK1903: option_nat > nat > vEBT_VEBT > nat ).
thf(func_def_3417,type,
sK1904: option_nat > nat > vEBT_VEBT > nat ).
thf(func_def_3418,type,
sK1905: option_nat > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3419,type,
sK1906: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3420,type,
sK1907: option_nat > nat > vEBT_VEBT > nat ).
thf(func_def_3421,type,
sK1908: vEBT_VEBT > $o ).
thf(func_def_3422,type,
sK1909: vEBT_VEBT > $o ).
thf(func_def_3423,type,
sK1910: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_3424,type,
sK1911: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_3425,type,
sK1912: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_3426,type,
sK1913: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_3427,type,
sK1914: nat > nat ).
thf(func_def_3428,type,
sK1915: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3429,type,
sK1916: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3430,type,
sK1917: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3431,type,
sK1918: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3432,type,
sK1919: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3433,type,
sK1920: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3434,type,
sK1921: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3435,type,
sK1922: vEBT_VEBT > nat ).
thf(func_def_3436,type,
sK1923: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3437,type,
sK1924: ( num > num > $o ) > num ).
thf(func_def_3438,type,
sK1925: ( num > num > $o ) > num ).
thf(func_def_3439,type,
sK1926: ( num > num > $o ) > num ).
thf(func_def_3440,type,
sK1927: ( num > num > $o ) > num ).
thf(func_def_3441,type,
sK1928: set_real > ( real > code_integer ) > real ).
thf(func_def_3442,type,
sK1929: set_Pr6192946355708809607T_VEBT > list_VEBT_VEBT > list_VEBT_VEBT > nat ).
thf(func_def_3443,type,
sK1930: real > ( real > $o ) > real ).
thf(func_def_3444,type,
sK1931: real > ( real > $o ) > real ).
thf(func_def_3445,type,
sK1932: ( real > $o ) > real > real ).
thf(func_def_3446,type,
sK1933: ( real > $o ) > real > real ).
thf(func_def_3447,type,
sK1934: ( nat > complex ) > set_nat > real > nat ).
thf(func_def_3448,type,
sK1935: real > list_real > list_nat > nat ).
thf(func_def_3449,type,
sK1936: set_int > set_int > ( int > complex ) > int ).
thf(func_def_3450,type,
sK1937: set_int > ( int > complex ) > ( int > complex ) > int ).
thf(func_def_3451,type,
sK1938: ( $o > $o ) > list_o > $o ).
thf(func_def_3452,type,
sK1939: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3453,type,
sK1940: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3454,type,
sK1941: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3455,type,
sK1942: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3456,type,
sK1943: ( complex > code_integer ) > ( code_integer > code_integer > $o ) > ( complex > code_integer ) > set_complex > complex ).
thf(func_def_3457,type,
sK1944: set_real > ( real > rat ) > real ).
thf(func_def_3458,type,
sK1945: rat > rat ).
thf(func_def_3459,type,
sK1946: real > ( real > real ) > real > real ).
thf(func_def_3460,type,
sK1947: real > ( real > real ) > real > real ).
thf(func_def_3461,type,
sK1948: real > real > ( real > real ) > real ).
thf(func_def_3462,type,
sK1949: set_int > set_int > ( int > rat ) > int ).
thf(func_def_3463,type,
sK1950: set_real > ( real > int ) > set_real > real ).
thf(func_def_3464,type,
sK1951: nat > set_int > int ).
thf(func_def_3465,type,
sK1952: nat > set_int > set_int ).
thf(func_def_3466,type,
sK1953: nat > nat > nat ).
thf(func_def_3467,type,
sK1954: ( nat > real ) > nat ).
thf(func_def_3468,type,
sK1955: ( nat > real ) > nat ).
thf(func_def_3469,type,
sK1956: nat > vEBT_VEBT > nat ).
thf(func_def_3470,type,
sK1957: ( nat > real ) > nat ).
thf(func_def_3471,type,
sK1958: ( nat > real ) > nat ).
thf(func_def_3472,type,
sK1959: set_complex > ( complex > real ) > complex ).
thf(func_def_3473,type,
sK1960: set_complex > real > ( complex > real ) > real > complex ).
thf(func_def_3474,type,
sK1961: list_int > nat > list_int ).
thf(func_def_3475,type,
sK1962: list_int > nat > int ).
thf(func_def_3476,type,
sK1963: ( rat > num ) > rat ).
thf(func_def_3477,type,
sK1964: ( rat > num ) > rat ).
thf(func_def_3478,type,
sK1965: produc7272778201969148633d_enat > list_VEBT_VEBT ).
thf(func_def_3479,type,
sK1966: produc7272778201969148633d_enat > nat ).
thf(func_def_3480,type,
sK1967: produc7272778201969148633d_enat > vEBT_VEBT ).
thf(func_def_3481,type,
sK1968: produc7272778201969148633d_enat > option4927543243414619207at_nat ).
thf(func_def_3482,type,
sK1969: produc7272778201969148633d_enat > option4927543243414619207at_nat ).
thf(func_def_3483,type,
sK1970: produc7272778201969148633d_enat > nat ).
thf(func_def_3484,type,
sK1971: produc7272778201969148633d_enat > list_VEBT_VEBT ).
thf(func_def_3485,type,
sK1972: produc7272778201969148633d_enat > vEBT_VEBT ).
thf(func_def_3486,type,
sK1973: produc7272778201969148633d_enat > nat ).
thf(func_def_3487,type,
sK1974: produc7272778201969148633d_enat > extended_enat ).
thf(func_def_3488,type,
sK1975: produc7272778201969148633d_enat > $o ).
thf(func_def_3489,type,
sK1976: produc7272778201969148633d_enat > $o ).
thf(func_def_3490,type,
sK1977: ( nat > real ) > nat ).
thf(func_def_3491,type,
sK1978: ( nat > real ) > nat ).
thf(func_def_3492,type,
sK1979: ( num > nat ) > num ).
thf(func_def_3493,type,
sK1980: ( num > nat ) > num ).
thf(func_def_3494,type,
sK1981: ( nat > nat > nat ) > nat ).
thf(func_def_3495,type,
sK1982: ( nat > nat > nat ) > nat ).
thf(func_def_3496,type,
sK1983: ( nat > nat > nat ) > nat ).
thf(func_def_3497,type,
sK1984: ( nat > nat > nat ) > nat ).
thf(func_def_3498,type,
sK1985: ( nat > nat > nat ) > nat ).
thf(func_def_3499,type,
sK1986: ( nat > nat > nat ) > nat ).
thf(func_def_3500,type,
sK1987: ( nat > nat > nat ) > nat ).
thf(func_def_3501,type,
sK1988: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_3502,type,
sK1989: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_3503,type,
sK1990: rat > rat > nat ).
thf(func_def_3504,type,
sK1991: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3505,type,
sK1992: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3506,type,
sK1993: vEBT_VEBT > nat ).
thf(func_def_3507,type,
sK1994: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3508,type,
sK1995: vEBT_VEBT > $o ).
thf(func_def_3509,type,
sK1996: vEBT_VEBT > $o ).
thf(func_def_3510,type,
sK1997: set_int > ( int > real ) > int ).
thf(func_def_3511,type,
sK1998: real > int ).
thf(func_def_3512,type,
sK1999: ( nat > real ) > nat ).
thf(func_def_3513,type,
sK2000: nat > nat > nat ).
thf(func_def_3514,type,
sK2001: set_real > ( real > real ) > set_real > real ).
thf(func_def_3515,type,
sK2002: set_real > ( real > real ) > real ).
thf(func_def_3516,type,
sK2003: ( int > $o ) > int > int ).
thf(func_def_3517,type,
sK2004: ( nat > int ) > nat ).
thf(func_def_3518,type,
sK2005: ( num > rat ) > num ).
thf(func_def_3519,type,
sK2006: ( num > rat ) > num ).
thf(func_def_3520,type,
sK2007: ( nat > real ) > nat > nat ).
thf(func_def_3521,type,
sK2008: ( nat > real ) > nat > nat ).
thf(func_def_3522,type,
sK2009: ( real > int ) > real ).
thf(func_def_3523,type,
sK2010: ( real > int ) > real ).
thf(func_def_3524,type,
sK2011: nat > set_complex > complex ).
thf(func_def_3525,type,
sK2012: nat > set_complex > set_complex ).
thf(func_def_3526,type,
sK2013: ( real > real ) > ( real > real ) > set_real > set_real > real ).
thf(func_def_3527,type,
sK2014: set_real > ( real > complex ) > ( real > complex ) > ( real > real ) > real ).
thf(func_def_3528,type,
sK2015: set_real > set_real > ( real > real ) > set_real > set_real > real ).
thf(func_def_3529,type,
sK2016: ( real > complex ) > set_real > real ).
thf(func_def_3530,type,
sK2017: ( real > real ) > ( real > real ) > set_real > set_real > real ).
thf(func_def_3531,type,
sK2018: ( real > real ) > set_real > set_real > set_real > set_real > real ).
thf(func_def_3532,type,
sK2019: ( real > complex ) > set_real > real ).
thf(func_def_3533,type,
sK2020: ( rat > rat ) > rat ).
thf(func_def_3534,type,
sK2021: ( rat > rat ) > rat ).
thf(func_def_3535,type,
sK2022: ( int > $o ) > int > int ).
thf(func_def_3536,type,
sK2023: ( int > $o ) > int > int ).
thf(func_def_3537,type,
sK2024: ( int > $o ) > int > int ).
thf(func_def_3538,type,
sK2025: ( int > $o ) > int ).
thf(func_def_3539,type,
sK2026: ( real > nat ) > set_real > real ).
thf(func_def_3540,type,
sK2027: ( int > complex ) > ( int > complex ) > set_int > int ).
thf(func_def_3541,type,
sK2028: ( int > complex ) > set_int > set_int > int ).
thf(func_def_3542,type,
sK2029: set_real > ( real > complex ) > ( real > complex ) > set_real > real ).
thf(func_def_3543,type,
sK2030: set_real > ( real > complex ) > set_real > real ).
thf(func_def_3544,type,
sK2031: set_real > ( real > complex ) > set_real > real ).
thf(func_def_3545,type,
sK2032: ( real > real ) > set_real > set_real > real ).
thf(func_def_3546,type,
sK2033: ( real > real ) > ( real > real ) > set_real > real ).
thf(func_def_3547,type,
sK2034: ( complex > real ) > set_complex > complex ).
thf(func_def_3548,type,
sK2035: ( nat > rat ) > rat > nat ).
thf(func_def_3549,type,
sK2036: set_nat > ( nat > nat ) > nat ).
thf(func_def_3550,type,
sK2037: set_int > ( int > complex ) > set_int > int ).
thf(func_def_3551,type,
sK2038: ( int > complex ) > set_int > set_int > int ).
thf(func_def_3552,type,
sK2039: nat > ( nat > rat ) > set_nat > nat ).
thf(func_def_3553,type,
sK2040: ( nat > $o ) > nat ).
thf(func_def_3554,type,
sK2041: nat > ( nat > real ) > real ).
thf(func_def_3555,type,
sK2042: nat > ( nat > real ) > nat ).
thf(func_def_3556,type,
sK2043: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3557,type,
sK2044: nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_3558,type,
sK2045: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3559,type,
sK2046: rat > set_rat > rat ).
thf(func_def_3560,type,
sK2047: set_real > ( real > real ) > real ).
thf(func_def_3561,type,
sK2048: ( rat > int ) > rat ).
thf(func_def_3562,type,
sK2049: ( rat > int ) > rat ).
thf(func_def_3563,type,
sK2050: nat > nat ).
thf(func_def_3564,type,
sK2051: vEBT_VEBT > $o ).
thf(func_def_3565,type,
sK2052: vEBT_VEBT > $o ).
thf(func_def_3566,type,
sK2053: nat > option_nat > vEBT_VEBT > nat ).
thf(func_def_3567,type,
sK2054: nat > option_nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3568,type,
sK2055: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3569,type,
sK2056: nat > option_nat > vEBT_VEBT > nat ).
thf(func_def_3570,type,
sK2057: nat > option_nat > vEBT_VEBT > nat ).
thf(func_def_3571,type,
sK2058: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_3572,type,
sK2059: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_3573,type,
sK2060: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3574,type,
sK2061: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3575,type,
sK2062: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3576,type,
sK2063: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3577,type,
sK2064: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3578,type,
sK2065: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3579,type,
sK2066: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3580,type,
sK2067: vEBT_VEBT > nat ).
thf(func_def_3581,type,
sK2068: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3582,type,
sK2069: set_int > set_int > ( real > int ) > ( int > real ) > int ).
thf(func_def_3583,type,
sK2070: ( int > complex ) > set_int > int ).
thf(func_def_3584,type,
sK2071: set_real > ( real > complex ) > ( int > complex ) > ( real > int ) > real ).
thf(func_def_3585,type,
sK2072: ( real > int ) > set_int > set_int > set_real > set_real > real ).
thf(func_def_3586,type,
sK2073: set_real > ( real > complex ) > real ).
thf(func_def_3587,type,
sK2074: set_int > set_real > set_real > set_int > ( int > real ) > int ).
thf(func_def_3588,type,
sK2075: ( real > int ) > set_real > set_real > ( int > real ) > real ).
thf(func_def_3589,type,
sK2076: set_Pr8693737435421807431at_nat > product_prod_nat_nat ).
thf(func_def_3590,type,
sK2077: list_nat > ( nat > $o ) > nat ).
thf(func_def_3591,type,
sK2078: product_prod_nat_nat > nat ).
thf(func_def_3592,type,
sK2079: product_prod_nat_nat > nat ).
thf(func_def_3593,type,
sK2080: set_int > int ).
thf(func_def_3594,type,
sK2081: produc8923325533196201883nteger > code_integer ).
thf(func_def_3595,type,
sK2082: produc8923325533196201883nteger > code_integer ).
thf(func_def_3596,type,
sK2083: set_complex > ( complex > rat ) > complex ).
thf(func_def_3597,type,
sK2084: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3598,type,
sK2085: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3599,type,
sK2086: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3600,type,
sK2087: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3601,type,
sK2088: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3602,type,
sK2089: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3603,type,
sK2090: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3604,type,
sK2091: set_int > ( int > rat ) > int ).
thf(func_def_3605,type,
sK2092: real > real ).
thf(func_def_3606,type,
sK2093: ( int > int > $o ) > int ).
thf(func_def_3607,type,
sK2094: set_complex > ( complex > nat ) > complex ).
thf(func_def_3608,type,
sK2095: set_nat > ( nat > complex ) > nat ).
thf(func_def_3609,type,
sK2096: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3610,type,
sK2097: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3611,type,
sK2098: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3612,type,
sK2099: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_3613,type,
sK2100: ( code_integer > code_integer > $o ) > ( int > code_integer ) > set_int > ( int > code_integer ) > int ).
thf(func_def_3614,type,
sK2101: ( option_nat > option_nat > $o ) > option_nat > option_nat > nat ).
thf(func_def_3615,type,
sK2102: ( option_nat > option_nat > $o ) > option_nat > option_nat > nat ).
thf(func_def_3616,type,
sK2103: ( int > real ) > set_int > set_int > int ).
thf(func_def_3617,type,
sK2104: ( int > real ) > set_int > ( int > real ) > int ).
thf(func_def_3618,type,
sK2105: nat > ( nat > $o ) > nat ).
thf(func_def_3619,type,
sK2106: nat > ( nat > $o ) > nat ).
thf(func_def_3620,type,
sK2107: ( rat > rat > rat ) > rat ).
thf(func_def_3621,type,
sK2108: ( rat > rat > rat ) > rat ).
thf(func_def_3622,type,
sK2109: ( rat > rat > rat ) > rat ).
thf(func_def_3623,type,
sK2110: ( rat > rat > rat ) > rat ).
thf(func_def_3624,type,
sK2111: ( rat > rat > rat ) > rat ).
thf(func_def_3625,type,
sK2112: ( rat > rat > rat ) > rat ).
thf(func_def_3626,type,
sK2113: ( rat > rat > rat ) > rat ).
thf(func_def_3627,type,
sK2114: ( int > $o ) > int > int > int ).
thf(func_def_3628,type,
sK2115: ( int > $o ) > int > int > int ).
thf(func_def_3629,type,
sK2116: int > int > ( int > $o ) > int ).
thf(func_def_3630,type,
sK2117: int > int > ( int > $o ) > int ).
thf(func_def_3631,type,
sK2118: ( nat > real ) > nat ).
thf(func_def_3632,type,
sK2119: list_real > list_int > real > int ).
thf(func_def_3633,type,
sK2120: ( real > rat ) > set_real > real ).
thf(func_def_3634,type,
sK2121: ( nat > $o ) > nat > nat ).
thf(func_def_3635,type,
sK2122: vEBT_VEBT > nat > $o > $o ).
thf(func_def_3636,type,
sK2123: vEBT_VEBT > nat > $o > $o ).
thf(func_def_3637,type,
sK2124: vEBT_VEBT > $o > nat > nat ).
thf(func_def_3638,type,
sK2125: vEBT_VEBT > $o > nat > nat ).
thf(func_def_3639,type,
sK2126: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).
thf(func_def_3640,type,
sK2127: vEBT_VEBT > $o > nat > nat ).
thf(func_def_3641,type,
sK2128: vEBT_VEBT > $o > nat > vEBT_VEBT ).
thf(func_def_3642,type,
sK2129: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3643,type,
sK2130: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3644,type,
sK2131: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3645,type,
sK2132: vEBT_VEBT > nat ).
thf(func_def_3646,type,
sK2133: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3647,type,
sK2134: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3648,type,
sK2135: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3649,type,
sK2136: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3650,type,
sK2137: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_3651,type,
sK2138: nat > list_o > $o ).
thf(func_def_3652,type,
sK2139: nat > list_o > list_o ).
thf(func_def_3653,type,
sK2140: rat > rat > rat > rat ).
thf(func_def_3654,type,
sK2141: set_list_nat > list_nat ).
thf(func_def_3655,type,
sK2142: set_list_nat > list_nat ).
thf(func_def_3656,type,
sK2143: set_list_nat > list_nat ).
thf(func_def_3657,type,
sK2144: ( int > rat ) > ( int > rat ) > set_int > int ).
thf(func_def_3658,type,
sK2145: ( int > rat ) > set_int > set_int > int ).
thf(func_def_3659,type,
sK2146: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > list_P6011104703257516679at_nat ).
thf(func_def_3660,type,
sK2147: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_3661,type,
sK2148: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > list_P6011104703257516679at_nat ).
thf(func_def_3662,type,
sK2149: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_3663,type,
sK2150: int > nat ).
thf(func_def_3664,type,
sK2151: set_real > ( real > rat ) > rat > real ).
thf(func_def_3665,type,
sK2152: real > list_real > nat ).
thf(func_def_3666,type,
sK2153: rat > ( rat > $o ) > rat ).
thf(func_def_3667,type,
sK2154: rat > ( rat > $o ) > rat ).
thf(func_def_3668,type,
sK2155: rat > ( rat > $o ) > rat ).
thf(func_def_3669,type,
sK2156: rat > ( rat > $o ) > rat ).
thf(func_def_3670,type,
sK2157: set_nat > nat > set_nat ).
thf(func_def_3671,type,
sK2158: set_nat > nat > nat ).
thf(func_def_3672,type,
sK2159: ( option_num > option4927543243414619207at_nat > $o ) > option_num > option4927543243414619207at_nat > num ).
thf(func_def_3673,type,
sK2160: ( option_num > option4927543243414619207at_nat > $o ) > option_num > option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_3674,type,
sK2161: ( nat > $o ) > nat ).
thf(func_def_3675,type,
sK2162: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_3676,type,
sK2163: set_nat > ( nat > nat ) > nat ).
thf(func_def_3677,type,
sK2164: nat > set_nat > ( nat > nat ) > nat ).
thf(func_def_3678,type,
sK2165: ( num > nat ) > num ).
thf(func_def_3679,type,
sK2166: ( num > nat ) > num ).
thf(func_def_3680,type,
sK2167: ( nat > $o ) > nat ).
thf(func_def_3681,type,
sK2168: ( nat > $o ) > nat > nat ).
thf(func_def_3682,type,
sK2169: ( nat > $o > $o ) > nat > list_o ).
thf(func_def_3683,type,
sK2170: ( nat > $o > $o ) > nat > nat ).
thf(func_def_3684,type,
sK2171: nat > ( nat > $o > $o ) > $o ).
thf(func_def_3685,type,
sK2172: list_o > ( nat > $o > $o ) > nat > nat ).
thf(func_def_3686,type,
sK2173: set_nat > nat > nat ).
thf(func_def_3687,type,
sK2174: ( produc8923325533196201883nteger > $o ) > code_integer ).
thf(func_def_3688,type,
sK2175: ( produc8923325533196201883nteger > $o ) > code_integer ).
thf(func_def_3689,type,
sK2176: nat > set_set_nat > set_set_nat ).
thf(func_def_3690,type,
sK2177: nat > set_set_nat > set_nat ).
thf(func_def_3691,type,
sK2178: set_real > ( real > nat ) > set_real > real ).
thf(func_def_3692,type,
sK2179: list_int > int > nat ).
thf(func_def_3693,type,
sK2180: nat > set_complex > complex ).
thf(func_def_3694,type,
sK2181: nat > set_complex > set_complex ).
thf(func_def_3695,type,
sK2182: ( num > $o ) > num ).
thf(func_def_3696,type,
sK2183: set_real > ( real > real ) > real ).
thf(func_def_3697,type,
sK2184: ( real > rat ) > real ).
thf(func_def_3698,type,
sK2185: ( real > rat ) > real ).
thf(func_def_3699,type,
sK2186: ( nat > int ) > nat ).
thf(func_def_3700,type,
sK2187: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > nat ).
thf(func_def_3701,type,
sK2188: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > list_nat ).
thf(func_def_3702,type,
sK2189: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > list_nat ).
thf(func_def_3703,type,
sK2190: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > nat ).
thf(func_def_3704,type,
sK2191: ( rat > rat ) > rat ).
thf(func_def_3705,type,
sK2192: ( rat > rat ) > rat ).
thf(func_def_3706,type,
sK2193: set_complex > ( complex > real ) > complex ).
thf(func_def_3707,type,
sK2194: ( int > int > $o ) > int > int > int ).
thf(func_def_3708,type,
sK2195: ( int > int > $o ) > int > int > int ).
thf(func_def_3709,type,
sK2196: ( nat > $o ) > nat > nat ).
thf(func_def_3710,type,
sK2197: ( nat > $o ) > nat > nat ).
thf(func_def_3711,type,
sK2198: real > nat ).
thf(func_def_3712,type,
sK2199: real > nat ).
thf(func_def_3713,type,
sK2200: nat > nat > nat ).
thf(func_def_3714,type,
sK2201: ( nat > real > real ) > real ).
thf(func_def_3715,type,
sK2202: ( nat > real > real ) > nat ).
thf(func_def_3716,type,
sK2203: real > nat > ( nat > real > real ) > ( real > real ) > real ).
thf(func_def_3717,type,
sK2204: set_complex > ( complex > real ) > complex ).
thf(func_def_3718,type,
sK2205: ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_3719,type,
sK2206: list_nat > list_nat ).
thf(func_def_3720,type,
sK2207: list_nat > nat ).
thf(func_def_3721,type,
sK2208: real > real > ( real > real ) > real ).
thf(func_def_3722,type,
sK2209: real > ( real > real ) > ( real > real ) > real > real ).
thf(func_def_3723,type,
sK2210: ( real > real ) > ( real > real ) > real > real > real ).
thf(func_def_3724,type,
sK2211: real > real > ( real > real ) > real ).
thf(func_def_3725,type,
sK2212: ( real > real ) > real > ( real > real ) > real > ( real > real ) > ( real > real ) > real ).
thf(func_def_3726,type,
sK2213: list_complex > complex > complex ).
thf(func_def_3727,type,
sK2214: list_o > list_o > nat ).
thf(func_def_3728,type,
sK2215: rat > set_real > ( real > rat ) > real ).
thf(func_def_3729,type,
sK2216: ( nat > nat > nat ) > nat ).
thf(func_def_3730,type,
sK2217: ( nat > nat > nat ) > nat ).
thf(func_def_3731,type,
sK2218: ( nat > nat > nat ) > nat ).
thf(func_def_3732,type,
sK2219: ( nat > nat > nat ) > nat ).
thf(func_def_3733,type,
sK2220: ( nat > nat > nat ) > nat ).
thf(func_def_3734,type,
sK2221: ( nat > nat > nat ) > nat ).
thf(func_def_3735,type,
sK2222: ( nat > nat > nat ) > nat ).
thf(func_def_3736,type,
sK2223: ( product_prod_nat_nat > complex ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat ).
thf(func_def_3737,type,
sK2224: set_complex > ( complex > rat ) > rat > complex ).
thf(func_def_3738,type,
sK2225: int > ( int > $o ) > int ).
thf(func_def_3739,type,
sK2226: int > ( int > $o ) > int ).
thf(func_def_3740,type,
sK2227: ( int > $o ) > int ).
thf(func_def_3741,type,
sK2228: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_3742,type,
sK2229: ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_3743,type,
sK2230: nat > real > ( nat > real > real ) > real > nat ).
thf(func_def_3744,type,
sK2231: nat > real > ( nat > real > real ) > real > real ).
thf(func_def_3745,type,
sK2232: real > ( real > real ) > ( nat > real > real ) > nat > real > real ).
thf(func_def_3746,type,
sK2233: set_real > set_real > ( real > rat ) > real ).
thf(func_def_3747,type,
sK2234: set_real > set_real > ( real > rat ) > real ).
thf(func_def_3748,type,
sK2235: ( complex > nat ) > ( set_complex > $o ) > complex ).
thf(func_def_3749,type,
sK2236: ( complex > nat ) > ( set_complex > $o ) > set_complex ).
thf(func_def_3750,type,
sK2237: nat > list_nat > nat ).
thf(func_def_3751,type,
sK2238: ( nat > $o ) > nat ).
thf(func_def_3752,type,
sK2239: ( nat > $o ) > nat ).
thf(func_def_3753,type,
sK2240: set_int > nat > set_int ).
thf(func_def_3754,type,
sK2241: ( nat > nat ) > nat ).
thf(func_def_3755,type,
sK2242: set_int > ( int > nat ) > int ).
thf(func_def_3756,type,
sK2243: set_int > ( int > rat ) > int ).
thf(func_def_3757,type,
sK2244: ( int > int > $o ) > int > int > int ).
thf(func_def_3758,type,
sK2245: ( int > int > $o ) > int > int > int ).
thf(func_def_3759,type,
sK2246: set_nat > nat > nat ).
thf(func_def_3760,type,
sK2247: ( rat > rat ) > rat ).
thf(func_def_3761,type,
sK2248: ( rat > rat ) > rat ).
thf(func_def_3762,type,
sK2249: list_int > ( int > $o ) > nat ).
thf(func_def_3763,type,
sK2250: list_int > ( int > $o ) > int ).
thf(func_def_3764,type,
sK2251: nat > list_int > list_int ).
thf(func_def_3765,type,
sK2252: nat > list_int > int ).
thf(func_def_3766,type,
sK2253: ( int > nat ) > ( nat > nat > $o ) > ( int > nat ) > set_int > int ).
thf(func_def_3767,type,
sK2254: ( nat > nat > $o ) > nat ).
thf(func_def_3768,type,
sK2255: ( nat > nat > $o ) > nat ).
thf(func_def_3769,type,
sK2256: ( nat > nat > $o ) > nat ).
thf(func_def_3770,type,
sK2257: ( nat > nat > $o ) > nat ).
thf(func_def_3771,type,
sK2258: set_int > set_int > ( int > real ) > int ).
thf(func_def_3772,type,
sK2259: set_int > set_int > ( int > real ) > int ).
thf(func_def_3773,type,
sK2260: ( real > real ) > ( nat > real > real ) > real > real > nat > real ).
thf(func_def_3774,type,
sK2261: nat > ( nat > real > real ) > real > real > nat ).
thf(func_def_3775,type,
sK2262: nat > ( nat > real > real ) > real > real > real ).
thf(func_def_3776,type,
sK2263: nat > nat > nat ).
thf(func_def_3777,type,
sK2264: real > ( int > real ) > set_int > int ).
thf(func_def_3778,type,
sK2265: ( nat > rat ) > rat ).
thf(func_def_3779,type,
sK2266: nat > ( nat > rat ) > nat ).
thf(func_def_3780,type,
sK2267: nat > ( nat > rat ) > nat ).
thf(func_def_3781,type,
sK2268: ( produc3843707927480180839at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3782,type,
sK2269: ( produc3843707927480180839at_nat > $o ) > set_Pr1261947904930325089at_nat ).
thf(func_def_3783,type,
sK2270: ( nat > rat ) > nat ).
thf(func_def_3784,type,
sK2271: ( nat > rat ) > nat ).
thf(func_def_3785,type,
sK2272: rat > ( complex > rat ) > set_complex > complex ).
thf(func_def_3786,type,
sK2273: ( rat > num ) > rat ).
thf(func_def_3787,type,
sK2274: ( rat > num ) > rat ).
thf(func_def_3788,type,
sK2275: vEBT_VEBT > $o > nat > $o ).
thf(func_def_3789,type,
sK2276: vEBT_VEBT > $o > nat > $o ).
thf(func_def_3790,type,
sK2277: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_3791,type,
sK2278: nat > $o > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_3792,type,
sK2279: nat > $o > vEBT_VEBT > nat ).
thf(func_def_3793,type,
sK2280: nat > $o > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3794,type,
sK2281: nat > $o > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3795,type,
sK2282: rat > set_nat > ( nat > rat ) > nat ).
thf(func_def_3796,type,
sK2283: option_num > num ).
thf(func_def_3797,type,
sK2284: ( rat > real ) > rat ).
thf(func_def_3798,type,
sK2285: ( rat > real ) > rat ).
thf(func_def_3799,type,
sK2286: set_list_nat > nat > set_list_nat ).
thf(func_def_3800,type,
sK2287: nat > nat ).
thf(func_def_3801,type,
sK2288: nat > set_nat > ( complex > nat > $o ) > set_complex > nat ).
thf(func_def_3802,type,
sK2289: nat > nat > nat ).
thf(func_def_3803,type,
sK2290: ( nat > $o ) > nat ).
thf(func_def_3804,type,
sK2291: ( nat > num ) > nat ).
thf(func_def_3805,type,
sK2292: nat > list_nat > list_nat ).
thf(func_def_3806,type,
sK2293: nat > list_nat > nat ).
thf(func_def_3807,type,
sK2294: nat > vEBT_VEBT > nat ).
thf(func_def_3808,type,
sK2295: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3809,type,
sK2296: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3810,type,
sK2297: nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_3811,type,
sK2298: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3812,type,
sK2299: nat > vEBT_VEBT > $o ).
thf(func_def_3813,type,
sK2300: nat > vEBT_VEBT > $o ).
thf(func_def_3814,type,
sK2301: set_set_nat > nat > set_set_nat ).
thf(func_def_3815,type,
sK2302: set_set_nat > nat > set_nat ).
thf(func_def_3816,type,
sK2303: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_3817,type,
sK2304: nat > real > ( nat > real ) > real ).
thf(func_def_3818,type,
sK2305: ( real > real ) > set_real > real ).
thf(func_def_3819,type,
sK2306: ( real > real ) > set_real > real ).
thf(func_def_3820,type,
sK2307: complex > ( nat > complex ) > nat > nat > complex ).
thf(func_def_3821,type,
sK2308: set_complex > ( complex > int ) > ( complex > int ) > complex ).
thf(func_def_3822,type,
sK2309: ( rat > $o ) > rat > rat ).
thf(func_def_3823,type,
sK2310: ( rat > $o ) > rat > rat ).
thf(func_def_3824,type,
sK2311: ( rat > $o ) > rat > rat ).
thf(func_def_3825,type,
sK2312: ( rat > $o ) > rat > rat ).
thf(func_def_3826,type,
sK2313: list_set_nat > ( set_nat > $o ) > set_nat ).
thf(func_def_3827,type,
sK2314: set_nat > ( nat > rat ) > nat ).
thf(func_def_3828,type,
sK2315: ( nat > $o ) > nat ).
thf(func_def_3829,type,
sK2316: ( nat > $o ) > nat > nat ).
thf(func_def_3830,type,
sK2317: ( int > real ) > set_int > int ).
thf(func_def_3831,type,
sK2318: set_int > ( int > real ) > set_int > int ).
thf(func_def_3832,type,
sK2319: set_nat > ( nat > rat ) > nat ).
thf(func_def_3833,type,
sK2320: ( nat > rat ) > set_nat > rat > rat > nat ).
thf(func_def_3834,type,
sK2321: set_set_nat > set_nat ).
thf(func_def_3835,type,
sK2322: set_set_nat > set_nat ).
thf(func_def_3836,type,
sK2323: set_set_nat > set_nat ).
thf(func_def_3837,type,
sK2324: ( real > rat ) > set_real > real ).
thf(func_def_3838,type,
sK2325: ( complex > real ) > ( int > real ) > set_int > ( complex > int ) > set_complex > int ).
thf(func_def_3839,type,
sK2326: ( complex > real ) > set_complex > complex ).
thf(func_def_3840,type,
sK2327: nat > extended_enat > nat ).
thf(func_def_3841,type,
sK2328: set_set_nat > set_nat ).
thf(func_def_3842,type,
sK2329: produc5491161045314408544at_nat > option4927543243414619207at_nat ).
thf(func_def_3843,type,
sK2330: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_3844,type,
sK2331: produc5491161045314408544at_nat > product_prod_nat_nat ).
thf(func_def_3845,type,
sK2332: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_3846,type,
sK2333: produc5491161045314408544at_nat > product_prod_nat_nat ).
thf(func_def_3847,type,
sK2334: produc5491161045314408544at_nat > product_prod_nat_nat ).
thf(func_def_3848,type,
sK2335: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o ).
thf(func_def_3849,type,
sK2336: list_nat > nat > list_nat ).
thf(func_def_3850,type,
sK2337: list_nat > nat > nat ).
thf(func_def_3851,type,
sK2338: set_complex > ( complex > code_integer ) > code_integer > code_integer > complex ).
thf(func_def_3852,type,
sK2339: ( complex > code_integer ) > set_complex > complex ).
thf(func_def_3853,type,
sK2340: real > real ).
thf(func_def_3854,type,
sK2341: rat > nat ).
thf(func_def_3855,type,
sK2342: set_int > ( int > rat ) > int ).
thf(func_def_3856,type,
sK2343: set_int > ( int > rat ) > int ).
thf(func_def_3857,type,
sK2344: set_complex > ( complex > rat ) > complex ).
thf(func_def_3858,type,
sK2345: set_int > ( int > nat ) > int ).
thf(func_def_3859,type,
sK2346: ( num > rat ) > num ).
thf(func_def_3860,type,
sK2347: ( num > rat ) > num ).
thf(func_def_3861,type,
sK2348: set_int > set_complex > ( int > complex > $o ) > nat > complex ).
thf(func_def_3862,type,
sK2349: set_int > set_int > ( int > complex ) > int ).
thf(func_def_3863,type,
sK2350: nat > real > ( nat > real > real ) > real ).
thf(func_def_3864,type,
sK2351: nat > real > ( nat > real > real ) > nat ).
thf(func_def_3865,type,
sK2352: ( nat > real > real ) > nat > ( real > real ) > real > real ).
thf(func_def_3866,type,
sK2353: set_int > ( int > rat ) > set_int > int ).
thf(func_def_3867,type,
sK2354: set_list_int > nat ).
thf(func_def_3868,type,
sK2355: nat > ( nat > real ) > real > nat > real ).
thf(func_def_3869,type,
sK2356: ( nat > $o ) > nat ).
thf(func_def_3870,type,
sK2357: nat > nat > nat ).
thf(func_def_3871,type,
sK2358: ( real > rat ) > set_real > set_real > real ).
thf(func_def_3872,type,
sK2359: ( real > rat ) > ( real > rat ) > set_real > real ).
thf(func_def_3873,type,
sK2360: ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_3874,type,
sK2361: set_complex > ( complex > real ) > set_complex > complex ).
thf(func_def_3875,type,
sK2362: set_int > int > int ).
thf(func_def_3876,type,
sK2363: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > list_int ).
thf(func_def_3877,type,
sK2364: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > int ).
thf(func_def_3878,type,
sK2365: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > int ).
thf(func_def_3879,type,
sK2366: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > list_int ).
thf(func_def_3880,type,
sK2367: ( list_int > $o ) > list_int ).
thf(func_def_3881,type,
sK2368: ( nat > num ) > nat ).
thf(func_def_3882,type,
sK2369: ( nat > num ) > nat ).
thf(func_def_3883,type,
sK2370: list_set_nat > set_nat > nat ).
thf(func_def_3884,type,
sK2371: set_nat > ( nat > int ) > ( nat > int ) > nat ).
thf(func_def_3885,type,
sK2372: set_nat > nat > set_nat ).
thf(func_def_3886,type,
sK2373: vEBT_VEBT > vEBT_VEBT > nat > option4927543243414619207at_nat ).
thf(func_def_3887,type,
sK2374: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_3888,type,
sK2375: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_3889,type,
sK2376: vEBT_VEBT > nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_3890,type,
sK2377: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3891,type,
sK2378: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3892,type,
sK2379: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3893,type,
sK2380: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_3894,type,
sK2381: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_3895,type,
sK2382: vEBT_VEBT > nat > vEBT_VEBT > nat ).
thf(func_def_3896,type,
sK2383: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3897,type,
sK2384: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_3898,type,
sK2385: vEBT_VEBT > vEBT_VEBT > nat > $o ).
thf(func_def_3899,type,
sK2386: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3900,type,
sK2387: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3901,type,
sK2388: nat > vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_3902,type,
sK2389: nat > ( nat > nat > $o ) > nat ).
thf(func_def_3903,type,
sK2390: list_nat > nat > ( nat > nat > $o ) > nat ).
thf(func_def_3904,type,
sK2391: nat > ( nat > nat > $o ) > list_nat ).
thf(func_def_3905,type,
sK2392: nat > ( nat > nat > $o ) > nat ).
thf(func_def_3906,type,
sK2393: ( nat > real > real ) > real > nat > real ).
thf(func_def_3907,type,
sK2394: ( nat > real > real ) > real > nat > nat ).
thf(func_def_3908,type,
sK2395: ( nat > real > real ) > real > nat > ( real > real ) > real ).
thf(func_def_3909,type,
sK2396: set_complex > ( complex > real ) > complex ).
thf(func_def_3910,type,
sK2397: ( nat > nat ) > set_nat > nat ).
thf(func_def_3911,type,
sK2398: nat > nat > nat > nat ).
thf(func_def_3912,type,
sK2399: nat > nat > nat > nat ).
thf(func_def_3913,type,
sK2400: ( rat > rat ) > rat ).
thf(func_def_3914,type,
sK2401: ( rat > rat ) > rat ).
thf(func_def_3915,type,
sK2402: ( complex > nat ) > set_complex > ( complex > nat ) > complex ).
thf(func_def_3916,type,
sK2403: ( num > num ) > num ).
thf(func_def_3917,type,
sK2404: ( num > num ) > num ).
thf(func_def_3918,type,
sK2405: ( num > rat ) > num ).
thf(func_def_3919,type,
sK2406: ( num > rat ) > num ).
thf(func_def_3920,type,
sK2407: ( rat > nat ) > rat ).
thf(func_def_3921,type,
sK2408: ( rat > nat ) > rat ).
thf(func_def_3922,type,
sK2409: rat > rat > rat ).
thf(func_def_3923,type,
sK2410: real > nat > ( nat > real > real ) > real > nat ).
thf(func_def_3924,type,
sK2411: real > nat > ( nat > real > real ) > real > real ).
thf(func_def_3925,type,
sK2412: ( real > real ) > nat > ( nat > real > real ) > real > real > real ).
thf(func_def_3926,type,
sK2413: set_nat > nat > set_nat ).
thf(func_def_3927,type,
sK2414: set_nat > nat > nat ).
thf(func_def_3928,type,
sK2415: ( nat > real ) > nat ).
thf(func_def_3929,type,
sK2416: ( nat > real ) > nat ).
thf(func_def_3930,type,
sK2417: ( complex > nat ) > set_complex > complex ).
thf(func_def_3931,type,
sK2418: list_VEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_3932,type,
sK2419: ( complex > rat ) > ( complex > rat ) > set_complex > ( rat > rat > $o ) > complex ).
thf(func_def_3933,type,
sK2420: ( rat > rat > $o ) > rat ).
thf(func_def_3934,type,
sK2421: ( rat > rat > $o ) > rat ).
thf(func_def_3935,type,
sK2422: ( rat > rat > $o ) > rat ).
thf(func_def_3936,type,
sK2423: ( rat > rat > $o ) > rat ).
thf(func_def_3937,type,
sK2424: ( real > real ) > real > set_real > real ).
thf(func_def_3938,type,
sK2425: nat > set_nat > set_int > ( int > nat > $o ) > nat ).
thf(func_def_3939,type,
sK2426: ( nat > nat ) > ( nat > nat ) > set_nat > nat ).
thf(func_def_3940,type,
sK2427: set_real > set_real > ( real > rat ) > real ).
thf(func_def_3941,type,
sK2428: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3942,type,
sK2429: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3943,type,
sK2430: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3944,type,
sK2431: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3945,type,
sK2432: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3946,type,
sK2433: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3947,type,
sK2434: ( set_nat > set_nat > set_nat ) > set_nat ).
thf(func_def_3948,type,
sK2435: code_integer > code_integer > code_integer ).
thf(func_def_3949,type,
sK2436: nat > nat > nat ).
thf(func_def_3950,type,
sK2437: set_complex > ( complex > rat ) > complex ).
thf(func_def_3951,type,
sK2438: nat > set_real > real ).
thf(func_def_3952,type,
sK2439: nat > set_real > set_real ).
thf(func_def_3953,type,
sK2440: ( nat > set_nat ) > nat ).
thf(func_def_3954,type,
sK2441: set_complex > ( complex > real ) > complex ).
thf(func_def_3955,type,
sK2442: ( complex > complex ) > ( complex > real ) > set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_3956,type,
sK2443: ( nat > rat ) > set_nat > nat ).
thf(func_def_3957,type,
sK2444: nat > nat > nat ).
thf(func_def_3958,type,
sK2445: ( nat > num ) > nat ).
thf(func_def_3959,type,
sK2446: ( real > real ) > real ).
thf(func_def_3960,type,
sK2447: ( real > real ) > real ).
thf(func_def_3961,type,
sK2448: set_real > real ).
thf(func_def_3962,type,
sK2449: set_real > real ).
thf(func_def_3963,type,
sK2450: set_real > real ).
thf(func_def_3964,type,
sK2451: real > nat > real ).
thf(func_def_3965,type,
sK2452: nat > ( nat > rat ) > rat > nat ).
thf(func_def_3966,type,
sK2453: nat > set_real > set_real ).
thf(func_def_3967,type,
sK2454: nat > set_real > real ).
thf(func_def_3968,type,
sK2455: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_3969,type,
sK2456: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_3970,type,
sK2457: vEBT_VEBT > nat ).
thf(func_def_3971,type,
sK2458: ( num > real ) > num ).
thf(func_def_3972,type,
sK2459: ( num > real ) > num ).
thf(func_def_3973,type,
sK2460: set_int > set_int > ( int > complex ) > set_complex > set_complex > int ).
thf(func_def_3974,type,
sK2461: set_complex > ( complex > complex ) > complex ).
thf(func_def_3975,type,
sK2462: ( complex > int ) > ( int > complex ) > set_int > set_int > int ).
thf(func_def_3976,type,
sK2463: set_complex > set_complex > ( complex > int ) > set_int > set_int > complex ).
thf(func_def_3977,type,
sK2464: set_int > ( int > complex ) > int ).
thf(func_def_3978,type,
sK2465: ( int > complex ) > set_int > ( int > complex ) > ( complex > complex ) > int ).
thf(func_def_3979,type,
sK2466: ( int > complex ) > set_complex > set_complex > ( complex > int ) > complex ).
thf(func_def_3980,type,
sK2467: ( nat > complex ) > nat > nat ).
thf(func_def_3981,type,
sK2468: set_int > ( int > real ) > real > int ).
thf(func_def_3982,type,
sK2469: ( real > nat ) > set_real > ( real > nat ) > real ).
thf(func_def_3983,type,
sK2470: list_Code_integer > code_integer > list_Code_integer > code_integer ).
thf(func_def_3984,type,
sK2471: rat > rat > set_complex > ( complex > rat ) > complex ).
thf(func_def_3985,type,
sK2472: ( complex > rat ) > set_complex > complex ).
thf(func_def_3986,type,
sK2473: ( real > int ) > real ).
thf(func_def_3987,type,
sK2474: ( real > int ) > real ).
thf(func_def_3988,type,
sK2475: vEBT_VEBT > $o ).
thf(func_def_3989,type,
sK2476: vEBT_VEBT > $o ).
thf(func_def_3990,type,
sK2477: real > real > real ).
thf(func_def_3991,type,
sK2478: real > nat > real ).
thf(func_def_3992,type,
sK2479: set_complex > ( complex > complex ) > set_complex > ( complex > complex ) > complex ).
thf(func_def_3993,type,
sK2480: set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_3994,type,
sK2481: set_complex > set_complex > ( complex > complex ) > complex ).
thf(func_def_3995,type,
sK2482: ( rat > rat ) > rat ).
thf(func_def_3996,type,
sK2483: ( rat > rat ) > rat ).
thf(func_def_3997,type,
sK2484: set_nat > ( nat > code_integer ) > nat ).
thf(func_def_3998,type,
sK2485: set_nat > code_integer > code_integer > ( nat > code_integer ) > nat ).
thf(func_def_3999,type,
sK2486: ( complex > nat ) > nat > set_complex > complex ).
thf(func_def_4000,type,
sK2487: ( num > rat ) > num ).
thf(func_def_4001,type,
sK2488: ( num > rat ) > num ).
thf(func_def_4002,type,
sK2489: ( real > $o ) > real ).
thf(func_def_4003,type,
sK2490: ( real > $o ) > real ).
thf(func_def_4004,type,
sK2491: ( real > $o ) > nat ).
thf(func_def_4005,type,
sK2492: ( nat > real ) > nat ).
thf(func_def_4006,type,
sK2493: ( nat > real ) > nat ).
thf(func_def_4007,type,
sK2494: set_set_nat > set_nat ).
thf(func_def_4008,type,
sK2495: set_set_nat > set_nat ).
thf(func_def_4009,type,
sK2496: nat > ( nat > $o ) > nat ).
thf(func_def_4010,type,
sK2497: nat > ( nat > $o ) > nat ).
thf(func_def_4011,type,
sK2498: ( num > num ) > num ).
thf(func_def_4012,type,
sK2499: ( num > num ) > num ).
thf(func_def_4013,type,
sK2500: set_real > nat > set_real ).
thf(func_def_4014,type,
sK2501: set_real > nat > real ).
thf(func_def_4015,type,
sK2502: ( num > int ) > num ).
thf(func_def_4016,type,
sK2503: ( num > int ) > num ).
thf(func_def_4017,type,
sK2504: ( num > num > $o ) > num ).
thf(func_def_4018,type,
sK2505: ( num > num > $o ) > num ).
thf(func_def_4019,type,
sK2506: ( num > num > $o ) > num ).
thf(func_def_4020,type,
sK2507: ( num > num > $o ) > num ).
thf(func_def_4021,type,
sK2508: ( num > num > $o ) > num ).
thf(func_def_4022,type,
sK2509: list_real > real > real ).
thf(func_def_4023,type,
sK2510: vEBT_VEBT > nat > $o ).
thf(func_def_4024,type,
sK2511: vEBT_VEBT > nat > $o ).
thf(func_def_4025,type,
sK2512: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_4026,type,
sK2513: vEBT_VEBT > nat > nat ).
thf(func_def_4027,type,
sK2514: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_4028,type,
sK2515: vEBT_VEBT > nat > nat ).
thf(func_def_4029,type,
sK2516: vEBT_VEBT > nat > nat ).
thf(func_def_4030,type,
sK2517: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4031,type,
sK2518: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4032,type,
sK2519: nat > vEBT_VEBT > nat ).
thf(func_def_4033,type,
sK2520: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4034,type,
sK2521: nat > vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_4035,type,
sK2522: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4036,type,
sK2523: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4037,type,
sK2524: nat > vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_4038,type,
sK2525: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4039,type,
sK2526: ( nat > $o ) > nat ).
thf(func_def_4040,type,
sK2527: set_complex > real > ( complex > real ) > complex ).
thf(func_def_4041,type,
sK2528: ( nat > nat ) > ( set_nat > $o ) > nat ).
thf(func_def_4042,type,
sK2529: ( nat > nat ) > ( set_nat > $o ) > set_nat ).
thf(func_def_4043,type,
sK2530: ( real > num ) > real ).
thf(func_def_4044,type,
sK2531: ( real > num ) > real ).
thf(func_def_4045,type,
sK2532: nat > nat > nat ).
thf(func_def_4046,type,
sK2533: nat > nat > nat ).
thf(func_def_4047,type,
sK2534: produc859450856879609959at_nat > nat ).
thf(func_def_4048,type,
sK2535: produc859450856879609959at_nat > product_prod_nat_nat ).
thf(func_def_4049,type,
sK2536: produc859450856879609959at_nat > nat ).
thf(func_def_4050,type,
sK2537: ( real > $o ) > real ).
thf(func_def_4051,type,
sK2538: ( real > $o ) > real ).
thf(func_def_4052,type,
sK2539: ( real > $o ) > nat ).
thf(func_def_4053,type,
sK2540: nat > nat ).
thf(func_def_4054,type,
sK2541: ( num > num ) > num ).
thf(func_def_4055,type,
sK2542: ( num > num ) > num ).
thf(func_def_4056,type,
sK2543: set_int > set_int > ( int > real ) > int ).
thf(func_def_4057,type,
sK2544: real > real > real ).
thf(func_def_4058,type,
sK2545: ( complex > code_integer ) > set_complex > set_complex > complex ).
thf(func_def_4059,type,
sK2546: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_4060,type,
sK2547: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_4061,type,
sK2548: option_num > num ).
thf(func_def_4062,type,
sK2549: set_complex > ( complex > nat ) > set_complex > complex ).
thf(func_def_4063,type,
sK2550: ( list_nat > $o ) > ( list_nat > $o ) > list_nat ).
thf(func_def_4064,type,
sK2551: ( rat > rat ) > rat ).
thf(func_def_4065,type,
sK2552: ( rat > rat ) > rat ).
thf(func_def_4066,type,
sK2553: ( real > real ) > real ).
thf(func_def_4067,type,
sK2554: ( real > real ) > real ).
thf(func_def_4068,type,
sK2555: list_real > real > list_o > $o ).
thf(func_def_4069,type,
sK2556: ( real > rat ) > set_real > real ).
thf(func_def_4070,type,
sK2557: option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_4071,type,
sK2558: set_Pr7543698050874017315T_VEBT > list_VEBT_VEBT > list_o > nat ).
thf(func_def_4072,type,
sK2559: set_set_nat > set_nat > set_nat ).
thf(func_def_4073,type,
sK2560: vEBT_VEBT > $o ).
thf(func_def_4074,type,
sK2561: vEBT_VEBT > $o ).
thf(func_def_4075,type,
sK2562: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4076,type,
sK2563: vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4077,type,
sK2564: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4078,type,
sK2565: vEBT_VEBT > nat ).
thf(func_def_4079,type,
sK2566: ( nat > nat > $o ) > nat ).
thf(func_def_4080,type,
sK2567: ( nat > nat > $o ) > nat ).
thf(func_def_4081,type,
sK2568: ( nat > nat > $o ) > nat ).
thf(func_def_4082,type,
sK2569: ( nat > nat > $o ) > nat ).
thf(func_def_4083,type,
sK2570: ( real > int ) > int > set_real > real ).
thf(func_def_4084,type,
sK2571: nat > nat > set_nat > nat ).
thf(func_def_4085,type,
sK2572: set_nat > nat ).
thf(func_def_4086,type,
sK2573: set_nat > nat ).
thf(func_def_4087,type,
sK2574: set_real > ( real > complex ) > real ).
thf(func_def_4088,type,
sK2575: ( nat > nat ) > nat ).
thf(func_def_4089,type,
sK2576: ( nat > nat ) > nat ).
thf(func_def_4090,type,
sK2577: nat > ( nat > complex ) > real > real ).
thf(func_def_4091,type,
sK2578: set_nat > set_nat > ( nat > real ) > nat ).
thf(func_def_4092,type,
sK2579: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat ).
thf(func_def_4093,type,
sK2580: set_int > set_real > ( real > int > $o ) > real ).
thf(func_def_4094,type,
sK2581: set_int > set_real > ( real > int > $o ) > real ).
thf(func_def_4095,type,
sK2582: set_int > set_real > ( real > int > $o ) > int ).
thf(func_def_4096,type,
sK2583: set_int > set_real > ( real > int > $o ) > real ).
thf(func_def_4097,type,
sK2584: set_int > ( int > nat ) > set_int > int ).
thf(func_def_4098,type,
sK2585: set_complex > ( complex > int ) > set_complex > complex ).
thf(func_def_4099,type,
sK2586: ( num > num ) > num ).
thf(func_def_4100,type,
sK2587: ( num > num ) > num ).
thf(func_def_4101,type,
sK2588: ( int > nat ) > set_int > int ).
thf(func_def_4102,type,
sK2589: ( num > num ) > num ).
thf(func_def_4103,type,
sK2590: ( num > num ) > num ).
thf(func_def_4104,type,
sK2591: set_int > ( int > rat ) > int ).
thf(func_def_4105,type,
sK2592: ( int > nat ) > set_int > int ).
thf(func_def_4106,type,
sK2593: ( int > nat ) > set_int > int ).
thf(func_def_4107,type,
sK2594: option_nat > nat ).
thf(func_def_4108,type,
sK2595: ( int > complex ) > set_int > int ).
thf(func_def_4109,type,
sK2596: ( complex > int ) > ( int > complex ) > set_int > set_int > int ).
thf(func_def_4110,type,
sK2597: ( complex > int ) > set_int > set_int > set_complex > set_complex > complex ).
thf(func_def_4111,type,
sK2598: set_complex > ( complex > complex ) > ( int > complex ) > ( complex > int ) > complex ).
thf(func_def_4112,type,
sK2599: set_complex > ( complex > complex ) > complex ).
thf(func_def_4113,type,
sK2600: set_complex > ( complex > int ) > ( int > complex ) > set_complex > complex ).
thf(func_def_4114,type,
sK2601: set_complex > ( int > complex ) > set_complex > set_int > set_int > int ).
thf(func_def_4115,type,
sK2602: rat > set_nat > ( nat > rat ) > nat ).
thf(func_def_4116,type,
sK2603: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4117,type,
sK2604: vEBT_VEBT > nat ).
thf(func_def_4118,type,
sK2605: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4119,type,
sK2606: vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_4120,type,
sK2607: vEBT_VEBT > $o ).
thf(func_def_4121,type,
sK2608: vEBT_VEBT > $o ).
thf(func_def_4122,type,
sK2609: rat > ( nat > rat ) > nat ).
thf(func_def_4123,type,
sK2610: int > int > int ).
thf(func_def_4124,type,
sK2611: ( complex > nat ) > set_complex > ( complex > nat ) > complex ).
thf(func_def_4125,type,
sK2612: real > real > real ).
thf(func_def_4126,type,
sK2613: ( nat > rat ) > nat ).
thf(func_def_4127,type,
sK2614: ( real > rat ) > set_real > real ).
thf(func_def_4128,type,
sK2615: list_o > $o > nat ).
thf(func_def_4129,type,
sK2616: rat > ( int > rat ) > set_int > int ).
thf(func_def_4130,type,
sK2617: set_int > set_int > ( int > real ) > int ).
thf(func_def_4131,type,
sK2618: ( complex > nat > $o ) > set_nat > set_complex > nat ).
thf(func_def_4132,type,
sK2619: ( complex > nat > $o ) > set_nat > set_complex > complex ).
thf(func_def_4133,type,
sK2620: ( complex > nat > $o ) > set_nat > set_complex > complex ).
thf(func_def_4134,type,
sK2621: ( complex > nat > $o ) > set_complex > set_nat > complex ).
thf(func_def_4135,type,
sK2622: vEBT_VEBT > nat > $o ).
thf(func_def_4136,type,
sK2623: vEBT_VEBT > nat > $o ).
thf(func_def_4137,type,
sK2624: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4138,type,
sK2625: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4139,type,
sK2626: nat > vEBT_VEBT > nat ).
thf(func_def_4140,type,
sK2627: nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4141,type,
sK2628: set_int > ( int > code_integer ) > int ).
thf(func_def_4142,type,
sK2629: ( nat > rat ) > nat > rat > nat > rat ).
thf(func_def_4143,type,
sK2630: set_complex > ( complex > complex ) > complex ).
thf(func_def_4144,type,
sK2631: set_complex > ( complex > rat ) > ( complex > rat ) > complex ).
thf(func_def_4145,type,
sK2632: complex > set_complex > ( complex > nat ) > complex ).
thf(func_def_4146,type,
sK2633: set_complex > ( complex > nat ) > complex ).
thf(func_def_4147,type,
sK2634: set_real > real ).
thf(func_def_4148,type,
sK2635: set_real > set_real > ( real > int ) > set_int > set_int > real ).
thf(func_def_4149,type,
sK2636: ( int > real ) > set_real > set_real > set_int > set_int > int ).
thf(func_def_4150,type,
sK2637: ( int > complex ) > ( real > complex ) > ( int > real ) > set_int > int ).
thf(func_def_4151,type,
sK2638: set_real > set_real > ( int > real ) > ( real > int ) > real ).
thf(func_def_4152,type,
sK2639: set_real > ( real > complex ) > real ).
thf(func_def_4153,type,
sK2640: ( int > real ) > set_int > ( real > int ) > set_int > int ).
thf(func_def_4154,type,
sK2641: ( int > complex ) > set_int > int ).
thf(func_def_4155,type,
sK2642: ( rat > int ) > rat ).
thf(func_def_4156,type,
sK2643: ( rat > int ) > rat ).
thf(func_def_4157,type,
sK2644: list_int > ( int > $o ) > nat ).
thf(func_def_4158,type,
sK2645: set_int > nat > set_int ).
thf(func_def_4159,type,
sK2646: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_4160,type,
sK2647: ( complex > nat ) > set_complex > nat > complex ).
thf(func_def_4161,type,
sK2648: vEBT_VEBT > nat > nat ).
thf(func_def_4162,type,
sK2649: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_4163,type,
sK2650: vEBT_VEBT > nat > nat ).
thf(func_def_4164,type,
sK2651: vEBT_VEBT > nat > nat ).
thf(func_def_4165,type,
sK2652: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_4166,type,
sK2653: vEBT_VEBT > nat > nat ).
thf(func_def_4167,type,
sK2654: vEBT_VEBT > nat > nat ).
thf(func_def_4168,type,
sK2655: nat > vEBT_VEBT > nat ).
thf(func_def_4169,type,
sK2656: nat > vEBT_VEBT > nat ).
thf(func_def_4170,type,
sK2657: nat > vEBT_VEBT > nat ).
thf(func_def_4171,type,
sK2658: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4172,type,
sK2659: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4173,type,
sK2660: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4174,type,
sK2661: nat > vEBT_VEBT > nat ).
thf(func_def_4175,type,
sK2662: nat > vEBT_VEBT > nat ).
thf(func_def_4176,type,
sK2663: nat > vEBT_VEBT > nat ).
thf(func_def_4177,type,
sK2664: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4178,type,
sK2665: nat > vEBT_VEBT > nat ).
thf(func_def_4179,type,
sK2666: nat > vEBT_VEBT > nat ).
thf(func_def_4180,type,
sK2667: nat > vEBT_VEBT > nat ).
thf(func_def_4181,type,
sK2668: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4182,type,
sK2669: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4183,type,
sK2670: nat > vEBT_VEBT > nat ).
thf(func_def_4184,type,
sK2671: nat > vEBT_VEBT > nat ).
thf(func_def_4185,type,
sK2672: nat > list_VEBT_VEBT > nat ).
thf(func_def_4186,type,
sK2673: nat > list_VEBT_VEBT > nat ).
thf(func_def_4187,type,
sK2674: vEBT_VEBT > $o ).
thf(func_def_4188,type,
sK2675: vEBT_VEBT > $o ).
thf(func_def_4189,type,
sK2676: list_list_VEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_4190,type,
sK2677: ( complex > $o ) > list_complex > complex ).
thf(func_def_4191,type,
sK2678: ( nat > rat ) > set_nat > ( nat > rat ) > nat ).
thf(func_def_4192,type,
sK2679: set_real > ( real > real ) > real > real ).
thf(func_def_4193,type,
sK2680: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_4194,type,
sK2681: ( product_prod_nat_nat > $o ) > nat ).
thf(func_def_4195,type,
sK2682: ( num > int ) > num ).
thf(func_def_4196,type,
sK2683: ( num > int ) > num ).
thf(func_def_4197,type,
sK2684: ( complex > complex ) > set_complex > real > complex ).
thf(func_def_4198,type,
sK2685: ( complex > rat ) > set_complex > complex ).
thf(func_def_4199,type,
sK2686: ( nat > rat ) > set_nat > nat ).
thf(func_def_4200,type,
sK2687: ( nat > rat ) > set_nat > nat ).
thf(func_def_4201,type,
sK2688: real > ( real > real ) > real > real ).
thf(func_def_4202,type,
sK2689: real > ( real > real ) > real > real ).
thf(func_def_4203,type,
sK2690: real > real > ( real > real ) > real ).
thf(func_def_4204,type,
sK2691: ( real > real ) > ( real > real ) > real > real > real ).
thf(func_def_4205,type,
sK2692: ( real > real ) > ( real > real ) > real > real > real ).
thf(func_def_4206,type,
sK2693: ( real > real ) > ( real > real ) > real > real > real ).
thf(func_def_4207,type,
sK2694: real > ( real > real ) > real > real ).
thf(func_def_4208,type,
sK2695: ( int > code_integer ) > set_int > int ).
thf(func_def_4209,type,
sK2696: set_int > ( int > code_integer ) > set_int > int ).
thf(func_def_4210,type,
sK2697: nat > nat ).
thf(func_def_4211,type,
sK2698: int > nat ).
thf(func_def_4212,type,
sK2699: int > nat ).
thf(func_def_4213,type,
sK2700: ( int > real ) > set_int > int ).
thf(func_def_4214,type,
sK2701: ( int > real ) > ( int > int ) > ( int > real ) > set_int > set_int > int ).
thf(func_def_4215,type,
sK2702: int > nat ).
thf(func_def_4216,type,
sK2703: set_nat > ( nat > real ) > nat ).
thf(func_def_4217,type,
sK2704: int > list_int > int ).
thf(func_def_4218,type,
sK2705: ( nat > nat ) > nat ).
thf(func_def_4219,type,
sK2706: ( complex > rat ) > ( complex > rat ) > set_complex > complex ).
thf(func_def_4220,type,
sK2707: ( int > real ) > set_int > ( real > real > $o ) > ( int > real ) > int ).
thf(func_def_4221,type,
sK2708: ( real > real > $o ) > real ).
thf(func_def_4222,type,
sK2709: ( real > real > $o ) > real ).
thf(func_def_4223,type,
sK2710: ( real > real > $o ) > real ).
thf(func_def_4224,type,
sK2711: ( real > real > $o ) > real ).
thf(func_def_4225,type,
sK2712: list_VEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4226,type,
sK2713: ( option_num > option_nat > $o ) > option_nat > option_num > nat ).
thf(func_def_4227,type,
sK2714: ( option_num > option_nat > $o ) > option_nat > option_num > num ).
thf(func_def_4228,type,
sK2715: set_nat > ( nat > rat ) > ( nat > rat ) > nat ).
thf(func_def_4229,type,
sK2716: nat > set_nat > nat ).
thf(func_def_4230,type,
sK2717: complex > complex ).
thf(func_def_4231,type,
sK2718: complex > real ).
thf(func_def_4232,type,
sK2719: option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_4233,type,
sK2720: option4927543243414619207at_nat > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_4234,type,
sK2721: option4927543243414619207at_nat > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_4235,type,
sK2722: ( num > real ) > num ).
thf(func_def_4236,type,
sK2723: ( num > real ) > num ).
thf(func_def_4237,type,
sK2724: set_list_VEBT_VEBT > nat ).
thf(func_def_4238,type,
sK2725: ( real > rat ) > ( real > rat ) > set_real > real ).
thf(func_def_4239,type,
sK2726: ( num > rat ) > num ).
thf(func_def_4240,type,
sK2727: ( num > rat ) > num ).
thf(func_def_4241,type,
sK2728: list_VEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_4242,type,
sK2729: set_nat > ( nat > rat ) > nat ).
thf(func_def_4243,type,
sK2730: set_int > ( int > code_integer ) > int ).
thf(func_def_4244,type,
sK2731: set_real > ( real > real ) > real > real ).
thf(func_def_4245,type,
sK2732: vEBT_VEBT > extended_enat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4246,type,
sK2733: vEBT_VEBT > extended_enat > vEBT_VEBT > nat ).
thf(func_def_4247,type,
sK2734: vEBT_VEBT > extended_enat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4248,type,
sK2735: vEBT_VEBT > extended_enat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4249,type,
sK2736: vEBT_VEBT > extended_enat > vEBT_VEBT > nat ).
thf(func_def_4250,type,
sK2737: vEBT_VEBT > vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(func_def_4251,type,
sK2738: vEBT_VEBT > vEBT_VEBT > extended_enat > list_VEBT_VEBT ).
thf(func_def_4252,type,
sK2739: vEBT_VEBT > vEBT_VEBT > extended_enat > nat ).
thf(func_def_4253,type,
sK2740: vEBT_VEBT > vEBT_VEBT > extended_enat > option4927543243414619207at_nat ).
thf(func_def_4254,type,
sK2741: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_4255,type,
sK2742: vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_4256,type,
sK2743: ( int > real ) > set_int > int ).
thf(func_def_4257,type,
sK2744: ( list_o > $o ) > list_o ).
thf(func_def_4258,type,
sK2745: ( int > int > $o ) > int ).
thf(func_def_4259,type,
sK2746: ( int > int > $o ) > int ).
thf(func_def_4260,type,
sK2747: ( int > int > $o ) > int ).
thf(func_def_4261,type,
sK2748: ( int > int > $o ) > int ).
thf(func_def_4262,type,
sK2749: set_int > ( int > nat ) > int ).
thf(func_def_4263,type,
sK2750: int > set_int > ( int > nat ) > int ).
thf(func_def_4264,type,
sK2751: ( rat > num ) > rat ).
thf(func_def_4265,type,
sK2752: ( rat > num ) > rat ).
thf(func_def_4266,type,
sK2753: int > ( int > $o ) > int ).
thf(func_def_4267,type,
sK2754: int > ( int > $o ) > int ).
thf(func_def_4268,type,
sK2755: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_4269,type,
sK2756: ( int > $o ) > int ).
thf(func_def_4270,type,
sK2757: ( real > rat ) > ( real > rat ) > set_real > set_real > real ).
thf(func_def_4271,type,
sK2758: ( real > rat ) > set_real > set_real > real ).
thf(func_def_4272,type,
sK2759: ( real > rat ) > set_real > set_real > real ).
thf(func_def_4273,type,
sK2760: ( nat > real ) > nat > nat ).
thf(func_def_4274,type,
sK2761: ( int > $o ) > int > int ).
thf(func_def_4275,type,
sK2762: ( int > $o ) > int > int ).
thf(func_def_4276,type,
sK2763: set_real > ( real > int ) > real ).
thf(func_def_4277,type,
sK2764: ( set_nat > real ) > real > set_set_nat > set_nat ).
thf(func_def_4278,type,
sK2765: ( int > real ) > set_int > set_int > int ).
thf(func_def_4279,type,
sK2766: set_real > set_real > ( real > nat ) > real ).
thf(func_def_4280,type,
sK2767: ( real > nat ) > set_real > set_real > real ).
thf(func_def_4281,type,
sK2768: ( complex > $o ) > ( complex > $o ) > complex ).
thf(func_def_4282,type,
sK2769: set_complex > ( complex > complex ) > set_complex > complex ).
thf(func_def_4283,type,
sK2770: set_complex > ( complex > complex ) > ( complex > complex ) > complex ).
thf(func_def_4284,type,
sK2771: ( int > $o ) > int ).
thf(func_def_4285,type,
sK2772: int > ( int > $o ) > set_int > int ).
thf(func_def_4286,type,
sK2773: int > ( int > $o ) > set_int > int ).
thf(func_def_4287,type,
sK2774: ( int > $o ) > int > int ).
thf(func_def_4288,type,
sK2775: int > ( int > $o ) > int ).
thf(func_def_4289,type,
sK2776: int > ( int > $o ) > int ).
thf(func_def_4290,type,
sK2777: int > ( int > $o ) > ( int > $o ) > int ).
thf(func_def_4291,type,
sK2778: int > set_int > ( int > $o ) > int ).
thf(func_def_4292,type,
sK2779: ( complex > int ) > set_complex > int > complex ).
thf(func_def_4293,type,
sK2780: nat > nat ).
thf(func_def_4294,type,
sK2781: ( nat > nat ) > nat ).
thf(func_def_4295,type,
sK2782: ( rat > nat ) > rat ).
thf(func_def_4296,type,
sK2783: ( rat > nat ) > rat ).
thf(func_def_4297,type,
sK2784: ( complex > real ) > ( complex > real ) > set_complex > ( real > real > $o ) > complex ).
thf(func_def_4298,type,
sK2785: ( real > real > $o ) > real ).
thf(func_def_4299,type,
sK2786: ( real > real > $o ) > real ).
thf(func_def_4300,type,
sK2787: ( real > real > $o ) > real ).
thf(func_def_4301,type,
sK2788: ( real > real > $o ) > real ).
thf(func_def_4302,type,
sK2789: ( rat > real ) > rat ).
thf(func_def_4303,type,
sK2790: ( rat > real ) > rat ).
thf(func_def_4304,type,
sK2791: set_real > ( real > real ) > real ).
thf(func_def_4305,type,
sK2792: ( int > real ) > set_int > int ).
thf(func_def_4306,type,
sK2793: ( complex > complex ) > set_complex > set_complex > complex ).
thf(func_def_4307,type,
sK2794: set_complex > set_complex > ( complex > complex ) > complex ).
thf(func_def_4308,type,
sK2795: nat > ( nat > $o ) > nat ).
thf(func_def_4309,type,
sK2796: nat > ( nat > $o ) > nat ).
thf(func_def_4310,type,
sK2797: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > list_Code_integer ).
thf(func_def_4311,type,
sK2798: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > code_integer ).
thf(func_def_4312,type,
sK2799: ( nat > num ) > nat ).
thf(func_def_4313,type,
sK2800: set_complex > ( complex > nat ) > complex ).
thf(func_def_4314,type,
sK2801: ( rat > num ) > rat ).
thf(func_def_4315,type,
sK2802: ( rat > num ) > rat ).
thf(func_def_4316,type,
sK2803: ( int > $o ) > int > list_int > nat ).
thf(func_def_4317,type,
sK2804: nat > ( int > $o ) > list_int > nat ).
thf(func_def_4318,type,
sK2805: set_real > ( real > real ) > real ).
thf(func_def_4319,type,
sK2806: nat > set_complex > set_complex ).
thf(func_def_4320,type,
sK2807: option_nat > nat ).
thf(func_def_4321,type,
sK2808: int > ( int > $o ) > list_int > nat ).
thf(func_def_4322,type,
sK2809: nat > ( int > $o ) > list_int > nat ).
thf(func_def_4323,type,
sK2810: vEBT_VEBT > nat > option4927543243414619207at_nat ).
thf(func_def_4324,type,
sK2811: vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_4325,type,
sK2812: vEBT_VEBT > nat > nat ).
thf(func_def_4326,type,
sK2813: vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_4327,type,
sK2814: vEBT_VEBT > nat > $o ).
thf(func_def_4328,type,
sK2815: vEBT_VEBT > nat > $o ).
thf(func_def_4329,type,
sK2816: set_int > ( int > rat ) > int ).
thf(func_def_4330,type,
sK2817: ( rat > nat ) > rat ).
thf(func_def_4331,type,
sK2818: ( rat > nat ) > rat ).
thf(func_def_4332,type,
sK2819: list_o > nat > $o ).
thf(func_def_4333,type,
sK2820: list_o > nat > list_o ).
thf(func_def_4334,type,
sK2821: real > real ).
thf(func_def_4335,type,
sK2822: set_nat > ( int > nat > $o ) > set_int > nat ).
thf(func_def_4336,type,
sK2823: set_nat > ( int > nat > $o ) > set_int > int ).
thf(func_def_4337,type,
sK2824: set_nat > ( int > nat > $o ) > set_int > int ).
thf(func_def_4338,type,
sK2825: set_nat > ( int > nat > $o ) > set_int > int ).
thf(func_def_4339,type,
sK2826: nat > nat > nat > nat ).
thf(func_def_4340,type,
sK2827: nat > nat > nat > nat ).
thf(func_def_4341,type,
sK2828: ( nat > rat ) > rat ).
thf(func_def_4342,type,
sK2829: nat > ( nat > rat ) > nat ).
thf(func_def_4343,type,
sK2830: nat > nat > ( nat > $o ) > nat ).
thf(func_def_4344,type,
sK2831: ( nat > int ) > set_nat > nat ).
thf(func_def_4345,type,
sK2832: ( nat > real > real ) > nat ).
thf(func_def_4346,type,
sK2833: ( nat > real > real ) > real ).
thf(func_def_4347,type,
sK2834: real > ( nat > real > real ) > nat > ( real > real ) > real ).
thf(func_def_4348,type,
sK2835: int > int > int ).
thf(func_def_4349,type,
sK2836: ( code_integer > code_integer > $o ) > code_integer ).
thf(func_def_4350,type,
sK2837: ( complex > real ) > set_complex > complex ).
thf(func_def_4351,type,
sK2838: ( int > complex ) > set_int > set_int > int ).
thf(func_def_4352,type,
sK2839: ( nat > real ) > real > ( real > nat > real ) > real > real ).
thf(func_def_4353,type,
sK2840: ( nat > real ) > real > ( real > nat > real ) > real > nat ).
thf(func_def_4354,type,
sK2841: ( nat > real ) > real > ( real > nat > real ) > real > real ).
thf(func_def_4355,type,
sK2842: real > ( real > nat > real ) > ( real > nat > real ) > nat ).
thf(func_def_4356,type,
sK2843: real > ( real > nat > real ) > real > real ).
thf(func_def_4357,type,
sK2844: nat > nat > nat ).
thf(func_def_4358,type,
sK2845: set_real > ( real > int ) > real ).
thf(func_def_4359,type,
sK2846: set_real > set_real > ( real > int ) > real ).
thf(func_def_4360,type,
sK2847: set_real > ( real > rat ) > real ).
thf(func_def_4361,type,
sK2848: ( int > real ) > int ).
thf(func_def_4362,type,
sK2849: ( int > real ) > int ).
thf(func_def_4363,type,
sK2850: ( option_nat > option4927543243414619207at_nat > $o ) > option_nat > option4927543243414619207at_nat > nat ).
thf(func_def_4364,type,
sK2851: ( option_nat > option4927543243414619207at_nat > $o ) > option_nat > option4927543243414619207at_nat > product_prod_nat_nat ).
thf(func_def_4365,type,
sK2852: ( nat > nat > $o ) > nat ).
thf(func_def_4366,type,
sK2853: ( nat > nat > $o ) > nat ).
thf(func_def_4367,type,
sK2854: ( nat > nat > $o ) > nat ).
thf(func_def_4368,type,
sK2855: ( nat > nat > $o ) > nat ).
thf(func_def_4369,type,
sK2856: nat > list_nat > nat ).
thf(func_def_4370,type,
sK2857: complex > list_VEBT_VEBT > list_complex > vEBT_VEBT ).
thf(func_def_4371,type,
sK2858: $o > list_o > $o ).
thf(func_def_4372,type,
sK2859: ( complex > nat ) > set_complex > complex ).
thf(func_def_4373,type,
sK2860: ( real > num ) > real ).
thf(func_def_4374,type,
sK2861: ( real > num ) > real ).
thf(func_def_4375,type,
sK2862: $o > nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4376,type,
sK2863: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4377,type,
sK2864: $o > nat > vEBT_VEBT > nat ).
thf(func_def_4378,type,
sK2865: $o > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4379,type,
sK2866: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4380,type,
sK2867: vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4381,type,
sK2868: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4382,type,
sK2869: $o > vEBT_VEBT > nat > $o ).
thf(func_def_4383,type,
sK2870: $o > vEBT_VEBT > nat > $o ).
thf(func_def_4384,type,
sK2871: nat > ( nat > complex ) > nat ).
thf(func_def_4385,type,
sK2872: nat > ( nat > complex ) > complex ).
thf(func_def_4386,type,
sK2873: ( nat > num ) > nat ).
thf(func_def_4387,type,
sK2874: ( complex > rat ) > ( complex > rat ) > set_complex > complex ).
thf(func_def_4388,type,
sK2875: set_complex > ( complex > rat ) > set_complex > complex ).
thf(func_def_4389,type,
sK2876: ( int > nat ) > set_int > ( int > nat ) > int ).
thf(func_def_4390,type,
sK2877: ( complex > real ) > ( complex > real ) > set_complex > complex ).
thf(func_def_4391,type,
sK2878: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > code_integer ).
thf(func_def_4392,type,
sK2879: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > list_Code_integer ).
thf(func_def_4393,type,
sK2880: nat > nat > nat > nat ).
thf(func_def_4394,type,
sK2881: ( int > complex ) > set_int > int ).
thf(func_def_4395,type,
sK2882: produc9072475918466114483BT_nat > $o ).
thf(func_def_4396,type,
sK2883: produc9072475918466114483BT_nat > nat ).
thf(func_def_4397,type,
sK2884: produc9072475918466114483BT_nat > $o ).
thf(func_def_4398,type,
sK2885: produc9072475918466114483BT_nat > $o ).
thf(func_def_4399,type,
sK2886: produc9072475918466114483BT_nat > $o ).
thf(func_def_4400,type,
sK2887: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_4401,type,
sK2888: produc9072475918466114483BT_nat > nat ).
thf(func_def_4402,type,
sK2889: produc9072475918466114483BT_nat > nat ).
thf(func_def_4403,type,
sK2890: produc9072475918466114483BT_nat > nat ).
thf(func_def_4404,type,
sK2891: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_4405,type,
sK2892: produc9072475918466114483BT_nat > nat ).
thf(func_def_4406,type,
sK2893: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_4407,type,
sK2894: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_4408,type,
sK2895: produc9072475918466114483BT_nat > nat ).
thf(func_def_4409,type,
sK2896: produc9072475918466114483BT_nat > $o ).
thf(func_def_4410,type,
sK2897: produc9072475918466114483BT_nat > $o ).
thf(func_def_4411,type,
sK2898: produc9072475918466114483BT_nat > nat ).
thf(func_def_4412,type,
sK2899: produc9072475918466114483BT_nat > nat ).
thf(func_def_4413,type,
sK2900: produc9072475918466114483BT_nat > nat ).
thf(func_def_4414,type,
sK2901: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_4415,type,
sK2902: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_4416,type,
sK2903: produc9072475918466114483BT_nat > vEBT_VEBT ).
thf(func_def_4417,type,
sK2904: produc9072475918466114483BT_nat > nat ).
thf(func_def_4418,type,
sK2905: produc9072475918466114483BT_nat > nat ).
thf(func_def_4419,type,
sK2906: produc9072475918466114483BT_nat > nat ).
thf(func_def_4420,type,
sK2907: produc9072475918466114483BT_nat > nat ).
thf(func_def_4421,type,
sK2908: produc9072475918466114483BT_nat > list_VEBT_VEBT ).
thf(func_def_4422,type,
sK2909: rat > ( rat > $o ) > rat ).
thf(func_def_4423,type,
sK2910: rat > ( rat > $o ) > rat ).
thf(func_def_4424,type,
sK2911: ( real > real ) > set_real > set_real > real ).
thf(func_def_4425,type,
sK2912: set_real > ( real > real ) > set_real > real ).
thf(func_def_4426,type,
sK2913: ( num > num ) > num ).
thf(func_def_4427,type,
sK2914: ( num > num ) > num ).
thf(func_def_4428,type,
sK2915: ( rat > real ) > rat ).
thf(func_def_4429,type,
sK2916: ( rat > real ) > rat ).
thf(func_def_4430,type,
sK2917: set_int > set_int > ( int > complex ) > int ).
thf(func_def_4431,type,
sK2918: ( int > complex ) > set_int > set_int > int ).
thf(func_def_4432,type,
sK2919: ( nat > $o ) > nat > nat ).
thf(func_def_4433,type,
sK2920: nat > nat > nat ).
thf(func_def_4434,type,
sK2921: nat > nat > nat ).
thf(func_def_4435,type,
sK2922: set_Pr958786334691620121nt_int > list_int > list_int > int > int ).
thf(func_def_4436,type,
sK2923: set_Pr958786334691620121nt_int > list_int > list_int > int > list_int ).
thf(func_def_4437,type,
sK2924: set_complex > ( complex > code_integer ) > complex ).
thf(func_def_4438,type,
sK2925: nat > real > real ).
thf(func_def_4439,type,
sK2926: set_int > ( int > nat ) > int ).
thf(func_def_4440,type,
sK2927: ( complex > rat ) > set_complex > ( complex > nat ) > set_nat > ( nat > rat ) > nat ).
thf(func_def_4441,type,
sK2928: ( complex > rat ) > set_complex > complex ).
thf(func_def_4442,type,
sK2929: real > real ).
thf(func_def_4443,type,
sK2930: ( num > int ) > num ).
thf(func_def_4444,type,
sK2931: ( num > int ) > num ).
thf(func_def_4445,type,
sK2932: ( nat > $o ) > nat ).
thf(func_def_4446,type,
sK2933: nat > ( nat > $o ) > nat ).
thf(func_def_4447,type,
sK2934: ( num > nat ) > num ).
thf(func_def_4448,type,
sK2935: ( num > nat ) > num ).
thf(func_def_4449,type,
sK2936: nat > set_nat > set_nat ).
thf(func_def_4450,type,
sK2937: list_complex > list_VEBT_VEBT > complex > vEBT_VEBT ).
thf(func_def_4451,type,
sK2938: nat > set_int > int ).
thf(func_def_4452,type,
sK2939: nat > set_int > set_int ).
thf(func_def_4453,type,
sK2940: ( num > nat ) > num ).
thf(func_def_4454,type,
sK2941: ( num > nat ) > num ).
thf(func_def_4455,type,
sK2942: nat > ( nat > $o ) > nat ).
thf(func_def_4456,type,
sK2943: ( int > real ) > set_int > int ).
thf(func_def_4457,type,
sK2944: ( int > real ) > ( int > complex ) > set_int > ( complex > real ) > set_complex > complex ).
thf(func_def_4458,type,
sK2945: set_nat > ( nat > rat ) > ( nat > rat ) > nat ).
thf(func_def_4459,type,
sK2946: ( int > $o ) > int ).
thf(func_def_4460,type,
sK2947: ( int > $o ) > $o ).
thf(func_def_4461,type,
sK2948: ( int > $o ) > int ).
thf(func_def_4462,type,
sK2949: nat > vEBT_VEBT > nat ).
thf(func_def_4463,type,
sK2950: ( complex > $o ) > list_complex > nat ).
thf(func_def_4464,type,
sK2951: set_nat > ( nat > real ) > real > nat ).
thf(func_def_4465,type,
sK2952: set_complex > ( complex > rat ) > ( complex > rat ) > complex ).
thf(func_def_4466,type,
sK2953: int > int > int ).
thf(func_def_4467,type,
sK2954: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_4468,type,
sK2955: nat > ( nat > $o ) > nat ).
thf(func_def_4469,type,
sK2956: nat > ( nat > $o ) > nat ).
thf(func_def_4470,type,
sK2957: nat > set_int > int ).
thf(func_def_4471,type,
sK2958: nat > set_int > set_int ).
thf(func_def_4472,type,
sK2959: set_complex > set_complex > ( complex > real ) > complex ).
thf(func_def_4473,type,
sK2960: set_complex > ( complex > real ) > ( complex > real ) > complex ).
thf(func_def_4474,type,
sK2961: set_Pr958786334691620121nt_int > int ).
thf(func_def_4475,type,
sK2962: set_int > ( int > int ) > int ).
thf(func_def_4476,type,
sK2963: set_int > set_real > ( int > real > $o ) > nat > real ).
thf(func_def_4477,type,
sK2964: set_nat > ( nat > real ) > nat ).
thf(func_def_4478,type,
sK2965: ( nat > rat ) > rat ).
thf(func_def_4479,type,
sK2966: ( nat > rat ) > nat ).
thf(func_def_4480,type,
sK2967: nat > rat > ( nat > rat ) > nat ).
thf(func_def_4481,type,
sK2968: ( real > nat ) > set_real > ( real > nat ) > real ).
thf(func_def_4482,type,
sK2969: list_o > set_Pr3175402225741728619VEBT_o > list_VEBT_VEBT > nat ).
thf(func_def_4483,type,
sK2970: vEBT_VEBT > vEBT_VEBT > extended_enat > list_VEBT_VEBT ).
thf(func_def_4484,type,
sK2971: vEBT_VEBT > vEBT_VEBT > extended_enat > nat ).
thf(func_def_4485,type,
sK2972: vEBT_VEBT > vEBT_VEBT > extended_enat > option4927543243414619207at_nat ).
thf(func_def_4486,type,
sK2973: vEBT_VEBT > vEBT_VEBT > extended_enat > vEBT_VEBT ).
thf(func_def_4487,type,
sK2974: vEBT_VEBT > vEBT_VEBT > extended_enat > nat ).
thf(func_def_4488,type,
sK2975: extended_enat > vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4489,type,
sK2976: extended_enat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4490,type,
sK2977: extended_enat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4491,type,
sK2978: extended_enat > vEBT_VEBT > vEBT_VEBT > nat ).
thf(func_def_4492,type,
sK2979: extended_enat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_4493,type,
sK2980: extended_enat > vEBT_VEBT > vEBT_VEBT > $o ).
thf(func_def_4494,type,
sK2981: ( nat > rat ) > rat ).
thf(func_def_4495,type,
sK2982: ( nat > rat ) > nat ).
thf(func_def_4496,type,
sK2983: nat > rat > ( nat > rat ) > nat ).
thf(func_def_4497,type,
sK2984: set_set_nat > nat > set_set_nat ).
thf(func_def_4498,type,
sK2985: set_set_nat > nat > set_nat ).
thf(func_def_4499,type,
sK2986: nat > ( nat > real ) > nat ).
thf(func_def_4500,type,
sK2987: ( nat > complex ) > set_nat > nat ).
thf(func_def_4501,type,
sK2988: ( rat > rat ) > rat ).
thf(func_def_4502,type,
sK2989: ( rat > rat ) > rat ).
thf(func_def_4503,type,
sK2990: set_real > rat > ( real > rat ) > real ).
thf(func_def_4504,type,
sK2991: set_complex > ( complex > nat ) > complex ).
thf(func_def_4505,type,
sK2992: set_complex > ( complex > nat ) > complex ).
thf(func_def_4506,type,
sK2993: real > ( complex > real ) > set_complex > complex ).
thf(func_def_4507,type,
sK2994: nat > nat ).
thf(func_def_4508,type,
sK2995: nat > list_VEBT_VEBT ).
thf(func_def_4509,type,
sK2996: nat > vEBT_VEBT > nat ).
thf(func_def_4510,type,
sK2997: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_4511,type,
sK2998: list_VEBT_VEBT > nat ).
thf(func_def_4512,type,
sK2999: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_4513,type,
sK3000: vEBT_VEBT > nat ).
thf(func_def_4514,type,
sK3001: set_int > ( int > nat ) > int ).
thf(func_def_4515,type,
sK3002: ( nat > real ) > nat > nat ).
thf(func_def_4516,type,
sK3003: ( nat > real ) > nat > nat ).
thf(func_def_4517,type,
sK3004: set_complex > nat > set_complex ).
thf(func_def_4518,type,
sK3005: set_complex > nat > complex ).
thf(func_def_4519,type,
sK3006: nat > ( nat > $o ) > nat ).
thf(func_def_4520,type,
sK3007: nat > ( nat > $o ) > nat ).
thf(func_def_4521,type,
sK3008: list_VEBT_VEBT > ( vEBT_VEBT > $o ) > nat ).
thf(func_def_4522,type,
sK3009: nat > ( nat > real ) > real > real ).
thf(func_def_4523,type,
sK3010: nat > ( nat > real ) > nat ).
thf(func_def_4524,type,
sK3011: list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_4525,type,
sK3012: list_VEBT_VEBT > nat ).
thf(func_def_4526,type,
sK3013: nat > list_VEBT_VEBT > nat > nat > nat > nat ).
thf(func_def_4527,type,
sK3014: nat > list_VEBT_VEBT > nat > nat > nat > nat ).
thf(func_def_4528,type,
sK3015: nat > list_VEBT_VEBT > vEBT_VEBT ).
thf(func_def_4529,type,
sK3016: vEBT_VEBT > nat > list_VEBT_VEBT > nat ).
thf(func_def_4530,type,
sK3017: vEBT_VEBT > nat > list_VEBT_VEBT > nat ).
thf(func_def_4531,type,
sK3018: ( option4927543243414619207at_nat > option_nat > $o ) > option4927543243414619207at_nat > option_nat > nat ).
thf(func_def_4532,type,
sK3019: ( option4927543243414619207at_nat > option_nat > $o ) > option4927543243414619207at_nat > option_nat > product_prod_nat_nat ).
thf(func_def_4533,type,
sK3020: rat > set_complex > ( complex > rat ) > complex ).
thf(func_def_4534,type,
sK3021: ( real > nat ) > set_real > real ).
thf(func_def_4535,type,
sK3022: ( nat > nat ) > nat > nat ).
thf(func_def_4536,type,
sK3023: ( nat > nat ) > nat > nat ).
thf(func_def_4537,type,
sK3024: ( int > rat ) > set_int > int ).
thf(func_def_4538,type,
sK3025: ( real > rat ) > set_real > set_real > real ).
thf(func_def_4539,type,
sK3026: ( real > rat ) > set_real > set_real > real ).
thf(func_def_4540,type,
sK3027: int > nat ).
thf(func_def_4541,type,
sK3028: int > list_int > int ).
thf(func_def_4542,type,
sK3029: ( int > rat ) > set_int > set_int > int ).
thf(func_def_4543,type,
sK3030: ( num > rat ) > num ).
thf(func_def_4544,type,
sK3031: ( num > rat ) > num ).
thf(func_def_4545,type,
sK3032: ( int > rat ) > ( int > rat ) > set_int > int ).
thf(func_def_4546,type,
sK3033: list_VEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_4547,type,
sK3034: list_VEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_4548,type,
sK3035: ( nat > int ) > set_nat > ( nat > int ) > nat ).
thf(func_def_4549,type,
sK3036: ( nat > $o ) > nat > nat > nat ).
thf(func_def_4550,type,
sK3037: ( nat > $o ) > nat > nat > nat ).
thf(func_def_4551,type,
sK3038: ( int > rat ) > set_int > ( int > rat ) > int ).
thf(func_def_4552,type,
sK3039: set_int > ( int > rat ) > set_int > int ).
thf(func_def_4553,type,
sK3040: set_real > set_real > ( real > rat ) > real ).
thf(func_def_4554,type,
sK3041: set_real > ( real > rat ) > real ).
thf(func_def_4555,type,
sK3042: real > real > nat ).
thf(func_def_4556,type,
sK3043: set_real > set_real > ( real > complex ) > set_complex > set_complex > real ).
thf(func_def_4557,type,
sK3044: set_real > ( real > complex ) > real ).
thf(func_def_4558,type,
sK3045: ( complex > complex ) > set_complex > complex ).
thf(func_def_4559,type,
sK3046: set_real > set_real > ( complex > real ) > ( real > complex ) > real ).
thf(func_def_4560,type,
sK3047: ( real > complex ) > ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_4561,type,
sK3048: ( real > complex ) > ( real > complex ) > ( complex > complex ) > set_real > real ).
thf(func_def_4562,type,
sK3049: set_real > set_real > ( complex > real ) > set_complex > set_complex > complex ).
thf(func_def_4563,type,
sK3050: ( nat > $o ) > nat > nat > nat ).
thf(func_def_4564,type,
sK3051: set_complex > ( complex > real ) > ( complex > real ) > complex ).
thf(func_def_4565,type,
sK3052: ( int > nat ) > set_int > int ).
thf(func_def_4566,type,
sK3053: vEBT_VEBT > option_nat > $o ).
thf(func_def_4567,type,
sK3054: vEBT_VEBT > option_nat > $o ).
thf(func_def_4568,type,
sK3055: option_nat > vEBT_VEBT > nat ).
thf(func_def_4569,type,
sK3056: option_nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4570,type,
sK3057: option_nat > vEBT_VEBT > nat ).
thf(func_def_4571,type,
sK3058: option_nat > vEBT_VEBT > nat ).
thf(func_def_4572,type,
sK3059: option_nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4573,type,
sK3060: vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4574,type,
sK3061: vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4575,type,
sK3062: vEBT_VEBT > nat ).
thf(func_def_4576,type,
sK3063: ( nat > nat > $o ) > nat ).
thf(func_def_4577,type,
sK3064: ( nat > nat > $o ) > nat ).
thf(func_def_4578,type,
sK3065: ( nat > nat > $o ) > nat ).
thf(func_def_4579,type,
sK3066: ( nat > nat > $o ) > nat ).
thf(func_def_4580,type,
sK3067: ( nat > nat > $o ) > nat ).
thf(func_def_4581,type,
sK3068: real > list_real > nat ).
thf(func_def_4582,type,
sK3069: list_nat > nat > nat ).
thf(func_def_4583,type,
sK3070: ( real > rat ) > real ).
thf(func_def_4584,type,
sK3071: ( real > rat ) > real ).
thf(func_def_4585,type,
sK3072: set_int > ( int > rat ) > int ).
thf(func_def_4586,type,
sK3073: option_nat > vEBT_VEBT > nat > list_VEBT_VEBT ).
thf(func_def_4587,type,
sK3074: option_nat > vEBT_VEBT > nat > product_prod_nat_nat ).
thf(func_def_4588,type,
sK3075: option_nat > vEBT_VEBT > nat > vEBT_VEBT ).
thf(func_def_4589,type,
sK3076: vEBT_VEBT > nat > option_nat > vEBT_VEBT ).
thf(func_def_4590,type,
sK3077: vEBT_VEBT > nat > option_nat > list_VEBT_VEBT ).
thf(func_def_4591,type,
sK3078: vEBT_VEBT > nat > option_nat > product_prod_nat_nat ).
thf(func_def_4592,type,
sK3079: vEBT_VEBT > nat > option_nat > $o ).
thf(func_def_4593,type,
sK3080: vEBT_VEBT > nat > option_nat > $o ).
thf(func_def_4594,type,
sK3081: vEBT_VEBT > nat > option_nat > nat ).
thf(func_def_4595,type,
sK3082: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4596,type,
sK3083: option_nat > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4597,type,
sK3084: option_nat > nat > vEBT_VEBT > nat ).
thf(func_def_4598,type,
sK3085: option_nat > nat > vEBT_VEBT > nat ).
thf(func_def_4599,type,
sK3086: option_nat > nat > vEBT_VEBT > nat ).
thf(func_def_4600,type,
sK3087: option_nat > vEBT_VEBT > nat > $o ).
thf(func_def_4601,type,
sK3088: option_nat > vEBT_VEBT > nat > $o ).
thf(func_def_4602,type,
sK3089: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT ).
thf(func_def_4603,type,
sK3090: vEBT_VEBT > option_nat > nat > vEBT_VEBT ).
thf(func_def_4604,type,
sK3091: vEBT_VEBT > option_nat > nat > nat ).
thf(func_def_4605,type,
sK3092: set_real > ( real > code_integer ) > set_real > real ).
thf(func_def_4606,type,
sK3093: ( real > code_integer ) > set_real > real ).
thf(func_def_4607,type,
sK3094: vEBT_VEBT > option_nat > nat > nat ).
thf(func_def_4608,type,
sK3095: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT ).
thf(func_def_4609,type,
sK3096: vEBT_VEBT > option_nat > nat > vEBT_VEBT ).
thf(func_def_4610,type,
sK3097: vEBT_VEBT > option_nat > nat > product_prod_nat_nat ).
thf(func_def_4611,type,
sK3098: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT ).
thf(func_def_4612,type,
sK3099: vEBT_VEBT > option_nat > nat > vEBT_VEBT ).
thf(func_def_4613,type,
sK3100: nat > vEBT_VEBT > option_nat > $o ).
thf(func_def_4614,type,
sK3101: nat > vEBT_VEBT > option_nat > $o ).
thf(func_def_4615,type,
sK3102: nat > option_nat > vEBT_VEBT > nat ).
thf(func_def_4616,type,
sK3103: nat > option_nat > vEBT_VEBT > nat ).
thf(func_def_4617,type,
sK3104: nat > option_nat > vEBT_VEBT > nat ).
thf(func_def_4618,type,
sK3105: nat > option_nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4619,type,
sK3106: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4620,type,
sK3107: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_4621,type,
sK3108: nat > option_nat > vEBT_VEBT > $o ).
thf(func_def_4622,type,
sK3109: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_4623,type,
sK3110: vEBT_VEBT > option_nat > nat > $o ).
thf(func_def_4624,type,
sK3111: vEBT_VEBT > option_nat > nat > nat ).
thf(func_def_4625,type,
sK3112: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4626,type,
sK3113: nat > option_nat > vEBT_VEBT > product_prod_nat_nat ).
thf(func_def_4627,type,
sK3114: nat > option_nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4628,type,
sK3115: ( nat > $o ) > nat > nat ).
thf(func_def_4629,type,
sK3116: ( nat > rat ) > nat > nat ).
thf(func_def_4630,type,
sK3117: ( nat > rat ) > nat > nat ).
thf(func_def_4631,type,
sK3118: int > int > int > int ).
thf(func_def_4632,type,
sK3119: int > int > int > int ).
thf(func_def_4633,type,
sK3120: list_nat > complex > list_complex > nat ).
thf(func_def_4634,type,
sK3121: set_int > set_int > ( int > code_integer ) > int ).
thf(func_def_4635,type,
sK3122: ( nat > $o ) > nat > nat > nat ).
thf(func_def_4636,type,
sK3123: ( nat > $o ) > nat > nat > nat ).
thf(func_def_4637,type,
sK3124: ( nat > real ) > nat > real ).
thf(func_def_4638,type,
sK3125: vEBT_VEBT > $o > nat > list_VEBT_VEBT ).
thf(func_def_4639,type,
sK3126: vEBT_VEBT > $o > nat > option4927543243414619207at_nat ).
thf(func_def_4640,type,
sK3127: vEBT_VEBT > $o > nat > vEBT_VEBT ).
thf(func_def_4641,type,
sK3128: $o > nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4642,type,
sK3129: $o > nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4643,type,
sK3130: $o > nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4644,type,
sK3131: $o > nat > vEBT_VEBT > nat ).
thf(func_def_4645,type,
sK3132: vEBT_VEBT > nat > $o > $o ).
thf(func_def_4646,type,
sK3133: vEBT_VEBT > nat > $o > $o ).
thf(func_def_4647,type,
sK3134: int > nat ).
thf(func_def_4648,type,
sK3135: ( rat > rat > rat ) > rat ).
thf(func_def_4649,type,
sK3136: ( rat > rat > rat ) > rat ).
thf(func_def_4650,type,
sK3137: ( rat > rat > rat ) > rat ).
thf(func_def_4651,type,
sK3138: ( rat > rat > rat ) > rat ).
thf(func_def_4652,type,
sK3139: ( rat > rat > rat ) > rat ).
thf(func_def_4653,type,
sK3140: ( rat > rat > rat ) > rat ).
thf(func_def_4654,type,
sK3141: ( rat > rat > rat ) > rat ).
thf(func_def_4655,type,
sK3142: ( int > int > int ) > int ).
thf(func_def_4656,type,
sK3143: ( int > int > int ) > int ).
thf(func_def_4657,type,
sK3144: ( int > int > int ) > int ).
thf(func_def_4658,type,
sK3145: ( int > int > int ) > int ).
thf(func_def_4659,type,
sK3146: ( int > int > int ) > int ).
thf(func_def_4660,type,
sK3147: ( int > int > int ) > int ).
thf(func_def_4661,type,
sK3148: ( int > int > int ) > int ).
thf(func_def_4662,type,
sK3149: set_nat > ( nat > nat ) > ( nat > nat ) > nat ).
thf(func_def_4663,type,
sK3150: rat > rat ).
thf(func_def_4664,type,
sK3151: ( real > nat ) > set_real > real ).
thf(func_def_4665,type,
sK3152: ( nat > real ) > set_nat > nat ).
thf(func_def_4666,type,
sK3153: list_P6011104703257516679at_nat > product_prod_nat_nat > set_Pr8693737435421807431at_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
thf(func_def_4667,type,
sK3154: list_P6011104703257516679at_nat > product_prod_nat_nat > set_Pr8693737435421807431at_nat > list_P6011104703257516679at_nat > product_prod_nat_nat ).
thf(func_def_4668,type,
sK3155: ( nat > rat ) > nat ).
thf(func_def_4669,type,
sK3156: ( nat > rat ) > nat ).
thf(func_def_4670,type,
sK3157: ( int > int ) > set_int > int ).
thf(func_def_4671,type,
sK3158: vEBT_VEBT > nat > $o ).
thf(func_def_4672,type,
sK3159: vEBT_VEBT > nat > $o ).
thf(func_def_4673,type,
sK3160: nat > vEBT_VEBT > nat ).
thf(func_def_4674,type,
sK3161: nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4675,type,
sK3162: nat > vEBT_VEBT > option4927543243414619207at_nat ).
thf(func_def_4676,type,
sK3163: nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4677,type,
sK3164: list_int > int > set_Pr958786334691620121nt_int > list_int > list_int ).
thf(func_def_4678,type,
sK3165: list_int > int > set_Pr958786334691620121nt_int > list_int > int ).
thf(func_def_4679,type,
sK3166: rat > rat > rat ).
thf(func_def_4680,type,
sK3167: set_nat > nat ).
thf(func_def_4681,type,
sK3168: set_nat > nat ).
thf(func_def_4682,type,
sK3169: set_nat > ( nat > nat ) > nat ).
thf(func_def_4683,type,
sK3170: ( nat > nat > $o ) > nat ).
thf(func_def_4684,type,
sK3171: ( nat > nat > $o ) > nat ).
thf(func_def_4685,type,
sK3172: ( nat > nat > $o ) > nat ).
thf(func_def_4686,type,
sK3173: ( nat > nat > $o ) > nat ).
thf(func_def_4687,type,
sK3174: ( nat > nat > $o ) > nat ).
thf(func_def_4688,type,
sK3175: int > ( nat > int ) > nat > nat > int ).
thf(func_def_4689,type,
sK3176: set_num > num ).
thf(func_def_4690,type,
sK3177: nat > set_complex > complex ).
thf(func_def_4691,type,
sK3178: nat > set_complex > set_complex ).
thf(func_def_4692,type,
sK3179: set_int > int ).
thf(func_def_4693,type,
sK3180: set_int > int ).
thf(func_def_4694,type,
sK3181: set_int > int ).
thf(func_def_4695,type,
sK3182: rat > nat ).
thf(func_def_4696,type,
sK3183: real > nat > real ).
thf(func_def_4697,type,
sK3184: set_int > set_int > ( int > real ) > int ).
thf(func_def_4698,type,
sK3185: set_set_nat > nat > set_set_nat ).
thf(func_def_4699,type,
sK3186: set_nat > ( nat > rat ) > nat ).
thf(func_def_4700,type,
sK3187: ( nat > real > real ) > real > nat > nat ).
thf(func_def_4701,type,
sK3188: ( nat > real > real ) > real > nat > real ).
thf(func_def_4702,type,
sK3189: ( nat > real > real ) > real > ( real > real ) > nat > real ).
thf(func_def_4703,type,
sK3190: set_complex > ( complex > code_integer ) > set_complex > complex ).
thf(func_def_4704,type,
sK3191: set_complex > ( complex > code_integer ) > complex ).
thf(func_def_4705,type,
sK3192: ( complex > complex > $o ) > complex ).
thf(func_def_4706,type,
sK3193: ( complex > complex > $o ) > complex ).
thf(func_def_4707,type,
sK3194: ( complex > complex > $o ) > complex ).
thf(func_def_4708,type,
sK3195: ( complex > complex > $o ) > complex ).
thf(func_def_4709,type,
sK3196: set_int > ( int > complex ) > ( int > complex ) > ( complex > complex > $o ) > int ).
thf(func_def_4710,type,
sK3197: set_int > int ).
thf(func_def_4711,type,
sK3198: set_int > int ).
thf(func_def_4712,type,
sK3199: product_prod_nat_nat > nat ).
thf(func_def_4713,type,
sK3200: product_prod_nat_nat > nat ).
thf(func_def_4714,type,
sK3201: set_nat > set_nat > nat ).
thf(func_def_4715,type,
sK3202: ( nat > rat ) > rat ).
thf(func_def_4716,type,
sK3203: ( nat > rat ) > nat ).
thf(func_def_4717,type,
sK3204: set_set_nat > set_nat ).
thf(func_def_4718,type,
sK3205: set_set_nat > set_nat ).
thf(func_def_4719,type,
sK3206: ( nat > $o ) > nat ).
thf(func_def_4720,type,
sK3207: produc8306885398267862888on_nat > nat > nat > nat ).
thf(func_def_4721,type,
sK3208: produc8306885398267862888on_nat > option_nat ).
thf(func_def_4722,type,
sK3209: produc8306885398267862888on_nat > nat ).
thf(func_def_4723,type,
sK3210: produc8306885398267862888on_nat > nat > nat > nat ).
thf(func_def_4724,type,
sK3211: produc8306885398267862888on_nat > nat ).
thf(func_def_4725,type,
sK3212: produc8306885398267862888on_nat > nat > nat > nat ).
thf(func_def_4726,type,
sK3213: produc8306885398267862888on_nat > nat ).
thf(func_def_4727,type,
sK3214: vEBT_VEBT > option_nat > nat ).
thf(func_def_4728,type,
sK3215: vEBT_VEBT > option_nat > vEBT_VEBT ).
thf(func_def_4729,type,
sK3216: vEBT_VEBT > option_nat > list_VEBT_VEBT ).
thf(func_def_4730,type,
sK3217: vEBT_VEBT > option_nat > nat ).
thf(func_def_4731,type,
sK3218: vEBT_VEBT > option_nat > nat ).
thf(func_def_4732,type,
sK3219: vEBT_VEBT > option_nat > $o ).
thf(func_def_4733,type,
sK3220: vEBT_VEBT > option_nat > $o ).
thf(func_def_4734,type,
sK3221: option_nat > vEBT_VEBT > vEBT_VEBT ).
thf(func_def_4735,type,
sK3222: option_nat > vEBT_VEBT > list_VEBT_VEBT ).
thf(func_def_4736,type,
sK3223: option_nat > vEBT_VEBT > nat ).
thf(func_def_4737,type,
sK3224: ( rat > num ) > rat ).
thf(func_def_4738,type,
sK3225: ( rat > num ) > rat ).
thf(func_def_4739,type,
sK3226: set_int > int ).
thf(func_def_4740,type,
sK3227: ( nat > int ) > int > nat > nat > nat ).
thf(func_def_4741,type,
sK3228: nat > nat > ( nat > int ) > nat ).
thf(func_def_4742,type,
sK3229: ( nat > real ) > nat ).
thf(func_def_4743,type,
sK3230: ( nat > real ) > nat ).
thf(func_def_4744,type,
sK3231: ( complex > rat ) > set_complex > complex ).
thf(func_def_4745,type,
sK3232: ( complex > rat ) > set_complex > complex ).
thf(func_def_4746,type,
sK3233: ( nat > $o ) > nat > nat > nat ).
thf(func_def_4747,type,
sK3234: real > ( real > $o ) > real ).
thf(func_def_4748,type,
sK3235: real > ( real > $o ) > real ).
thf(func_def_4749,type,
sK3236: real > real > real ).
thf(func_def_4750,type,
sK3237: real > real > real ).
thf(func_def_4751,type,
sK3238: set_complex > set_complex > ( complex > rat ) > complex ).
thf(func_def_4753,type,
ph3240:
!>[X0: $tType] : X0 ).
thf(f60782,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f60781,f55785]) ).
thf(f55785,plain,
! [X0: nat] :
( ( ord_less_eq_nat @ ( suc @ X0 ) @ X0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f25931]) ).
thf(f25931,plain,
! [X0: nat] :
( ( ord_less_eq_nat @ ( suc @ X0 ) @ X0 )
!= $true ),
inference(flattening,[status(thm)],[f21359]) ).
thf(f21359,plain,
! [X0: nat] :
( ( ord_less_eq_nat @ ( suc @ X0 ) @ X0 )
!= $true ),
inference(fool_elimination,[status(thm)],[f21358]) ).
thf(f21358,plain,
! [X0: nat] :
~ ( ord_less_eq_nat @ ( suc @ X0 ) @ X0 ),
inference(rectify,[status(thm)],[f104]) ).
thf(f104,axiom,
! [X29: nat] :
~ ( ord_less_eq_nat @ ( suc @ X29 ) @ X29 ),
file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_103_Suc__n__not__le__n) ).
thf(f60781,plain,
( ( ord_less_eq_nat @ ( suc @ one_one_nat ) @ one_one_nat )
= $true ),
inference(forward_demodulation,[status(thm)],[f60780,f60489]) ).
thf(f60489,plain,
deg = one_one_nat,
inference(backward_demodulation,[status(thm)],[f53864,f41780]) ).
thf(f41780,plain,
( ( suc @ zero_zero_nat )
= one_one_nat ),
inference(cnf_transformation,[status(thm)],[f1159]) ).
thf(f1159,axiom,
( ( suc @ zero_zero_nat )
= one_one_nat ),
file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_1158_One__nat__def) ).
thf(f53864,plain,
( deg
= ( suc @ zero_zero_nat ) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f76,axiom,
( deg
= ( suc @ zero_zero_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_75__C1_C_I2_J) ).
thf(f60780,plain,
( ( ord_less_eq_nat @ ( suc @ one_one_nat ) @ deg )
= $true ),
inference(forward_demodulation,[status(thm)],[f40310,f48221]) ).
thf(f48221,plain,
( ( numeral_numeral_nat @ ( bit0 @ one ) )
= ( suc @ one_one_nat ) ),
inference(cnf_transformation,[status(thm)],[f3213]) ).
thf(f3213,axiom,
( ( numeral_numeral_nat @ ( bit0 @ one ) )
= ( suc @ one_one_nat ) ),
file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_3212_Suc__1) ).
thf(f40310,plain,
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
= $true ),
inference(cnf_transformation,[status(thm)],[f16210]) ).
thf(f16210,plain,
( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg )
= $true ),
inference(fool_elimination,[status(thm)],[f16209]) ).
thf(f16209,plain,
ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg,
inference(rectify,[status(thm)],[f2987]) ).
thf(f2987,axiom,
ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg,
file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_2986_a0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP276^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.35 % Computer : n013.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri Feb 27 13:42:38 EST 2026
% 0.21/0.36 % CPUTime :
% 0.21/0.36 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.50 ---- Original DTF file ---
% 0.30/0.50 thf(spec,logic,$$dhol).
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 % File : ITP276^3 : TPTP v9.2.1. Bugfixed v9.2.1.
% 0.30/0.50 % Domain : Interactive Theorem Proving
% 0.30/0.50 % Problem : Sledgehammer problem VEBT_Uniqueness 00216_013627
% 0.30/0.50 % Version : [Des22] axioms.
% 0.30/0.50 % English :
% 0.30/0.50
% 0.30/0.50 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.30/0.50 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 0.30/0.50 % Source : [Des22]
% 0.30/0.50 % Names : 0075_VEBT_Uniqueness_00216_013627 [Des22]
% 0.30/0.50
% 0.30/0.50 % Status : ContradictoryAxioms
% 0.30/0.50 % Rating : ? v9.2.1
% 0.30/0.50 % Syntax : Number of formulae : 11045 (5080 unt;1495 typ; 0 def)
% 0.30/0.50 % Number of atoms : 27536 (12178 equ; 0 cnn)
% 0.30/0.50 % Maximal formula atoms : 71 ( 2 avg)
% 0.30/0.50 % Number of connectives : 116044 (2818 ~; 487 |;2080 &;99931 @)
% 0.30/0.50 % ( 0 <=>;10728 =>; 0 <=; 0 <~>)
% 0.30/0.50 % Maximal formula depth : 39 ( 6 avg)
% 0.30/0.50 % Number of types : 212 ( 211 usr)
% 0.30/0.50 % Number of type conns : 4874 (4874 >; 0 *; 0 +; 0 <<)
% 0.30/0.50 % Number of symbols : 1287 (1284 usr; 72 con; 0-8 aty)
% 0.30/0.50 % Number of variables : 25413 (2067 ^;22644 !; 702 ?;25413 :)
% 0.30/0.50 % SPC : TH0_CAX_EQU_NAR
% 0.30/0.50
% 0.30/0.50 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.30/0.50 % from the van Emde Boas Trees session in the Archive of Formal
% 0.30/0.50 % proofs -
% 0.30/0.50 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 0.30/0.50 % 2022-02-18 15:42:08.029
% 0.30/0.50 % Bugfixes : Added ()s around negated sides of equations.
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 % Could-be-implicit typings (211)
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.30/0.50 produc5542196010084753463at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.30/0.50 produc5491161045314408544at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 0.30/0.50 set_Pr4333006031979791559at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.30/0.50 produc424102278133772007at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.30/0.50 set_Pr1542805901266377927at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.30/0.50 list_P5464809261938338413at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 0.30/0.50 set_Pr4329608150637261639at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 0.30/0.50 produc1193250871479095198on_num: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 0.30/0.50 produc8306885398267862888on_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.30/0.50 produc6121120109295599847at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.30/0.50 produc4471711990508489141at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.30/0.50 produc6392793444374437607at_nat: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 0.30/0.50 produc7036089656553540234on_num: $tType ).
% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
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% 0.30/0.50 thf(ty_n_t__Set__Oset_It__Int__Oint_J,type,
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% 0.30/0.50 thf(ty_n_t__Code____Numeral__Onatural,type,
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% 0.30/0.50
% 0.30/0.50 thf(ty_n_t__String__Ochar,type,
% 0.30/0.50 char: $tType ).
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% 0.30/0.50
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% 0.30/0.50 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
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% 0.30/0.50 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.30/0.50 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.30/0.51 listrel_VEBT_VEBT_o: set_Pr3175402225741728619VEBT_o > set_Pr7508168486584781291list_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.30/0.51 listre5900670229112895443BT_nat: set_Pr7556676689462069481BT_nat > set_Pr8894456036836396799st_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Olistrel_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 listre1230615542750757617T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Omeasures_001t__Code____Numeral__Ointeger,type,
% 0.30/0.51 measur8870801148506250077nteger: list_C4705013386053401436er_nat > set_Pr4811707699266497531nteger ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Omeasures_001t__Int__Oint,type,
% 0.30/0.51 measures_int: list_int_nat > set_Pr958786334691620121nt_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Omeasures_001t__Nat__Onat,type,
% 0.30/0.51 measures_nat: list_nat_nat > set_Pr1261947904930325089at_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Omeasures_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.51 measur2679027848233739777at_nat: list_P9162950289778280392at_nat > set_Pr8693737435421807431at_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Omeasures_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 0.30/0.51 measur2694323259624372065at_nat: list_s9130966667114977576at_nat > set_Pr4329608150637261639at_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001_Eo,type,
% 0.30/0.51 nth_o: list_o > nat > $o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 0.30/0.51 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 0.30/0.51 nth_complex: list_complex > nat > complex ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 0.30/0.51 nth_int: list_int > nat > int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 0.30/0.51 nth_nat: list_nat > nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 0.30/0.51 nth_num: list_num > nat > num ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 0.30/0.51 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 0.30/0.51 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 0.30/0.51 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.30/0.51 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 0.30/0.51 nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 0.30/0.51 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.51 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.30/0.51 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 0.30/0.51 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 0.30/0.51 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 0.30/0.51 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 0.30/0.51 nth_real: list_real > nat > real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.51 nth_set_nat: list_set_nat > nat > set_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 0.30/0.51 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 0.30/0.51 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 0.30/0.51 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 0.30/0.51 produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 0.30/0.51 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 0.30/0.51 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 0.30/0.51 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 0.30/0.51 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct__lists_001_Eo,type,
% 0.30/0.51 product_lists_o: list_list_o > list_list_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct__lists_001t__Int__Oint,type,
% 0.30/0.51 product_lists_int: list_list_int > list_list_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct__lists_001t__Nat__Onat,type,
% 0.30/0.51 product_lists_nat: list_list_nat > list_list_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oproduct__lists_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 produc3021084454716106787T_VEBT: list_list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oreplicate_001_Eo,type,
% 0.30/0.51 replicate_o: nat > $o > list_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 0.30/0.51 replicate_complex: nat > complex > list_complex ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 0.30/0.51 replicate_int: nat > int > list_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 0.30/0.51 replicate_nat: nat > nat > list_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 0.30/0.51 replicate_real: nat > real > list_real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.51 replicate_set_nat: nat > set_nat > list_set_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Orotate1_001_Eo,type,
% 0.30/0.51 rotate1_o: list_o > list_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 0.30/0.51 rotate1_int: list_int > list_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 0.30/0.51 rotate1_nat: list_nat > list_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 0.30/0.51 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 0.30/0.51 take_nat: nat > list_nat > list_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oupt,type,
% 0.30/0.51 upt: nat > nat > list_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Oupto,type,
% 0.30/0.51 upto: int > int > list_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001_Eo_001_Eo,type,
% 0.30/0.51 zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001_Eo_001t__Complex__Ocomplex,type,
% 0.30/0.51 zip_o_complex: list_o > list_complex > list_P3924974545808530565omplex ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 0.30/0.51 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001_Eo_001t__Nat__Onat,type,
% 0.30/0.51 zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001_Eo_001t__Real__Oreal,type,
% 0.30/0.51 zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001_Eo,type,
% 0.30/0.51 zip_complex_o: list_complex > list_o > list_P7942624414058669295plex_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 0.30/0.51 zip_complex_complex: list_complex > list_complex > list_P7664491975274850627omplex ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 0.30/0.51 zip_complex_int: list_complex > list_int > list_P2206113689347244737ex_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 0.30/0.51 zip_complex_nat: list_complex > list_nat > list_P4696196834278971493ex_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 0.30/0.51 zip_complex_real: list_complex > list_real > list_P7647014805210017729x_real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__VEBT____Definitions__OVEBT,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Complex__Ocomplex,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Real__Oreal,type,
% 0.30/0.51 zip_int_real: list_int > list_real > list_P6863124054624500543t_real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 0.30/0.51 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 0.30/0.51 zip_Pr4664179122662387191at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Real__Oreal_001_Eo,type,
% 0.30/0.51 zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 0.30/0.51 zip_real_complex: list_real > list_complex > list_P3881527313128557121omplex ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Int__Oint,type,
% 0.30/0.51 zip_real_int: list_real > list_int > list_P4344331454722006975al_int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Nat__Onat,type,
% 0.30/0.51 zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Real__Oreal,type,
% 0.30/0.51 zip_real_real: list_real > list_real > list_P8689742595348180415l_real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 0.30/0.51 zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat ).
% 0.30/0.51
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001_Eo,type,
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% 0.30/0.51 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Complex__Ocomplex,type,
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% 0.30/0.51 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
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% 0.30/0.51 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_OSuc,type,
% 0.30/0.51 suc: nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 0.30/0.51 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 0.30/0.51 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Onat_Opred,type,
% 0.30/0.51 pred: nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 0.30/0.51 semiri4939895301339042750nteger: nat > code_integer ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Onatural,type,
% 0.30/0.51 semiri3763490453095760265atural: nat > code_natural ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 0.30/0.51 semiri1314217659103216013at_int: nat > int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
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% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
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% 0.30/0.51 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 0.30/0.51 size_size_list_int: list_int > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 0.30/0.51 size_s2710708370519433104list_o: list_list_o > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
% 0.30/0.51 size_s533118279054570080st_int: list_list_int > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
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% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
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% 0.30/0.51 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
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% 0.30/0.51 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
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% 0.30/0.51 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
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% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 0.30/0.51 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 0.30/0.51 size_size_list_real: list_real > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 0.30/0.51 size_s3254054031482475050et_nat: list_set_nat > nat ).
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% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 0.30/0.51 size_s8736152011456118867at_nat: list_s1210847774152347623at_nat > nat ).
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% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 0.30/0.51 size_size_num: num > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 0.30/0.51 size_size_option_nat: option_nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 0.30/0.51 size_size_option_num: option_num > nat ).
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% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 0.30/0.51 size_size_char: char > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__Typerep__Otyperep,type,
% 0.30/0.51 size_size_typerep: typerep > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 0.30/0.51 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oint__decode,type,
% 0.30/0.51 nat_int_decode: nat > int ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oint__encode,type,
% 0.30/0.51 nat_int_encode: int > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Olist__decode,type,
% 0.30/0.51 nat_list_decode: nat > list_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 0.30/0.51 nat_list_decode_rel: nat > nat > $o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 0.30/0.51 nat_list_encode: list_nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 0.30/0.51 nat_list_encode_rel: list_nat > list_nat > $o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 0.30/0.51 nat_prod_decode: nat > product_prod_nat_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 0.30/0.51 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 0.30/0.51 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 0.30/0.51 nat_prod_encode: product_prod_nat_nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 0.30/0.51 nat_set_decode: nat > set_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 0.30/0.51 nat_set_encode: set_nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Osum__decode,type,
% 0.30/0.51 nat_sum_decode: nat > sum_sum_nat_nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Osum__encode,type,
% 0.30/0.51 nat_sum_encode: sum_sum_nat_nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Nat__Bijection_Otriangle,type,
% 0.30/0.51 nat_triangle: nat > nat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_NthRoot_Oroot,type,
% 0.30/0.51 root: nat > real > real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_NthRoot_Osqrt,type,
% 0.30/0.51 sqrt: real > real ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Num_OBitM,type,
% 0.30/0.51 bitM: num > num ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Num_Oinc,type,
% 0.30/0.51 inc: num > num ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Num_Onat__of__num,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
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% 0.30/0.51
% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 0.30/0.51 neg_numeral_dbl_rat: rat > rat ).
% 0.30/0.51
% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 0.30/0.51 neg_nu6511756317524482435omplex: complex > complex ).
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 0.30/0.51 neg_nu8557863876264182079omplex: complex > complex ).
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
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% 0.30/0.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
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% 0.30/0.51 thf(fact_8_prod_Oinject,axiom,
% 0.30/0.51 ! [X1: int,X2: int,Y1: int,Y2: int] :
% 0.30/0.51 ( ( ( product_Pair_int_int @ X1 @ X2 )
% 0.30/0.51 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 0.30/0.51 = ( ( X1 = Y1 )
% 0.30/0.51 & ( X2 = Y2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod.inject
% 0.30/0.51 thf(fact_9_old_Oprod_Oinject,axiom,
% 0.30/0.51 ! [A: code_integer,B: code_integer,A2: code_integer,B2: code_integer] :
% 0.30/0.51 ( ( ( produc1086072967326762835nteger @ A @ B )
% 0.30/0.51 = ( produc1086072967326762835nteger @ A2 @ B2 ) )
% 0.30/0.51 = ( ( A = A2 )
% 0.30/0.51 & ( B = B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.inject
% 0.30/0.51 thf(fact_10_old_Oprod_Oinject,axiom,
% 0.30/0.51 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 0.30/0.51 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 0.30/0.51 = ( produc6161850002892822231at_nat @ A2 @ B2 ) )
% 0.30/0.51 = ( ( A = A2 )
% 0.30/0.51 & ( B = B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.inject
% 0.30/0.51 thf(fact_11_old_Oprod_Oinject,axiom,
% 0.30/0.51 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.51 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 0.30/0.51 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 0.30/0.51 = ( ( A = A2 )
% 0.30/0.51 & ( B = B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.inject
% 0.30/0.51 thf(fact_12_old_Oprod_Oinject,axiom,
% 0.30/0.51 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.30/0.51 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.30/0.51 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.30/0.51 = ( ( A = A2 )
% 0.30/0.51 & ( B = B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.inject
% 0.30/0.51 thf(fact_13_old_Oprod_Oinject,axiom,
% 0.30/0.51 ! [A: int,B: int,A2: int,B2: int] :
% 0.30/0.51 ( ( ( product_Pair_int_int @ A @ B )
% 0.30/0.51 = ( product_Pair_int_int @ A2 @ B2 ) )
% 0.30/0.51 = ( ( A = A2 )
% 0.30/0.51 & ( B = B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.inject
% 0.30/0.51 thf(fact_14_prod__decode__aux_Ocases,axiom,
% 0.30/0.51 ! [X: product_prod_nat_nat] :
% 0.30/0.51 ~ ! [K: nat,M: nat] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( product_Pair_nat_nat @ K @ M ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_decode_aux.cases
% 0.30/0.51 thf(fact_15_old_Oprod_Oexhaust,axiom,
% 0.30/0.51 ! [Y: produc8923325533196201883nteger] :
% 0.30/0.51 ~ ! [A3: code_integer,B3: code_integer] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( produc1086072967326762835nteger @ A3 @ B3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.exhaust
% 0.30/0.51 thf(fact_16_old_Oprod_Oexhaust,axiom,
% 0.30/0.51 ! [Y: produc859450856879609959at_nat] :
% 0.30/0.51 ~ ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( produc6161850002892822231at_nat @ A3 @ B3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.exhaust
% 0.30/0.51 thf(fact_17_old_Oprod_Oexhaust,axiom,
% 0.30/0.51 ! [Y: produc3843707927480180839at_nat] :
% 0.30/0.51 ~ ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( produc2922128104949294807at_nat @ A3 @ B3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.exhaust
% 0.30/0.51 thf(fact_18_old_Oprod_Oexhaust,axiom,
% 0.30/0.51 ! [Y: product_prod_nat_nat] :
% 0.30/0.51 ~ ! [A3: nat,B3: nat] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.exhaust
% 0.30/0.51 thf(fact_19_old_Oprod_Oexhaust,axiom,
% 0.30/0.51 ! [Y: product_prod_int_int] :
% 0.30/0.51 ~ ! [A3: int,B3: int] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.prod.exhaust
% 0.30/0.51 thf(fact_20_surj__pair,axiom,
% 0.30/0.51 ! [P: produc8923325533196201883nteger] :
% 0.30/0.51 ? [X3: code_integer,Y3: code_integer] :
% 0.30/0.51 ( P
% 0.30/0.51 = ( produc1086072967326762835nteger @ X3 @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % surj_pair
% 0.30/0.51 thf(fact_21_surj__pair,axiom,
% 0.30/0.51 ! [P: produc859450856879609959at_nat] :
% 0.30/0.51 ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.30/0.51 ( P
% 0.30/0.51 = ( produc6161850002892822231at_nat @ X3 @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % surj_pair
% 0.30/0.51 thf(fact_22_surj__pair,axiom,
% 0.30/0.51 ! [P: produc3843707927480180839at_nat] :
% 0.30/0.51 ? [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 0.30/0.51 ( P
% 0.30/0.51 = ( produc2922128104949294807at_nat @ X3 @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % surj_pair
% 0.30/0.51 thf(fact_23_surj__pair,axiom,
% 0.30/0.51 ! [P: product_prod_nat_nat] :
% 0.30/0.51 ? [X3: nat,Y3: nat] :
% 0.30/0.51 ( P
% 0.30/0.51 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % surj_pair
% 0.30/0.51 thf(fact_24_surj__pair,axiom,
% 0.30/0.51 ! [P: product_prod_int_int] :
% 0.30/0.51 ? [X3: int,Y3: int] :
% 0.30/0.51 ( P
% 0.30/0.51 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 0.30/0.51
% 0.30/0.51 % surj_pair
% 0.30/0.51 thf(fact_25_prod__cases,axiom,
% 0.30/0.51 ! [P2: produc8923325533196201883nteger > $o,P: produc8923325533196201883nteger] :
% 0.30/0.51 ( ! [A3: code_integer,B3: code_integer] : ( P2 @ ( produc1086072967326762835nteger @ A3 @ B3 ) )
% 0.30/0.51 => ( P2 @ P ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases
% 0.30/0.51 thf(fact_26_prod__cases,axiom,
% 0.30/0.51 ! [P2: produc859450856879609959at_nat > $o,P: produc859450856879609959at_nat] :
% 0.30/0.51 ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] : ( P2 @ ( produc6161850002892822231at_nat @ A3 @ B3 ) )
% 0.30/0.51 => ( P2 @ P ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases
% 0.30/0.51 thf(fact_27_prod__cases,axiom,
% 0.30/0.51 ! [P2: produc3843707927480180839at_nat > $o,P: produc3843707927480180839at_nat] :
% 0.30/0.51 ( ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( P2 @ ( produc2922128104949294807at_nat @ A3 @ B3 ) )
% 0.30/0.51 => ( P2 @ P ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases
% 0.30/0.51 thf(fact_28_prod__cases,axiom,
% 0.30/0.51 ! [P2: product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 0.30/0.51 ( ! [A3: nat,B3: nat] : ( P2 @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 0.30/0.51 => ( P2 @ P ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases
% 0.30/0.51 thf(fact_29_prod__cases,axiom,
% 0.30/0.51 ! [P2: product_prod_int_int > $o,P: product_prod_int_int] :
% 0.30/0.51 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 0.30/0.51 => ( P2 @ P ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases
% 0.30/0.51 thf(fact_30_Pair__inject,axiom,
% 0.30/0.51 ! [A: code_integer,B: code_integer,A2: code_integer,B2: code_integer] :
% 0.30/0.51 ( ( ( produc1086072967326762835nteger @ A @ B )
% 0.30/0.51 = ( produc1086072967326762835nteger @ A2 @ B2 ) )
% 0.30/0.51 => ~ ( ( A = A2 )
% 0.30/0.51 => ( B != B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Pair_inject
% 0.30/0.51 thf(fact_31_Pair__inject,axiom,
% 0.30/0.51 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 0.30/0.51 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 0.30/0.51 = ( produc6161850002892822231at_nat @ A2 @ B2 ) )
% 0.30/0.51 => ~ ( ( A = A2 )
% 0.30/0.51 => ( B != B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Pair_inject
% 0.30/0.51 thf(fact_32_Pair__inject,axiom,
% 0.30/0.51 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 0.30/0.51 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 0.30/0.51 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 0.30/0.51 => ~ ( ( A = A2 )
% 0.30/0.51 => ( B != B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Pair_inject
% 0.30/0.51 thf(fact_33_Pair__inject,axiom,
% 0.30/0.51 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 0.30/0.51 ( ( ( product_Pair_nat_nat @ A @ B )
% 0.30/0.51 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 0.30/0.51 => ~ ( ( A = A2 )
% 0.30/0.51 => ( B != B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Pair_inject
% 0.30/0.51 thf(fact_34_Pair__inject,axiom,
% 0.30/0.51 ! [A: int,B: int,A2: int,B2: int] :
% 0.30/0.51 ( ( ( product_Pair_int_int @ A @ B )
% 0.30/0.51 = ( product_Pair_int_int @ A2 @ B2 ) )
% 0.30/0.51 => ~ ( ( A = A2 )
% 0.30/0.51 => ( B != B2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Pair_inject
% 0.30/0.51 thf(fact_35_prod__cases3,axiom,
% 0.30/0.51 ! [Y: produc859450856879609959at_nat] :
% 0.30/0.51 ~ ! [A3: product_prod_nat_nat,B3: nat,C: nat] :
% 0.30/0.51 ( Y
% 0.30/0.51 != ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ C ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_cases3
% 0.30/0.51 thf(fact_36_max__in__set__def,axiom,
% 0.30/0.51 ( vEBT_VEBT_max_in_set
% 0.30/0.51 = ( ^ [Xs: set_nat,X4: nat] :
% 0.30/0.51 ( ( member_nat @ X4 @ Xs )
% 0.30/0.51 & ! [Y4: nat] :
% 0.30/0.51 ( ( member_nat @ Y4 @ Xs )
% 0.30/0.51 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % max_in_set_def
% 0.30/0.51 thf(fact_37_min__in__set__def,axiom,
% 0.30/0.51 ( vEBT_VEBT_min_in_set
% 0.30/0.51 = ( ^ [Xs: set_nat,X4: nat] :
% 0.30/0.51 ( ( member_nat @ X4 @ Xs )
% 0.30/0.51 & ! [Y4: nat] :
% 0.30/0.51 ( ( member_nat @ Y4 @ Xs )
% 0.30/0.51 => ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % min_in_set_def
% 0.30/0.51 thf(fact_38_lesseq__shift,axiom,
% 0.30/0.51 ( ord_less_eq_nat
% 0.30/0.51 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lesseq_shift
% 0.30/0.51 thf(fact_39_prod__induct3,axiom,
% 0.30/0.51 ! [P2: produc859450856879609959at_nat > $o,X: produc859450856879609959at_nat] :
% 0.30/0.51 ( ! [A3: product_prod_nat_nat,B3: nat,C: nat] : ( P2 @ ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ C ) ) )
% 0.30/0.51 => ( P2 @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_induct3
% 0.30/0.51 thf(fact_40_order__refl,axiom,
% 0.30/0.51 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 0.30/0.51
% 0.30/0.51 % order_refl
% 0.30/0.51 thf(fact_41_order__refl,axiom,
% 0.30/0.51 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 0.30/0.51
% 0.30/0.51 % order_refl
% 0.30/0.51 thf(fact_42_order__refl,axiom,
% 0.30/0.51 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 0.30/0.51
% 0.30/0.51 % order_refl
% 0.30/0.51 thf(fact_43_order__refl,axiom,
% 0.30/0.51 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 0.30/0.51
% 0.30/0.51 % order_refl
% 0.30/0.51 thf(fact_44_order__refl,axiom,
% 0.30/0.51 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 0.30/0.51
% 0.30/0.51 % order_refl
% 0.30/0.51 thf(fact_45_dual__order_Orefl,axiom,
% 0.30/0.51 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.30/0.51
% 0.30/0.51 % dual_order.refl
% 0.30/0.51 thf(fact_46_dual__order_Orefl,axiom,
% 0.30/0.51 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.30/0.51
% 0.30/0.51 % dual_order.refl
% 0.30/0.51 thf(fact_47_dual__order_Orefl,axiom,
% 0.30/0.51 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.30/0.51
% 0.30/0.51 % dual_order.refl
% 0.30/0.51 thf(fact_48_dual__order_Orefl,axiom,
% 0.30/0.51 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.30/0.51
% 0.30/0.51 % dual_order.refl
% 0.30/0.51 thf(fact_49_dual__order_Orefl,axiom,
% 0.30/0.51 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.30/0.51
% 0.30/0.51 % dual_order.refl
% 0.30/0.51 thf(fact_50_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca8354645632395198811er_rat
% 0.30/0.51 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > rat] :
% 0.30/0.51 ! [I: code_integer,J: code_integer] :
% 0.30/0.51 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_51_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca333620267926924494at_rat
% 0.30/0.51 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > rat] :
% 0.30/0.51 ! [I: nat,J: nat] :
% 0.30/0.51 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_52_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca1332973979827979050nt_rat
% 0.30/0.51 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > rat] :
% 0.30/0.51 ! [I: int,J: int] :
% 0.30/0.51 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_53_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca5547107478637473181er_num
% 0.30/0.51 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > num] :
% 0.30/0.51 ! [I: code_integer,J: code_integer] :
% 0.30/0.51 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_54_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca6749454151023974672at_num
% 0.30/0.51 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > num] :
% 0.30/0.51 ! [I: nat,J: nat] :
% 0.30/0.51 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_55_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca7748807862925029228nt_num
% 0.30/0.51 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > num] :
% 0.30/0.51 ! [I: int,J: int] :
% 0.30/0.51 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_56_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca8989775692481694547er_nat
% 0.30/0.51 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > nat] :
% 0.30/0.51 ! [I: code_integer,J: code_integer] :
% 0.30/0.51 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_57_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca968750328013420230at_nat
% 0.30/0.51 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > nat] :
% 0.30/0.51 ! [I: nat,J: nat] :
% 0.30/0.51 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_58_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca1968104039914474786nt_nat
% 0.30/0.51 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > nat] :
% 0.30/0.51 ! [I: int,J: int] :
% 0.30/0.51 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_59_relChain__def,axiom,
% 0.30/0.51 ( bNF_Ca8987285221972644271er_int
% 0.30/0.51 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > int] :
% 0.30/0.51 ! [I: code_integer,J: code_integer] :
% 0.30/0.51 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 0.30/0.51 => ( ord_less_eq_int @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % relChain_def
% 0.30/0.51 thf(fact_60_fold__atLeastAtMost__nat_Ocases,axiom,
% 0.30/0.51 ! [X: produc4471711990508489141at_nat] :
% 0.30/0.51 ~ ! [F: nat > nat > nat,A3: nat,B3: nat,Acc: nat] :
% 0.30/0.51 ( X
% 0.30/0.51 != ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % fold_atLeastAtMost_nat.cases
% 0.30/0.51 thf(fact_61_le__prod__encode__1,axiom,
% 0.30/0.51 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_prod_encode_1
% 0.30/0.51 thf(fact_62_le__prod__encode__2,axiom,
% 0.30/0.51 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_prod_encode_2
% 0.30/0.51 thf(fact_63_lift__Suc__mono__le,axiom,
% 0.30/0.51 ! [F2: nat > set_nat,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_set_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_mono_le
% 0.30/0.51 thf(fact_64_lift__Suc__mono__le,axiom,
% 0.30/0.51 ! [F2: nat > rat,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_mono_le
% 0.30/0.51 thf(fact_65_lift__Suc__mono__le,axiom,
% 0.30/0.51 ! [F2: nat > num,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_mono_le
% 0.30/0.51 thf(fact_66_lift__Suc__mono__le,axiom,
% 0.30/0.51 ! [F2: nat > nat,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_mono_le
% 0.30/0.51 thf(fact_67_lift__Suc__mono__le,axiom,
% 0.30/0.51 ! [F2: nat > int,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_mono_le
% 0.30/0.51 thf(fact_68_lift__Suc__antimono__le,axiom,
% 0.30/0.51 ! [F2: nat > set_nat,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_set_nat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_antimono_le
% 0.30/0.51 thf(fact_69_lift__Suc__antimono__le,axiom,
% 0.30/0.51 ! [F2: nat > rat,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_antimono_le
% 0.30/0.51 thf(fact_70_lift__Suc__antimono__le,axiom,
% 0.30/0.51 ! [F2: nat > num,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_num @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_antimono_le
% 0.30/0.51 thf(fact_71_lift__Suc__antimono__le,axiom,
% 0.30/0.51 ! [F2: nat > nat,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_nat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_antimono_le
% 0.30/0.51 thf(fact_72_lift__Suc__antimono__le,axiom,
% 0.30/0.51 ! [F2: nat > int,N: nat,N2: nat] :
% 0.30/0.51 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 0.30/0.51 => ( ( ord_less_eq_nat @ N @ N2 )
% 0.30/0.51 => ( ord_less_eq_int @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % lift_Suc_antimono_le
% 0.30/0.51 thf(fact_73_le__refl,axiom,
% 0.30/0.51 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.30/0.51
% 0.30/0.51 % le_refl
% 0.30/0.51 thf(fact_74_le__trans,axiom,
% 0.30/0.51 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.51 => ( ( ord_less_eq_nat @ J2 @ K2 )
% 0.30/0.51 => ( ord_less_eq_nat @ I2 @ K2 ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_trans
% 0.30/0.51 thf(fact_75__C1_C_I2_J,axiom,
% 0.30/0.51 ( deg
% 0.30/0.51 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.51
% 0.30/0.51 % "1"(2)
% 0.30/0.51 thf(fact_76_old_Onat_Oinject,axiom,
% 0.30/0.51 ! [Nat: nat,Nat2: nat] :
% 0.30/0.51 ( ( ( suc @ Nat )
% 0.30/0.51 = ( suc @ Nat2 ) )
% 0.30/0.51 = ( Nat = Nat2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % old.nat.inject
% 0.30/0.51 thf(fact_77_nat_Oinject,axiom,
% 0.30/0.51 ! [X2: nat,Y2: nat] :
% 0.30/0.51 ( ( ( suc @ X2 )
% 0.30/0.51 = ( suc @ Y2 ) )
% 0.30/0.51 = ( X2 = Y2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % nat.inject
% 0.30/0.51 thf(fact_78_prod__encode__eq,axiom,
% 0.30/0.51 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.30/0.51 ( ( ( nat_prod_encode @ X )
% 0.30/0.51 = ( nat_prod_encode @ Y ) )
% 0.30/0.51 = ( X = Y ) ) ).
% 0.30/0.51
% 0.30/0.51 % prod_encode_eq
% 0.30/0.51 thf(fact_79_Suc__le__mono,axiom,
% 0.30/0.51 ! [N: nat,M2: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) )
% 0.30/0.51 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % Suc_le_mono
% 0.30/0.51 thf(fact_80_n__not__Suc__n,axiom,
% 0.30/0.51 ! [N: nat] :
% 0.30/0.51 ( N
% 0.30/0.51 != ( suc @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % n_not_Suc_n
% 0.30/0.51 thf(fact_81_Suc__inject,axiom,
% 0.30/0.51 ! [X: nat,Y: nat] :
% 0.30/0.51 ( ( ( suc @ X )
% 0.30/0.51 = ( suc @ Y ) )
% 0.30/0.51 => ( X = Y ) ) ).
% 0.30/0.51
% 0.30/0.51 % Suc_inject
% 0.30/0.51 thf(fact_82_transitive__stepwise__le,axiom,
% 0.30/0.51 ! [M2: nat,N: nat,R2: nat > nat > $o] :
% 0.30/0.51 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.51 => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 0.30/0.51 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 0.30/0.51 ( ( R2 @ X3 @ Y3 )
% 0.30/0.51 => ( ( R2 @ Y3 @ Z )
% 0.30/0.51 => ( R2 @ X3 @ Z ) ) )
% 0.30/0.51 => ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
% 0.30/0.51 => ( R2 @ M2 @ N ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % transitive_stepwise_le
% 0.30/0.51 thf(fact_83_nat__induct__at__least,axiom,
% 0.30/0.51 ! [M2: nat,N: nat,P2: nat > $o] :
% 0.30/0.51 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.51 => ( ( P2 @ M2 )
% 0.30/0.51 => ( ! [N3: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ M2 @ N3 )
% 0.30/0.51 => ( ( P2 @ N3 )
% 0.30/0.51 => ( P2 @ ( suc @ N3 ) ) ) )
% 0.30/0.51 => ( P2 @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % nat_induct_at_least
% 0.30/0.51 thf(fact_84_mem__Collect__eq,axiom,
% 0.30/0.51 ! [A: int,P2: int > $o] :
% 0.30/0.51 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 0.30/0.51 = ( P2 @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 % mem_Collect_eq
% 0.30/0.51 thf(fact_85_mem__Collect__eq,axiom,
% 0.30/0.51 ! [A: complex,P2: complex > $o] :
% 0.30/0.51 ( ( member_complex @ A @ ( collect_complex @ P2 ) )
% 0.30/0.51 = ( P2 @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 % mem_Collect_eq
% 0.30/0.51 thf(fact_86_mem__Collect__eq,axiom,
% 0.30/0.51 ! [A: real,P2: real > $o] :
% 0.30/0.51 ( ( member_real @ A @ ( collect_real @ P2 ) )
% 0.30/0.51 = ( P2 @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 % mem_Collect_eq
% 0.30/0.51 thf(fact_87_mem__Collect__eq,axiom,
% 0.30/0.51 ! [A: list_nat,P2: list_nat > $o] :
% 0.30/0.51 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 0.30/0.51 = ( P2 @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 % mem_Collect_eq
% 0.30/0.51 thf(fact_88_mem__Collect__eq,axiom,
% 0.30/0.51 ! [A: set_nat,P2: set_nat > $o] :
% 0.30/0.51 ( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 0.30/0.51 = ( P2 @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 % mem_Collect_eq
% 0.30/0.51 thf(fact_89_mem__Collect__eq,axiom,
% 0.30/0.51 ! [A: nat,P2: nat > $o] :
% 0.30/0.51 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 0.30/0.51 = ( P2 @ A ) ) ).
% 0.30/0.51
% 0.30/0.51 % mem_Collect_eq
% 0.30/0.51 thf(fact_90_Collect__mem__eq,axiom,
% 0.30/0.51 ! [A4: set_int] :
% 0.30/0.51 ( ( collect_int
% 0.30/0.51 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 0.30/0.51 = A4 ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_mem_eq
% 0.30/0.51 thf(fact_91_Collect__mem__eq,axiom,
% 0.30/0.51 ! [A4: set_complex] :
% 0.30/0.51 ( ( collect_complex
% 0.30/0.51 @ ^ [X4: complex] : ( member_complex @ X4 @ A4 ) )
% 0.30/0.51 = A4 ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_mem_eq
% 0.30/0.51 thf(fact_92_Collect__mem__eq,axiom,
% 0.30/0.51 ! [A4: set_real] :
% 0.30/0.51 ( ( collect_real
% 0.30/0.51 @ ^ [X4: real] : ( member_real @ X4 @ A4 ) )
% 0.30/0.51 = A4 ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_mem_eq
% 0.30/0.51 thf(fact_93_Collect__mem__eq,axiom,
% 0.30/0.51 ! [A4: set_list_nat] :
% 0.30/0.51 ( ( collect_list_nat
% 0.30/0.51 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A4 ) )
% 0.30/0.51 = A4 ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_mem_eq
% 0.30/0.51 thf(fact_94_Collect__mem__eq,axiom,
% 0.30/0.51 ! [A4: set_set_nat] :
% 0.30/0.51 ( ( collect_set_nat
% 0.30/0.51 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 0.30/0.51 = A4 ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_mem_eq
% 0.30/0.51 thf(fact_95_Collect__mem__eq,axiom,
% 0.30/0.51 ! [A4: set_nat] :
% 0.30/0.51 ( ( collect_nat
% 0.30/0.51 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 0.30/0.51 = A4 ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_mem_eq
% 0.30/0.51 thf(fact_96_Collect__cong,axiom,
% 0.30/0.51 ! [P2: complex > $o,Q: complex > $o] :
% 0.30/0.51 ( ! [X3: complex] :
% 0.30/0.51 ( ( P2 @ X3 )
% 0.30/0.51 = ( Q @ X3 ) )
% 0.30/0.51 => ( ( collect_complex @ P2 )
% 0.30/0.51 = ( collect_complex @ Q ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_cong
% 0.30/0.51 thf(fact_97_Collect__cong,axiom,
% 0.30/0.51 ! [P2: real > $o,Q: real > $o] :
% 0.30/0.51 ( ! [X3: real] :
% 0.30/0.51 ( ( P2 @ X3 )
% 0.30/0.51 = ( Q @ X3 ) )
% 0.30/0.51 => ( ( collect_real @ P2 )
% 0.30/0.51 = ( collect_real @ Q ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_cong
% 0.30/0.51 thf(fact_98_Collect__cong,axiom,
% 0.30/0.51 ! [P2: list_nat > $o,Q: list_nat > $o] :
% 0.30/0.51 ( ! [X3: list_nat] :
% 0.30/0.51 ( ( P2 @ X3 )
% 0.30/0.51 = ( Q @ X3 ) )
% 0.30/0.51 => ( ( collect_list_nat @ P2 )
% 0.30/0.51 = ( collect_list_nat @ Q ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_cong
% 0.30/0.51 thf(fact_99_Collect__cong,axiom,
% 0.30/0.51 ! [P2: set_nat > $o,Q: set_nat > $o] :
% 0.30/0.51 ( ! [X3: set_nat] :
% 0.30/0.51 ( ( P2 @ X3 )
% 0.30/0.51 = ( Q @ X3 ) )
% 0.30/0.51 => ( ( collect_set_nat @ P2 )
% 0.30/0.51 = ( collect_set_nat @ Q ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_cong
% 0.30/0.51 thf(fact_100_Collect__cong,axiom,
% 0.30/0.51 ! [P2: nat > $o,Q: nat > $o] :
% 0.30/0.51 ( ! [X3: nat] :
% 0.30/0.51 ( ( P2 @ X3 )
% 0.30/0.51 = ( Q @ X3 ) )
% 0.30/0.51 => ( ( collect_nat @ P2 )
% 0.30/0.51 = ( collect_nat @ Q ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Collect_cong
% 0.30/0.51 thf(fact_101_full__nat__induct,axiom,
% 0.30/0.51 ! [P2: nat > $o,N: nat] :
% 0.30/0.51 ( ! [N3: nat] :
% 0.30/0.51 ( ! [M3: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 0.30/0.51 => ( P2 @ M3 ) )
% 0.30/0.51 => ( P2 @ N3 ) )
% 0.30/0.51 => ( P2 @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % full_nat_induct
% 0.30/0.51 thf(fact_102_not__less__eq__eq,axiom,
% 0.30/0.51 ! [M2: nat,N: nat] :
% 0.30/0.51 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) )
% 0.30/0.51 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ).
% 0.30/0.51
% 0.30/0.51 % not_less_eq_eq
% 0.30/0.51 thf(fact_103_Suc__n__not__le__n,axiom,
% 0.30/0.51 ! [N: nat] :
% 0.30/0.51 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 0.30/0.51
% 0.30/0.51 % Suc_n_not_le_n
% 0.30/0.51 thf(fact_104_le__Suc__eq,axiom,
% 0.30/0.51 ! [M2: nat,N: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.30/0.51 = ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.51 | ( M2
% 0.30/0.51 = ( suc @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_Suc_eq
% 0.30/0.51 thf(fact_105_Suc__le__D,axiom,
% 0.30/0.51 ! [N: nat,M4: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 0.30/0.51 => ? [M: nat] :
% 0.30/0.51 ( M4
% 0.30/0.51 = ( suc @ M ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % Suc_le_D
% 0.30/0.51 thf(fact_106_le__SucI,axiom,
% 0.30/0.51 ! [M2: nat,N: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.51 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_SucI
% 0.30/0.51 thf(fact_107_le__SucE,axiom,
% 0.30/0.51 ! [M2: nat,N: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.30/0.51 => ( ~ ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.51 => ( M2
% 0.30/0.51 = ( suc @ N ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % le_SucE
% 0.30/0.51 thf(fact_108_Suc__leD,axiom,
% 0.30/0.51 ! [M2: nat,N: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.30/0.51 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.51
% 0.30/0.51 % Suc_leD
% 0.30/0.51 thf(fact_109_order__antisym__conv,axiom,
% 0.30/0.51 ! [Y: set_nat,X: set_nat] :
% 0.30/0.51 ( ( ord_less_eq_set_nat @ Y @ X )
% 0.30/0.51 => ( ( ord_less_eq_set_nat @ X @ Y )
% 0.30/0.51 = ( X = Y ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % order_antisym_conv
% 0.30/0.51 thf(fact_110_order__antisym__conv,axiom,
% 0.30/0.51 ! [Y: rat,X: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ Y @ X )
% 0.30/0.51 => ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.51 = ( X = Y ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % order_antisym_conv
% 0.30/0.51 thf(fact_111_order__antisym__conv,axiom,
% 0.30/0.51 ! [Y: num,X: num] :
% 0.30/0.51 ( ( ord_less_eq_num @ Y @ X )
% 0.30/0.51 => ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.51 = ( X = Y ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % order_antisym_conv
% 0.30/0.51 thf(fact_112_order__antisym__conv,axiom,
% 0.30/0.51 ! [Y: nat,X: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ Y @ X )
% 0.30/0.51 => ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.51 = ( X = Y ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % order_antisym_conv
% 0.30/0.51 thf(fact_113_order__antisym__conv,axiom,
% 0.30/0.51 ! [Y: int,X: int] :
% 0.30/0.51 ( ( ord_less_eq_int @ Y @ X )
% 0.30/0.51 => ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.51 = ( X = Y ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % order_antisym_conv
% 0.30/0.51 thf(fact_114_linorder__le__cases,axiom,
% 0.30/0.51 ! [X: rat,Y: rat] :
% 0.30/0.51 ( ~ ( ord_less_eq_rat @ X @ Y )
% 0.30/0.51 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % linorder_le_cases
% 0.30/0.51 thf(fact_115_linorder__le__cases,axiom,
% 0.30/0.51 ! [X: num,Y: num] :
% 0.30/0.51 ( ~ ( ord_less_eq_num @ X @ Y )
% 0.30/0.51 => ( ord_less_eq_num @ Y @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % linorder_le_cases
% 0.30/0.51 thf(fact_116_linorder__le__cases,axiom,
% 0.30/0.51 ! [X: nat,Y: nat] :
% 0.30/0.51 ( ~ ( ord_less_eq_nat @ X @ Y )
% 0.30/0.51 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % linorder_le_cases
% 0.30/0.51 thf(fact_117_linorder__le__cases,axiom,
% 0.30/0.51 ! [X: int,Y: int] :
% 0.30/0.51 ( ~ ( ord_less_eq_int @ X @ Y )
% 0.30/0.51 => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.30/0.51
% 0.30/0.51 % linorder_le_cases
% 0.30/0.51 thf(fact_118_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_119_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 0.30/0.51 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_120_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_121_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 0.30/0.51 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_122_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 0.30/0.51 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: num,Y3: num] :
% 0.30/0.51 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_123_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: num,B: num,F2: num > num,C2: num] :
% 0.30/0.51 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: num,Y3: num] :
% 0.30/0.51 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_124_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 0.30/0.51 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: num,Y3: num] :
% 0.30/0.51 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_125_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: num,B: num,F2: num > int,C2: int] :
% 0.30/0.51 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: num,Y3: num] :
% 0.30/0.51 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_126_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_127_ord__le__eq__subst,axiom,
% 0.30/0.51 ! [A: nat,B: nat,F2: nat > num,C2: num] :
% 0.30/0.51 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.51 => ( ( ( F2 @ B )
% 0.30/0.51 = C2 )
% 0.30/0.51 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.51 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_le_eq_subst
% 0.30/0.51 thf(fact_128_ord__eq__le__subst,axiom,
% 0.30/0.51 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 0.30/0.51 ( ( A
% 0.30/0.51 = ( F2 @ B ) )
% 0.30/0.51 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.51 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_eq_le_subst
% 0.30/0.51 thf(fact_129_ord__eq__le__subst,axiom,
% 0.30/0.51 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 0.30/0.51 ( ( A
% 0.30/0.51 = ( F2 @ B ) )
% 0.30/0.51 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.51 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.51 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.51 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.51
% 0.30/0.51 % ord_eq_le_subst
% 0.30/0.51 thf(fact_130_ord__eq__le__subst,axiom,
% 0.30/0.51 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 0.30/0.51 ( ( A
% 0.30/0.51 = ( F2 @ B ) )
% 0.30/0.51 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.51 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.51 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_131_ord__eq__le__subst,axiom,
% 0.30/0.52 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_132_ord__eq__le__subst,axiom,
% 0.30/0.52 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_133_ord__eq__le__subst,axiom,
% 0.30/0.52 ! [A: num,F2: num > num,B: num,C2: num] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_134_ord__eq__le__subst,axiom,
% 0.30/0.52 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_135_ord__eq__le__subst,axiom,
% 0.30/0.52 ! [A: int,F2: num > int,B: num,C2: num] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_136_ord__eq__le__subst,axiom,
% 0.30/0.52 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_137_ord__eq__le__subst,axiom,
% 0.30/0.52 ! [A: num,F2: nat > num,B: nat,C2: nat] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_subst
% 0.30/0.52 thf(fact_138_linorder__linear,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.52 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_linear
% 0.30/0.52 thf(fact_139_linorder__linear,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.52 | ( ord_less_eq_num @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_linear
% 0.30/0.52 thf(fact_140_linorder__linear,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.52 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_linear
% 0.30/0.52 thf(fact_141_linorder__linear,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.52 | ( ord_less_eq_int @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_linear
% 0.30/0.52 thf(fact_142_order__eq__refl,axiom,
% 0.30/0.52 ! [X: set_nat,Y: set_nat] :
% 0.30/0.52 ( ( X = Y )
% 0.30/0.52 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_eq_refl
% 0.30/0.52 thf(fact_143_order__eq__refl,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( X = Y )
% 0.30/0.52 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_eq_refl
% 0.30/0.52 thf(fact_144_order__eq__refl,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( X = Y )
% 0.30/0.52 => ( ord_less_eq_num @ X @ Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_eq_refl
% 0.30/0.52 thf(fact_145_order__eq__refl,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( X = Y )
% 0.30/0.52 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_eq_refl
% 0.30/0.52 thf(fact_146_order__eq__refl,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( X = Y )
% 0.30/0.52 => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_eq_refl
% 0.30/0.52 thf(fact_147_order__subst2,axiom,
% 0.30/0.52 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_148_order__subst2,axiom,
% 0.30/0.52 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_149_order__subst2,axiom,
% 0.30/0.52 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_150_order__subst2,axiom,
% 0.30/0.52 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_151_order__subst2,axiom,
% 0.30/0.52 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_152_order__subst2,axiom,
% 0.30/0.52 ! [A: num,B: num,F2: num > num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_153_order__subst2,axiom,
% 0.30/0.52 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_154_order__subst2,axiom,
% 0.30/0.52 ! [A: num,B: num,F2: num > int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_155_order__subst2,axiom,
% 0.30/0.52 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_156_order__subst2,axiom,
% 0.30/0.52 ! [A: nat,B: nat,F2: nat > num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 0.30/0.52 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst2
% 0.30/0.52 thf(fact_157_order__subst1,axiom,
% 0.30/0.52 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_158_order__subst1,axiom,
% 0.30/0.52 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_159_order__subst1,axiom,
% 0.30/0.52 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_160_order__subst1,axiom,
% 0.30/0.52 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ C2 )
% 0.30/0.52 => ( ! [X3: int,Y3: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_161_order__subst1,axiom,
% 0.30/0.52 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_162_order__subst1,axiom,
% 0.30/0.52 ! [A: num,F2: num > num,B: num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_163_order__subst1,axiom,
% 0.30/0.52 ! [A: num,F2: nat > num,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_164_order__subst1,axiom,
% 0.30/0.52 ! [A: num,F2: int > num,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ C2 )
% 0.30/0.52 => ( ! [X3: int,Y3: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_165_order__subst1,axiom,
% 0.30/0.52 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_166_order__subst1,axiom,
% 0.30/0.52 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ! [X3: num,Y3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_subst1
% 0.30/0.52 thf(fact_167_Orderings_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 0.30/0.52 & ( ord_less_eq_set_nat @ B4 @ A5 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % Orderings.order_eq_iff
% 0.30/0.52 thf(fact_168_Orderings_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: rat,B4: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A5 @ B4 )
% 0.30/0.52 & ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % Orderings.order_eq_iff
% 0.30/0.52 thf(fact_169_Orderings_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: num,B4: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ A5 @ B4 )
% 0.30/0.52 & ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % Orderings.order_eq_iff
% 0.30/0.52 thf(fact_170_Orderings_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: nat,B4: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A5 @ B4 )
% 0.30/0.52 & ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % Orderings.order_eq_iff
% 0.30/0.52 thf(fact_171_Orderings_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: int,B4: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A5 @ B4 )
% 0.30/0.52 & ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % Orderings.order_eq_iff
% 0.30/0.52 thf(fact_172_antisym,axiom,
% 0.30/0.52 ! [A: set_nat,B: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_set_nat @ B @ A )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym
% 0.30/0.52 thf(fact_173_antisym,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym
% 0.30/0.52 thf(fact_174_antisym,axiom,
% 0.30/0.52 ! [A: num,B: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ A )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym
% 0.30/0.52 thf(fact_175_antisym,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym
% 0.30/0.52 thf(fact_176_antisym,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ A )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym
% 0.30/0.52 thf(fact_177_dual__order_Otrans,axiom,
% 0.30/0.52 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 0.30/0.52 => ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.trans
% 0.30/0.52 thf(fact_178_dual__order_Otrans,axiom,
% 0.30/0.52 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ C2 @ B )
% 0.30/0.52 => ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.trans
% 0.30/0.52 thf(fact_179_dual__order_Otrans,axiom,
% 0.30/0.52 ! [B: num,A: num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_num @ C2 @ B )
% 0.30/0.52 => ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.trans
% 0.30/0.52 thf(fact_180_dual__order_Otrans,axiom,
% 0.30/0.52 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.30/0.52 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.trans
% 0.30/0.52 thf(fact_181_dual__order_Otrans,axiom,
% 0.30/0.52 ! [B: int,A: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ C2 @ B )
% 0.30/0.52 => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.trans
% 0.30/0.52 thf(fact_182_dual__order_Oantisym,axiom,
% 0.30/0.52 ! [B: set_nat,A: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.antisym
% 0.30/0.52 thf(fact_183_dual__order_Oantisym,axiom,
% 0.30/0.52 ! [B: rat,A: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.antisym
% 0.30/0.52 thf(fact_184_dual__order_Oantisym,axiom,
% 0.30/0.52 ! [B: num,A: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.antisym
% 0.30/0.52 thf(fact_185_dual__order_Oantisym,axiom,
% 0.30/0.52 ! [B: nat,A: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.antisym
% 0.30/0.52 thf(fact_186_dual__order_Oantisym,axiom,
% 0.30/0.52 ! [B: int,A: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.antisym
% 0.30/0.52 thf(fact_187_dual__order_Oeq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 0.30/0.52 & ( ord_less_eq_set_nat @ A5 @ B4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.eq_iff
% 0.30/0.52 thf(fact_188_dual__order_Oeq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: rat,B4: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ B4 @ A5 )
% 0.30/0.52 & ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.eq_iff
% 0.30/0.52 thf(fact_189_dual__order_Oeq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: num,B4: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ B4 @ A5 )
% 0.30/0.52 & ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.eq_iff
% 0.30/0.52 thf(fact_190_dual__order_Oeq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: nat,B4: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ B4 @ A5 )
% 0.30/0.52 & ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.eq_iff
% 0.30/0.52 thf(fact_191_dual__order_Oeq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [A5: int,B4: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ B4 @ A5 )
% 0.30/0.52 & ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.eq_iff
% 0.30/0.52 thf(fact_192_linorder__wlog,axiom,
% 0.30/0.52 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 0.30/0.52 ( ! [A3: rat,B3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: rat,B3: rat] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_wlog
% 0.30/0.52 thf(fact_193_linorder__wlog,axiom,
% 0.30/0.52 ! [P2: num > num > $o,A: num,B: num] :
% 0.30/0.52 ( ! [A3: num,B3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: num,B3: num] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_wlog
% 0.30/0.52 thf(fact_194_linorder__wlog,axiom,
% 0.30/0.52 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 0.30/0.52 ( ! [A3: nat,B3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: nat,B3: nat] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_wlog
% 0.30/0.52 thf(fact_195_linorder__wlog,axiom,
% 0.30/0.52 ! [P2: int > int > $o,A: int,B: int] :
% 0.30/0.52 ( ! [A3: int,B3: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: int,B3: int] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_wlog
% 0.30/0.52 thf(fact_196_order__trans,axiom,
% 0.30/0.52 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_trans
% 0.30/0.52 thf(fact_197_order__trans,axiom,
% 0.30/0.52 ! [X: rat,Y: rat,Z3: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_trans
% 0.30/0.52 thf(fact_198_order__trans,axiom,
% 0.30/0.52 ! [X: num,Y: num,Z3: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_num @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_eq_num @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_trans
% 0.30/0.52 thf(fact_199_order__trans,axiom,
% 0.30/0.52 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_trans
% 0.30/0.52 thf(fact_200_order__trans,axiom,
% 0.30/0.52 ! [X: int,Y: int,Z3: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_int @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_trans
% 0.30/0.52 thf(fact_201_order_Otrans,axiom,
% 0.30/0.52 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.trans
% 0.30/0.52 thf(fact_202_order_Otrans,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.trans
% 0.30/0.52 thf(fact_203_order_Otrans,axiom,
% 0.30/0.52 ! [A: num,B: num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.trans
% 0.30/0.52 thf(fact_204_order_Otrans,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.trans
% 0.30/0.52 thf(fact_205_order_Otrans,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.trans
% 0.30/0.52 thf(fact_206_order__antisym,axiom,
% 0.30/0.52 ! [X: set_nat,Y: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_set_nat @ Y @ X )
% 0.30/0.52 => ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_antisym
% 0.30/0.52 thf(fact_207_order__antisym,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_rat @ Y @ X )
% 0.30/0.52 => ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_antisym
% 0.30/0.52 thf(fact_208_order__antisym,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_num @ Y @ X )
% 0.30/0.52 => ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_antisym
% 0.30/0.52 thf(fact_209_order__antisym,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_nat @ Y @ X )
% 0.30/0.52 => ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_antisym
% 0.30/0.52 thf(fact_210_order__antisym,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.52 => ( ( ord_less_eq_int @ Y @ X )
% 0.30/0.52 => ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_antisym
% 0.30/0.52 thf(fact_211_ord__le__eq__trans,axiom,
% 0.30/0.52 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_le_eq_trans
% 0.30/0.52 thf(fact_212_ord__le__eq__trans,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_le_eq_trans
% 0.30/0.52 thf(fact_213_ord__le__eq__trans,axiom,
% 0.30/0.52 ! [A: num,B: num,C2: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_le_eq_trans
% 0.30/0.52 thf(fact_214_ord__le__eq__trans,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_le_eq_trans
% 0.30/0.52 thf(fact_215_ord__le__eq__trans,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_le_eq_trans
% 0.30/0.52 thf(fact_216_ord__eq__le__trans,axiom,
% 0.30/0.52 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_trans
% 0.30/0.52 thf(fact_217_ord__eq__le__trans,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_trans
% 0.30/0.52 thf(fact_218_ord__eq__le__trans,axiom,
% 0.30/0.52 ! [A: num,B: num,C2: num] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_trans
% 0.30/0.52 thf(fact_219_ord__eq__le__trans,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_trans
% 0.30/0.52 thf(fact_220_ord__eq__le__trans,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ C2 )
% 0.30/0.52 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_le_trans
% 0.30/0.52 thf(fact_221_order__class_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [X4: set_nat,Y4: set_nat] :
% 0.30/0.52 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 0.30/0.52 & ( ord_less_eq_set_nat @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_class.order_eq_iff
% 0.30/0.52 thf(fact_222_order__class_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [X4: rat,Y4: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.30/0.52 & ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_class.order_eq_iff
% 0.30/0.52 thf(fact_223_order__class_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [X4: num,Y4: num] :
% 0.30/0.52 ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.30/0.52 & ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_class.order_eq_iff
% 0.30/0.52 thf(fact_224_order__class_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [X4: nat,Y4: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.30/0.52 & ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_class.order_eq_iff
% 0.30/0.52 thf(fact_225_order__class_Oorder__eq__iff,axiom,
% 0.30/0.52 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.30/0.52 = ( ^ [X4: int,Y4: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.30/0.52 & ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_class.order_eq_iff
% 0.30/0.52 thf(fact_226_le__cases3,axiom,
% 0.30/0.52 ! [X: rat,Y: rat,Z3: rat] :
% 0.30/0.52 ( ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_rat @ Y @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_rat @ Y @ X )
% 0.30/0.52 => ~ ( ord_less_eq_rat @ X @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_rat @ X @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_rat @ Z3 @ Y ) )
% 0.30/0.52 => ( ( ( ord_less_eq_rat @ Z3 @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 0.30/0.52 => ( ( ( ord_less_eq_rat @ Y @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_rat @ Z3 @ X ) )
% 0.30/0.52 => ~ ( ( ord_less_eq_rat @ Z3 @ X )
% 0.30/0.52 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_cases3
% 0.30/0.52 thf(fact_227_le__cases3,axiom,
% 0.30/0.52 ! [X: num,Y: num,Z3: num] :
% 0.30/0.52 ( ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_num @ Y @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_num @ Y @ X )
% 0.30/0.52 => ~ ( ord_less_eq_num @ X @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_num @ X @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_num @ Z3 @ Y ) )
% 0.30/0.52 => ( ( ( ord_less_eq_num @ Z3 @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_num @ Y @ X ) )
% 0.30/0.52 => ( ( ( ord_less_eq_num @ Y @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_num @ Z3 @ X ) )
% 0.30/0.52 => ~ ( ( ord_less_eq_num @ Z3 @ X )
% 0.30/0.52 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_cases3
% 0.30/0.52 thf(fact_228_le__cases3,axiom,
% 0.30/0.52 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.52 ( ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_nat @ Y @ X )
% 0.30/0.52 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 0.30/0.52 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 0.30/0.52 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 0.30/0.52 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 0.30/0.52 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_cases3
% 0.30/0.52 thf(fact_229_le__cases3,axiom,
% 0.30/0.52 ! [X: int,Y: int,Z3: int] :
% 0.30/0.52 ( ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_int @ Y @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_int @ Y @ X )
% 0.30/0.52 => ~ ( ord_less_eq_int @ X @ Z3 ) )
% 0.30/0.52 => ( ( ( ord_less_eq_int @ X @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_int @ Z3 @ Y ) )
% 0.30/0.52 => ( ( ( ord_less_eq_int @ Z3 @ Y )
% 0.30/0.52 => ~ ( ord_less_eq_int @ Y @ X ) )
% 0.30/0.52 => ( ( ( ord_less_eq_int @ Y @ Z3 )
% 0.30/0.52 => ~ ( ord_less_eq_int @ Z3 @ X ) )
% 0.30/0.52 => ~ ( ( ord_less_eq_int @ Z3 @ X )
% 0.30/0.52 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_cases3
% 0.30/0.52 thf(fact_230_nle__le,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 0.30/0.52 = ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.52 & ( B != A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nle_le
% 0.30/0.52 thf(fact_231_nle__le,axiom,
% 0.30/0.52 ! [A: num,B: num] :
% 0.30/0.52 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 0.30/0.52 = ( ( ord_less_eq_num @ B @ A )
% 0.30/0.52 & ( B != A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nle_le
% 0.30/0.52 thf(fact_232_nle__le,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 0.30/0.52 = ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.52 & ( B != A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nle_le
% 0.30/0.52 thf(fact_233_nle__le,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 0.30/0.52 = ( ( ord_less_eq_int @ B @ A )
% 0.30/0.52 & ( B != A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nle_le
% 0.30/0.52 thf(fact_234_bounded__Max__nat,axiom,
% 0.30/0.52 ! [P2: nat > $o,X: nat,M5: nat] :
% 0.30/0.52 ( ( P2 @ X )
% 0.30/0.52 => ( ! [X3: nat] :
% 0.30/0.52 ( ( P2 @ X3 )
% 0.30/0.52 => ( ord_less_eq_nat @ X3 @ M5 ) )
% 0.30/0.52 => ~ ! [M: nat] :
% 0.30/0.52 ( ( P2 @ M )
% 0.30/0.52 => ~ ! [X5: nat] :
% 0.30/0.52 ( ( P2 @ X5 )
% 0.30/0.52 => ( ord_less_eq_nat @ X5 @ M ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % bounded_Max_nat
% 0.30/0.52 thf(fact_235_Nat_Oex__has__greatest__nat,axiom,
% 0.30/0.52 ! [P2: nat > $o,K2: nat,B: nat] :
% 0.30/0.52 ( ( P2 @ K2 )
% 0.30/0.52 => ( ! [Y3: nat] :
% 0.30/0.52 ( ( P2 @ Y3 )
% 0.30/0.52 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.30/0.52 => ? [X3: nat] :
% 0.30/0.52 ( ( P2 @ X3 )
% 0.30/0.52 & ! [Y6: nat] :
% 0.30/0.52 ( ( P2 @ Y6 )
% 0.30/0.52 => ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % Nat.ex_has_greatest_nat
% 0.30/0.52 thf(fact_236_nat__le__linear,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.52 | ( ord_less_eq_nat @ N @ M2 ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_le_linear
% 0.30/0.52 thf(fact_237_le__antisym,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.52 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.30/0.52 => ( M2 = N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_antisym
% 0.30/0.52 thf(fact_238_eq__imp__le,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( M2 = N )
% 0.30/0.52 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % eq_imp_le
% 0.30/0.52 thf(fact_239_le0,axiom,
% 0.30/0.52 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.30/0.52
% 0.30/0.52 % le0
% 0.30/0.52 thf(fact_240_bot__nat__0_Oextremum,axiom,
% 0.30/0.52 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 0.30/0.52
% 0.30/0.52 % bot_nat_0.extremum
% 0.30/0.52 thf(fact_241_le__0__eq,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.30/0.52 = ( N = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_0_eq
% 0.30/0.52 thf(fact_242_bot__nat__0_Oextremum__uniqueI,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.52 => ( A = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % bot_nat_0.extremum_uniqueI
% 0.30/0.52 thf(fact_243_bot__nat__0_Oextremum__unique,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.52 = ( A = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % bot_nat_0.extremum_unique
% 0.30/0.52 thf(fact_244_less__eq__nat_Osimps_I1_J,axiom,
% 0.30/0.52 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.30/0.52
% 0.30/0.52 % less_eq_nat.simps(1)
% 0.30/0.52 thf(fact_245_not0__implies__Suc,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( N != zero_zero_nat )
% 0.30/0.52 => ? [M: nat] :
% 0.30/0.52 ( N
% 0.30/0.52 = ( suc @ M ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % not0_implies_Suc
% 0.30/0.52 thf(fact_246_Zero__not__Suc,axiom,
% 0.30/0.52 ! [M2: nat] :
% 0.30/0.52 ( zero_zero_nat
% 0.30/0.52 != ( suc @ M2 ) ) ).
% 0.30/0.52
% 0.30/0.52 % Zero_not_Suc
% 0.30/0.52 thf(fact_247_Zero__neq__Suc,axiom,
% 0.30/0.52 ! [M2: nat] :
% 0.30/0.52 ( zero_zero_nat
% 0.30/0.52 != ( suc @ M2 ) ) ).
% 0.30/0.52
% 0.30/0.52 % Zero_neq_Suc
% 0.30/0.52 thf(fact_248_Suc__neq__Zero,axiom,
% 0.30/0.52 ! [M2: nat] :
% 0.30/0.52 ( ( suc @ M2 )
% 0.30/0.52 != zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % Suc_neq_Zero
% 0.30/0.52 thf(fact_249_zero__induct,axiom,
% 0.30/0.52 ! [P2: nat > $o,K2: nat] :
% 0.30/0.52 ( ( P2 @ K2 )
% 0.30/0.52 => ( ! [N3: nat] :
% 0.30/0.52 ( ( P2 @ ( suc @ N3 ) )
% 0.30/0.52 => ( P2 @ N3 ) )
% 0.30/0.52 => ( P2 @ zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_induct
% 0.30/0.52 thf(fact_250_diff__induct,axiom,
% 0.30/0.52 ! [P2: nat > nat > $o,M2: nat,N: nat] :
% 0.30/0.52 ( ! [X3: nat] : ( P2 @ X3 @ zero_zero_nat )
% 0.30/0.52 => ( ! [Y3: nat] : ( P2 @ zero_zero_nat @ ( suc @ Y3 ) )
% 0.30/0.52 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.52 ( ( P2 @ X3 @ Y3 )
% 0.30/0.52 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 0.30/0.52 => ( P2 @ M2 @ N ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % diff_induct
% 0.30/0.52 thf(fact_251_list__decode_Ocases,axiom,
% 0.30/0.52 ! [X: nat] :
% 0.30/0.52 ( ( X != zero_zero_nat )
% 0.30/0.52 => ~ ! [N3: nat] :
% 0.30/0.52 ( X
% 0.30/0.52 != ( suc @ N3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % list_decode.cases
% 0.30/0.52 thf(fact_252_nat_Odistinct_I1_J,axiom,
% 0.30/0.52 ! [X2: nat] :
% 0.30/0.52 ( zero_zero_nat
% 0.30/0.52 != ( suc @ X2 ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat.distinct(1)
% 0.30/0.52 thf(fact_253_old_Onat_Odistinct_I2_J,axiom,
% 0.30/0.52 ! [Nat2: nat] :
% 0.30/0.52 ( ( suc @ Nat2 )
% 0.30/0.52 != zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % old.nat.distinct(2)
% 0.30/0.52 thf(fact_254_old_Onat_Odistinct_I1_J,axiom,
% 0.30/0.52 ! [Nat2: nat] :
% 0.30/0.52 ( zero_zero_nat
% 0.30/0.52 != ( suc @ Nat2 ) ) ).
% 0.30/0.52
% 0.30/0.52 % old.nat.distinct(1)
% 0.30/0.52 thf(fact_255_nat_OdiscI,axiom,
% 0.30/0.52 ! [Nat: nat,X2: nat] :
% 0.30/0.52 ( ( Nat
% 0.30/0.52 = ( suc @ X2 ) )
% 0.30/0.52 => ( Nat != zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat.discI
% 0.30/0.52 thf(fact_256_old_Onat_Oexhaust,axiom,
% 0.30/0.52 ! [Y: nat] :
% 0.30/0.52 ( ( Y != zero_zero_nat )
% 0.30/0.52 => ~ ! [Nat3: nat] :
% 0.30/0.52 ( Y
% 0.30/0.52 != ( suc @ Nat3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % old.nat.exhaust
% 0.30/0.52 thf(fact_257_nat__induct,axiom,
% 0.30/0.52 ! [P2: nat > $o,N: nat] :
% 0.30/0.52 ( ( P2 @ zero_zero_nat )
% 0.30/0.52 => ( ! [N3: nat] :
% 0.30/0.52 ( ( P2 @ N3 )
% 0.30/0.52 => ( P2 @ ( suc @ N3 ) ) )
% 0.30/0.52 => ( P2 @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_induct
% 0.30/0.52 thf(fact_258_case4_I12_J,axiom,
% 0.30/0.52 vEBT_invar_vebt @ sa @ deg ).
% 0.30/0.52
% 0.30/0.52 % case4(12)
% 0.30/0.52 thf(fact_259_le__zero__eq,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.30/0.52 = ( N = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_zero_eq
% 0.30/0.52 thf(fact_260_option_Osize_I4_J,axiom,
% 0.30/0.52 ! [X2: product_prod_nat_nat] :
% 0.30/0.52 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 0.30/0.52 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % option.size(4)
% 0.30/0.52 thf(fact_261_option_Osize_I4_J,axiom,
% 0.30/0.52 ! [X2: nat] :
% 0.30/0.52 ( ( size_size_option_nat @ ( some_nat @ X2 ) )
% 0.30/0.52 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % option.size(4)
% 0.30/0.52 thf(fact_262_option_Osize_I4_J,axiom,
% 0.30/0.52 ! [X2: num] :
% 0.30/0.52 ( ( size_size_option_num @ ( some_num @ X2 ) )
% 0.30/0.52 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % option.size(4)
% 0.30/0.52 thf(fact_263_vebt__buildup_Ocases,axiom,
% 0.30/0.52 ! [X: nat] :
% 0.30/0.52 ( ( X != zero_zero_nat )
% 0.30/0.52 => ( ( X
% 0.30/0.52 != ( suc @ zero_zero_nat ) )
% 0.30/0.52 => ~ ! [Va: nat] :
% 0.30/0.52 ( X
% 0.30/0.52 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % vebt_buildup.cases
% 0.30/0.52 thf(fact_264_exists__least__lemma,axiom,
% 0.30/0.52 ! [P2: nat > $o] :
% 0.30/0.52 ( ~ ( P2 @ zero_zero_nat )
% 0.30/0.52 => ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.30/0.52 => ? [N3: nat] :
% 0.30/0.52 ( ~ ( P2 @ N3 )
% 0.30/0.52 & ( P2 @ ( suc @ N3 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % exists_least_lemma
% 0.30/0.52 thf(fact_265_le__numeral__extra_I3_J,axiom,
% 0.30/0.52 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 0.30/0.52
% 0.30/0.52 % le_numeral_extra(3)
% 0.30/0.52 thf(fact_266_le__numeral__extra_I3_J,axiom,
% 0.30/0.52 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 0.30/0.52
% 0.30/0.52 % le_numeral_extra(3)
% 0.30/0.52 thf(fact_267_le__numeral__extra_I3_J,axiom,
% 0.30/0.52 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 0.30/0.52
% 0.30/0.52 % le_numeral_extra(3)
% 0.30/0.52 thf(fact_268_le__numeral__extra_I3_J,axiom,
% 0.30/0.52 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.30/0.52
% 0.30/0.52 % le_numeral_extra(3)
% 0.30/0.52 thf(fact_269_zero__le,axiom,
% 0.30/0.52 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 0.30/0.52
% 0.30/0.52 % zero_le
% 0.30/0.52 thf(fact_270_divides__aux__eq,axiom,
% 0.30/0.52 ! [Q2: code_integer,R3: code_integer] :
% 0.30/0.52 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 0.30/0.52 = ( R3 = zero_z3403309356797280102nteger ) ) ).
% 0.30/0.52
% 0.30/0.52 % divides_aux_eq
% 0.30/0.52 thf(fact_271_divides__aux__eq,axiom,
% 0.30/0.52 ! [Q2: nat,R3: nat] :
% 0.30/0.52 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 0.30/0.52 = ( R3 = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % divides_aux_eq
% 0.30/0.52 thf(fact_272_divides__aux__eq,axiom,
% 0.30/0.52 ! [Q2: int,R3: int] :
% 0.30/0.52 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.30/0.52 = ( R3 = zero_zero_int ) ) ).
% 0.30/0.52
% 0.30/0.52 % divides_aux_eq
% 0.30/0.52 thf(fact_273_one__le__mult__iff,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.52 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 0.30/0.52 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % one_le_mult_iff
% 0.30/0.52 thf(fact_274__C1_C_I1_J,axiom,
% 0.30/0.52 ( sa
% 0.30/0.52 = ( vEBT_Leaf @ a @ b ) ) ).
% 0.30/0.52
% 0.30/0.52 % "1"(1)
% 0.30/0.52 thf(fact_275_valid__tree__deg__neq__0,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT] :
% 0.30/0.52 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % valid_tree_deg_neq_0
% 0.30/0.52 thf(fact_276_valid__0__not,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT] :
% 0.30/0.52 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % valid_0_not
% 0.30/0.52 thf(fact_277_Leaf__0__not,axiom,
% 0.30/0.52 ! [A: $o,B: $o] :
% 0.30/0.52 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % Leaf_0_not
% 0.30/0.52 thf(fact_278_prod__decode__eq,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( ( nat_prod_decode @ X )
% 0.30/0.52 = ( nat_prod_decode @ Y ) )
% 0.30/0.52 = ( X = Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % prod_decode_eq
% 0.30/0.52 thf(fact_279_insert_H__pres__valid,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.52 => ( vEBT_invar_vebt @ ( vEBT_VEBT_insert @ T @ X ) @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % insert'_pres_valid
% 0.30/0.52 thf(fact_280_mult__is__0,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ M2 @ N )
% 0.30/0.52 = zero_zero_nat )
% 0.30/0.52 = ( ( M2 = zero_zero_nat )
% 0.30/0.52 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_is_0
% 0.30/0.52 thf(fact_281_mult__0__right,axiom,
% 0.30/0.52 ! [M2: nat] :
% 0.30/0.52 ( ( times_times_nat @ M2 @ zero_zero_nat )
% 0.30/0.52 = zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % mult_0_right
% 0.30/0.52 thf(fact_282_mult__cancel1,axiom,
% 0.30/0.52 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ K2 @ M2 )
% 0.30/0.52 = ( times_times_nat @ K2 @ N ) )
% 0.30/0.52 = ( ( M2 = N )
% 0.30/0.52 | ( K2 = zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel1
% 0.30/0.52 thf(fact_283_mult__cancel2,axiom,
% 0.30/0.52 ! [M2: nat,K2: nat,N: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ M2 @ K2 )
% 0.30/0.52 = ( times_times_nat @ N @ K2 ) )
% 0.30/0.52 = ( ( M2 = N )
% 0.30/0.52 | ( K2 = zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel2
% 0.30/0.52 thf(fact_284_prod__decode__inverse,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( nat_prod_encode @ ( nat_prod_decode @ N ) )
% 0.30/0.52 = N ) ).
% 0.30/0.52
% 0.30/0.52 % prod_decode_inverse
% 0.30/0.52 thf(fact_285_prod__encode__inverse,axiom,
% 0.30/0.52 ! [X: product_prod_nat_nat] :
% 0.30/0.52 ( ( nat_prod_decode @ ( nat_prod_encode @ X ) )
% 0.30/0.52 = X ) ).
% 0.30/0.52
% 0.30/0.52 % prod_encode_inverse
% 0.30/0.52 thf(fact_286_one__eq__mult__iff,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ( suc @ zero_zero_nat )
% 0.30/0.52 = ( times_times_nat @ M2 @ N ) )
% 0.30/0.52 = ( ( M2
% 0.30/0.52 = ( suc @ zero_zero_nat ) )
% 0.30/0.52 & ( N
% 0.30/0.52 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % one_eq_mult_iff
% 0.30/0.52 thf(fact_287_mult__eq__1__iff,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ M2 @ N )
% 0.30/0.52 = ( suc @ zero_zero_nat ) )
% 0.30/0.52 = ( ( M2
% 0.30/0.52 = ( suc @ zero_zero_nat ) )
% 0.30/0.52 & ( N
% 0.30/0.52 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_eq_1_iff
% 0.30/0.52 thf(fact_288_mult_Oleft__commute,axiom,
% 0.30/0.52 ! [B: real,A: real,C2: real] :
% 0.30/0.52 ( ( times_times_real @ B @ ( times_times_real @ A @ C2 ) )
% 0.30/0.52 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.left_commute
% 0.30/0.52 thf(fact_289_mult_Oleft__commute,axiom,
% 0.30/0.52 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.52 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C2 ) )
% 0.30/0.52 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.left_commute
% 0.30/0.52 thf(fact_290_mult_Oleft__commute,axiom,
% 0.30/0.52 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.52 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C2 ) )
% 0.30/0.52 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.left_commute
% 0.30/0.52 thf(fact_291_mult_Oleft__commute,axiom,
% 0.30/0.52 ! [B: int,A: int,C2: int] :
% 0.30/0.52 ( ( times_times_int @ B @ ( times_times_int @ A @ C2 ) )
% 0.30/0.52 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.left_commute
% 0.30/0.52 thf(fact_292_mult_Ocommute,axiom,
% 0.30/0.52 ( times_times_real
% 0.30/0.52 = ( ^ [A5: real,B4: real] : ( times_times_real @ B4 @ A5 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.commute
% 0.30/0.52 thf(fact_293_mult_Ocommute,axiom,
% 0.30/0.52 ( times_times_rat
% 0.30/0.52 = ( ^ [A5: rat,B4: rat] : ( times_times_rat @ B4 @ A5 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.commute
% 0.30/0.52 thf(fact_294_mult_Ocommute,axiom,
% 0.30/0.52 ( times_times_nat
% 0.30/0.52 = ( ^ [A5: nat,B4: nat] : ( times_times_nat @ B4 @ A5 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.commute
% 0.30/0.52 thf(fact_295_mult_Ocommute,axiom,
% 0.30/0.52 ( times_times_int
% 0.30/0.52 = ( ^ [A5: int,B4: int] : ( times_times_int @ B4 @ A5 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.commute
% 0.30/0.52 thf(fact_296_mult_Oassoc,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.assoc
% 0.30/0.52 thf(fact_297_mult_Oassoc,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.assoc
% 0.30/0.52 thf(fact_298_mult_Oassoc,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.assoc
% 0.30/0.52 thf(fact_299_mult_Oassoc,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult.assoc
% 0.30/0.52 thf(fact_300_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ab_semigroup_mult_class.mult_ac(1)
% 0.30/0.52 thf(fact_301_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ab_semigroup_mult_class.mult_ac(1)
% 0.30/0.52 thf(fact_302_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ab_semigroup_mult_class.mult_ac(1)
% 0.30/0.52 thf(fact_303_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.30/0.52 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ab_semigroup_mult_class.mult_ac(1)
% 0.30/0.52 thf(fact_304_size__neq__size__imp__neq,axiom,
% 0.30/0.52 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 0.30/0.52 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 0.30/0.52 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % size_neq_size_imp_neq
% 0.30/0.52 thf(fact_305_size__neq__size__imp__neq,axiom,
% 0.30/0.52 ! [X: list_o,Y: list_o] :
% 0.30/0.52 ( ( ( size_size_list_o @ X )
% 0.30/0.52 != ( size_size_list_o @ Y ) )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % size_neq_size_imp_neq
% 0.30/0.52 thf(fact_306_size__neq__size__imp__neq,axiom,
% 0.30/0.52 ! [X: list_nat,Y: list_nat] :
% 0.30/0.52 ( ( ( size_size_list_nat @ X )
% 0.30/0.52 != ( size_size_list_nat @ Y ) )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % size_neq_size_imp_neq
% 0.30/0.52 thf(fact_307_size__neq__size__imp__neq,axiom,
% 0.30/0.52 ! [X: list_int,Y: list_int] :
% 0.30/0.52 ( ( ( size_size_list_int @ X )
% 0.30/0.52 != ( size_size_list_int @ Y ) )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % size_neq_size_imp_neq
% 0.30/0.52 thf(fact_308_size__neq__size__imp__neq,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( ( size_size_num @ X )
% 0.30/0.52 != ( size_size_num @ Y ) )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % size_neq_size_imp_neq
% 0.30/0.52 thf(fact_309_Suc__mult__cancel1,axiom,
% 0.30/0.52 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ ( suc @ K2 ) @ M2 )
% 0.30/0.52 = ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 0.30/0.52 = ( M2 = N ) ) ).
% 0.30/0.52
% 0.30/0.52 % Suc_mult_cancel1
% 0.30/0.52 thf(fact_310_mult__0,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.30/0.52 = zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % mult_0
% 0.30/0.52 thf(fact_311_mult__le__mono2,axiom,
% 0.30/0.52 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_le_mono2
% 0.30/0.52 thf(fact_312_mult__le__mono1,axiom,
% 0.30/0.52 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_le_mono1
% 0.30/0.52 thf(fact_313_mult__le__mono,axiom,
% 0.30/0.52 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.52 => ( ( ord_less_eq_nat @ K2 @ L )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ L ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_le_mono
% 0.30/0.52 thf(fact_314_le__square,axiom,
% 0.30/0.52 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_square
% 0.30/0.52 thf(fact_315_le__cube,axiom,
% 0.30/0.52 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % le_cube
% 0.30/0.52 thf(fact_316_Suc__mult__le__cancel1,axiom,
% 0.30/0.52 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K2 ) @ M2 ) @ ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 0.30/0.52 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % Suc_mult_le_cancel1
% 0.30/0.52 thf(fact_317_zero__reorient,axiom,
% 0.30/0.52 ! [X: complex] :
% 0.30/0.52 ( ( zero_zero_complex = X )
% 0.30/0.52 = ( X = zero_zero_complex ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_reorient
% 0.30/0.52 thf(fact_318_zero__reorient,axiom,
% 0.30/0.52 ! [X: real] :
% 0.30/0.52 ( ( zero_zero_real = X )
% 0.30/0.52 = ( X = zero_zero_real ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_reorient
% 0.30/0.52 thf(fact_319_zero__reorient,axiom,
% 0.30/0.52 ! [X: rat] :
% 0.30/0.52 ( ( zero_zero_rat = X )
% 0.30/0.52 = ( X = zero_zero_rat ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_reorient
% 0.30/0.52 thf(fact_320_zero__reorient,axiom,
% 0.30/0.52 ! [X: nat] :
% 0.30/0.52 ( ( zero_zero_nat = X )
% 0.30/0.52 = ( X = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_reorient
% 0.30/0.52 thf(fact_321_zero__reorient,axiom,
% 0.30/0.52 ! [X: int] :
% 0.30/0.52 ( ( zero_zero_int = X )
% 0.30/0.52 = ( X = zero_zero_int ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_reorient
% 0.30/0.52 thf(fact_322_mult__cancel__right,axiom,
% 0.30/0.52 ! [A: complex,C2: complex,B: complex] :
% 0.30/0.52 ( ( ( times_times_complex @ A @ C2 )
% 0.30/0.52 = ( times_times_complex @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_complex )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right
% 0.30/0.52 thf(fact_323_mult__cancel__right,axiom,
% 0.30/0.52 ! [A: real,C2: real,B: real] :
% 0.30/0.52 ( ( ( times_times_real @ A @ C2 )
% 0.30/0.52 = ( times_times_real @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_real )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right
% 0.30/0.52 thf(fact_324_mult__cancel__right,axiom,
% 0.30/0.52 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.52 ( ( ( times_times_rat @ A @ C2 )
% 0.30/0.52 = ( times_times_rat @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_rat )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right
% 0.30/0.52 thf(fact_325_mult__cancel__right,axiom,
% 0.30/0.52 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ A @ C2 )
% 0.30/0.52 = ( times_times_nat @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_nat )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right
% 0.30/0.52 thf(fact_326_mult__cancel__right,axiom,
% 0.30/0.52 ! [A: int,C2: int,B: int] :
% 0.30/0.52 ( ( ( times_times_int @ A @ C2 )
% 0.30/0.52 = ( times_times_int @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_int )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right
% 0.30/0.52 thf(fact_327_mult__cancel__left,axiom,
% 0.30/0.52 ! [C2: complex,A: complex,B: complex] :
% 0.30/0.52 ( ( ( times_times_complex @ C2 @ A )
% 0.30/0.52 = ( times_times_complex @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_complex )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left
% 0.30/0.52 thf(fact_328_mult__cancel__left,axiom,
% 0.30/0.52 ! [C2: real,A: real,B: real] :
% 0.30/0.52 ( ( ( times_times_real @ C2 @ A )
% 0.30/0.52 = ( times_times_real @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_real )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left
% 0.30/0.52 thf(fact_329_mult__cancel__left,axiom,
% 0.30/0.52 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.52 ( ( ( times_times_rat @ C2 @ A )
% 0.30/0.52 = ( times_times_rat @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_rat )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left
% 0.30/0.52 thf(fact_330_mult__cancel__left,axiom,
% 0.30/0.52 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ C2 @ A )
% 0.30/0.52 = ( times_times_nat @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_nat )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left
% 0.30/0.52 thf(fact_331_mult__cancel__left,axiom,
% 0.30/0.52 ! [C2: int,A: int,B: int] :
% 0.30/0.52 ( ( ( times_times_int @ C2 @ A )
% 0.30/0.52 = ( times_times_int @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_int )
% 0.30/0.52 | ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left
% 0.30/0.52 thf(fact_332_mult__eq__0__iff,axiom,
% 0.30/0.52 ! [A: complex,B: complex] :
% 0.30/0.52 ( ( ( times_times_complex @ A @ B )
% 0.30/0.52 = zero_zero_complex )
% 0.30/0.52 = ( ( A = zero_zero_complex )
% 0.30/0.52 | ( B = zero_zero_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_eq_0_iff
% 0.30/0.52 thf(fact_333_mult__eq__0__iff,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ( times_times_real @ A @ B )
% 0.30/0.52 = zero_zero_real )
% 0.30/0.52 = ( ( A = zero_zero_real )
% 0.30/0.52 | ( B = zero_zero_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_eq_0_iff
% 0.30/0.52 thf(fact_334_mult__eq__0__iff,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ( times_times_rat @ A @ B )
% 0.30/0.52 = zero_zero_rat )
% 0.30/0.52 = ( ( A = zero_zero_rat )
% 0.30/0.52 | ( B = zero_zero_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_eq_0_iff
% 0.30/0.52 thf(fact_335_mult__eq__0__iff,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ A @ B )
% 0.30/0.52 = zero_zero_nat )
% 0.30/0.52 = ( ( A = zero_zero_nat )
% 0.30/0.52 | ( B = zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_eq_0_iff
% 0.30/0.52 thf(fact_336_mult__eq__0__iff,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ( times_times_int @ A @ B )
% 0.30/0.52 = zero_zero_int )
% 0.30/0.52 = ( ( A = zero_zero_int )
% 0.30/0.52 | ( B = zero_zero_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_eq_0_iff
% 0.30/0.52 thf(fact_337_mult__zero__right,axiom,
% 0.30/0.52 ! [A: complex] :
% 0.30/0.52 ( ( times_times_complex @ A @ zero_zero_complex )
% 0.30/0.52 = zero_zero_complex ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_right
% 0.30/0.52 thf(fact_338_mult__zero__right,axiom,
% 0.30/0.52 ! [A: real] :
% 0.30/0.52 ( ( times_times_real @ A @ zero_zero_real )
% 0.30/0.52 = zero_zero_real ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_right
% 0.30/0.52 thf(fact_339_mult__zero__right,axiom,
% 0.30/0.52 ! [A: rat] :
% 0.30/0.52 ( ( times_times_rat @ A @ zero_zero_rat )
% 0.30/0.52 = zero_zero_rat ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_right
% 0.30/0.52 thf(fact_340_mult__zero__right,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ( ( times_times_nat @ A @ zero_zero_nat )
% 0.30/0.52 = zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_right
% 0.30/0.52 thf(fact_341_mult__zero__right,axiom,
% 0.30/0.52 ! [A: int] :
% 0.30/0.52 ( ( times_times_int @ A @ zero_zero_int )
% 0.30/0.52 = zero_zero_int ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_right
% 0.30/0.52 thf(fact_342_mult__zero__left,axiom,
% 0.30/0.52 ! [A: complex] :
% 0.30/0.52 ( ( times_times_complex @ zero_zero_complex @ A )
% 0.30/0.52 = zero_zero_complex ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_left
% 0.30/0.52 thf(fact_343_mult__zero__left,axiom,
% 0.30/0.52 ! [A: real] :
% 0.30/0.52 ( ( times_times_real @ zero_zero_real @ A )
% 0.30/0.52 = zero_zero_real ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_left
% 0.30/0.52 thf(fact_344_mult__zero__left,axiom,
% 0.30/0.52 ! [A: rat] :
% 0.30/0.52 ( ( times_times_rat @ zero_zero_rat @ A )
% 0.30/0.52 = zero_zero_rat ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_left
% 0.30/0.52 thf(fact_345_mult__zero__left,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ( ( times_times_nat @ zero_zero_nat @ A )
% 0.30/0.52 = zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_left
% 0.30/0.52 thf(fact_346_mult__zero__left,axiom,
% 0.30/0.52 ! [A: int] :
% 0.30/0.52 ( ( times_times_int @ zero_zero_int @ A )
% 0.30/0.52 = zero_zero_int ) ).
% 0.30/0.52
% 0.30/0.52 % mult_zero_left
% 0.30/0.52 thf(fact_347_mul__shift,axiom,
% 0.30/0.52 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ X @ Y )
% 0.30/0.52 = Z3 )
% 0.30/0.52 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.30/0.52 = ( some_nat @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mul_shift
% 0.30/0.52 thf(fact_348_invar__vebt_Ointros_I1_J,axiom,
% 0.30/0.52 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % invar_vebt.intros(1)
% 0.30/0.52 thf(fact_349_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.52 thf(fact_350_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.52 thf(fact_351_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.52 thf(fact_352_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ordered_comm_semiring_class.comm_mult_left_mono
% 0.30/0.52 thf(fact_353_zero__le__mult__iff,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.30/0.52 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.30/0.52 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.52 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_le_mult_iff
% 0.30/0.52 thf(fact_354_zero__le__mult__iff,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.52 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.30/0.52 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.52 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_le_mult_iff
% 0.30/0.52 thf(fact_355_zero__le__mult__iff,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.30/0.52 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.30/0.52 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.52 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_le_mult_iff
% 0.30/0.52 thf(fact_356_mult__nonneg__nonpos2,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos2
% 0.30/0.52 thf(fact_357_mult__nonneg__nonpos2,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos2
% 0.30/0.52 thf(fact_358_mult__nonneg__nonpos2,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos2
% 0.30/0.52 thf(fact_359_mult__nonneg__nonpos2,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos2
% 0.30/0.52 thf(fact_360_mult__nonpos__nonneg,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonpos_nonneg
% 0.30/0.52 thf(fact_361_mult__nonpos__nonneg,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonpos_nonneg
% 0.30/0.52 thf(fact_362_mult__nonpos__nonneg,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonpos_nonneg
% 0.30/0.52 thf(fact_363_mult__nonpos__nonneg,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonpos_nonneg
% 0.30/0.52 thf(fact_364_mult__nonneg__nonpos,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos
% 0.30/0.52 thf(fact_365_mult__nonneg__nonpos,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos
% 0.30/0.52 thf(fact_366_mult__nonneg__nonpos,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.52 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos
% 0.30/0.52 thf(fact_367_mult__nonneg__nonpos,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonpos
% 0.30/0.52 thf(fact_368_VEBT_Oinject_I2_J,axiom,
% 0.30/0.52 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 0.30/0.52 ( ( ( vEBT_Leaf @ X21 @ X22 )
% 0.30/0.52 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 0.30/0.52 = ( ( X21 = Y21 )
% 0.30/0.52 & ( X22 = Y22 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % VEBT.inject(2)
% 0.30/0.52 thf(fact_369_mul__def,axiom,
% 0.30/0.52 ( vEBT_VEBT_mul
% 0.30/0.52 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % mul_def
% 0.30/0.52 thf(fact_370_VEBT_Osize_I4_J,axiom,
% 0.30/0.52 ! [X21: $o,X22: $o] :
% 0.30/0.52 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 0.30/0.52 = zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % VEBT.size(4)
% 0.30/0.52 thf(fact_371_mult__not__zero,axiom,
% 0.30/0.52 ! [A: complex,B: complex] :
% 0.30/0.52 ( ( ( times_times_complex @ A @ B )
% 0.30/0.52 != zero_zero_complex )
% 0.30/0.52 => ( ( A != zero_zero_complex )
% 0.30/0.52 & ( B != zero_zero_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_not_zero
% 0.30/0.52 thf(fact_372_mult__not__zero,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ( times_times_real @ A @ B )
% 0.30/0.52 != zero_zero_real )
% 0.30/0.52 => ( ( A != zero_zero_real )
% 0.30/0.52 & ( B != zero_zero_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_not_zero
% 0.30/0.52 thf(fact_373_mult__not__zero,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ( times_times_rat @ A @ B )
% 0.30/0.52 != zero_zero_rat )
% 0.30/0.52 => ( ( A != zero_zero_rat )
% 0.30/0.52 & ( B != zero_zero_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_not_zero
% 0.30/0.52 thf(fact_374_mult__not__zero,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ A @ B )
% 0.30/0.52 != zero_zero_nat )
% 0.30/0.52 => ( ( A != zero_zero_nat )
% 0.30/0.52 & ( B != zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_not_zero
% 0.30/0.52 thf(fact_375_mult__not__zero,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ( times_times_int @ A @ B )
% 0.30/0.52 != zero_zero_int )
% 0.30/0.52 => ( ( A != zero_zero_int )
% 0.30/0.52 & ( B != zero_zero_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_not_zero
% 0.30/0.52 thf(fact_376_divisors__zero,axiom,
% 0.30/0.52 ! [A: complex,B: complex] :
% 0.30/0.52 ( ( ( times_times_complex @ A @ B )
% 0.30/0.52 = zero_zero_complex )
% 0.30/0.52 => ( ( A = zero_zero_complex )
% 0.30/0.52 | ( B = zero_zero_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % divisors_zero
% 0.30/0.52 thf(fact_377_divisors__zero,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ( times_times_real @ A @ B )
% 0.30/0.52 = zero_zero_real )
% 0.30/0.52 => ( ( A = zero_zero_real )
% 0.30/0.52 | ( B = zero_zero_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % divisors_zero
% 0.30/0.52 thf(fact_378_divisors__zero,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ( times_times_rat @ A @ B )
% 0.30/0.52 = zero_zero_rat )
% 0.30/0.52 => ( ( A = zero_zero_rat )
% 0.30/0.52 | ( B = zero_zero_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % divisors_zero
% 0.30/0.52 thf(fact_379_divisors__zero,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ A @ B )
% 0.30/0.52 = zero_zero_nat )
% 0.30/0.52 => ( ( A = zero_zero_nat )
% 0.30/0.52 | ( B = zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % divisors_zero
% 0.30/0.52 thf(fact_380_divisors__zero,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ( times_times_int @ A @ B )
% 0.30/0.52 = zero_zero_int )
% 0.30/0.52 => ( ( A = zero_zero_int )
% 0.30/0.52 | ( B = zero_zero_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % divisors_zero
% 0.30/0.52 thf(fact_381_no__zero__divisors,axiom,
% 0.30/0.52 ! [A: complex,B: complex] :
% 0.30/0.52 ( ( A != zero_zero_complex )
% 0.30/0.52 => ( ( B != zero_zero_complex )
% 0.30/0.52 => ( ( times_times_complex @ A @ B )
% 0.30/0.52 != zero_zero_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % no_zero_divisors
% 0.30/0.52 thf(fact_382_no__zero__divisors,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( A != zero_zero_real )
% 0.30/0.52 => ( ( B != zero_zero_real )
% 0.30/0.52 => ( ( times_times_real @ A @ B )
% 0.30/0.52 != zero_zero_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % no_zero_divisors
% 0.30/0.52 thf(fact_383_no__zero__divisors,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( A != zero_zero_rat )
% 0.30/0.52 => ( ( B != zero_zero_rat )
% 0.30/0.52 => ( ( times_times_rat @ A @ B )
% 0.30/0.52 != zero_zero_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % no_zero_divisors
% 0.30/0.52 thf(fact_384_no__zero__divisors,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( A != zero_zero_nat )
% 0.30/0.52 => ( ( B != zero_zero_nat )
% 0.30/0.52 => ( ( times_times_nat @ A @ B )
% 0.30/0.52 != zero_zero_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % no_zero_divisors
% 0.30/0.52 thf(fact_385_no__zero__divisors,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( A != zero_zero_int )
% 0.30/0.52 => ( ( B != zero_zero_int )
% 0.30/0.52 => ( ( times_times_int @ A @ B )
% 0.30/0.52 != zero_zero_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % no_zero_divisors
% 0.30/0.52 thf(fact_386_mult__left__cancel,axiom,
% 0.30/0.52 ! [C2: complex,A: complex,B: complex] :
% 0.30/0.52 ( ( C2 != zero_zero_complex )
% 0.30/0.52 => ( ( ( times_times_complex @ C2 @ A )
% 0.30/0.52 = ( times_times_complex @ C2 @ B ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_cancel
% 0.30/0.52 thf(fact_387_mult__left__cancel,axiom,
% 0.30/0.52 ! [C2: real,A: real,B: real] :
% 0.30/0.52 ( ( C2 != zero_zero_real )
% 0.30/0.52 => ( ( ( times_times_real @ C2 @ A )
% 0.30/0.52 = ( times_times_real @ C2 @ B ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_cancel
% 0.30/0.52 thf(fact_388_mult__left__cancel,axiom,
% 0.30/0.52 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.52 ( ( C2 != zero_zero_rat )
% 0.30/0.52 => ( ( ( times_times_rat @ C2 @ A )
% 0.30/0.52 = ( times_times_rat @ C2 @ B ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_cancel
% 0.30/0.52 thf(fact_389_mult__left__cancel,axiom,
% 0.30/0.52 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.52 ( ( C2 != zero_zero_nat )
% 0.30/0.52 => ( ( ( times_times_nat @ C2 @ A )
% 0.30/0.52 = ( times_times_nat @ C2 @ B ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_cancel
% 0.30/0.52 thf(fact_390_mult__left__cancel,axiom,
% 0.30/0.52 ! [C2: int,A: int,B: int] :
% 0.30/0.52 ( ( C2 != zero_zero_int )
% 0.30/0.52 => ( ( ( times_times_int @ C2 @ A )
% 0.30/0.52 = ( times_times_int @ C2 @ B ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_cancel
% 0.30/0.52 thf(fact_391_mult__right__cancel,axiom,
% 0.30/0.52 ! [C2: complex,A: complex,B: complex] :
% 0.30/0.52 ( ( C2 != zero_zero_complex )
% 0.30/0.52 => ( ( ( times_times_complex @ A @ C2 )
% 0.30/0.52 = ( times_times_complex @ B @ C2 ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_cancel
% 0.30/0.52 thf(fact_392_mult__right__cancel,axiom,
% 0.30/0.52 ! [C2: real,A: real,B: real] :
% 0.30/0.52 ( ( C2 != zero_zero_real )
% 0.30/0.52 => ( ( ( times_times_real @ A @ C2 )
% 0.30/0.52 = ( times_times_real @ B @ C2 ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_cancel
% 0.30/0.52 thf(fact_393_mult__right__cancel,axiom,
% 0.30/0.52 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.52 ( ( C2 != zero_zero_rat )
% 0.30/0.52 => ( ( ( times_times_rat @ A @ C2 )
% 0.30/0.52 = ( times_times_rat @ B @ C2 ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_cancel
% 0.30/0.52 thf(fact_394_mult__right__cancel,axiom,
% 0.30/0.52 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.52 ( ( C2 != zero_zero_nat )
% 0.30/0.52 => ( ( ( times_times_nat @ A @ C2 )
% 0.30/0.52 = ( times_times_nat @ B @ C2 ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_cancel
% 0.30/0.52 thf(fact_395_mult__right__cancel,axiom,
% 0.30/0.52 ! [C2: int,A: int,B: int] :
% 0.30/0.52 ( ( C2 != zero_zero_int )
% 0.30/0.52 => ( ( ( times_times_int @ A @ C2 )
% 0.30/0.52 = ( times_times_int @ B @ C2 ) )
% 0.30/0.52 = ( A = B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_cancel
% 0.30/0.52 thf(fact_396_mult__mono,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_real @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono
% 0.30/0.52 thf(fact_397_mult__mono,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono
% 0.30/0.52 thf(fact_398_mult__mono,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono
% 0.30/0.52 thf(fact_399_mult__mono,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono
% 0.30/0.52 thf(fact_400_mult__mono_H,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_real @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono'
% 0.30/0.52 thf(fact_401_mult__mono_H,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono'
% 0.30/0.52 thf(fact_402_mult__mono_H,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono'
% 0.30/0.52 thf(fact_403_mult__mono_H,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ C2 @ D )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_mono'
% 0.30/0.52 thf(fact_404_zero__le__square,axiom,
% 0.30/0.52 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_le_square
% 0.30/0.52 thf(fact_405_zero__le__square,axiom,
% 0.30/0.52 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_le_square
% 0.30/0.52 thf(fact_406_zero__le__square,axiom,
% 0.30/0.52 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_le_square
% 0.30/0.52 thf(fact_407_split__mult__pos__le,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.30/0.52 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.52 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.30/0.52 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % split_mult_pos_le
% 0.30/0.52 thf(fact_408_split__mult__pos__le,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.30/0.52 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.52 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % split_mult_pos_le
% 0.30/0.52 thf(fact_409_split__mult__pos__le,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 0.30/0.52 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.52 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.30/0.52 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % split_mult_pos_le
% 0.30/0.52 thf(fact_410_mult__left__mono__neg,axiom,
% 0.30/0.52 ! [B: real,A: real,C2: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_mono_neg
% 0.30/0.52 thf(fact_411_mult__left__mono__neg,axiom,
% 0.30/0.52 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_mono_neg
% 0.30/0.52 thf(fact_412_mult__left__mono__neg,axiom,
% 0.30/0.52 ! [B: int,A: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_mono_neg
% 0.30/0.52 thf(fact_413_mult__nonpos__nonpos,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.52 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.30/0.52 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonpos_nonpos
% 0.30/0.52 thf(fact_414_mult__nonpos__nonpos,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.52 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.52 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonpos_nonpos
% 0.30/0.52 thf(fact_415_mult__nonpos__nonpos,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.52 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.52 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonpos_nonpos
% 0.30/0.52 thf(fact_416_mult__left__mono,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_mono
% 0.30/0.52 thf(fact_417_mult__left__mono,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_mono
% 0.30/0.52 thf(fact_418_mult__left__mono,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_mono
% 0.30/0.52 thf(fact_419_mult__left__mono,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_left_mono
% 0.30/0.52 thf(fact_420_mult__right__mono__neg,axiom,
% 0.30/0.52 ! [B: real,A: real,C2: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_mono_neg
% 0.30/0.52 thf(fact_421_mult__right__mono__neg,axiom,
% 0.30/0.52 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_mono_neg
% 0.30/0.52 thf(fact_422_mult__right__mono__neg,axiom,
% 0.30/0.52 ! [B: int,A: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_mono_neg
% 0.30/0.52 thf(fact_423_mult__right__mono,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_mono
% 0.30/0.52 thf(fact_424_mult__right__mono,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_mono
% 0.30/0.52 thf(fact_425_mult__right__mono,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_mono
% 0.30/0.52 thf(fact_426_mult__right__mono,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_right_mono
% 0.30/0.52 thf(fact_427_mult__le__0__iff,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.30/0.52 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.30/0.52 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.52 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_le_0_iff
% 0.30/0.52 thf(fact_428_mult__le__0__iff,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.30/0.52 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.30/0.52 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.52 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_le_0_iff
% 0.30/0.52 thf(fact_429_mult__le__0__iff,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.30/0.52 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.30/0.52 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.52 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_le_0_iff
% 0.30/0.52 thf(fact_430_split__mult__neg__le,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.30/0.52 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.52 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 0.30/0.52 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 0.30/0.52
% 0.30/0.52 % split_mult_neg_le
% 0.30/0.52 thf(fact_431_split__mult__neg__le,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.30/0.52 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.52 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 0.30/0.52 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 0.30/0.52
% 0.30/0.52 % split_mult_neg_le
% 0.30/0.52 thf(fact_432_split__mult__neg__le,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.52 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 0.30/0.52 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.52 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 0.30/0.52 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % split_mult_neg_le
% 0.30/0.52 thf(fact_433_split__mult__neg__le,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 0.30/0.52 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.52 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 0.30/0.52 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.30/0.52
% 0.30/0.52 % split_mult_neg_le
% 0.30/0.52 thf(fact_434_mult__nonneg__nonneg,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.52 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.52 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonneg
% 0.30/0.52 thf(fact_435_mult__nonneg__nonneg,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.52 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonneg
% 0.30/0.52 thf(fact_436_mult__nonneg__nonneg,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.52 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.52 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonneg
% 0.30/0.52 thf(fact_437_mult__nonneg__nonneg,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.52 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.52 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_nonneg_nonneg
% 0.30/0.52 thf(fact_438_valid__eq,axiom,
% 0.30/0.52 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 0.30/0.52
% 0.30/0.52 % valid_eq
% 0.30/0.52 thf(fact_439_valid__eq1,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT,D: nat] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ T @ D )
% 0.30/0.52 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 0.30/0.52
% 0.30/0.52 % valid_eq1
% 0.30/0.52 thf(fact_440_valid__eq2,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT,D: nat] :
% 0.30/0.52 ( ( vEBT_VEBT_valid @ T @ D )
% 0.30/0.52 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 0.30/0.52
% 0.30/0.52 % valid_eq2
% 0.30/0.52 thf(fact_441_deg1Leaf,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.30/0.52 = ( ? [A5: $o,B4: $o] :
% 0.30/0.52 ( T
% 0.30/0.52 = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % deg1Leaf
% 0.30/0.52 thf(fact_442_deg__1__Leaf,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 0.30/0.52 => ? [A3: $o,B3: $o] :
% 0.30/0.52 ( T
% 0.30/0.52 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % deg_1_Leaf
% 0.30/0.52 thf(fact_443_deg__1__Leafy,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT,N: nat] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.52 => ( ( N = one_one_nat )
% 0.30/0.52 => ? [A3: $o,B3: $o] :
% 0.30/0.52 ( T
% 0.30/0.52 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % deg_1_Leafy
% 0.30/0.52 thf(fact_444_nat__mult__eq__cancel__disj,axiom,
% 0.30/0.52 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ K2 @ M2 )
% 0.30/0.52 = ( times_times_nat @ K2 @ N ) )
% 0.30/0.52 = ( ( K2 = zero_zero_nat )
% 0.30/0.52 | ( M2 = N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_mult_eq_cancel_disj
% 0.30/0.52 thf(fact_445_deg__not__0,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT,N: nat] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.52 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % deg_not_0
% 0.30/0.52 thf(fact_446_VEBT_Osize__gen_I2_J,axiom,
% 0.30/0.52 ! [X21: $o,X22: $o] :
% 0.30/0.52 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 0.30/0.52 = zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % VEBT.size_gen(2)
% 0.30/0.52 thf(fact_447_deg__SUcn__Node,axiom,
% 0.30/0.52 ! [Tree: vEBT_VEBT,N: nat] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 0.30/0.52 => ? [Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.30/0.52 ( Tree
% 0.30/0.52 = ( vEBT_Node @ Info @ ( suc @ ( suc @ N ) ) @ TreeList @ S ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % deg_SUcn_Node
% 0.30/0.52 thf(fact_448_case4_I13_J,axiom,
% 0.30/0.52 ( ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) )
% 0.30/0.52 = ( vEBT_VEBT_set_vebt @ sa ) ) ).
% 0.30/0.52
% 0.30/0.52 % case4(13)
% 0.30/0.52 thf(fact_449_deg__deg__n,axiom,
% 0.30/0.52 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 0.30/0.52 => ( Deg = N ) ) ).
% 0.30/0.52
% 0.30/0.52 % deg_deg_n
% 0.30/0.52 thf(fact_450_VEBT_Oinject_I1_J,axiom,
% 0.30/0.52 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 0.30/0.52 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.30/0.52 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 0.30/0.52 = ( ( X11 = Y11 )
% 0.30/0.52 & ( X12 = Y12 )
% 0.30/0.52 & ( X13 = Y13 )
% 0.30/0.52 & ( X14 = Y14 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % VEBT.inject(1)
% 0.30/0.52 thf(fact_451_not__gr__zero,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.30/0.52 = ( N = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % not_gr_zero
% 0.30/0.52 thf(fact_452_mult__1,axiom,
% 0.30/0.52 ! [A: code_integer] :
% 0.30/0.52 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult_1
% 0.30/0.52 thf(fact_453_mult__1,axiom,
% 0.30/0.52 ! [A: complex] :
% 0.30/0.52 ( ( times_times_complex @ one_one_complex @ A )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult_1
% 0.30/0.52 thf(fact_454_mult__1,axiom,
% 0.30/0.52 ! [A: real] :
% 0.30/0.52 ( ( times_times_real @ one_one_real @ A )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult_1
% 0.30/0.52 thf(fact_455_mult__1,axiom,
% 0.30/0.52 ! [A: rat] :
% 0.30/0.52 ( ( times_times_rat @ one_one_rat @ A )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult_1
% 0.30/0.52 thf(fact_456_mult__1,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ( ( times_times_nat @ one_one_nat @ A )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult_1
% 0.30/0.52 thf(fact_457_mult__1,axiom,
% 0.30/0.52 ! [A: int] :
% 0.30/0.52 ( ( times_times_int @ one_one_int @ A )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult_1
% 0.30/0.52 thf(fact_458_mult_Oright__neutral,axiom,
% 0.30/0.52 ! [A: code_integer] :
% 0.30/0.52 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult.right_neutral
% 0.30/0.52 thf(fact_459_mult_Oright__neutral,axiom,
% 0.30/0.52 ! [A: complex] :
% 0.30/0.52 ( ( times_times_complex @ A @ one_one_complex )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult.right_neutral
% 0.30/0.52 thf(fact_460_mult_Oright__neutral,axiom,
% 0.30/0.52 ! [A: real] :
% 0.30/0.52 ( ( times_times_real @ A @ one_one_real )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult.right_neutral
% 0.30/0.52 thf(fact_461_mult_Oright__neutral,axiom,
% 0.30/0.52 ! [A: rat] :
% 0.30/0.52 ( ( times_times_rat @ A @ one_one_rat )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult.right_neutral
% 0.30/0.52 thf(fact_462_mult_Oright__neutral,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ( ( times_times_nat @ A @ one_one_nat )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult.right_neutral
% 0.30/0.52 thf(fact_463_mult_Oright__neutral,axiom,
% 0.30/0.52 ! [A: int] :
% 0.30/0.52 ( ( times_times_int @ A @ one_one_int )
% 0.30/0.52 = A ) ).
% 0.30/0.52
% 0.30/0.52 % mult.right_neutral
% 0.30/0.52 thf(fact_464_Suc__less__eq,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.30/0.52 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % Suc_less_eq
% 0.30/0.52 thf(fact_465_Suc__mono,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.52 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % Suc_mono
% 0.30/0.52 thf(fact_466_lessI,axiom,
% 0.30/0.52 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % lessI
% 0.30/0.52 thf(fact_467_bot__nat__0_Onot__eq__extremum,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ( ( A != zero_zero_nat )
% 0.30/0.52 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % bot_nat_0.not_eq_extremum
% 0.30/0.52 thf(fact_468_neq0__conv,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( N != zero_zero_nat )
% 0.30/0.52 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % neq0_conv
% 0.30/0.52 thf(fact_469_less__nat__zero__code,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.52
% 0.30/0.52 % less_nat_zero_code
% 0.30/0.52 thf(fact_470_nat__1__eq__mult__iff,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( one_one_nat
% 0.30/0.52 = ( times_times_nat @ M2 @ N ) )
% 0.30/0.52 = ( ( M2 = one_one_nat )
% 0.30/0.52 & ( N = one_one_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_1_eq_mult_iff
% 0.30/0.52 thf(fact_471_nat__mult__eq__1__iff,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ( times_times_nat @ M2 @ N )
% 0.30/0.52 = one_one_nat )
% 0.30/0.52 = ( ( M2 = one_one_nat )
% 0.30/0.52 & ( N = one_one_nat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_mult_eq_1_iff
% 0.30/0.52 thf(fact_472_case4_I3_J,axiom,
% 0.30/0.52 vEBT_invar_vebt @ summary2 @ m ).
% 0.30/0.52
% 0.30/0.52 % case4(3)
% 0.30/0.52 thf(fact_473_mult__cancel__left1,axiom,
% 0.30/0.52 ! [C2: code_integer,B: code_integer] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_3573771949741848930nteger @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_z3403309356797280102nteger )
% 0.30/0.52 | ( B = one_one_Code_integer ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left1
% 0.30/0.52 thf(fact_474_mult__cancel__left1,axiom,
% 0.30/0.52 ! [C2: complex,B: complex] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_complex @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_complex )
% 0.30/0.52 | ( B = one_one_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left1
% 0.30/0.52 thf(fact_475_mult__cancel__left1,axiom,
% 0.30/0.52 ! [C2: real,B: real] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_real @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_real )
% 0.30/0.52 | ( B = one_one_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left1
% 0.30/0.52 thf(fact_476_mult__cancel__left1,axiom,
% 0.30/0.52 ! [C2: rat,B: rat] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_rat @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_rat )
% 0.30/0.52 | ( B = one_one_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left1
% 0.30/0.52 thf(fact_477_mult__cancel__left1,axiom,
% 0.30/0.52 ! [C2: int,B: int] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_int @ C2 @ B ) )
% 0.30/0.52 = ( ( C2 = zero_zero_int )
% 0.30/0.52 | ( B = one_one_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left1
% 0.30/0.52 thf(fact_478_mult__cancel__left2,axiom,
% 0.30/0.52 ! [C2: code_integer,A: code_integer] :
% 0.30/0.52 ( ( ( times_3573771949741848930nteger @ C2 @ A )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_z3403309356797280102nteger )
% 0.30/0.52 | ( A = one_one_Code_integer ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left2
% 0.30/0.52 thf(fact_479_mult__cancel__left2,axiom,
% 0.30/0.52 ! [C2: complex,A: complex] :
% 0.30/0.52 ( ( ( times_times_complex @ C2 @ A )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_complex )
% 0.30/0.52 | ( A = one_one_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left2
% 0.30/0.52 thf(fact_480_mult__cancel__left2,axiom,
% 0.30/0.52 ! [C2: real,A: real] :
% 0.30/0.52 ( ( ( times_times_real @ C2 @ A )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_real )
% 0.30/0.52 | ( A = one_one_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left2
% 0.30/0.52 thf(fact_481_mult__cancel__left2,axiom,
% 0.30/0.52 ! [C2: rat,A: rat] :
% 0.30/0.52 ( ( ( times_times_rat @ C2 @ A )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_rat )
% 0.30/0.52 | ( A = one_one_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left2
% 0.30/0.52 thf(fact_482_mult__cancel__left2,axiom,
% 0.30/0.52 ! [C2: int,A: int] :
% 0.30/0.52 ( ( ( times_times_int @ C2 @ A )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_int )
% 0.30/0.52 | ( A = one_one_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_left2
% 0.30/0.52 thf(fact_483_mult__cancel__right1,axiom,
% 0.30/0.52 ! [C2: code_integer,B: code_integer] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_3573771949741848930nteger @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_z3403309356797280102nteger )
% 0.30/0.52 | ( B = one_one_Code_integer ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right1
% 0.30/0.52 thf(fact_484_mult__cancel__right1,axiom,
% 0.30/0.52 ! [C2: complex,B: complex] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_complex @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_complex )
% 0.30/0.52 | ( B = one_one_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right1
% 0.30/0.52 thf(fact_485_mult__cancel__right1,axiom,
% 0.30/0.52 ! [C2: real,B: real] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_real @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_real )
% 0.30/0.52 | ( B = one_one_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right1
% 0.30/0.52 thf(fact_486_mult__cancel__right1,axiom,
% 0.30/0.52 ! [C2: rat,B: rat] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_rat @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_rat )
% 0.30/0.52 | ( B = one_one_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right1
% 0.30/0.52 thf(fact_487_mult__cancel__right1,axiom,
% 0.30/0.52 ! [C2: int,B: int] :
% 0.30/0.52 ( ( C2
% 0.30/0.52 = ( times_times_int @ B @ C2 ) )
% 0.30/0.52 = ( ( C2 = zero_zero_int )
% 0.30/0.52 | ( B = one_one_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right1
% 0.30/0.52 thf(fact_488_mult__cancel__right2,axiom,
% 0.30/0.52 ! [A: code_integer,C2: code_integer] :
% 0.30/0.52 ( ( ( times_3573771949741848930nteger @ A @ C2 )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_z3403309356797280102nteger )
% 0.30/0.52 | ( A = one_one_Code_integer ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right2
% 0.30/0.52 thf(fact_489_mult__cancel__right2,axiom,
% 0.30/0.52 ! [A: complex,C2: complex] :
% 0.30/0.52 ( ( ( times_times_complex @ A @ C2 )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_complex )
% 0.30/0.52 | ( A = one_one_complex ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right2
% 0.30/0.52 thf(fact_490_mult__cancel__right2,axiom,
% 0.30/0.52 ! [A: real,C2: real] :
% 0.30/0.52 ( ( ( times_times_real @ A @ C2 )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_real )
% 0.30/0.52 | ( A = one_one_real ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right2
% 0.30/0.52 thf(fact_491_mult__cancel__right2,axiom,
% 0.30/0.52 ! [A: rat,C2: rat] :
% 0.30/0.52 ( ( ( times_times_rat @ A @ C2 )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_rat )
% 0.30/0.52 | ( A = one_one_rat ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right2
% 0.30/0.52 thf(fact_492_mult__cancel__right2,axiom,
% 0.30/0.52 ! [A: int,C2: int] :
% 0.30/0.52 ( ( ( times_times_int @ A @ C2 )
% 0.30/0.52 = C2 )
% 0.30/0.52 = ( ( C2 = zero_zero_int )
% 0.30/0.52 | ( A = one_one_int ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_cancel_right2
% 0.30/0.52 thf(fact_493_zero__less__Suc,axiom,
% 0.30/0.52 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % zero_less_Suc
% 0.30/0.52 thf(fact_494_less__Suc0,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.30/0.52 = ( N = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_Suc0
% 0.30/0.52 thf(fact_495_nat__mult__less__cancel__disj,axiom,
% 0.30/0.52 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.30/0.52 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.52 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_mult_less_cancel_disj
% 0.30/0.52 thf(fact_496_mult__less__cancel2,axiom,
% 0.30/0.52 ! [M2: nat,K2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) )
% 0.30/0.52 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.52 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_less_cancel2
% 0.30/0.52 thf(fact_497_nat__0__less__mult__iff,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.52 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.30/0.52 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_0_less_mult_iff
% 0.30/0.52 thf(fact_498_less__one,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ( ( ord_less_nat @ N @ one_one_nat )
% 0.30/0.52 = ( N = zero_zero_nat ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_one
% 0.30/0.52 thf(fact_499_nat__mult__le__cancel__disj,axiom,
% 0.30/0.52 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.30/0.52 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.52 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_mult_le_cancel_disj
% 0.30/0.52 thf(fact_500_mult__le__cancel2,axiom,
% 0.30/0.52 ! [M2: nat,K2: nat,N: nat] :
% 0.30/0.52 ( ( ord_less_eq_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) )
% 0.30/0.52 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.52 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % mult_le_cancel2
% 0.30/0.52 thf(fact_501_set__vebt__set__vebt_H__valid,axiom,
% 0.30/0.52 ! [T: vEBT_VEBT,N: nat] :
% 0.30/0.52 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.52 => ( ( vEBT_set_vebt @ T )
% 0.30/0.52 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % set_vebt_set_vebt'_valid
% 0.30/0.52 thf(fact_502_linorder__neqE__linordered__idom,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_real @ X @ Y )
% 0.30/0.52 => ( ord_less_real @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE_linordered_idom
% 0.30/0.52 thf(fact_503_linorder__neqE__linordered__idom,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_rat @ X @ Y )
% 0.30/0.52 => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE_linordered_idom
% 0.30/0.52 thf(fact_504_linorder__neqE__linordered__idom,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_int @ X @ Y )
% 0.30/0.52 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE_linordered_idom
% 0.30/0.52 thf(fact_505_lt__ex,axiom,
% 0.30/0.52 ! [X: real] :
% 0.30/0.52 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 0.30/0.52
% 0.30/0.52 % lt_ex
% 0.30/0.52 thf(fact_506_lt__ex,axiom,
% 0.30/0.52 ! [X: rat] :
% 0.30/0.52 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 0.30/0.52
% 0.30/0.52 % lt_ex
% 0.30/0.52 thf(fact_507_lt__ex,axiom,
% 0.30/0.52 ! [X: int] :
% 0.30/0.52 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 0.30/0.52
% 0.30/0.52 % lt_ex
% 0.30/0.52 thf(fact_508_gt__ex,axiom,
% 0.30/0.52 ! [X: real] :
% 0.30/0.52 ? [X_12: real] : ( ord_less_real @ X @ X_12 ) ).
% 0.30/0.52
% 0.30/0.52 % gt_ex
% 0.30/0.52 thf(fact_509_gt__ex,axiom,
% 0.30/0.52 ! [X: rat] :
% 0.30/0.52 ? [X_12: rat] : ( ord_less_rat @ X @ X_12 ) ).
% 0.30/0.52
% 0.30/0.52 % gt_ex
% 0.30/0.52 thf(fact_510_gt__ex,axiom,
% 0.30/0.52 ! [X: nat] :
% 0.30/0.52 ? [X_12: nat] : ( ord_less_nat @ X @ X_12 ) ).
% 0.30/0.52
% 0.30/0.52 % gt_ex
% 0.30/0.52 thf(fact_511_gt__ex,axiom,
% 0.30/0.52 ! [X: int] :
% 0.30/0.52 ? [X_12: int] : ( ord_less_int @ X @ X_12 ) ).
% 0.30/0.52
% 0.30/0.52 % gt_ex
% 0.30/0.52 thf(fact_512_dense,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ( ord_less_real @ X @ Y )
% 0.30/0.52 => ? [Z: real] :
% 0.30/0.52 ( ( ord_less_real @ X @ Z )
% 0.30/0.52 & ( ord_less_real @ Z @ Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dense
% 0.30/0.52 thf(fact_513_dense,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( ord_less_rat @ X @ Y )
% 0.30/0.52 => ? [Z: rat] :
% 0.30/0.52 ( ( ord_less_rat @ X @ Z )
% 0.30/0.52 & ( ord_less_rat @ Z @ Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dense
% 0.30/0.52 thf(fact_514_less__imp__neq,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ( ord_less_real @ X @ Y )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_imp_neq
% 0.30/0.52 thf(fact_515_less__imp__neq,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( ord_less_rat @ X @ Y )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_imp_neq
% 0.30/0.52 thf(fact_516_less__imp__neq,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( ord_less_num @ X @ Y )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_imp_neq
% 0.30/0.52 thf(fact_517_less__imp__neq,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( ord_less_nat @ X @ Y )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_imp_neq
% 0.30/0.52 thf(fact_518_less__imp__neq,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( ord_less_int @ X @ Y )
% 0.30/0.52 => ( X != Y ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_imp_neq
% 0.30/0.52 thf(fact_519_order_Oasym,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_real @ A @ B )
% 0.30/0.52 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.asym
% 0.30/0.52 thf(fact_520_order_Oasym,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_rat @ A @ B )
% 0.30/0.52 => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.asym
% 0.30/0.52 thf(fact_521_order_Oasym,axiom,
% 0.30/0.52 ! [A: num,B: num] :
% 0.30/0.52 ( ( ord_less_num @ A @ B )
% 0.30/0.52 => ~ ( ord_less_num @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.asym
% 0.30/0.52 thf(fact_522_order_Oasym,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_nat @ A @ B )
% 0.30/0.52 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.asym
% 0.30/0.52 thf(fact_523_order_Oasym,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_int @ A @ B )
% 0.30/0.52 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.asym
% 0.30/0.52 thf(fact_524_ord__eq__less__trans,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.52 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_trans
% 0.30/0.52 thf(fact_525_ord__eq__less__trans,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.52 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_trans
% 0.30/0.52 thf(fact_526_ord__eq__less__trans,axiom,
% 0.30/0.52 ! [A: num,B: num,C2: num] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_num @ B @ C2 )
% 0.30/0.52 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_trans
% 0.30/0.52 thf(fact_527_ord__eq__less__trans,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.52 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_trans
% 0.30/0.52 thf(fact_528_ord__eq__less__trans,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( A = B )
% 0.30/0.52 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.52 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_trans
% 0.30/0.52 thf(fact_529_ord__less__eq__trans,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( ord_less_real @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_less_eq_trans
% 0.30/0.52 thf(fact_530_ord__less__eq__trans,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_rat @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_less_eq_trans
% 0.30/0.52 thf(fact_531_ord__less__eq__trans,axiom,
% 0.30/0.52 ! [A: num,B: num,C2: num] :
% 0.30/0.52 ( ( ord_less_num @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_less_eq_trans
% 0.30/0.52 thf(fact_532_ord__less__eq__trans,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_nat @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_less_eq_trans
% 0.30/0.52 thf(fact_533_ord__less__eq__trans,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_int @ A @ B )
% 0.30/0.52 => ( ( B = C2 )
% 0.30/0.52 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_less_eq_trans
% 0.30/0.52 thf(fact_534_less__induct,axiom,
% 0.30/0.52 ! [P2: nat > $o,A: nat] :
% 0.30/0.52 ( ! [X3: nat] :
% 0.30/0.52 ( ! [Y6: nat] :
% 0.30/0.52 ( ( ord_less_nat @ Y6 @ X3 )
% 0.30/0.52 => ( P2 @ Y6 ) )
% 0.30/0.52 => ( P2 @ X3 ) )
% 0.30/0.52 => ( P2 @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_induct
% 0.30/0.52 thf(fact_535_antisym__conv3,axiom,
% 0.30/0.52 ! [Y: real,X: real] :
% 0.30/0.52 ( ~ ( ord_less_real @ Y @ X )
% 0.30/0.52 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.30/0.52 = ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym_conv3
% 0.30/0.52 thf(fact_536_antisym__conv3,axiom,
% 0.30/0.52 ! [Y: rat,X: rat] :
% 0.30/0.52 ( ~ ( ord_less_rat @ Y @ X )
% 0.30/0.52 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.30/0.52 = ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym_conv3
% 0.30/0.52 thf(fact_537_antisym__conv3,axiom,
% 0.30/0.52 ! [Y: num,X: num] :
% 0.30/0.52 ( ~ ( ord_less_num @ Y @ X )
% 0.30/0.52 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.30/0.52 = ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym_conv3
% 0.30/0.52 thf(fact_538_antisym__conv3,axiom,
% 0.30/0.52 ! [Y: nat,X: nat] :
% 0.30/0.52 ( ~ ( ord_less_nat @ Y @ X )
% 0.30/0.52 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.30/0.52 = ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym_conv3
% 0.30/0.52 thf(fact_539_antisym__conv3,axiom,
% 0.30/0.52 ! [Y: int,X: int] :
% 0.30/0.52 ( ~ ( ord_less_int @ Y @ X )
% 0.30/0.52 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.30/0.52 = ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % antisym_conv3
% 0.30/0.52 thf(fact_540_linorder__cases,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ~ ( ord_less_real @ X @ Y )
% 0.30/0.52 => ( ( X != Y )
% 0.30/0.52 => ( ord_less_real @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_cases
% 0.30/0.52 thf(fact_541_linorder__cases,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ~ ( ord_less_rat @ X @ Y )
% 0.30/0.52 => ( ( X != Y )
% 0.30/0.52 => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_cases
% 0.30/0.52 thf(fact_542_linorder__cases,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ~ ( ord_less_num @ X @ Y )
% 0.30/0.52 => ( ( X != Y )
% 0.30/0.52 => ( ord_less_num @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_cases
% 0.30/0.52 thf(fact_543_linorder__cases,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ~ ( ord_less_nat @ X @ Y )
% 0.30/0.52 => ( ( X != Y )
% 0.30/0.52 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_cases
% 0.30/0.52 thf(fact_544_linorder__cases,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ~ ( ord_less_int @ X @ Y )
% 0.30/0.52 => ( ( X != Y )
% 0.30/0.52 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_cases
% 0.30/0.52 thf(fact_545_dual__order_Oasym,axiom,
% 0.30/0.52 ! [B: real,A: real] :
% 0.30/0.52 ( ( ord_less_real @ B @ A )
% 0.30/0.52 => ~ ( ord_less_real @ A @ B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.asym
% 0.30/0.52 thf(fact_546_dual__order_Oasym,axiom,
% 0.30/0.52 ! [B: rat,A: rat] :
% 0.30/0.52 ( ( ord_less_rat @ B @ A )
% 0.30/0.52 => ~ ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.asym
% 0.30/0.52 thf(fact_547_dual__order_Oasym,axiom,
% 0.30/0.52 ! [B: num,A: num] :
% 0.30/0.52 ( ( ord_less_num @ B @ A )
% 0.30/0.52 => ~ ( ord_less_num @ A @ B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.asym
% 0.30/0.52 thf(fact_548_dual__order_Oasym,axiom,
% 0.30/0.52 ! [B: nat,A: nat] :
% 0.30/0.52 ( ( ord_less_nat @ B @ A )
% 0.30/0.52 => ~ ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.asym
% 0.30/0.52 thf(fact_549_dual__order_Oasym,axiom,
% 0.30/0.52 ! [B: int,A: int] :
% 0.30/0.52 ( ( ord_less_int @ B @ A )
% 0.30/0.52 => ~ ( ord_less_int @ A @ B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.asym
% 0.30/0.52 thf(fact_550_dual__order_Oirrefl,axiom,
% 0.30/0.52 ! [A: real] :
% 0.30/0.52 ~ ( ord_less_real @ A @ A ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.irrefl
% 0.30/0.52 thf(fact_551_dual__order_Oirrefl,axiom,
% 0.30/0.52 ! [A: rat] :
% 0.30/0.52 ~ ( ord_less_rat @ A @ A ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.irrefl
% 0.30/0.52 thf(fact_552_dual__order_Oirrefl,axiom,
% 0.30/0.52 ! [A: num] :
% 0.30/0.52 ~ ( ord_less_num @ A @ A ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.irrefl
% 0.30/0.52 thf(fact_553_dual__order_Oirrefl,axiom,
% 0.30/0.52 ! [A: nat] :
% 0.30/0.52 ~ ( ord_less_nat @ A @ A ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.irrefl
% 0.30/0.52 thf(fact_554_dual__order_Oirrefl,axiom,
% 0.30/0.52 ! [A: int] :
% 0.30/0.52 ~ ( ord_less_int @ A @ A ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.irrefl
% 0.30/0.52 thf(fact_555_exists__least__iff,axiom,
% 0.30/0.52 ( ( ^ [P3: nat > $o] :
% 0.30/0.52 ? [X6: nat] : ( P3 @ X6 ) )
% 0.30/0.52 = ( ^ [P4: nat > $o] :
% 0.30/0.52 ? [N4: nat] :
% 0.30/0.52 ( ( P4 @ N4 )
% 0.30/0.52 & ! [M6: nat] :
% 0.30/0.52 ( ( ord_less_nat @ M6 @ N4 )
% 0.30/0.52 => ~ ( P4 @ M6 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % exists_least_iff
% 0.30/0.52 thf(fact_556_linorder__less__wlog,axiom,
% 0.30/0.52 ! [P2: real > real > $o,A: real,B: real] :
% 0.30/0.52 ( ! [A3: real,B3: real] :
% 0.30/0.52 ( ( ord_less_real @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: real] : ( P2 @ A3 @ A3 )
% 0.30/0.52 => ( ! [A3: real,B3: real] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_less_wlog
% 0.30/0.52 thf(fact_557_linorder__less__wlog,axiom,
% 0.30/0.52 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 0.30/0.52 ( ! [A3: rat,B3: rat] :
% 0.30/0.52 ( ( ord_less_rat @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: rat] : ( P2 @ A3 @ A3 )
% 0.30/0.52 => ( ! [A3: rat,B3: rat] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_less_wlog
% 0.30/0.52 thf(fact_558_linorder__less__wlog,axiom,
% 0.30/0.52 ! [P2: num > num > $o,A: num,B: num] :
% 0.30/0.52 ( ! [A3: num,B3: num] :
% 0.30/0.52 ( ( ord_less_num @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: num] : ( P2 @ A3 @ A3 )
% 0.30/0.52 => ( ! [A3: num,B3: num] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_less_wlog
% 0.30/0.52 thf(fact_559_linorder__less__wlog,axiom,
% 0.30/0.52 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 0.30/0.52 ( ! [A3: nat,B3: nat] :
% 0.30/0.52 ( ( ord_less_nat @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: nat] : ( P2 @ A3 @ A3 )
% 0.30/0.52 => ( ! [A3: nat,B3: nat] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_less_wlog
% 0.30/0.52 thf(fact_560_linorder__less__wlog,axiom,
% 0.30/0.52 ! [P2: int > int > $o,A: int,B: int] :
% 0.30/0.52 ( ! [A3: int,B3: int] :
% 0.30/0.52 ( ( ord_less_int @ A3 @ B3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( ! [A3: int] : ( P2 @ A3 @ A3 )
% 0.30/0.52 => ( ! [A3: int,B3: int] :
% 0.30/0.52 ( ( P2 @ B3 @ A3 )
% 0.30/0.52 => ( P2 @ A3 @ B3 ) )
% 0.30/0.52 => ( P2 @ A @ B ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_less_wlog
% 0.30/0.52 thf(fact_561_order_Ostrict__trans,axiom,
% 0.30/0.52 ! [A: real,B: real,C2: real] :
% 0.30/0.52 ( ( ord_less_real @ A @ B )
% 0.30/0.52 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.52 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_trans
% 0.30/0.52 thf(fact_562_order_Ostrict__trans,axiom,
% 0.30/0.52 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_rat @ A @ B )
% 0.30/0.52 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.52 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_trans
% 0.30/0.52 thf(fact_563_order_Ostrict__trans,axiom,
% 0.30/0.52 ! [A: num,B: num,C2: num] :
% 0.30/0.52 ( ( ord_less_num @ A @ B )
% 0.30/0.52 => ( ( ord_less_num @ B @ C2 )
% 0.30/0.52 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_trans
% 0.30/0.52 thf(fact_564_order_Ostrict__trans,axiom,
% 0.30/0.52 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_nat @ A @ B )
% 0.30/0.52 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.52 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_trans
% 0.30/0.52 thf(fact_565_order_Ostrict__trans,axiom,
% 0.30/0.52 ! [A: int,B: int,C2: int] :
% 0.30/0.52 ( ( ord_less_int @ A @ B )
% 0.30/0.52 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.52 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_trans
% 0.30/0.52 thf(fact_566_not__less__iff__gr__or__eq,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.30/0.52 = ( ( ord_less_real @ Y @ X )
% 0.30/0.52 | ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % not_less_iff_gr_or_eq
% 0.30/0.52 thf(fact_567_not__less__iff__gr__or__eq,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.30/0.52 = ( ( ord_less_rat @ Y @ X )
% 0.30/0.52 | ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % not_less_iff_gr_or_eq
% 0.30/0.52 thf(fact_568_not__less__iff__gr__or__eq,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.30/0.52 = ( ( ord_less_num @ Y @ X )
% 0.30/0.52 | ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % not_less_iff_gr_or_eq
% 0.30/0.52 thf(fact_569_not__less__iff__gr__or__eq,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.30/0.52 = ( ( ord_less_nat @ Y @ X )
% 0.30/0.52 | ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % not_less_iff_gr_or_eq
% 0.30/0.52 thf(fact_570_not__less__iff__gr__or__eq,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.30/0.52 = ( ( ord_less_int @ Y @ X )
% 0.30/0.52 | ( X = Y ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % not_less_iff_gr_or_eq
% 0.30/0.52 thf(fact_571_dual__order_Ostrict__trans,axiom,
% 0.30/0.52 ! [B: real,A: real,C2: real] :
% 0.30/0.52 ( ( ord_less_real @ B @ A )
% 0.30/0.52 => ( ( ord_less_real @ C2 @ B )
% 0.30/0.52 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_trans
% 0.30/0.52 thf(fact_572_dual__order_Ostrict__trans,axiom,
% 0.30/0.52 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.52 ( ( ord_less_rat @ B @ A )
% 0.30/0.52 => ( ( ord_less_rat @ C2 @ B )
% 0.30/0.52 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_trans
% 0.30/0.52 thf(fact_573_dual__order_Ostrict__trans,axiom,
% 0.30/0.52 ! [B: num,A: num,C2: num] :
% 0.30/0.52 ( ( ord_less_num @ B @ A )
% 0.30/0.52 => ( ( ord_less_num @ C2 @ B )
% 0.30/0.52 => ( ord_less_num @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_trans
% 0.30/0.52 thf(fact_574_dual__order_Ostrict__trans,axiom,
% 0.30/0.52 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.52 ( ( ord_less_nat @ B @ A )
% 0.30/0.52 => ( ( ord_less_nat @ C2 @ B )
% 0.30/0.52 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_trans
% 0.30/0.52 thf(fact_575_dual__order_Ostrict__trans,axiom,
% 0.30/0.52 ! [B: int,A: int,C2: int] :
% 0.30/0.52 ( ( ord_less_int @ B @ A )
% 0.30/0.52 => ( ( ord_less_int @ C2 @ B )
% 0.30/0.52 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_trans
% 0.30/0.52 thf(fact_576_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_real @ A @ B )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_implies_not_eq
% 0.30/0.52 thf(fact_577_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_rat @ A @ B )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_implies_not_eq
% 0.30/0.52 thf(fact_578_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [A: num,B: num] :
% 0.30/0.52 ( ( ord_less_num @ A @ B )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_implies_not_eq
% 0.30/0.52 thf(fact_579_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_nat @ A @ B )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_implies_not_eq
% 0.30/0.52 thf(fact_580_order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_int @ A @ B )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % order.strict_implies_not_eq
% 0.30/0.52 thf(fact_581_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [B: real,A: real] :
% 0.30/0.52 ( ( ord_less_real @ B @ A )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_implies_not_eq
% 0.30/0.52 thf(fact_582_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [B: rat,A: rat] :
% 0.30/0.52 ( ( ord_less_rat @ B @ A )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_implies_not_eq
% 0.30/0.52 thf(fact_583_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [B: num,A: num] :
% 0.30/0.52 ( ( ord_less_num @ B @ A )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_implies_not_eq
% 0.30/0.52 thf(fact_584_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [B: nat,A: nat] :
% 0.30/0.52 ( ( ord_less_nat @ B @ A )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_implies_not_eq
% 0.30/0.52 thf(fact_585_dual__order_Ostrict__implies__not__eq,axiom,
% 0.30/0.52 ! [B: int,A: int] :
% 0.30/0.52 ( ( ord_less_int @ B @ A )
% 0.30/0.52 => ( A != B ) ) ).
% 0.30/0.52
% 0.30/0.52 % dual_order.strict_implies_not_eq
% 0.30/0.52 thf(fact_586_nat__neq__iff,axiom,
% 0.30/0.52 ! [M2: nat,N: nat] :
% 0.30/0.52 ( ( M2 != N )
% 0.30/0.52 = ( ( ord_less_nat @ M2 @ N )
% 0.30/0.52 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_neq_iff
% 0.30/0.52 thf(fact_587_less__not__refl,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.52
% 0.30/0.52 % less_not_refl
% 0.30/0.52 thf(fact_588_less__not__refl2,axiom,
% 0.30/0.52 ! [N: nat,M2: nat] :
% 0.30/0.52 ( ( ord_less_nat @ N @ M2 )
% 0.30/0.52 => ( M2 != N ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_not_refl2
% 0.30/0.52 thf(fact_589_less__not__refl3,axiom,
% 0.30/0.52 ! [S2: nat,T: nat] :
% 0.30/0.52 ( ( ord_less_nat @ S2 @ T )
% 0.30/0.52 => ( S2 != T ) ) ).
% 0.30/0.52
% 0.30/0.52 % less_not_refl3
% 0.30/0.52 thf(fact_590_less__irrefl__nat,axiom,
% 0.30/0.52 ! [N: nat] :
% 0.30/0.52 ~ ( ord_less_nat @ N @ N ) ).
% 0.30/0.52
% 0.30/0.52 % less_irrefl_nat
% 0.30/0.52 thf(fact_591_nat__less__induct,axiom,
% 0.30/0.52 ! [P2: nat > $o,N: nat] :
% 0.30/0.52 ( ! [N3: nat] :
% 0.30/0.52 ( ! [M3: nat] :
% 0.30/0.52 ( ( ord_less_nat @ M3 @ N3 )
% 0.30/0.52 => ( P2 @ M3 ) )
% 0.30/0.52 => ( P2 @ N3 ) )
% 0.30/0.52 => ( P2 @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % nat_less_induct
% 0.30/0.52 thf(fact_592_infinite__descent,axiom,
% 0.30/0.52 ! [P2: nat > $o,N: nat] :
% 0.30/0.52 ( ! [N3: nat] :
% 0.30/0.52 ( ~ ( P2 @ N3 )
% 0.30/0.52 => ? [M3: nat] :
% 0.30/0.52 ( ( ord_less_nat @ M3 @ N3 )
% 0.30/0.52 & ~ ( P2 @ M3 ) ) )
% 0.30/0.52 => ( P2 @ N ) ) ).
% 0.30/0.52
% 0.30/0.52 % infinite_descent
% 0.30/0.52 thf(fact_593_linorder__neqE__nat,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_nat @ X @ Y )
% 0.30/0.52 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE_nat
% 0.30/0.52 thf(fact_594_linorder__neqE,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_real @ X @ Y )
% 0.30/0.52 => ( ord_less_real @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE
% 0.30/0.52 thf(fact_595_linorder__neqE,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_rat @ X @ Y )
% 0.30/0.52 => ( ord_less_rat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE
% 0.30/0.52 thf(fact_596_linorder__neqE,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_num @ X @ Y )
% 0.30/0.52 => ( ord_less_num @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE
% 0.30/0.52 thf(fact_597_linorder__neqE,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_nat @ X @ Y )
% 0.30/0.52 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE
% 0.30/0.52 thf(fact_598_linorder__neqE,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 => ( ~ ( ord_less_int @ X @ Y )
% 0.30/0.52 => ( ord_less_int @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neqE
% 0.30/0.52 thf(fact_599_order__less__asym,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ( ord_less_real @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym
% 0.30/0.52 thf(fact_600_order__less__asym,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( ord_less_rat @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym
% 0.30/0.52 thf(fact_601_order__less__asym,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( ord_less_num @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym
% 0.30/0.52 thf(fact_602_order__less__asym,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( ord_less_nat @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym
% 0.30/0.52 thf(fact_603_order__less__asym,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( ord_less_int @ X @ Y )
% 0.30/0.52 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym
% 0.30/0.52 thf(fact_604_linorder__neq__iff,axiom,
% 0.30/0.52 ! [X: real,Y: real] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 = ( ( ord_less_real @ X @ Y )
% 0.30/0.52 | ( ord_less_real @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neq_iff
% 0.30/0.52 thf(fact_605_linorder__neq__iff,axiom,
% 0.30/0.52 ! [X: rat,Y: rat] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 = ( ( ord_less_rat @ X @ Y )
% 0.30/0.52 | ( ord_less_rat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neq_iff
% 0.30/0.52 thf(fact_606_linorder__neq__iff,axiom,
% 0.30/0.52 ! [X: num,Y: num] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 = ( ( ord_less_num @ X @ Y )
% 0.30/0.52 | ( ord_less_num @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neq_iff
% 0.30/0.52 thf(fact_607_linorder__neq__iff,axiom,
% 0.30/0.52 ! [X: nat,Y: nat] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 = ( ( ord_less_nat @ X @ Y )
% 0.30/0.52 | ( ord_less_nat @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neq_iff
% 0.30/0.52 thf(fact_608_linorder__neq__iff,axiom,
% 0.30/0.52 ! [X: int,Y: int] :
% 0.30/0.52 ( ( X != Y )
% 0.30/0.52 = ( ( ord_less_int @ X @ Y )
% 0.30/0.52 | ( ord_less_int @ Y @ X ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % linorder_neq_iff
% 0.30/0.52 thf(fact_609_order__less__asym_H,axiom,
% 0.30/0.52 ! [A: real,B: real] :
% 0.30/0.52 ( ( ord_less_real @ A @ B )
% 0.30/0.52 => ~ ( ord_less_real @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym'
% 0.30/0.52 thf(fact_610_order__less__asym_H,axiom,
% 0.30/0.52 ! [A: rat,B: rat] :
% 0.30/0.52 ( ( ord_less_rat @ A @ B )
% 0.30/0.52 => ~ ( ord_less_rat @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym'
% 0.30/0.52 thf(fact_611_order__less__asym_H,axiom,
% 0.30/0.52 ! [A: num,B: num] :
% 0.30/0.52 ( ( ord_less_num @ A @ B )
% 0.30/0.52 => ~ ( ord_less_num @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym'
% 0.30/0.52 thf(fact_612_order__less__asym_H,axiom,
% 0.30/0.52 ! [A: nat,B: nat] :
% 0.30/0.52 ( ( ord_less_nat @ A @ B )
% 0.30/0.52 => ~ ( ord_less_nat @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym'
% 0.30/0.52 thf(fact_613_order__less__asym_H,axiom,
% 0.30/0.52 ! [A: int,B: int] :
% 0.30/0.52 ( ( ord_less_int @ A @ B )
% 0.30/0.52 => ~ ( ord_less_int @ B @ A ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_asym'
% 0.30/0.52 thf(fact_614_order__less__trans,axiom,
% 0.30/0.52 ! [X: real,Y: real,Z3: real] :
% 0.30/0.52 ( ( ord_less_real @ X @ Y )
% 0.30/0.52 => ( ( ord_less_real @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_trans
% 0.30/0.52 thf(fact_615_order__less__trans,axiom,
% 0.30/0.52 ! [X: rat,Y: rat,Z3: rat] :
% 0.30/0.52 ( ( ord_less_rat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_rat @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_trans
% 0.30/0.52 thf(fact_616_order__less__trans,axiom,
% 0.30/0.52 ! [X: num,Y: num,Z3: num] :
% 0.30/0.52 ( ( ord_less_num @ X @ Y )
% 0.30/0.52 => ( ( ord_less_num @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_trans
% 0.30/0.52 thf(fact_617_order__less__trans,axiom,
% 0.30/0.52 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.52 ( ( ord_less_nat @ X @ Y )
% 0.30/0.52 => ( ( ord_less_nat @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_trans
% 0.30/0.52 thf(fact_618_order__less__trans,axiom,
% 0.30/0.52 ! [X: int,Y: int,Z3: int] :
% 0.30/0.52 ( ( ord_less_int @ X @ Y )
% 0.30/0.52 => ( ( ord_less_int @ Y @ Z3 )
% 0.30/0.52 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % order_less_trans
% 0.30/0.52 thf(fact_619_ord__eq__less__subst,axiom,
% 0.30/0.52 ! [A: real,F2: real > real,B: real,C2: real] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.52 => ( ! [X3: real,Y3: real] :
% 0.30/0.52 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_subst
% 0.30/0.52 thf(fact_620_ord__eq__less__subst,axiom,
% 0.30/0.52 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.52 => ( ! [X3: real,Y3: real] :
% 0.30/0.52 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_subst
% 0.30/0.52 thf(fact_621_ord__eq__less__subst,axiom,
% 0.30/0.52 ! [A: num,F2: real > num,B: real,C2: real] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.52 => ( ! [X3: real,Y3: real] :
% 0.30/0.52 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_subst
% 0.30/0.52 thf(fact_622_ord__eq__less__subst,axiom,
% 0.30/0.52 ! [A: nat,F2: real > nat,B: real,C2: real] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.52 => ( ! [X3: real,Y3: real] :
% 0.30/0.52 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_subst
% 0.30/0.52 thf(fact_623_ord__eq__less__subst,axiom,
% 0.30/0.52 ! [A: int,F2: real > int,B: real,C2: real] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.52 => ( ! [X3: real,Y3: real] :
% 0.30/0.52 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.52 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.52 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.52
% 0.30/0.52 % ord_eq_less_subst
% 0.30/0.52 thf(fact_624_ord__eq__less__subst,axiom,
% 0.30/0.52 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 0.30/0.52 ( ( A
% 0.30/0.52 = ( F2 @ B ) )
% 0.30/0.52 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.52 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_eq_less_subst
% 0.30/0.53 thf(fact_625_ord__eq__less__subst,axiom,
% 0.30/0.53 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 0.30/0.53 ( ( A
% 0.30/0.53 = ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_eq_less_subst
% 0.30/0.53 thf(fact_626_ord__eq__less__subst,axiom,
% 0.30/0.53 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 0.30/0.53 ( ( A
% 0.30/0.53 = ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_eq_less_subst
% 0.30/0.53 thf(fact_627_ord__eq__less__subst,axiom,
% 0.30/0.53 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 0.30/0.53 ( ( A
% 0.30/0.53 = ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_eq_less_subst
% 0.30/0.53 thf(fact_628_ord__eq__less__subst,axiom,
% 0.30/0.53 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 0.30/0.53 ( ( A
% 0.30/0.53 = ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_eq_less_subst
% 0.30/0.53 thf(fact_629_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_630_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_631_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > num,C2: num] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_632_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_633_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > int,C2: int] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_634_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_635_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_636_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_637_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_638_ord__less__eq__subst,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ( F2 @ B )
% 0.30/0.53 = C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % ord_less_eq_subst
% 0.30/0.53 thf(fact_639_order__less__irrefl,axiom,
% 0.30/0.53 ! [X: real] :
% 0.30/0.53 ~ ( ord_less_real @ X @ X ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_irrefl
% 0.30/0.53 thf(fact_640_order__less__irrefl,axiom,
% 0.30/0.53 ! [X: rat] :
% 0.30/0.53 ~ ( ord_less_rat @ X @ X ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_irrefl
% 0.30/0.53 thf(fact_641_order__less__irrefl,axiom,
% 0.30/0.53 ! [X: num] :
% 0.30/0.53 ~ ( ord_less_num @ X @ X ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_irrefl
% 0.30/0.53 thf(fact_642_order__less__irrefl,axiom,
% 0.30/0.53 ! [X: nat] :
% 0.30/0.53 ~ ( ord_less_nat @ X @ X ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_irrefl
% 0.30/0.53 thf(fact_643_order__less__irrefl,axiom,
% 0.30/0.53 ! [X: int] :
% 0.30/0.53 ~ ( ord_less_int @ X @ X ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_irrefl
% 0.30/0.53 thf(fact_644_order__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: real > real,B: real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_645_order__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_646_order__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: num > real,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_647_order__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: nat > real,B: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_648_order__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: int > real,B: int,C2: int] :
% 0.30/0.53 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.53 => ( ! [X3: int,Y3: int] :
% 0.30/0.53 ( ( ord_less_int @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_649_order__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 0.30/0.53 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_650_order__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_651_order__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_652_order__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_653_order__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 0.30/0.53 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.53 => ( ! [X3: int,Y3: int] :
% 0.30/0.53 ( ( ord_less_int @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst1
% 0.30/0.53 thf(fact_654_order__less__subst2,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_655_order__less__subst2,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_656_order__less__subst2,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > num,C2: num] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_657_order__less__subst2,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_658_order__less__subst2,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > int,C2: int] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_659_order__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_660_order__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_661_order__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_662_order__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_663_order__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_subst2
% 0.30/0.53 thf(fact_664_order__less__not__sym,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_not_sym
% 0.30/0.53 thf(fact_665_order__less__not__sym,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_not_sym
% 0.30/0.53 thf(fact_666_order__less__not__sym,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_not_sym
% 0.30/0.53 thf(fact_667_order__less__not__sym,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_not_sym
% 0.30/0.53 thf(fact_668_order__less__not__sym,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_not_sym
% 0.30/0.53 thf(fact_669_order__less__imp__triv,axiom,
% 0.30/0.53 ! [X: real,Y: real,P2: $o] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( ( ord_less_real @ Y @ X )
% 0.30/0.53 => P2 ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_triv
% 0.30/0.53 thf(fact_670_order__less__imp__triv,axiom,
% 0.30/0.53 ! [X: rat,Y: rat,P2: $o] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_rat @ Y @ X )
% 0.30/0.53 => P2 ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_triv
% 0.30/0.53 thf(fact_671_order__less__imp__triv,axiom,
% 0.30/0.53 ! [X: num,Y: num,P2: $o] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 => ( ( ord_less_num @ Y @ X )
% 0.30/0.53 => P2 ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_triv
% 0.30/0.53 thf(fact_672_order__less__imp__triv,axiom,
% 0.30/0.53 ! [X: nat,Y: nat,P2: $o] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_nat @ Y @ X )
% 0.30/0.53 => P2 ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_triv
% 0.30/0.53 thf(fact_673_order__less__imp__triv,axiom,
% 0.30/0.53 ! [X: int,Y: int,P2: $o] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 => ( ( ord_less_int @ Y @ X )
% 0.30/0.53 => P2 ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_triv
% 0.30/0.53 thf(fact_674_linorder__less__linear,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 | ( X = Y )
% 0.30/0.53 | ( ord_less_real @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_less_linear
% 0.30/0.53 thf(fact_675_linorder__less__linear,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 | ( X = Y )
% 0.30/0.53 | ( ord_less_rat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_less_linear
% 0.30/0.53 thf(fact_676_linorder__less__linear,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 | ( X = Y )
% 0.30/0.53 | ( ord_less_num @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_less_linear
% 0.30/0.53 thf(fact_677_linorder__less__linear,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 | ( X = Y )
% 0.30/0.53 | ( ord_less_nat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_less_linear
% 0.30/0.53 thf(fact_678_linorder__less__linear,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 | ( X = Y )
% 0.30/0.53 | ( ord_less_int @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_less_linear
% 0.30/0.53 thf(fact_679_order__less__imp__not__eq,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( X != Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq
% 0.30/0.53 thf(fact_680_order__less__imp__not__eq,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( X != Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq
% 0.30/0.53 thf(fact_681_order__less__imp__not__eq,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 => ( X != Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq
% 0.30/0.53 thf(fact_682_order__less__imp__not__eq,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ( X != Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq
% 0.30/0.53 thf(fact_683_order__less__imp__not__eq,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 => ( X != Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq
% 0.30/0.53 thf(fact_684_order__less__imp__not__eq2,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( Y != X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq2
% 0.30/0.53 thf(fact_685_order__less__imp__not__eq2,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( Y != X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq2
% 0.30/0.53 thf(fact_686_order__less__imp__not__eq2,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 => ( Y != X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq2
% 0.30/0.53 thf(fact_687_order__less__imp__not__eq2,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ( Y != X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq2
% 0.30/0.53 thf(fact_688_order__less__imp__not__eq2,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 => ( Y != X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_eq2
% 0.30/0.53 thf(fact_689_order__less__imp__not__less,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_real @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_less
% 0.30/0.53 thf(fact_690_order__less__imp__not__less,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_less
% 0.30/0.53 thf(fact_691_order__less__imp__not__less,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_num @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_less
% 0.30/0.53 thf(fact_692_order__less__imp__not__less,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_less
% 0.30/0.53 thf(fact_693_order__less__imp__not__less,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 => ~ ( ord_less_int @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_not_less
% 0.30/0.53 thf(fact_694_less__numeral__extra_I4_J,axiom,
% 0.30/0.53 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(4)
% 0.30/0.53 thf(fact_695_less__numeral__extra_I4_J,axiom,
% 0.30/0.53 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(4)
% 0.30/0.53 thf(fact_696_less__numeral__extra_I4_J,axiom,
% 0.30/0.53 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(4)
% 0.30/0.53 thf(fact_697_less__numeral__extra_I4_J,axiom,
% 0.30/0.53 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(4)
% 0.30/0.53 thf(fact_698_less__numeral__extra_I4_J,axiom,
% 0.30/0.53 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(4)
% 0.30/0.53 thf(fact_699_one__reorient,axiom,
% 0.30/0.53 ! [X: code_integer] :
% 0.30/0.53 ( ( one_one_Code_integer = X )
% 0.30/0.53 = ( X = one_one_Code_integer ) ) ).
% 0.30/0.53
% 0.30/0.53 % one_reorient
% 0.30/0.53 thf(fact_700_one__reorient,axiom,
% 0.30/0.53 ! [X: complex] :
% 0.30/0.53 ( ( one_one_complex = X )
% 0.30/0.53 = ( X = one_one_complex ) ) ).
% 0.30/0.53
% 0.30/0.53 % one_reorient
% 0.30/0.53 thf(fact_701_one__reorient,axiom,
% 0.30/0.53 ! [X: real] :
% 0.30/0.53 ( ( one_one_real = X )
% 0.30/0.53 = ( X = one_one_real ) ) ).
% 0.30/0.53
% 0.30/0.53 % one_reorient
% 0.30/0.53 thf(fact_702_one__reorient,axiom,
% 0.30/0.53 ! [X: nat] :
% 0.30/0.53 ( ( one_one_nat = X )
% 0.30/0.53 = ( X = one_one_nat ) ) ).
% 0.30/0.53
% 0.30/0.53 % one_reorient
% 0.30/0.53 thf(fact_703_one__reorient,axiom,
% 0.30/0.53 ! [X: int] :
% 0.30/0.53 ( ( one_one_int = X )
% 0.30/0.53 = ( X = one_one_int ) ) ).
% 0.30/0.53
% 0.30/0.53 % one_reorient
% 0.30/0.53 thf(fact_704_less__numeral__extra_I1_J,axiom,
% 0.30/0.53 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(1)
% 0.30/0.53 thf(fact_705_less__numeral__extra_I1_J,axiom,
% 0.30/0.53 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(1)
% 0.30/0.53 thf(fact_706_less__numeral__extra_I1_J,axiom,
% 0.30/0.53 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(1)
% 0.30/0.53 thf(fact_707_less__numeral__extra_I1_J,axiom,
% 0.30/0.53 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(1)
% 0.30/0.53 thf(fact_708_less__numeral__extra_I1_J,axiom,
% 0.30/0.53 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(1)
% 0.30/0.53 thf(fact_709_not__one__less__zero,axiom,
% 0.30/0.53 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.30/0.53
% 0.30/0.53 % not_one_less_zero
% 0.30/0.53 thf(fact_710_not__one__less__zero,axiom,
% 0.30/0.53 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.30/0.53
% 0.30/0.53 % not_one_less_zero
% 0.30/0.53 thf(fact_711_not__one__less__zero,axiom,
% 0.30/0.53 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.30/0.53
% 0.30/0.53 % not_one_less_zero
% 0.30/0.53 thf(fact_712_not__one__less__zero,axiom,
% 0.30/0.53 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.30/0.53
% 0.30/0.53 % not_one_less_zero
% 0.30/0.53 thf(fact_713_not__one__less__zero,axiom,
% 0.30/0.53 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.30/0.53
% 0.30/0.53 % not_one_less_zero
% 0.30/0.53 thf(fact_714_zero__less__one,axiom,
% 0.30/0.53 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.53
% 0.30/0.53 % zero_less_one
% 0.30/0.53 thf(fact_715_zero__less__one,axiom,
% 0.30/0.53 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.30/0.53
% 0.30/0.53 % zero_less_one
% 0.30/0.53 thf(fact_716_zero__less__one,axiom,
% 0.30/0.53 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.53
% 0.30/0.53 % zero_less_one
% 0.30/0.53 thf(fact_717_zero__less__one,axiom,
% 0.30/0.53 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.53
% 0.30/0.53 % zero_less_one
% 0.30/0.53 thf(fact_718_zero__less__one,axiom,
% 0.30/0.53 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.30/0.53
% 0.30/0.53 % zero_less_one
% 0.30/0.53 thf(fact_719_lift__Suc__mono__less__iff,axiom,
% 0.30/0.53 ! [F2: nat > real,N: nat,M2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_real @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 0.30/0.53 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less_iff
% 0.30/0.53 thf(fact_720_lift__Suc__mono__less__iff,axiom,
% 0.30/0.53 ! [F2: nat > rat,N: nat,M2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_rat @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 0.30/0.53 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less_iff
% 0.30/0.53 thf(fact_721_lift__Suc__mono__less__iff,axiom,
% 0.30/0.53 ! [F2: nat > num,N: nat,M2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_num @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 0.30/0.53 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less_iff
% 0.30/0.53 thf(fact_722_lift__Suc__mono__less__iff,axiom,
% 0.30/0.53 ! [F2: nat > nat,N: nat,M2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 0.30/0.53 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less_iff
% 0.30/0.53 thf(fact_723_lift__Suc__mono__less__iff,axiom,
% 0.30/0.53 ! [F2: nat > int,N: nat,M2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_int @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 0.30/0.53 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less_iff
% 0.30/0.53 thf(fact_724_lift__Suc__mono__less,axiom,
% 0.30/0.53 ! [F2: nat > real,N: nat,N2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_nat @ N @ N2 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less
% 0.30/0.53 thf(fact_725_lift__Suc__mono__less,axiom,
% 0.30/0.53 ! [F2: nat > rat,N: nat,N2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_nat @ N @ N2 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less
% 0.30/0.53 thf(fact_726_lift__Suc__mono__less,axiom,
% 0.30/0.53 ! [F2: nat > num,N: nat,N2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_nat @ N @ N2 )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less
% 0.30/0.53 thf(fact_727_lift__Suc__mono__less,axiom,
% 0.30/0.53 ! [F2: nat > nat,N: nat,N2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_nat @ N @ N2 )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less
% 0.30/0.53 thf(fact_728_lift__Suc__mono__less,axiom,
% 0.30/0.53 ! [F2: nat > int,N: nat,N2: nat] :
% 0.30/0.53 ( ! [N3: nat] : ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.30/0.53 => ( ( ord_less_nat @ N @ N2 )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % lift_Suc_mono_less
% 0.30/0.53 thf(fact_729_less__1__mult,axiom,
% 0.30/0.53 ! [M2: code_integer,N: code_integer] :
% 0.30/0.53 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M2 )
% 0.30/0.53 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M2 @ N ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_1_mult
% 0.30/0.53 thf(fact_730_less__1__mult,axiom,
% 0.30/0.53 ! [M2: real,N: real] :
% 0.30/0.53 ( ( ord_less_real @ one_one_real @ M2 )
% 0.30/0.53 => ( ( ord_less_real @ one_one_real @ N )
% 0.30/0.53 => ( ord_less_real @ one_one_real @ ( times_times_real @ M2 @ N ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_1_mult
% 0.30/0.53 thf(fact_731_less__1__mult,axiom,
% 0.30/0.53 ! [M2: rat,N: rat] :
% 0.30/0.53 ( ( ord_less_rat @ one_one_rat @ M2 )
% 0.30/0.53 => ( ( ord_less_rat @ one_one_rat @ N )
% 0.30/0.53 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_1_mult
% 0.30/0.53 thf(fact_732_less__1__mult,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ one_one_nat @ M2 )
% 0.30/0.53 => ( ( ord_less_nat @ one_one_nat @ N )
% 0.30/0.53 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_1_mult
% 0.30/0.53 thf(fact_733_less__1__mult,axiom,
% 0.30/0.53 ! [M2: int,N: int] :
% 0.30/0.53 ( ( ord_less_int @ one_one_int @ M2 )
% 0.30/0.53 => ( ( ord_less_int @ one_one_int @ N )
% 0.30/0.53 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_1_mult
% 0.30/0.53 thf(fact_734_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 0.30/0.53 ! [Uu: $o,Uv: $o,D: nat] :
% 0.30/0.53 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 0.30/0.53 = ( D = one_one_nat ) ) ).
% 0.30/0.53
% 0.30/0.53 % VEBT_internal.valid'.simps(1)
% 0.30/0.53 thf(fact_735_nat__induct__non__zero,axiom,
% 0.30/0.53 ! [N: nat,P2: nat > $o] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.53 => ( ( P2 @ one_one_nat )
% 0.30/0.53 => ( ! [N3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.30/0.53 => ( ( P2 @ N3 )
% 0.30/0.53 => ( P2 @ ( suc @ N3 ) ) ) )
% 0.30/0.53 => ( P2 @ N ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nat_induct_non_zero
% 0.30/0.53 thf(fact_736_order__le__imp__less__or__eq,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ X @ Y )
% 0.30/0.53 => ( ( ord_less_real @ X @ Y )
% 0.30/0.53 | ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_imp_less_or_eq
% 0.30/0.53 thf(fact_737_order__le__imp__less__or__eq,axiom,
% 0.30/0.53 ! [X: set_nat,Y: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_set_nat @ X @ Y )
% 0.30/0.53 | ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_imp_less_or_eq
% 0.30/0.53 thf(fact_738_order__le__imp__less__or__eq,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 | ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_imp_less_or_eq
% 0.30/0.53 thf(fact_739_order__le__imp__less__or__eq,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.53 => ( ( ord_less_num @ X @ Y )
% 0.30/0.53 | ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_imp_less_or_eq
% 0.30/0.53 thf(fact_740_order__le__imp__less__or__eq,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 | ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_imp_less_or_eq
% 0.30/0.53 thf(fact_741_order__le__imp__less__or__eq,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.53 => ( ( ord_less_int @ X @ Y )
% 0.30/0.53 | ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_imp_less_or_eq
% 0.30/0.53 thf(fact_742_linorder__le__less__linear,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ X @ Y )
% 0.30/0.53 | ( ord_less_real @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_le_less_linear
% 0.30/0.53 thf(fact_743_linorder__le__less__linear,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.53 | ( ord_less_rat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_le_less_linear
% 0.30/0.53 thf(fact_744_linorder__le__less__linear,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.53 | ( ord_less_num @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_le_less_linear
% 0.30/0.53 thf(fact_745_linorder__le__less__linear,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.53 | ( ord_less_nat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_le_less_linear
% 0.30/0.53 thf(fact_746_linorder__le__less__linear,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.53 | ( ord_less_int @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_le_less_linear
% 0.30/0.53 thf(fact_747_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_748_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_749_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: num,B: num,F2: num > real,C2: real] :
% 0.30/0.53 ( ( ord_less_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_750_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: nat,B: nat,F2: nat > real,C2: real] :
% 0.30/0.53 ( ( ord_less_nat @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_751_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: int,B: int,F2: int > real,C2: real] :
% 0.30/0.53 ( ( ord_less_int @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: int,Y3: int] :
% 0.30/0.53 ( ( ord_less_int @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_752_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_753_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_754_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_755_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_nat @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_756_order__less__le__subst2,axiom,
% 0.30/0.53 ! [A: int,B: int,F2: int > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_int @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: int,Y3: int] :
% 0.30/0.53 ( ( ord_less_int @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst2
% 0.30/0.53 thf(fact_757_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_758_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_759_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_num @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_760_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_761_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_int @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_762_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: num > real,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_763_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_764_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: num,F2: num > num,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_num @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_765_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_766_order__less__le__subst1,axiom,
% 0.30/0.53 ! [A: int,F2: num > int,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_int @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_subst1
% 0.30/0.53 thf(fact_767_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_768_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_769_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_770_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_771_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_772_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: num,B: num,F2: num > real,C2: real] :
% 0.30/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_773_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_774_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: num,B: num,F2: num > num,C2: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_775_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_776_order__le__less__subst2,axiom,
% 0.30/0.53 ! [A: num,B: num,F2: num > int,C2: int] :
% 0.30/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst2
% 0.30/0.53 thf(fact_777_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: real > real,B: real,C2: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_778_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_779_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: num > real,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_780_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: nat > real,B: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_781_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: real,F2: int > real,B: int,C2: int] :
% 0.30/0.53 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.53 => ( ! [X3: int,Y3: int] :
% 0.30/0.53 ( ( ord_less_int @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_782_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.53 => ( ! [X3: real,Y3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_783_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: rat,Y3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_784_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_num @ B @ C2 )
% 0.30/0.53 => ( ! [X3: num,Y3: num] :
% 0.30/0.53 ( ( ord_less_num @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_785_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.53 => ( ! [X3: nat,Y3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_786_order__le__less__subst1,axiom,
% 0.30/0.53 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 0.30/0.53 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.53 => ( ! [X3: int,Y3: int] :
% 0.30/0.53 ( ( ord_less_int @ X3 @ Y3 )
% 0.30/0.53 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 0.30/0.53 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_subst1
% 0.30/0.53 thf(fact_787_order__less__le__trans,axiom,
% 0.30/0.53 ! [X: real,Y: real,Z3: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_real @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_trans
% 0.30/0.53 thf(fact_788_order__less__le__trans,axiom,
% 0.30/0.53 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_trans
% 0.30/0.53 thf(fact_789_order__less__le__trans,axiom,
% 0.30/0.53 ! [X: rat,Y: rat,Z3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_trans
% 0.30/0.53 thf(fact_790_order__less__le__trans,axiom,
% 0.30/0.53 ! [X: num,Y: num,Z3: num] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_num @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_trans
% 0.30/0.53 thf(fact_791_order__less__le__trans,axiom,
% 0.30/0.53 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_trans
% 0.30/0.53 thf(fact_792_order__less__le__trans,axiom,
% 0.30/0.53 ! [X: int,Y: int,Z3: int] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_int @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le_trans
% 0.30/0.53 thf(fact_793_order__le__less__trans,axiom,
% 0.30/0.53 ! [X: real,Y: real,Z3: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ X @ Y )
% 0.30/0.53 => ( ( ord_less_real @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_trans
% 0.30/0.53 thf(fact_794_order__le__less__trans,axiom,
% 0.30/0.53 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_set_nat @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_trans
% 0.30/0.53 thf(fact_795_order__le__less__trans,axiom,
% 0.30/0.53 ! [X: rat,Y: rat,Z3: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_rat @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_trans
% 0.30/0.53 thf(fact_796_order__le__less__trans,axiom,
% 0.30/0.53 ! [X: num,Y: num,Z3: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.53 => ( ( ord_less_num @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_trans
% 0.30/0.53 thf(fact_797_order__le__less__trans,axiom,
% 0.30/0.53 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_nat @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_trans
% 0.30/0.53 thf(fact_798_order__le__less__trans,axiom,
% 0.30/0.53 ! [X: int,Y: int,Z3: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.53 => ( ( ord_less_int @ Y @ Z3 )
% 0.30/0.53 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less_trans
% 0.30/0.53 thf(fact_799_order__neq__le__trans,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( A != B )
% 0.30/0.53 => ( ( ord_less_eq_real @ A @ B )
% 0.30/0.53 => ( ord_less_real @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_neq_le_trans
% 0.30/0.53 thf(fact_800_order__neq__le__trans,axiom,
% 0.30/0.53 ! [A: set_nat,B: set_nat] :
% 0.30/0.53 ( ( A != B )
% 0.30/0.53 => ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.53 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_neq_le_trans
% 0.30/0.53 thf(fact_801_order__neq__le__trans,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( A != B )
% 0.30/0.53 => ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_neq_le_trans
% 0.30/0.53 thf(fact_802_order__neq__le__trans,axiom,
% 0.30/0.53 ! [A: num,B: num] :
% 0.30/0.53 ( ( A != B )
% 0.30/0.53 => ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ord_less_num @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_neq_le_trans
% 0.30/0.53 thf(fact_803_order__neq__le__trans,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( A != B )
% 0.30/0.53 => ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.53 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_neq_le_trans
% 0.30/0.53 thf(fact_804_order__neq__le__trans,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( A != B )
% 0.30/0.53 => ( ( ord_less_eq_int @ A @ B )
% 0.30/0.53 => ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_neq_le_trans
% 0.30/0.53 thf(fact_805_order__le__neq__trans,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.53 => ( ( A != B )
% 0.30/0.53 => ( ord_less_real @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_neq_trans
% 0.30/0.53 thf(fact_806_order__le__neq__trans,axiom,
% 0.30/0.53 ! [A: set_nat,B: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.53 => ( ( A != B )
% 0.30/0.53 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_neq_trans
% 0.30/0.53 thf(fact_807_order__le__neq__trans,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ( A != B )
% 0.30/0.53 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_neq_trans
% 0.30/0.53 thf(fact_808_order__le__neq__trans,axiom,
% 0.30/0.53 ! [A: num,B: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ( A != B )
% 0.30/0.53 => ( ord_less_num @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_neq_trans
% 0.30/0.53 thf(fact_809_order__le__neq__trans,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.53 => ( ( A != B )
% 0.30/0.53 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_neq_trans
% 0.30/0.53 thf(fact_810_order__le__neq__trans,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.53 => ( ( A != B )
% 0.30/0.53 => ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_neq_trans
% 0.30/0.53 thf(fact_811_order__less__imp__le,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_le
% 0.30/0.53 thf(fact_812_order__less__imp__le,axiom,
% 0.30/0.53 ! [X: set_nat,Y: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_le
% 0.30/0.53 thf(fact_813_order__less__imp__le,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_le
% 0.30/0.53 thf(fact_814_order__less__imp__le,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_num @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_num @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_le
% 0.30/0.53 thf(fact_815_order__less__imp__le,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_le
% 0.30/0.53 thf(fact_816_order__less__imp__le,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_int @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_int @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_imp_le
% 0.30/0.53 thf(fact_817_linorder__not__less,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.30/0.53 = ( ord_less_eq_real @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_less
% 0.30/0.53 thf(fact_818_linorder__not__less,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.30/0.53 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_less
% 0.30/0.53 thf(fact_819_linorder__not__less,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.30/0.53 = ( ord_less_eq_num @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_less
% 0.30/0.53 thf(fact_820_linorder__not__less,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.30/0.53 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_less
% 0.30/0.53 thf(fact_821_linorder__not__less,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.30/0.53 = ( ord_less_eq_int @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_less
% 0.30/0.53 thf(fact_822_linorder__not__le,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 0.30/0.53 = ( ord_less_real @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_le
% 0.30/0.53 thf(fact_823_linorder__not__le,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 0.30/0.53 = ( ord_less_rat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_le
% 0.30/0.53 thf(fact_824_linorder__not__le,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 0.30/0.53 = ( ord_less_num @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_le
% 0.30/0.53 thf(fact_825_linorder__not__le,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 0.30/0.53 = ( ord_less_nat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_le
% 0.30/0.53 thf(fact_826_linorder__not__le,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 0.30/0.53 = ( ord_less_int @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % linorder_not_le
% 0.30/0.53 thf(fact_827_order__less__le,axiom,
% 0.30/0.53 ( ord_less_real
% 0.30/0.53 = ( ^ [X4: real,Y4: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.30/0.53 & ( X4 != Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le
% 0.30/0.53 thf(fact_828_order__less__le,axiom,
% 0.30/0.53 ( ord_less_set_nat
% 0.30/0.53 = ( ^ [X4: set_nat,Y4: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 0.30/0.53 & ( X4 != Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le
% 0.30/0.53 thf(fact_829_order__less__le,axiom,
% 0.30/0.53 ( ord_less_rat
% 0.30/0.53 = ( ^ [X4: rat,Y4: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.30/0.53 & ( X4 != Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le
% 0.30/0.53 thf(fact_830_order__less__le,axiom,
% 0.30/0.53 ( ord_less_num
% 0.30/0.53 = ( ^ [X4: num,Y4: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.30/0.53 & ( X4 != Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le
% 0.30/0.53 thf(fact_831_order__less__le,axiom,
% 0.30/0.53 ( ord_less_nat
% 0.30/0.53 = ( ^ [X4: nat,Y4: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.30/0.53 & ( X4 != Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le
% 0.30/0.53 thf(fact_832_order__less__le,axiom,
% 0.30/0.53 ( ord_less_int
% 0.30/0.53 = ( ^ [X4: int,Y4: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.30/0.53 & ( X4 != Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_less_le
% 0.30/0.53 thf(fact_833_order__le__less,axiom,
% 0.30/0.53 ( ord_less_eq_real
% 0.30/0.53 = ( ^ [X4: real,Y4: real] :
% 0.30/0.53 ( ( ord_less_real @ X4 @ Y4 )
% 0.30/0.53 | ( X4 = Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less
% 0.30/0.53 thf(fact_834_order__le__less,axiom,
% 0.30/0.53 ( ord_less_eq_set_nat
% 0.30/0.53 = ( ^ [X4: set_nat,Y4: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ X4 @ Y4 )
% 0.30/0.53 | ( X4 = Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less
% 0.30/0.53 thf(fact_835_order__le__less,axiom,
% 0.30/0.53 ( ord_less_eq_rat
% 0.30/0.53 = ( ^ [X4: rat,Y4: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X4 @ Y4 )
% 0.30/0.53 | ( X4 = Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less
% 0.30/0.53 thf(fact_836_order__le__less,axiom,
% 0.30/0.53 ( ord_less_eq_num
% 0.30/0.53 = ( ^ [X4: num,Y4: num] :
% 0.30/0.53 ( ( ord_less_num @ X4 @ Y4 )
% 0.30/0.53 | ( X4 = Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less
% 0.30/0.53 thf(fact_837_order__le__less,axiom,
% 0.30/0.53 ( ord_less_eq_nat
% 0.30/0.53 = ( ^ [X4: nat,Y4: nat] :
% 0.30/0.53 ( ( ord_less_nat @ X4 @ Y4 )
% 0.30/0.53 | ( X4 = Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less
% 0.30/0.53 thf(fact_838_order__le__less,axiom,
% 0.30/0.53 ( ord_less_eq_int
% 0.30/0.53 = ( ^ [X4: int,Y4: int] :
% 0.30/0.53 ( ( ord_less_int @ X4 @ Y4 )
% 0.30/0.53 | ( X4 = Y4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order_le_less
% 0.30/0.53 thf(fact_839_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [B: real,A: real] :
% 0.30/0.53 ( ( ord_less_real @ B @ A )
% 0.30/0.53 => ( ord_less_eq_real @ B @ A ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_implies_order
% 0.30/0.53 thf(fact_840_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [B: set_nat,A: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ B @ A )
% 0.30/0.53 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_implies_order
% 0.30/0.53 thf(fact_841_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [B: rat,A: rat] :
% 0.30/0.53 ( ( ord_less_rat @ B @ A )
% 0.30/0.53 => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_implies_order
% 0.30/0.53 thf(fact_842_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [B: num,A: num] :
% 0.30/0.53 ( ( ord_less_num @ B @ A )
% 0.30/0.53 => ( ord_less_eq_num @ B @ A ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_implies_order
% 0.30/0.53 thf(fact_843_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [B: nat,A: nat] :
% 0.30/0.53 ( ( ord_less_nat @ B @ A )
% 0.30/0.53 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_implies_order
% 0.30/0.53 thf(fact_844_dual__order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [B: int,A: int] :
% 0.30/0.53 ( ( ord_less_int @ B @ A )
% 0.30/0.53 => ( ord_less_eq_int @ B @ A ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_implies_order
% 0.30/0.53 thf(fact_845_order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_implies_order
% 0.30/0.53 thf(fact_846_order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [A: set_nat,B: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ A @ B )
% 0.30/0.53 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_implies_order
% 0.30/0.53 thf(fact_847_order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_implies_order
% 0.30/0.53 thf(fact_848_order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [A: num,B: num] :
% 0.30/0.53 ( ( ord_less_num @ A @ B )
% 0.30/0.53 => ( ord_less_eq_num @ A @ B ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_implies_order
% 0.30/0.53 thf(fact_849_order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ord_less_nat @ A @ B )
% 0.30/0.53 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_implies_order
% 0.30/0.53 thf(fact_850_order_Ostrict__implies__order,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ A @ B )
% 0.30/0.53 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_implies_order
% 0.30/0.53 thf(fact_851_dual__order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_real
% 0.30/0.53 = ( ^ [B4: real,A5: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ B4 @ A5 )
% 0.30/0.53 & ~ ( ord_less_eq_real @ A5 @ B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_not
% 0.30/0.53 thf(fact_852_dual__order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_set_nat
% 0.30/0.53 = ( ^ [B4: set_nat,A5: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 0.30/0.53 & ~ ( ord_less_eq_set_nat @ A5 @ B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_not
% 0.30/0.53 thf(fact_853_dual__order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_rat
% 0.30/0.53 = ( ^ [B4: rat,A5: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ B4 @ A5 )
% 0.30/0.53 & ~ ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_not
% 0.30/0.53 thf(fact_854_dual__order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_num
% 0.30/0.53 = ( ^ [B4: num,A5: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ B4 @ A5 )
% 0.30/0.53 & ~ ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_not
% 0.30/0.53 thf(fact_855_dual__order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_nat
% 0.30/0.53 = ( ^ [B4: nat,A5: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ B4 @ A5 )
% 0.30/0.53 & ~ ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_not
% 0.30/0.53 thf(fact_856_dual__order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_int
% 0.30/0.53 = ( ^ [B4: int,A5: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ B4 @ A5 )
% 0.30/0.53 & ~ ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_not
% 0.30/0.53 thf(fact_857_dual__order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [B: real,A: real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ B @ A )
% 0.30/0.53 => ( ( ord_less_eq_real @ C2 @ B )
% 0.30/0.53 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans2
% 0.30/0.53 thf(fact_858_dual__order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ B @ A )
% 0.30/0.53 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 0.30/0.53 => ( ord_less_set_nat @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans2
% 0.30/0.53 thf(fact_859_dual__order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ B @ A )
% 0.30/0.53 => ( ( ord_less_eq_rat @ C2 @ B )
% 0.30/0.53 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans2
% 0.30/0.53 thf(fact_860_dual__order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [B: num,A: num,C2: num] :
% 0.30/0.53 ( ( ord_less_num @ B @ A )
% 0.30/0.53 => ( ( ord_less_eq_num @ C2 @ B )
% 0.30/0.53 => ( ord_less_num @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans2
% 0.30/0.53 thf(fact_861_dual__order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_nat @ B @ A )
% 0.30/0.53 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.30/0.53 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans2
% 0.30/0.53 thf(fact_862_dual__order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [B: int,A: int,C2: int] :
% 0.30/0.53 ( ( ord_less_int @ B @ A )
% 0.30/0.53 => ( ( ord_less_eq_int @ C2 @ B )
% 0.30/0.53 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans2
% 0.30/0.53 thf(fact_863_dual__order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [B: real,A: real,C2: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ B @ A )
% 0.30/0.53 => ( ( ord_less_real @ C2 @ B )
% 0.30/0.53 => ( ord_less_real @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans1
% 0.30/0.53 thf(fact_864_dual__order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ B @ A )
% 0.30/0.53 => ( ( ord_less_set_nat @ C2 @ B )
% 0.30/0.53 => ( ord_less_set_nat @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans1
% 0.30/0.53 thf(fact_865_dual__order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.53 => ( ( ord_less_rat @ C2 @ B )
% 0.30/0.53 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans1
% 0.30/0.53 thf(fact_866_dual__order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [B: num,A: num,C2: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ B @ A )
% 0.30/0.53 => ( ( ord_less_num @ C2 @ B )
% 0.30/0.53 => ( ord_less_num @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans1
% 0.30/0.53 thf(fact_867_dual__order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.53 => ( ( ord_less_nat @ C2 @ B )
% 0.30/0.53 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans1
% 0.30/0.53 thf(fact_868_dual__order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [B: int,A: int,C2: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.53 => ( ( ord_less_int @ C2 @ B )
% 0.30/0.53 => ( ord_less_int @ C2 @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_trans1
% 0.30/0.53 thf(fact_869_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_real
% 0.30/0.53 = ( ^ [B4: real,A5: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ B4 @ A5 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_order
% 0.30/0.53 thf(fact_870_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_set_nat
% 0.30/0.53 = ( ^ [B4: set_nat,A5: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_order
% 0.30/0.53 thf(fact_871_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_rat
% 0.30/0.53 = ( ^ [B4: rat,A5: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ B4 @ A5 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_order
% 0.30/0.53 thf(fact_872_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_num
% 0.30/0.53 = ( ^ [B4: num,A5: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ B4 @ A5 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_order
% 0.30/0.53 thf(fact_873_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_nat
% 0.30/0.53 = ( ^ [B4: nat,A5: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ B4 @ A5 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_order
% 0.30/0.53 thf(fact_874_dual__order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_int
% 0.30/0.53 = ( ^ [B4: int,A5: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ B4 @ A5 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.strict_iff_order
% 0.30/0.53 thf(fact_875_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_real
% 0.30/0.53 = ( ^ [B4: real,A5: real] :
% 0.30/0.53 ( ( ord_less_real @ B4 @ A5 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.order_iff_strict
% 0.30/0.53 thf(fact_876_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_set_nat
% 0.30/0.53 = ( ^ [B4: set_nat,A5: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ B4 @ A5 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.order_iff_strict
% 0.30/0.53 thf(fact_877_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_rat
% 0.30/0.53 = ( ^ [B4: rat,A5: rat] :
% 0.30/0.53 ( ( ord_less_rat @ B4 @ A5 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.order_iff_strict
% 0.30/0.53 thf(fact_878_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_num
% 0.30/0.53 = ( ^ [B4: num,A5: num] :
% 0.30/0.53 ( ( ord_less_num @ B4 @ A5 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.order_iff_strict
% 0.30/0.53 thf(fact_879_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_nat
% 0.30/0.53 = ( ^ [B4: nat,A5: nat] :
% 0.30/0.53 ( ( ord_less_nat @ B4 @ A5 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.order_iff_strict
% 0.30/0.53 thf(fact_880_dual__order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_int
% 0.30/0.53 = ( ^ [B4: int,A5: int] :
% 0.30/0.53 ( ( ord_less_int @ B4 @ A5 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dual_order.order_iff_strict
% 0.30/0.53 thf(fact_881_dense__le__bounded,axiom,
% 0.30/0.53 ! [X: real,Y: real,Z3: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( ! [W: real] :
% 0.30/0.53 ( ( ord_less_real @ X @ W )
% 0.30/0.53 => ( ( ord_less_real @ W @ Y )
% 0.30/0.53 => ( ord_less_eq_real @ W @ Z3 ) ) )
% 0.30/0.53 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_le_bounded
% 0.30/0.53 thf(fact_882_dense__le__bounded,axiom,
% 0.30/0.53 ! [X: rat,Y: rat,Z3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( ! [W: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X @ W )
% 0.30/0.53 => ( ( ord_less_rat @ W @ Y )
% 0.30/0.53 => ( ord_less_eq_rat @ W @ Z3 ) ) )
% 0.30/0.53 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_le_bounded
% 0.30/0.53 thf(fact_883_dense__ge__bounded,axiom,
% 0.30/0.53 ! [Z3: real,X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_real @ Z3 @ X )
% 0.30/0.53 => ( ! [W: real] :
% 0.30/0.53 ( ( ord_less_real @ Z3 @ W )
% 0.30/0.53 => ( ( ord_less_real @ W @ X )
% 0.30/0.53 => ( ord_less_eq_real @ Y @ W ) ) )
% 0.30/0.53 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_ge_bounded
% 0.30/0.53 thf(fact_884_dense__ge__bounded,axiom,
% 0.30/0.53 ! [Z3: rat,X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_rat @ Z3 @ X )
% 0.30/0.53 => ( ! [W: rat] :
% 0.30/0.53 ( ( ord_less_rat @ Z3 @ W )
% 0.30/0.53 => ( ( ord_less_rat @ W @ X )
% 0.30/0.53 => ( ord_less_eq_rat @ Y @ W ) ) )
% 0.30/0.53 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_ge_bounded
% 0.30/0.53 thf(fact_885_order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_real
% 0.30/0.53 = ( ^ [A5: real,B4: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ A5 @ B4 )
% 0.30/0.53 & ~ ( ord_less_eq_real @ B4 @ A5 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_not
% 0.30/0.53 thf(fact_886_order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_set_nat
% 0.30/0.53 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 0.30/0.53 & ~ ( ord_less_eq_set_nat @ B4 @ A5 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_not
% 0.30/0.53 thf(fact_887_order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_rat
% 0.30/0.53 = ( ^ [A5: rat,B4: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A5 @ B4 )
% 0.30/0.53 & ~ ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_not
% 0.30/0.53 thf(fact_888_order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_num
% 0.30/0.53 = ( ^ [A5: num,B4: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ A5 @ B4 )
% 0.30/0.53 & ~ ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_not
% 0.30/0.53 thf(fact_889_order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_nat
% 0.30/0.53 = ( ^ [A5: nat,B4: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ A5 @ B4 )
% 0.30/0.53 & ~ ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_not
% 0.30/0.53 thf(fact_890_order_Ostrict__iff__not,axiom,
% 0.30/0.53 ( ord_less_int
% 0.30/0.53 = ( ^ [A5: int,B4: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ A5 @ B4 )
% 0.30/0.53 & ~ ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_not
% 0.30/0.53 thf(fact_891_order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [A: real,B: real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_real @ B @ C2 )
% 0.30/0.53 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans2
% 0.30/0.53 thf(fact_892_order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 0.30/0.53 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans2
% 0.30/0.53 thf(fact_893_order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.53 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans2
% 0.30/0.53 thf(fact_894_order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [A: num,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_num @ B @ C2 )
% 0.30/0.53 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans2
% 0.30/0.53 thf(fact_895_order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_nat @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.53 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans2
% 0.30/0.53 thf(fact_896_order_Ostrict__trans2,axiom,
% 0.30/0.53 ! [A: int,B: int,C2: int] :
% 0.30/0.53 ( ( ord_less_int @ A @ B )
% 0.30/0.53 => ( ( ord_less_eq_int @ B @ C2 )
% 0.30/0.53 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans2
% 0.30/0.53 thf(fact_897_order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [A: real,B: real,C2: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.53 => ( ord_less_real @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans1
% 0.30/0.53 thf(fact_898_order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.53 => ( ( ord_less_set_nat @ B @ C2 )
% 0.30/0.53 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans1
% 0.30/0.53 thf(fact_899_order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.53 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans1
% 0.30/0.53 thf(fact_900_order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [A: num,B: num,C2: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ A @ B )
% 0.30/0.53 => ( ( ord_less_num @ B @ C2 )
% 0.30/0.53 => ( ord_less_num @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans1
% 0.30/0.53 thf(fact_901_order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.53 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.53 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans1
% 0.30/0.53 thf(fact_902_order_Ostrict__trans1,axiom,
% 0.30/0.53 ! [A: int,B: int,C2: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.53 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.53 => ( ord_less_int @ A @ C2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_trans1
% 0.30/0.53 thf(fact_903_order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_real
% 0.30/0.53 = ( ^ [A5: real,B4: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ A5 @ B4 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_order
% 0.30/0.53 thf(fact_904_order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_set_nat
% 0.30/0.53 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_order
% 0.30/0.53 thf(fact_905_order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_rat
% 0.30/0.53 = ( ^ [A5: rat,B4: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ A5 @ B4 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_order
% 0.30/0.53 thf(fact_906_order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_num
% 0.30/0.53 = ( ^ [A5: num,B4: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ A5 @ B4 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_order
% 0.30/0.53 thf(fact_907_order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_nat
% 0.30/0.53 = ( ^ [A5: nat,B4: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ A5 @ B4 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_order
% 0.30/0.53 thf(fact_908_order_Ostrict__iff__order,axiom,
% 0.30/0.53 ( ord_less_int
% 0.30/0.53 = ( ^ [A5: int,B4: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ A5 @ B4 )
% 0.30/0.53 & ( A5 != B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.strict_iff_order
% 0.30/0.53 thf(fact_909_order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_real
% 0.30/0.53 = ( ^ [A5: real,B4: real] :
% 0.30/0.53 ( ( ord_less_real @ A5 @ B4 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.order_iff_strict
% 0.30/0.53 thf(fact_910_order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_set_nat
% 0.30/0.53 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.30/0.53 ( ( ord_less_set_nat @ A5 @ B4 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.order_iff_strict
% 0.30/0.53 thf(fact_911_order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_rat
% 0.30/0.53 = ( ^ [A5: rat,B4: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A5 @ B4 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.order_iff_strict
% 0.30/0.53 thf(fact_912_order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_num
% 0.30/0.53 = ( ^ [A5: num,B4: num] :
% 0.30/0.53 ( ( ord_less_num @ A5 @ B4 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.order_iff_strict
% 0.30/0.53 thf(fact_913_order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_nat
% 0.30/0.53 = ( ^ [A5: nat,B4: nat] :
% 0.30/0.53 ( ( ord_less_nat @ A5 @ B4 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.order_iff_strict
% 0.30/0.53 thf(fact_914_order_Oorder__iff__strict,axiom,
% 0.30/0.53 ( ord_less_eq_int
% 0.30/0.53 = ( ^ [A5: int,B4: int] :
% 0.30/0.53 ( ( ord_less_int @ A5 @ B4 )
% 0.30/0.53 | ( A5 = B4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % order.order_iff_strict
% 0.30/0.53 thf(fact_915_not__le__imp__less,axiom,
% 0.30/0.53 ! [Y: real,X: real] :
% 0.30/0.53 ( ~ ( ord_less_eq_real @ Y @ X )
% 0.30/0.53 => ( ord_less_real @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_le_imp_less
% 0.30/0.53 thf(fact_916_not__le__imp__less,axiom,
% 0.30/0.53 ! [Y: rat,X: rat] :
% 0.30/0.53 ( ~ ( ord_less_eq_rat @ Y @ X )
% 0.30/0.53 => ( ord_less_rat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_le_imp_less
% 0.30/0.53 thf(fact_917_not__le__imp__less,axiom,
% 0.30/0.53 ! [Y: num,X: num] :
% 0.30/0.53 ( ~ ( ord_less_eq_num @ Y @ X )
% 0.30/0.53 => ( ord_less_num @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_le_imp_less
% 0.30/0.53 thf(fact_918_not__le__imp__less,axiom,
% 0.30/0.53 ! [Y: nat,X: nat] :
% 0.30/0.53 ( ~ ( ord_less_eq_nat @ Y @ X )
% 0.30/0.53 => ( ord_less_nat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_le_imp_less
% 0.30/0.53 thf(fact_919_not__le__imp__less,axiom,
% 0.30/0.53 ! [Y: int,X: int] :
% 0.30/0.53 ( ~ ( ord_less_eq_int @ Y @ X )
% 0.30/0.53 => ( ord_less_int @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_le_imp_less
% 0.30/0.53 thf(fact_920_less__le__not__le,axiom,
% 0.30/0.53 ( ord_less_real
% 0.30/0.53 = ( ^ [X4: real,Y4: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ X4 @ Y4 )
% 0.30/0.53 & ~ ( ord_less_eq_real @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_le_not_le
% 0.30/0.53 thf(fact_921_less__le__not__le,axiom,
% 0.30/0.53 ( ord_less_set_nat
% 0.30/0.53 = ( ^ [X4: set_nat,Y4: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 0.30/0.53 & ~ ( ord_less_eq_set_nat @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_le_not_le
% 0.30/0.53 thf(fact_922_less__le__not__le,axiom,
% 0.30/0.53 ( ord_less_rat
% 0.30/0.53 = ( ^ [X4: rat,Y4: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 0.30/0.53 & ~ ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_le_not_le
% 0.30/0.53 thf(fact_923_less__le__not__le,axiom,
% 0.30/0.53 ( ord_less_num
% 0.30/0.53 = ( ^ [X4: num,Y4: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X4 @ Y4 )
% 0.30/0.53 & ~ ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_le_not_le
% 0.30/0.53 thf(fact_924_less__le__not__le,axiom,
% 0.30/0.53 ( ord_less_nat
% 0.30/0.53 = ( ^ [X4: nat,Y4: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 0.30/0.53 & ~ ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_le_not_le
% 0.30/0.53 thf(fact_925_less__le__not__le,axiom,
% 0.30/0.53 ( ord_less_int
% 0.30/0.53 = ( ^ [X4: int,Y4: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ X4 @ Y4 )
% 0.30/0.53 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_le_not_le
% 0.30/0.53 thf(fact_926_dense__le,axiom,
% 0.30/0.53 ! [Y: real,Z3: real] :
% 0.30/0.53 ( ! [X3: real] :
% 0.30/0.53 ( ( ord_less_real @ X3 @ Y )
% 0.30/0.53 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 0.30/0.53 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_le
% 0.30/0.53 thf(fact_927_dense__le,axiom,
% 0.30/0.53 ! [Y: rat,Z3: rat] :
% 0.30/0.53 ( ! [X3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ X3 @ Y )
% 0.30/0.53 => ( ord_less_eq_rat @ X3 @ Z3 ) )
% 0.30/0.53 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_le
% 0.30/0.53 thf(fact_928_dense__ge,axiom,
% 0.30/0.53 ! [Z3: real,Y: real] :
% 0.30/0.53 ( ! [X3: real] :
% 0.30/0.53 ( ( ord_less_real @ Z3 @ X3 )
% 0.30/0.53 => ( ord_less_eq_real @ Y @ X3 ) )
% 0.30/0.53 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_ge
% 0.30/0.53 thf(fact_929_dense__ge,axiom,
% 0.30/0.53 ! [Z3: rat,Y: rat] :
% 0.30/0.53 ( ! [X3: rat] :
% 0.30/0.53 ( ( ord_less_rat @ Z3 @ X3 )
% 0.30/0.53 => ( ord_less_eq_rat @ Y @ X3 ) )
% 0.30/0.53 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 0.30/0.53
% 0.30/0.53 % dense_ge
% 0.30/0.53 thf(fact_930_antisym__conv2,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ X @ Y )
% 0.30/0.53 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv2
% 0.30/0.53 thf(fact_931_antisym__conv2,axiom,
% 0.30/0.53 ! [X: set_nat,Y: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.30/0.53 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv2
% 0.30/0.53 thf(fact_932_antisym__conv2,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.53 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv2
% 0.30/0.53 thf(fact_933_antisym__conv2,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.53 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv2
% 0.30/0.53 thf(fact_934_antisym__conv2,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.53 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv2
% 0.30/0.53 thf(fact_935_antisym__conv2,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.53 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv2
% 0.30/0.53 thf(fact_936_antisym__conv1,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ~ ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_real @ X @ Y )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv1
% 0.30/0.53 thf(fact_937_antisym__conv1,axiom,
% 0.30/0.53 ! [X: set_nat,Y: set_nat] :
% 0.30/0.53 ( ~ ( ord_less_set_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_set_nat @ X @ Y )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv1
% 0.30/0.53 thf(fact_938_antisym__conv1,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ~ ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_rat @ X @ Y )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv1
% 0.30/0.53 thf(fact_939_antisym__conv1,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ~ ( ord_less_num @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_num @ X @ Y )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv1
% 0.30/0.53 thf(fact_940_antisym__conv1,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ~ ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_nat @ X @ Y )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv1
% 0.30/0.53 thf(fact_941_antisym__conv1,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ~ ( ord_less_int @ X @ Y )
% 0.30/0.53 => ( ( ord_less_eq_int @ X @ Y )
% 0.30/0.53 = ( X = Y ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % antisym_conv1
% 0.30/0.53 thf(fact_942_nless__le,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ~ ( ord_less_real @ A @ B ) )
% 0.30/0.53 = ( ~ ( ord_less_eq_real @ A @ B )
% 0.30/0.53 | ( A = B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nless_le
% 0.30/0.53 thf(fact_943_nless__le,axiom,
% 0.30/0.53 ! [A: set_nat,B: set_nat] :
% 0.30/0.53 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 0.30/0.53 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.30/0.53 | ( A = B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nless_le
% 0.30/0.53 thf(fact_944_nless__le,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ~ ( ord_less_rat @ A @ B ) )
% 0.30/0.53 = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.30/0.53 | ( A = B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nless_le
% 0.30/0.53 thf(fact_945_nless__le,axiom,
% 0.30/0.53 ! [A: num,B: num] :
% 0.30/0.53 ( ( ~ ( ord_less_num @ A @ B ) )
% 0.30/0.53 = ( ~ ( ord_less_eq_num @ A @ B )
% 0.30/0.53 | ( A = B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nless_le
% 0.30/0.53 thf(fact_946_nless__le,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ~ ( ord_less_nat @ A @ B ) )
% 0.30/0.53 = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.30/0.53 | ( A = B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nless_le
% 0.30/0.53 thf(fact_947_nless__le,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ~ ( ord_less_int @ A @ B ) )
% 0.30/0.53 = ( ~ ( ord_less_eq_int @ A @ B )
% 0.30/0.53 | ( A = B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nless_le
% 0.30/0.53 thf(fact_948_leI,axiom,
% 0.30/0.53 ! [X: real,Y: real] :
% 0.30/0.53 ( ~ ( ord_less_real @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_real @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % leI
% 0.30/0.53 thf(fact_949_leI,axiom,
% 0.30/0.53 ! [X: rat,Y: rat] :
% 0.30/0.53 ( ~ ( ord_less_rat @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % leI
% 0.30/0.53 thf(fact_950_leI,axiom,
% 0.30/0.53 ! [X: num,Y: num] :
% 0.30/0.53 ( ~ ( ord_less_num @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_num @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % leI
% 0.30/0.53 thf(fact_951_leI,axiom,
% 0.30/0.53 ! [X: nat,Y: nat] :
% 0.30/0.53 ( ~ ( ord_less_nat @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % leI
% 0.30/0.53 thf(fact_952_leI,axiom,
% 0.30/0.53 ! [X: int,Y: int] :
% 0.30/0.53 ( ~ ( ord_less_int @ X @ Y )
% 0.30/0.53 => ( ord_less_eq_int @ Y @ X ) ) ).
% 0.30/0.53
% 0.30/0.53 % leI
% 0.30/0.53 thf(fact_953_leD,axiom,
% 0.30/0.53 ! [Y: real,X: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ Y @ X )
% 0.30/0.53 => ~ ( ord_less_real @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % leD
% 0.30/0.53 thf(fact_954_leD,axiom,
% 0.30/0.53 ! [Y: set_nat,X: set_nat] :
% 0.30/0.53 ( ( ord_less_eq_set_nat @ Y @ X )
% 0.30/0.53 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % leD
% 0.30/0.53 thf(fact_955_leD,axiom,
% 0.30/0.53 ! [Y: rat,X: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ Y @ X )
% 0.30/0.53 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % leD
% 0.30/0.53 thf(fact_956_leD,axiom,
% 0.30/0.53 ! [Y: num,X: num] :
% 0.30/0.53 ( ( ord_less_eq_num @ Y @ X )
% 0.30/0.53 => ~ ( ord_less_num @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % leD
% 0.30/0.53 thf(fact_957_leD,axiom,
% 0.30/0.53 ! [Y: nat,X: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ Y @ X )
% 0.30/0.53 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % leD
% 0.30/0.53 thf(fact_958_leD,axiom,
% 0.30/0.53 ! [Y: int,X: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ Y @ X )
% 0.30/0.53 => ~ ( ord_less_int @ X @ Y ) ) ).
% 0.30/0.53
% 0.30/0.53 % leD
% 0.30/0.53 thf(fact_959_zero__less__iff__neq__zero,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.53 = ( N != zero_zero_nat ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_iff_neq_zero
% 0.30/0.53 thf(fact_960_gr__implies__not__zero,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.53 => ( N != zero_zero_nat ) ) ).
% 0.30/0.53
% 0.30/0.53 % gr_implies_not_zero
% 0.30/0.53 thf(fact_961_not__less__zero,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.53
% 0.30/0.53 % not_less_zero
% 0.30/0.53 thf(fact_962_gr__zeroI,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ( ( N != zero_zero_nat )
% 0.30/0.53 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.30/0.53
% 0.30/0.53 % gr_zeroI
% 0.30/0.53 thf(fact_963_less__numeral__extra_I3_J,axiom,
% 0.30/0.53 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(3)
% 0.30/0.53 thf(fact_964_less__numeral__extra_I3_J,axiom,
% 0.30/0.53 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(3)
% 0.30/0.53 thf(fact_965_less__numeral__extra_I3_J,axiom,
% 0.30/0.53 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(3)
% 0.30/0.53 thf(fact_966_less__numeral__extra_I3_J,axiom,
% 0.30/0.53 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 0.30/0.53
% 0.30/0.53 % less_numeral_extra(3)
% 0.30/0.53 thf(fact_967_not__less__less__Suc__eq,axiom,
% 0.30/0.53 ! [N: nat,M2: nat] :
% 0.30/0.53 ( ~ ( ord_less_nat @ N @ M2 )
% 0.30/0.53 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 0.30/0.53 = ( N = M2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_less_less_Suc_eq
% 0.30/0.53 thf(fact_968_strict__inc__induct,axiom,
% 0.30/0.53 ! [I2: nat,J2: nat,P2: nat > $o] :
% 0.30/0.53 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.53 => ( ! [I3: nat] :
% 0.30/0.53 ( ( J2
% 0.30/0.53 = ( suc @ I3 ) )
% 0.30/0.53 => ( P2 @ I3 ) )
% 0.30/0.53 => ( ! [I3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I3 @ J2 )
% 0.30/0.53 => ( ( P2 @ ( suc @ I3 ) )
% 0.30/0.53 => ( P2 @ I3 ) ) )
% 0.30/0.53 => ( P2 @ I2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % strict_inc_induct
% 0.30/0.53 thf(fact_969_less__Suc__induct,axiom,
% 0.30/0.53 ! [I2: nat,J2: nat,P2: nat > nat > $o] :
% 0.30/0.53 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.53 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 0.30/0.53 => ( ! [I3: nat,J3: nat,K: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I3 @ J3 )
% 0.30/0.53 => ( ( ord_less_nat @ J3 @ K )
% 0.30/0.53 => ( ( P2 @ I3 @ J3 )
% 0.30/0.53 => ( ( P2 @ J3 @ K )
% 0.30/0.53 => ( P2 @ I3 @ K ) ) ) ) )
% 0.30/0.53 => ( P2 @ I2 @ J2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_Suc_induct
% 0.30/0.53 thf(fact_970_less__trans__Suc,axiom,
% 0.30/0.53 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.53 => ( ( ord_less_nat @ J2 @ K2 )
% 0.30/0.53 => ( ord_less_nat @ ( suc @ I2 ) @ K2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_trans_Suc
% 0.30/0.53 thf(fact_971_Suc__less__SucD,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.30/0.53 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.53
% 0.30/0.53 % Suc_less_SucD
% 0.30/0.53 thf(fact_972_less__antisym,axiom,
% 0.30/0.53 ! [N: nat,M2: nat] :
% 0.30/0.53 ( ~ ( ord_less_nat @ N @ M2 )
% 0.30/0.53 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 0.30/0.53 => ( M2 = N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_antisym
% 0.30/0.53 thf(fact_973_Suc__less__eq2,axiom,
% 0.30/0.53 ! [N: nat,M2: nat] :
% 0.30/0.53 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.30/0.53 = ( ? [M7: nat] :
% 0.30/0.53 ( ( M2
% 0.30/0.53 = ( suc @ M7 ) )
% 0.30/0.53 & ( ord_less_nat @ N @ M7 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % Suc_less_eq2
% 0.30/0.53 thf(fact_974_All__less__Suc,axiom,
% 0.30/0.53 ! [N: nat,P2: nat > $o] :
% 0.30/0.53 ( ( ! [I: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 0.30/0.53 => ( P2 @ I ) ) )
% 0.30/0.53 = ( ( P2 @ N )
% 0.30/0.53 & ! [I: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I @ N )
% 0.30/0.53 => ( P2 @ I ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % All_less_Suc
% 0.30/0.53 thf(fact_975_not__less__eq,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 0.30/0.53 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_less_eq
% 0.30/0.53 thf(fact_976_less__Suc__eq,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 0.30/0.53 = ( ( ord_less_nat @ M2 @ N )
% 0.30/0.53 | ( M2 = N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_Suc_eq
% 0.30/0.53 thf(fact_977_Ex__less__Suc,axiom,
% 0.30/0.53 ! [N: nat,P2: nat > $o] :
% 0.30/0.53 ( ( ? [I: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 0.30/0.53 & ( P2 @ I ) ) )
% 0.30/0.53 = ( ( P2 @ N )
% 0.30/0.53 | ? [I: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I @ N )
% 0.30/0.53 & ( P2 @ I ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % Ex_less_Suc
% 0.30/0.53 thf(fact_978_less__SucI,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.53 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_SucI
% 0.30/0.53 thf(fact_979_less__SucE,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 0.30/0.53 => ( ~ ( ord_less_nat @ M2 @ N )
% 0.30/0.53 => ( M2 = N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_SucE
% 0.30/0.53 thf(fact_980_Suc__lessI,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.53 => ( ( ( suc @ M2 )
% 0.30/0.53 != N )
% 0.30/0.53 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % Suc_lessI
% 0.30/0.53 thf(fact_981_Suc__lessE,axiom,
% 0.30/0.53 ! [I2: nat,K2: nat] :
% 0.30/0.53 ( ( ord_less_nat @ ( suc @ I2 ) @ K2 )
% 0.30/0.53 => ~ ! [J3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I2 @ J3 )
% 0.30/0.53 => ( K2
% 0.30/0.53 != ( suc @ J3 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % Suc_lessE
% 0.30/0.53 thf(fact_982_Suc__lessD,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 0.30/0.53 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.53
% 0.30/0.53 % Suc_lessD
% 0.30/0.53 thf(fact_983_Nat_OlessE,axiom,
% 0.30/0.53 ! [I2: nat,K2: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I2 @ K2 )
% 0.30/0.53 => ( ( K2
% 0.30/0.53 != ( suc @ I2 ) )
% 0.30/0.53 => ~ ! [J3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I2 @ J3 )
% 0.30/0.53 => ( K2
% 0.30/0.53 != ( suc @ J3 ) ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % Nat.lessE
% 0.30/0.53 thf(fact_984_VEBT_Odistinct_I1_J,axiom,
% 0.30/0.53 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 0.30/0.53 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 0.30/0.53 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 0.30/0.53
% 0.30/0.53 % VEBT.distinct(1)
% 0.30/0.53 thf(fact_985_VEBT_Oexhaust,axiom,
% 0.30/0.53 ! [Y: vEBT_VEBT] :
% 0.30/0.53 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 0.30/0.53 ( Y
% 0.30/0.53 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 0.30/0.53 => ~ ! [X212: $o,X222: $o] :
% 0.30/0.53 ( Y
% 0.30/0.53 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % VEBT.exhaust
% 0.30/0.53 thf(fact_986_le__numeral__extra_I4_J,axiom,
% 0.30/0.53 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 0.30/0.53
% 0.30/0.53 % le_numeral_extra(4)
% 0.30/0.53 thf(fact_987_le__numeral__extra_I4_J,axiom,
% 0.30/0.53 ord_less_eq_real @ one_one_real @ one_one_real ).
% 0.30/0.53
% 0.30/0.53 % le_numeral_extra(4)
% 0.30/0.53 thf(fact_988_le__numeral__extra_I4_J,axiom,
% 0.30/0.53 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 0.30/0.53
% 0.30/0.53 % le_numeral_extra(4)
% 0.30/0.53 thf(fact_989_le__numeral__extra_I4_J,axiom,
% 0.30/0.53 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 0.30/0.53
% 0.30/0.53 % le_numeral_extra(4)
% 0.30/0.53 thf(fact_990_le__numeral__extra_I4_J,axiom,
% 0.30/0.53 ord_less_eq_int @ one_one_int @ one_one_int ).
% 0.30/0.53
% 0.30/0.53 % le_numeral_extra(4)
% 0.30/0.53 thf(fact_991_zero__neq__one,axiom,
% 0.30/0.53 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 0.30/0.53
% 0.30/0.53 % zero_neq_one
% 0.30/0.53 thf(fact_992_zero__neq__one,axiom,
% 0.30/0.53 zero_zero_complex != one_one_complex ).
% 0.30/0.53
% 0.30/0.53 % zero_neq_one
% 0.30/0.53 thf(fact_993_zero__neq__one,axiom,
% 0.30/0.53 zero_zero_real != one_one_real ).
% 0.30/0.53
% 0.30/0.53 % zero_neq_one
% 0.30/0.53 thf(fact_994_zero__neq__one,axiom,
% 0.30/0.53 zero_zero_rat != one_one_rat ).
% 0.30/0.53
% 0.30/0.53 % zero_neq_one
% 0.30/0.53 thf(fact_995_zero__neq__one,axiom,
% 0.30/0.53 zero_zero_nat != one_one_nat ).
% 0.30/0.53
% 0.30/0.53 % zero_neq_one
% 0.30/0.53 thf(fact_996_zero__neq__one,axiom,
% 0.30/0.53 zero_zero_int != one_one_int ).
% 0.30/0.53
% 0.30/0.53 % zero_neq_one
% 0.30/0.53 thf(fact_997_bot__nat__0_Oextremum__strict,axiom,
% 0.30/0.53 ! [A: nat] :
% 0.30/0.53 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 0.30/0.53
% 0.30/0.53 % bot_nat_0.extremum_strict
% 0.30/0.53 thf(fact_998_gr0I,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ( ( N != zero_zero_nat )
% 0.30/0.53 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.30/0.53
% 0.30/0.53 % gr0I
% 0.30/0.53 thf(fact_999_not__gr0,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 0.30/0.53 = ( N = zero_zero_nat ) ) ).
% 0.30/0.53
% 0.30/0.53 % not_gr0
% 0.30/0.53 thf(fact_1000_not__less0,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.53
% 0.30/0.53 % not_less0
% 0.30/0.53 thf(fact_1001_less__zeroE,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.30/0.53
% 0.30/0.53 % less_zeroE
% 0.30/0.53 thf(fact_1002_gr__implies__not0,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.53 => ( N != zero_zero_nat ) ) ).
% 0.30/0.53
% 0.30/0.53 % gr_implies_not0
% 0.30/0.53 thf(fact_1003_infinite__descent0,axiom,
% 0.30/0.53 ! [P2: nat > $o,N: nat] :
% 0.30/0.53 ( ( P2 @ zero_zero_nat )
% 0.30/0.53 => ( ! [N3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.30/0.53 => ( ~ ( P2 @ N3 )
% 0.30/0.53 => ? [M3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M3 @ N3 )
% 0.30/0.53 & ~ ( P2 @ M3 ) ) ) )
% 0.30/0.53 => ( P2 @ N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % infinite_descent0
% 0.30/0.53 thf(fact_1004_mult_Ocomm__neutral,axiom,
% 0.30/0.53 ! [A: code_integer] :
% 0.30/0.53 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % mult.comm_neutral
% 0.30/0.53 thf(fact_1005_mult_Ocomm__neutral,axiom,
% 0.30/0.53 ! [A: complex] :
% 0.30/0.53 ( ( times_times_complex @ A @ one_one_complex )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % mult.comm_neutral
% 0.30/0.53 thf(fact_1006_mult_Ocomm__neutral,axiom,
% 0.30/0.53 ! [A: real] :
% 0.30/0.53 ( ( times_times_real @ A @ one_one_real )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % mult.comm_neutral
% 0.30/0.53 thf(fact_1007_mult_Ocomm__neutral,axiom,
% 0.30/0.53 ! [A: rat] :
% 0.30/0.53 ( ( times_times_rat @ A @ one_one_rat )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % mult.comm_neutral
% 0.30/0.53 thf(fact_1008_mult_Ocomm__neutral,axiom,
% 0.30/0.53 ! [A: nat] :
% 0.30/0.53 ( ( times_times_nat @ A @ one_one_nat )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % mult.comm_neutral
% 0.30/0.53 thf(fact_1009_mult_Ocomm__neutral,axiom,
% 0.30/0.53 ! [A: int] :
% 0.30/0.53 ( ( times_times_int @ A @ one_one_int )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % mult.comm_neutral
% 0.30/0.53 thf(fact_1010_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.53 ! [A: code_integer] :
% 0.30/0.53 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % comm_monoid_mult_class.mult_1
% 0.30/0.53 thf(fact_1011_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.53 ! [A: complex] :
% 0.30/0.53 ( ( times_times_complex @ one_one_complex @ A )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % comm_monoid_mult_class.mult_1
% 0.30/0.53 thf(fact_1012_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.53 ! [A: real] :
% 0.30/0.53 ( ( times_times_real @ one_one_real @ A )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % comm_monoid_mult_class.mult_1
% 0.30/0.53 thf(fact_1013_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.53 ! [A: rat] :
% 0.30/0.53 ( ( times_times_rat @ one_one_rat @ A )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % comm_monoid_mult_class.mult_1
% 0.30/0.53 thf(fact_1014_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.53 ! [A: nat] :
% 0.30/0.53 ( ( times_times_nat @ one_one_nat @ A )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % comm_monoid_mult_class.mult_1
% 0.30/0.53 thf(fact_1015_comm__monoid__mult__class_Omult__1,axiom,
% 0.30/0.53 ! [A: int] :
% 0.30/0.53 ( ( times_times_int @ one_one_int @ A )
% 0.30/0.53 = A ) ).
% 0.30/0.53
% 0.30/0.53 % comm_monoid_mult_class.mult_1
% 0.30/0.53 thf(fact_1016_less__mono__imp__le__mono,axiom,
% 0.30/0.53 ! [F2: nat > nat,I2: nat,J2: nat] :
% 0.30/0.53 ( ! [I3: nat,J3: nat] :
% 0.30/0.53 ( ( ord_less_nat @ I3 @ J3 )
% 0.30/0.53 => ( ord_less_nat @ ( F2 @ I3 ) @ ( F2 @ J3 ) ) )
% 0.30/0.53 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.53 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( F2 @ J2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_mono_imp_le_mono
% 0.30/0.53 thf(fact_1017_le__neq__implies__less,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.53 => ( ( M2 != N )
% 0.30/0.53 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % le_neq_implies_less
% 0.30/0.53 thf(fact_1018_less__or__eq__imp__le,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ( ord_less_nat @ M2 @ N )
% 0.30/0.53 | ( M2 = N ) )
% 0.30/0.53 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_or_eq_imp_le
% 0.30/0.53 thf(fact_1019_le__eq__less__or__eq,axiom,
% 0.30/0.53 ( ord_less_eq_nat
% 0.30/0.53 = ( ^ [M6: nat,N4: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M6 @ N4 )
% 0.30/0.53 | ( M6 = N4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % le_eq_less_or_eq
% 0.30/0.53 thf(fact_1020_less__imp__le__nat,axiom,
% 0.30/0.53 ! [M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.53 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.53
% 0.30/0.53 % less_imp_le_nat
% 0.30/0.53 thf(fact_1021_nat__less__le,axiom,
% 0.30/0.53 ( ord_less_nat
% 0.30/0.53 = ( ^ [M6: nat,N4: nat] :
% 0.30/0.53 ( ( ord_less_eq_nat @ M6 @ N4 )
% 0.30/0.53 & ( M6 != N4 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nat_less_le
% 0.30/0.53 thf(fact_1022_nat__mult__1,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ( ( times_times_nat @ one_one_nat @ N )
% 0.30/0.53 = N ) ).
% 0.30/0.53
% 0.30/0.53 % nat_mult_1
% 0.30/0.53 thf(fact_1023_nat__mult__1__right,axiom,
% 0.30/0.53 ! [N: nat] :
% 0.30/0.53 ( ( times_times_nat @ N @ one_one_nat )
% 0.30/0.53 = N ) ).
% 0.30/0.53
% 0.30/0.53 % nat_mult_1_right
% 0.30/0.53 thf(fact_1024_nat__mult__eq__cancel1,axiom,
% 0.30/0.53 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.53 => ( ( ( times_times_nat @ K2 @ M2 )
% 0.30/0.53 = ( times_times_nat @ K2 @ N ) )
% 0.30/0.53 = ( M2 = N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nat_mult_eq_cancel1
% 0.30/0.53 thf(fact_1025_nat__mult__less__cancel1,axiom,
% 0.30/0.53 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.53 => ( ( ord_less_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.30/0.53 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % nat_mult_less_cancel1
% 0.30/0.53 thf(fact_1026_mult__less__cancel__right2,axiom,
% 0.30/0.53 ! [A: code_integer,C2: code_integer] :
% 0.30/0.53 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.30/0.53 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right2
% 0.30/0.53 thf(fact_1027_mult__less__cancel__right2,axiom,
% 0.30/0.53 ! [A: real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_real @ A @ one_one_real ) )
% 0.30/0.53 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right2
% 0.30/0.53 thf(fact_1028_mult__less__cancel__right2,axiom,
% 0.30/0.53 ! [A: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_rat @ A @ one_one_rat ) )
% 0.30/0.53 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right2
% 0.30/0.53 thf(fact_1029_mult__less__cancel__right2,axiom,
% 0.30/0.53 ! [A: int,C2: int] :
% 0.30/0.53 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_int @ A @ one_one_int ) )
% 0.30/0.53 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right2
% 0.30/0.53 thf(fact_1030_mult__less__cancel__right1,axiom,
% 0.30/0.53 ! [C2: code_integer,B: code_integer] :
% 0.30/0.53 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.30/0.53 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right1
% 0.30/0.53 thf(fact_1031_mult__less__cancel__right1,axiom,
% 0.30/0.53 ! [C2: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_real @ one_one_real @ B ) )
% 0.30/0.53 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right1
% 0.30/0.53 thf(fact_1032_mult__less__cancel__right1,axiom,
% 0.30/0.53 ! [C2: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_rat @ one_one_rat @ B ) )
% 0.30/0.53 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right1
% 0.30/0.53 thf(fact_1033_mult__less__cancel__right1,axiom,
% 0.30/0.53 ! [C2: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_int @ one_one_int @ B ) )
% 0.30/0.53 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_right1
% 0.30/0.53 thf(fact_1034_mult__less__cancel__left2,axiom,
% 0.30/0.53 ! [C2: code_integer,A: code_integer] :
% 0.30/0.53 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 0.30/0.53 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left2
% 0.30/0.53 thf(fact_1035_mult__less__cancel__left2,axiom,
% 0.30/0.53 ! [C2: real,A: real] :
% 0.30/0.53 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_real @ A @ one_one_real ) )
% 0.30/0.53 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left2
% 0.30/0.53 thf(fact_1036_mult__less__cancel__left2,axiom,
% 0.30/0.53 ! [C2: rat,A: rat] :
% 0.30/0.53 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_rat @ A @ one_one_rat ) )
% 0.30/0.53 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left2
% 0.30/0.53 thf(fact_1037_mult__less__cancel__left2,axiom,
% 0.30/0.53 ! [C2: int,A: int] :
% 0.30/0.53 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_int @ A @ one_one_int ) )
% 0.30/0.53 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left2
% 0.30/0.53 thf(fact_1038_mult__less__cancel__left1,axiom,
% 0.30/0.53 ! [C2: code_integer,B: code_integer] :
% 0.30/0.53 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 0.30/0.53 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left1
% 0.30/0.53 thf(fact_1039_mult__less__cancel__left1,axiom,
% 0.30/0.53 ! [C2: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_real @ one_one_real @ B ) )
% 0.30/0.53 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left1
% 0.30/0.53 thf(fact_1040_mult__less__cancel__left1,axiom,
% 0.30/0.53 ! [C2: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_rat @ one_one_rat @ B ) )
% 0.30/0.53 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left1
% 0.30/0.53 thf(fact_1041_mult__less__cancel__left1,axiom,
% 0.30/0.53 ! [C2: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_int @ one_one_int @ B ) )
% 0.30/0.53 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left1
% 0.30/0.53 thf(fact_1042_mult__le__cancel__right2,axiom,
% 0.30/0.53 ! [A: code_integer,C2: code_integer] :
% 0.30/0.53 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.30/0.53 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right2
% 0.30/0.53 thf(fact_1043_mult__le__cancel__right2,axiom,
% 0.30/0.53 ! [A: real,C2: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.30/0.53 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right2
% 0.30/0.53 thf(fact_1044_mult__le__cancel__right2,axiom,
% 0.30/0.53 ! [A: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.30/0.53 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right2
% 0.30/0.53 thf(fact_1045_mult__le__cancel__right2,axiom,
% 0.30/0.53 ! [A: int,C2: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.30/0.53 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right2
% 0.30/0.53 thf(fact_1046_mult__le__cancel__right1,axiom,
% 0.30/0.53 ! [C2: code_integer,B: code_integer] :
% 0.30/0.53 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.30/0.53 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right1
% 0.30/0.53 thf(fact_1047_mult__le__cancel__right1,axiom,
% 0.30/0.53 ! [C2: real,B: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.30/0.53 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right1
% 0.30/0.53 thf(fact_1048_mult__le__cancel__right1,axiom,
% 0.30/0.53 ! [C2: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.30/0.53 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right1
% 0.30/0.53 thf(fact_1049_mult__le__cancel__right1,axiom,
% 0.30/0.53 ! [C2: int,B: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 0.30/0.53 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.30/0.53 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_right1
% 0.30/0.53 thf(fact_1050_mult__le__cancel__left2,axiom,
% 0.30/0.53 ! [C2: code_integer,A: code_integer] :
% 0.30/0.53 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 0.30/0.53 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left2
% 0.30/0.53 thf(fact_1051_mult__le__cancel__left2,axiom,
% 0.30/0.53 ! [C2: real,A: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_eq_real @ A @ one_one_real ) )
% 0.30/0.53 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left2
% 0.30/0.53 thf(fact_1052_mult__le__cancel__left2,axiom,
% 0.30/0.53 ! [C2: rat,A: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 0.30/0.53 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left2
% 0.30/0.53 thf(fact_1053_mult__le__cancel__left2,axiom,
% 0.30/0.53 ! [C2: int,A: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 0.30/0.53 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_eq_int @ A @ one_one_int ) )
% 0.30/0.53 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left2
% 0.30/0.53 thf(fact_1054_mult__le__cancel__left1,axiom,
% 0.30/0.53 ! [C2: code_integer,B: code_integer] :
% 0.30/0.53 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 0.30/0.53 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 0.30/0.53 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left1
% 0.30/0.53 thf(fact_1055_mult__le__cancel__left1,axiom,
% 0.30/0.53 ! [C2: real,B: real] :
% 0.30/0.53 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_eq_real @ one_one_real @ B ) )
% 0.30/0.53 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left1
% 0.30/0.53 thf(fact_1056_mult__le__cancel__left1,axiom,
% 0.30/0.53 ! [C2: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 0.30/0.53 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left1
% 0.30/0.53 thf(fact_1057_mult__le__cancel__left1,axiom,
% 0.30/0.53 ! [C2: int,B: int] :
% 0.30/0.53 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_eq_int @ one_one_int @ B ) )
% 0.30/0.53 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_le_cancel_left1
% 0.30/0.53 thf(fact_1058_mult__neg__neg,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ zero_zero_real )
% 0.30/0.53 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_neg_neg
% 0.30/0.53 thf(fact_1059_mult__neg__neg,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.53 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_neg_neg
% 0.30/0.53 thf(fact_1060_mult__neg__neg,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.53 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_neg_neg
% 0.30/0.53 thf(fact_1061_not__square__less__zero,axiom,
% 0.30/0.53 ! [A: real] :
% 0.30/0.53 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 0.30/0.53
% 0.30/0.53 % not_square_less_zero
% 0.30/0.53 thf(fact_1062_not__square__less__zero,axiom,
% 0.30/0.53 ! [A: rat] :
% 0.30/0.53 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 0.30/0.53
% 0.30/0.53 % not_square_less_zero
% 0.30/0.53 thf(fact_1063_not__square__less__zero,axiom,
% 0.30/0.53 ! [A: int] :
% 0.30/0.53 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 0.30/0.53
% 0.30/0.53 % not_square_less_zero
% 0.30/0.53 thf(fact_1064_mult__less__0__iff,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 0.30/0.53 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.53 & ( ord_less_real @ B @ zero_zero_real ) )
% 0.30/0.53 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.30/0.53 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_0_iff
% 0.30/0.53 thf(fact_1065_mult__less__0__iff,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 0.30/0.53 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.53 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.30/0.53 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.53 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_0_iff
% 0.30/0.53 thf(fact_1066_mult__less__0__iff,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 0.30/0.53 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.53 & ( ord_less_int @ B @ zero_zero_int ) )
% 0.30/0.53 | ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.53 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_0_iff
% 0.30/0.53 thf(fact_1067_mult__neg__pos,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ zero_zero_real )
% 0.30/0.53 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.30/0.53 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_neg_pos
% 0.30/0.53 thf(fact_1068_mult__neg__pos,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.53 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.53 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_neg_pos
% 0.30/0.53 thf(fact_1069_mult__neg__pos,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.30/0.53 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.53 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_neg_pos
% 0.30/0.53 thf(fact_1070_mult__neg__pos,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.53 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.53 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_neg_pos
% 0.30/0.53 thf(fact_1071_mult__pos__neg,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.53 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg
% 0.30/0.53 thf(fact_1072_mult__pos__neg,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.53 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg
% 0.30/0.53 thf(fact_1073_mult__pos__neg,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.53 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.53 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg
% 0.30/0.53 thf(fact_1074_mult__pos__neg,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.53 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg
% 0.30/0.53 thf(fact_1075_mult__pos__pos,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.53 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.30/0.53 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_pos
% 0.30/0.53 thf(fact_1076_mult__pos__pos,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.53 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.53 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_pos
% 0.30/0.53 thf(fact_1077_mult__pos__pos,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.53 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.53 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_pos
% 0.30/0.53 thf(fact_1078_mult__pos__pos,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.53 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.53 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_pos
% 0.30/0.53 thf(fact_1079_mult__pos__neg2,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.53 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg2
% 0.30/0.53 thf(fact_1080_mult__pos__neg2,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.53 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg2
% 0.30/0.53 thf(fact_1081_mult__pos__neg2,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.53 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.53 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg2
% 0.30/0.53 thf(fact_1082_mult__pos__neg2,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.53 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_pos_neg2
% 0.30/0.53 thf(fact_1083_zero__less__mult__iff,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.30/0.53 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.53 & ( ord_less_real @ zero_zero_real @ B ) )
% 0.30/0.53 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.30/0.53 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_iff
% 0.30/0.53 thf(fact_1084_zero__less__mult__iff,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.53 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.53 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.30/0.53 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.53 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_iff
% 0.30/0.53 thf(fact_1085_zero__less__mult__iff,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.30/0.53 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.53 & ( ord_less_int @ zero_zero_int @ B ) )
% 0.30/0.53 | ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.53 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_iff
% 0.30/0.53 thf(fact_1086_zero__less__mult__pos,axiom,
% 0.30/0.53 ! [A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.30/0.53 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.53 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos
% 0.30/0.53 thf(fact_1087_zero__less__mult__pos,axiom,
% 0.30/0.53 ! [A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.30/0.53 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.53 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos
% 0.30/0.53 thf(fact_1088_zero__less__mult__pos,axiom,
% 0.30/0.53 ! [A: nat,B: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 0.30/0.53 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.53 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos
% 0.30/0.53 thf(fact_1089_zero__less__mult__pos,axiom,
% 0.30/0.53 ! [A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.30/0.53 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.53 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos
% 0.30/0.53 thf(fact_1090_zero__less__mult__pos2,axiom,
% 0.30/0.53 ! [B: real,A: real] :
% 0.30/0.53 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 0.30/0.53 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.53 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos2
% 0.30/0.53 thf(fact_1091_zero__less__mult__pos2,axiom,
% 0.30/0.53 ! [B: rat,A: rat] :
% 0.30/0.53 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 0.30/0.53 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.53 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos2
% 0.30/0.53 thf(fact_1092_zero__less__mult__pos2,axiom,
% 0.30/0.53 ! [B: nat,A: nat] :
% 0.30/0.53 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 0.30/0.53 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.53 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos2
% 0.30/0.53 thf(fact_1093_zero__less__mult__pos2,axiom,
% 0.30/0.53 ! [B: int,A: int] :
% 0.30/0.53 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 0.30/0.53 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.53 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % zero_less_mult_pos2
% 0.30/0.53 thf(fact_1094_mult__less__cancel__left__neg,axiom,
% 0.30/0.53 ! [C2: real,A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.53 = ( ord_less_real @ B @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_neg
% 0.30/0.53 thf(fact_1095_mult__less__cancel__left__neg,axiom,
% 0.30/0.53 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.53 = ( ord_less_rat @ B @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_neg
% 0.30/0.53 thf(fact_1096_mult__less__cancel__left__neg,axiom,
% 0.30/0.53 ! [C2: int,A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.53 = ( ord_less_int @ B @ A ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_neg
% 0.30/0.53 thf(fact_1097_mult__less__cancel__left__pos,axiom,
% 0.30/0.53 ! [C2: real,A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.53 = ( ord_less_real @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_pos
% 0.30/0.53 thf(fact_1098_mult__less__cancel__left__pos,axiom,
% 0.30/0.53 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.53 = ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_pos
% 0.30/0.53 thf(fact_1099_mult__less__cancel__left__pos,axiom,
% 0.30/0.53 ! [C2: int,A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.53 = ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_pos
% 0.30/0.53 thf(fact_1100_mult__strict__left__mono__neg,axiom,
% 0.30/0.53 ! [B: real,A: real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ B @ A )
% 0.30/0.53 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_left_mono_neg
% 0.30/0.53 thf(fact_1101_mult__strict__left__mono__neg,axiom,
% 0.30/0.53 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ B @ A )
% 0.30/0.53 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_left_mono_neg
% 0.30/0.53 thf(fact_1102_mult__strict__left__mono__neg,axiom,
% 0.30/0.53 ! [B: int,A: int,C2: int] :
% 0.30/0.53 ( ( ord_less_int @ B @ A )
% 0.30/0.53 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.53 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_left_mono_neg
% 0.30/0.53 thf(fact_1103_mult__strict__left__mono,axiom,
% 0.30/0.53 ! [A: real,B: real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ A @ B )
% 0.30/0.53 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.53 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_left_mono
% 0.30/0.53 thf(fact_1104_mult__strict__left__mono,axiom,
% 0.30/0.53 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ A @ B )
% 0.30/0.53 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_left_mono
% 0.30/0.53 thf(fact_1105_mult__strict__left__mono,axiom,
% 0.30/0.53 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.53 ( ( ord_less_nat @ A @ B )
% 0.30/0.53 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.30/0.53 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_left_mono
% 0.30/0.53 thf(fact_1106_mult__strict__left__mono,axiom,
% 0.30/0.53 ! [A: int,B: int,C2: int] :
% 0.30/0.53 ( ( ord_less_int @ A @ B )
% 0.30/0.53 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.53 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_left_mono
% 0.30/0.53 thf(fact_1107_mult__less__cancel__left__disj,axiom,
% 0.30/0.53 ! [C2: real,A: real,B: real] :
% 0.30/0.53 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.53 & ( ord_less_real @ A @ B ) )
% 0.30/0.53 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_disj
% 0.30/0.53 thf(fact_1108_mult__less__cancel__left__disj,axiom,
% 0.30/0.53 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.53 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.53 & ( ord_less_rat @ A @ B ) )
% 0.30/0.53 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.53 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_disj
% 0.30/0.53 thf(fact_1109_mult__less__cancel__left__disj,axiom,
% 0.30/0.53 ! [C2: int,A: int,B: int] :
% 0.30/0.53 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.53 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.53 & ( ord_less_int @ A @ B ) )
% 0.30/0.53 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.53 & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_less_cancel_left_disj
% 0.30/0.53 thf(fact_1110_mult__strict__right__mono__neg,axiom,
% 0.30/0.53 ! [B: real,A: real,C2: real] :
% 0.30/0.53 ( ( ord_less_real @ B @ A )
% 0.30/0.53 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.53 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.30/0.53
% 0.30/0.53 % mult_strict_right_mono_neg
% 0.30/0.53 thf(fact_1111_mult__strict__right__mono__neg,axiom,
% 0.30/0.53 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.53 ( ( ord_less_rat @ B @ A )
% 0.30/0.54 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.54 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_right_mono_neg
% 0.30/0.54 thf(fact_1112_mult__strict__right__mono__neg,axiom,
% 0.30/0.54 ! [B: int,A: int,C2: int] :
% 0.30/0.54 ( ( ord_less_int @ B @ A )
% 0.30/0.54 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.54 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_right_mono_neg
% 0.30/0.54 thf(fact_1113_mult__strict__right__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_right_mono
% 0.30/0.54 thf(fact_1114_mult__strict__right__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_right_mono
% 0.30/0.54 thf(fact_1115_mult__strict__right__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_right_mono
% 0.30/0.54 thf(fact_1116_mult__strict__right__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_right_mono
% 0.30/0.54 thf(fact_1117_mult__less__cancel__right__disj,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 & ( ord_less_real @ A @ B ) )
% 0.30/0.54 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.54 & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_right_disj
% 0.30/0.54 thf(fact_1118_mult__less__cancel__right__disj,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 & ( ord_less_rat @ A @ B ) )
% 0.30/0.54 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.54 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_right_disj
% 0.30/0.54 thf(fact_1119_mult__less__cancel__right__disj,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 & ( ord_less_int @ A @ B ) )
% 0.30/0.54 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.54 & ( ord_less_int @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_right_disj
% 0.30/0.54 thf(fact_1120_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.54 thf(fact_1121_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.54 thf(fact_1122_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.54 thf(fact_1123_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 0.30/0.54 thf(fact_1124_not__one__le__zero,axiom,
% 0.30/0.54 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 0.30/0.54
% 0.30/0.54 % not_one_le_zero
% 0.30/0.54 thf(fact_1125_not__one__le__zero,axiom,
% 0.30/0.54 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 0.30/0.54
% 0.30/0.54 % not_one_le_zero
% 0.30/0.54 thf(fact_1126_not__one__le__zero,axiom,
% 0.30/0.54 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 0.30/0.54
% 0.30/0.54 % not_one_le_zero
% 0.30/0.54 thf(fact_1127_not__one__le__zero,axiom,
% 0.30/0.54 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.30/0.54
% 0.30/0.54 % not_one_le_zero
% 0.30/0.54 thf(fact_1128_not__one__le__zero,axiom,
% 0.30/0.54 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 0.30/0.54
% 0.30/0.54 % not_one_le_zero
% 0.30/0.54 thf(fact_1129_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.54
% 0.30/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.54 thf(fact_1130_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.30/0.54
% 0.30/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.54 thf(fact_1131_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.54
% 0.30/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.54 thf(fact_1132_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.54
% 0.30/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.54 thf(fact_1133_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.30/0.54
% 0.30/0.54 % linordered_nonzero_semiring_class.zero_le_one
% 0.30/0.54 thf(fact_1134_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 0.30/0.54
% 0.30/0.54 % zero_less_one_class.zero_le_one
% 0.30/0.54 thf(fact_1135_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 0.30/0.54
% 0.30/0.54 % zero_less_one_class.zero_le_one
% 0.30/0.54 thf(fact_1136_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 0.30/0.54
% 0.30/0.54 % zero_less_one_class.zero_le_one
% 0.30/0.54 thf(fact_1137_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 0.30/0.54
% 0.30/0.54 % zero_less_one_class.zero_le_one
% 0.30/0.54 thf(fact_1138_zero__less__one__class_Ozero__le__one,axiom,
% 0.30/0.54 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.30/0.54
% 0.30/0.54 % zero_less_one_class.zero_le_one
% 0.30/0.54 thf(fact_1139_nat__mult__le__cancel1,axiom,
% 0.30/0.54 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.54 => ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.30/0.54 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % nat_mult_le_cancel1
% 0.30/0.54 thf(fact_1140_less__Suc__eq__0__disj,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 0.30/0.54 = ( ( M2 = zero_zero_nat )
% 0.30/0.54 | ? [J: nat] :
% 0.30/0.54 ( ( M2
% 0.30/0.54 = ( suc @ J ) )
% 0.30/0.54 & ( ord_less_nat @ J @ N ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_Suc_eq_0_disj
% 0.30/0.54 thf(fact_1141_gr0__implies__Suc,axiom,
% 0.30/0.54 ! [N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.54 => ? [M: nat] :
% 0.30/0.54 ( N
% 0.30/0.54 = ( suc @ M ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % gr0_implies_Suc
% 0.30/0.54 thf(fact_1142_All__less__Suc2,axiom,
% 0.30/0.54 ! [N: nat,P2: nat > $o] :
% 0.30/0.54 ( ( ! [I: nat] :
% 0.30/0.54 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 0.30/0.54 => ( P2 @ I ) ) )
% 0.30/0.54 = ( ( P2 @ zero_zero_nat )
% 0.30/0.54 & ! [I: nat] :
% 0.30/0.54 ( ( ord_less_nat @ I @ N )
% 0.30/0.54 => ( P2 @ ( suc @ I ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % All_less_Suc2
% 0.30/0.54 thf(fact_1143_gr0__conv__Suc,axiom,
% 0.30/0.54 ! [N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.54 = ( ? [M6: nat] :
% 0.30/0.54 ( N
% 0.30/0.54 = ( suc @ M6 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % gr0_conv_Suc
% 0.30/0.54 thf(fact_1144_Ex__less__Suc2,axiom,
% 0.30/0.54 ! [N: nat,P2: nat > $o] :
% 0.30/0.54 ( ( ? [I: nat] :
% 0.30/0.54 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 0.30/0.54 & ( P2 @ I ) ) )
% 0.30/0.54 = ( ( P2 @ zero_zero_nat )
% 0.30/0.54 | ? [I: nat] :
% 0.30/0.54 ( ( ord_less_nat @ I @ N )
% 0.30/0.54 & ( P2 @ ( suc @ I ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % Ex_less_Suc2
% 0.30/0.54 thf(fact_1145_le__imp__less__Suc,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.54 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_imp_less_Suc
% 0.30/0.54 thf(fact_1146_less__eq__Suc__le,axiom,
% 0.30/0.54 ( ord_less_nat
% 0.30/0.54 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_eq_Suc_le
% 0.30/0.54 thf(fact_1147_less__Suc__eq__le,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 0.30/0.54 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_Suc_eq_le
% 0.30/0.54 thf(fact_1148_le__less__Suc__eq,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.54 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 0.30/0.54 = ( N = M2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_less_Suc_eq
% 0.30/0.54 thf(fact_1149_Suc__le__lessD,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.30/0.54 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % Suc_le_lessD
% 0.30/0.54 thf(fact_1150_inc__induct,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,P2: nat > $o] :
% 0.30/0.54 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.54 => ( ( P2 @ J2 )
% 0.30/0.54 => ( ! [N3: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ I2 @ N3 )
% 0.30/0.54 => ( ( ord_less_nat @ N3 @ J2 )
% 0.30/0.54 => ( ( P2 @ ( suc @ N3 ) )
% 0.30/0.54 => ( P2 @ N3 ) ) ) )
% 0.30/0.54 => ( P2 @ I2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % inc_induct
% 0.30/0.54 thf(fact_1151_dec__induct,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,P2: nat > $o] :
% 0.30/0.54 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.54 => ( ( P2 @ I2 )
% 0.30/0.54 => ( ! [N3: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ I2 @ N3 )
% 0.30/0.54 => ( ( ord_less_nat @ N3 @ J2 )
% 0.30/0.54 => ( ( P2 @ N3 )
% 0.30/0.54 => ( P2 @ ( suc @ N3 ) ) ) ) )
% 0.30/0.54 => ( P2 @ J2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % dec_induct
% 0.30/0.54 thf(fact_1152_Suc__le__eq,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.30/0.54 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % Suc_le_eq
% 0.30/0.54 thf(fact_1153_Suc__leI,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.54 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % Suc_leI
% 0.30/0.54 thf(fact_1154_ex__least__nat__le,axiom,
% 0.30/0.54 ! [P2: nat > $o,N: nat] :
% 0.30/0.54 ( ( P2 @ N )
% 0.30/0.54 => ( ~ ( P2 @ zero_zero_nat )
% 0.30/0.54 => ? [K: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.54 & ! [I4: nat] :
% 0.30/0.54 ( ( ord_less_nat @ I4 @ K )
% 0.30/0.54 => ~ ( P2 @ I4 ) )
% 0.30/0.54 & ( P2 @ K ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ex_least_nat_le
% 0.30/0.54 thf(fact_1155_Suc__mult__less__cancel1,axiom,
% 0.30/0.54 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K2 ) @ M2 ) @ ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 0.30/0.54 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % Suc_mult_less_cancel1
% 0.30/0.54 thf(fact_1156_mult__less__mono1,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_mono1
% 0.30/0.54 thf(fact_1157_mult__less__mono2,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_mono2
% 0.30/0.54 thf(fact_1158_One__nat__def,axiom,
% 0.30/0.54 ( one_one_nat
% 0.30/0.54 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % One_nat_def
% 0.30/0.54 thf(fact_1159_mult__eq__self__implies__10,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( M2
% 0.30/0.54 = ( times_times_nat @ M2 @ N ) )
% 0.30/0.54 => ( ( N = one_one_nat )
% 0.30/0.54 | ( M2 = zero_zero_nat ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_eq_self_implies_10
% 0.30/0.54 thf(fact_1160_mult__less__le__imp__less,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_real @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.54 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_le_imp_less
% 0.30/0.54 thf(fact_1161_mult__less__le__imp__less,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.54 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_le_imp_less
% 0.30/0.54 thf(fact_1162_mult__less__le__imp__less,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_le_imp_less
% 0.30/0.54 thf(fact_1163_mult__less__le__imp__less,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_int @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.54 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_le_imp_less
% 0.30/0.54 thf(fact_1164_mult__le__less__imp__less,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_real @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_less_imp_less
% 0.30/0.54 thf(fact_1165_mult__le__less__imp__less,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_rat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_less_imp_less
% 0.30/0.54 thf(fact_1166_mult__le__less__imp__less,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_nat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_less_imp_less
% 0.30/0.54 thf(fact_1167_mult__le__less__imp__less,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_int @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_less_imp_less
% 0.30/0.54 thf(fact_1168_mult__right__le__imp__le,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_imp_le
% 0.30/0.54 thf(fact_1169_mult__right__le__imp__le,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_imp_le
% 0.30/0.54 thf(fact_1170_mult__right__le__imp__le,axiom,
% 0.30/0.54 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_imp_le
% 0.30/0.54 thf(fact_1171_mult__right__le__imp__le,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_imp_le
% 0.30/0.54 thf(fact_1172_mult__left__le__imp__le,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_imp_le
% 0.30/0.54 thf(fact_1173_mult__left__le__imp__le,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_imp_le
% 0.30/0.54 thf(fact_1174_mult__left__le__imp__le,axiom,
% 0.30/0.54 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_imp_le
% 0.30/0.54 thf(fact_1175_mult__left__le__imp__le,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_imp_le
% 0.30/0.54 thf(fact_1176_mult__le__cancel__left__pos,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left_pos
% 0.30/0.54 thf(fact_1177_mult__le__cancel__left__pos,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left_pos
% 0.30/0.54 thf(fact_1178_mult__le__cancel__left__pos,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left_pos
% 0.30/0.54 thf(fact_1179_mult__le__cancel__left__neg,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.54 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left_neg
% 0.30/0.54 thf(fact_1180_mult__le__cancel__left__neg,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.54 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left_neg
% 0.30/0.54 thf(fact_1181_mult__le__cancel__left__neg,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.54 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left_neg
% 0.30/0.54 thf(fact_1182_mult__less__cancel__right,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.54 => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_right
% 0.30/0.54 thf(fact_1183_mult__less__cancel__right,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.54 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_right
% 0.30/0.54 thf(fact_1184_mult__less__cancel__right,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.54 => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_right
% 0.30/0.54 thf(fact_1185_mult__strict__mono_H,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_real @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono'
% 0.30/0.54 thf(fact_1186_mult__strict__mono_H,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_rat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono'
% 0.30/0.54 thf(fact_1187_mult__strict__mono_H,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_nat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono'
% 0.30/0.54 thf(fact_1188_mult__strict__mono_H,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_int @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono'
% 0.30/0.54 thf(fact_1189_mult__right__less__imp__less,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_less_imp_less
% 0.30/0.54 thf(fact_1190_mult__right__less__imp__less,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_less_imp_less
% 0.30/0.54 thf(fact_1191_mult__right__less__imp__less,axiom,
% 0.30/0.54 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_less_imp_less
% 0.30/0.54 thf(fact_1192_mult__right__less__imp__less,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_less_imp_less
% 0.30/0.54 thf(fact_1193_mult__less__cancel__left,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.54 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.54 => ( ord_less_real @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_left
% 0.30/0.54 thf(fact_1194_mult__less__cancel__left,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.54 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.54 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_left
% 0.30/0.54 thf(fact_1195_mult__less__cancel__left,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.54 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.54 => ( ord_less_int @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_cancel_left
% 0.30/0.54 thf(fact_1196_mult__strict__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_real @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono
% 0.30/0.54 thf(fact_1197_mult__strict__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_rat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono
% 0.30/0.54 thf(fact_1198_mult__strict__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_nat @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono
% 0.30/0.54 thf(fact_1199_mult__strict__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_int @ C2 @ D )
% 0.30/0.54 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_strict_mono
% 0.30/0.54 thf(fact_1200_mult__left__less__imp__less,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_real @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_less_imp_less
% 0.30/0.54 thf(fact_1201_mult__left__less__imp__less,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_less_imp_less
% 0.30/0.54 thf(fact_1202_mult__left__less__imp__less,axiom,
% 0.30/0.54 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.54 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_less_imp_less
% 0.30/0.54 thf(fact_1203_mult__left__less__imp__less,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_less_imp_less
% 0.30/0.54 thf(fact_1204_mult__le__cancel__right,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_eq_real @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.54 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_right
% 0.30/0.54 thf(fact_1205_mult__le__cancel__right,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_eq_rat @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.54 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_right
% 0.30/0.54 thf(fact_1206_mult__le__cancel__right,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.30/0.54 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_eq_int @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.54 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_right
% 0.30/0.54 thf(fact_1207_mult__le__cancel__left,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.30/0.54 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.30/0.54 => ( ord_less_eq_real @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.30/0.54 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left
% 0.30/0.54 thf(fact_1208_mult__le__cancel__left,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.30/0.54 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.30/0.54 => ( ord_less_eq_rat @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.30/0.54 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left
% 0.30/0.54 thf(fact_1209_mult__le__cancel__left,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.30/0.54 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 0.30/0.54 => ( ord_less_eq_int @ A @ B ) )
% 0.30/0.54 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 0.30/0.54 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_left
% 0.30/0.54 thf(fact_1210_VEBT__internal_Onaive__member_Ocases,axiom,
% 0.30/0.54 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.54 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.30/0.54 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Ux ) )
% 0.30/0.54 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X3 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.naive_member.cases
% 0.30/0.54 thf(fact_1211_mult__left__le,axiom,
% 0.30/0.54 ! [C2: code_integer,A: code_integer] :
% 0.30/0.54 ( ( ord_le3102999989581377725nteger @ C2 @ one_one_Code_integer )
% 0.30/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.54 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le
% 0.30/0.54 thf(fact_1212_mult__left__le,axiom,
% 0.30/0.54 ! [C2: real,A: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ C2 @ one_one_real )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.54 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le
% 0.30/0.54 thf(fact_1213_mult__left__le,axiom,
% 0.30/0.54 ! [C2: rat,A: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ C2 @ one_one_rat )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.54 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le
% 0.30/0.54 thf(fact_1214_mult__left__le,axiom,
% 0.30/0.54 ! [C2: nat,A: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ C2 @ one_one_nat )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.54 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le
% 0.30/0.54 thf(fact_1215_mult__left__le,axiom,
% 0.30/0.54 ! [C2: int,A: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ C2 @ one_one_int )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.54 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ A ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le
% 0.30/0.54 thf(fact_1216_mult__le__one,axiom,
% 0.30/0.54 ! [A: code_integer,B: code_integer] :
% 0.30/0.54 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.54 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 0.30/0.54 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_one
% 0.30/0.54 thf(fact_1217_mult__le__one,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ A @ one_one_real )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.54 => ( ( ord_less_eq_real @ B @ one_one_real )
% 0.30/0.54 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_one
% 0.30/0.54 thf(fact_1218_mult__le__one,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.54 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 0.30/0.54 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_one
% 0.30/0.54 thf(fact_1219_mult__le__one,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.54 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.54 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 0.30/0.54 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_one
% 0.30/0.54 thf(fact_1220_mult__le__one,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.54 => ( ( ord_less_eq_int @ B @ one_one_int )
% 0.30/0.54 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_one
% 0.30/0.54 thf(fact_1221_mult__right__le__one__le,axiom,
% 0.30/0.54 ! [X: code_integer,Y: code_integer] :
% 0.30/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.30/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.30/0.54 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.30/0.54 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_one_le
% 0.30/0.54 thf(fact_1222_mult__right__le__one__le,axiom,
% 0.30/0.54 ! [X: real,Y: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.30/0.54 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.30/0.54 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_one_le
% 0.30/0.54 thf(fact_1223_mult__right__le__one__le,axiom,
% 0.30/0.54 ! [X: rat,Y: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.30/0.54 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.30/0.54 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_one_le
% 0.30/0.54 thf(fact_1224_mult__right__le__one__le,axiom,
% 0.30/0.54 ! [X: int,Y: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.54 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.30/0.54 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_right_le_one_le
% 0.30/0.54 thf(fact_1225_mult__left__le__one__le,axiom,
% 0.30/0.54 ! [X: code_integer,Y: code_integer] :
% 0.30/0.54 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.30/0.54 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.30/0.54 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 0.30/0.54 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_one_le
% 0.30/0.54 thf(fact_1226_mult__left__le__one__le,axiom,
% 0.30/0.54 ! [X: real,Y: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.30/0.54 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.30/0.54 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 0.30/0.54 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_one_le
% 0.30/0.54 thf(fact_1227_mult__left__le__one__le,axiom,
% 0.30/0.54 ! [X: rat,Y: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.54 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.30/0.54 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 0.30/0.54 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_one_le
% 0.30/0.54 thf(fact_1228_mult__left__le__one__le,axiom,
% 0.30/0.54 ! [X: int,Y: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.54 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.54 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 0.30/0.54 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_left_le_one_le
% 0.30/0.54 thf(fact_1229_ex__least__nat__less,axiom,
% 0.30/0.54 ! [P2: nat > $o,N: nat] :
% 0.30/0.54 ( ( P2 @ N )
% 0.30/0.54 => ( ~ ( P2 @ zero_zero_nat )
% 0.30/0.54 => ? [K: nat] :
% 0.30/0.54 ( ( ord_less_nat @ K @ N )
% 0.30/0.54 & ! [I4: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ I4 @ K )
% 0.30/0.54 => ~ ( P2 @ I4 ) )
% 0.30/0.54 & ( P2 @ ( suc @ K ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ex_least_nat_less
% 0.30/0.54 thf(fact_1230_n__less__n__mult__m,axiom,
% 0.30/0.54 ! [N: nat,M2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.54 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 0.30/0.54 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % n_less_n_mult_m
% 0.30/0.54 thf(fact_1231_n__less__m__mult__n,axiom,
% 0.30/0.54 ! [N: nat,M2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.54 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 0.30/0.54 => ( ord_less_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % n_less_m_mult_n
% 0.30/0.54 thf(fact_1232_one__less__mult,axiom,
% 0.30/0.54 ! [N: nat,M2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.30/0.54 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 0.30/0.54 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % one_less_mult
% 0.30/0.54 thf(fact_1233_greater__shift,axiom,
% 0.30/0.54 ( ord_less_nat
% 0.30/0.54 = ( ^ [Y4: nat,X4: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % greater_shift
% 0.30/0.54 thf(fact_1234_less__shift,axiom,
% 0.30/0.54 ( ord_less_nat
% 0.30/0.54 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_less @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_shift
% 0.30/0.54 thf(fact_1235_buildup__gives__valid,axiom,
% 0.30/0.54 ! [N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.54 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % buildup_gives_valid
% 0.30/0.54 thf(fact_1236_field__le__mult__one__interval,axiom,
% 0.30/0.54 ! [X: real,Y: real] :
% 0.30/0.54 ( ! [Z: real] :
% 0.30/0.54 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.30/0.54 => ( ( ord_less_real @ Z @ one_one_real )
% 0.30/0.54 => ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ Y ) ) )
% 0.30/0.54 => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.30/0.54
% 0.30/0.54 % field_le_mult_one_interval
% 0.30/0.54 thf(fact_1237_field__le__mult__one__interval,axiom,
% 0.30/0.54 ! [X: rat,Y: rat] :
% 0.30/0.54 ( ! [Z: rat] :
% 0.30/0.54 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 0.30/0.54 => ( ( ord_less_rat @ Z @ one_one_rat )
% 0.30/0.54 => ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ Y ) ) )
% 0.30/0.54 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.30/0.54
% 0.30/0.54 % field_le_mult_one_interval
% 0.30/0.54 thf(fact_1238_case4_I2_J,axiom,
% 0.30/0.54 ! [S2: vEBT_VEBT] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ S2 @ m )
% 0.30/0.54 => ( ( ( vEBT_VEBT_set_vebt @ summary2 )
% 0.30/0.54 = ( vEBT_VEBT_set_vebt @ S2 ) )
% 0.30/0.54 => ( S2 = summary2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % case4(2)
% 0.30/0.54 thf(fact_1239_maxt__corr,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_maxt @ T )
% 0.30/0.54 = ( some_nat @ X ) )
% 0.30/0.54 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % maxt_corr
% 0.30/0.54 thf(fact_1240_maxt__sound,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.30/0.54 => ( ( vEBT_vebt_maxt @ T )
% 0.30/0.54 = ( some_nat @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % maxt_sound
% 0.30/0.54 thf(fact_1241_mint__corr,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_mint @ T )
% 0.30/0.54 = ( some_nat @ X ) )
% 0.30/0.54 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mint_corr
% 0.30/0.54 thf(fact_1242_mint__sound,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 0.30/0.54 => ( ( vEBT_vebt_mint @ T )
% 0.30/0.54 = ( some_nat @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mint_sound
% 0.30/0.54 thf(fact_1243_mult__le__cancel__iff2,axiom,
% 0.30/0.54 ! [Z3: real,X: real,Y: real] :
% 0.30/0.54 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.30/0.54 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ ( times_times_real @ Z3 @ Y ) )
% 0.30/0.54 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_iff2
% 0.30/0.54 thf(fact_1244_mult__le__cancel__iff2,axiom,
% 0.30/0.54 ! [Z3: rat,X: rat,Y: rat] :
% 0.30/0.54 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.30/0.54 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ ( times_times_rat @ Z3 @ Y ) )
% 0.30/0.54 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_iff2
% 0.30/0.54 thf(fact_1245_mult__le__cancel__iff2,axiom,
% 0.30/0.54 ! [Z3: int,X: int,Y: int] :
% 0.30/0.54 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 0.30/0.54 => ( ( ord_less_eq_int @ ( times_times_int @ Z3 @ X ) @ ( times_times_int @ Z3 @ Y ) )
% 0.30/0.54 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_iff2
% 0.30/0.54 thf(fact_1246_mult__le__cancel__iff1,axiom,
% 0.30/0.54 ! [Z3: real,X: real,Y: real] :
% 0.30/0.54 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.30/0.54 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 0.30/0.54 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_iff1
% 0.30/0.54 thf(fact_1247_mult__le__cancel__iff1,axiom,
% 0.30/0.54 ! [Z3: rat,X: rat,Y: rat] :
% 0.30/0.54 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.30/0.54 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 0.30/0.54 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_iff1
% 0.30/0.54 thf(fact_1248_mult__le__cancel__iff1,axiom,
% 0.30/0.54 ! [Z3: int,X: int,Y: int] :
% 0.30/0.54 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 0.30/0.54 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 0.30/0.54 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_le_cancel_iff1
% 0.30/0.54 thf(fact_1249_ac,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,H: nat,K2: vEBT_VEBT] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ H )
% 0.30/0.54 => ( ( vEBT_invar_vebt @ K2 @ H )
% 0.30/0.54 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 0.30/0.54 = ( vEBT_VEBT_set_vebt @ K2 ) )
% 0.30/0.54 => ( ( vEBT_vebt_mint @ T )
% 0.30/0.54 = ( vEBT_vebt_mint @ K2 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ac
% 0.30/0.54 thf(fact_1250_ad,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,H: nat,K2: vEBT_VEBT] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ H )
% 0.30/0.54 => ( ( vEBT_invar_vebt @ K2 @ H )
% 0.30/0.54 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 0.30/0.54 = ( vEBT_VEBT_set_vebt @ K2 ) )
% 0.30/0.54 => ( ( vEBT_vebt_maxt @ T )
% 0.30/0.54 = ( vEBT_vebt_maxt @ K2 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ad
% 0.30/0.54 thf(fact_1251_case4_I5_J,axiom,
% 0.30/0.54 m = na ).
% 0.30/0.54
% 0.30/0.54 % case4(5)
% 0.30/0.54 thf(fact_1252_vebt__buildup_Osimps_I1_J,axiom,
% 0.30/0.54 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 0.30/0.54 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.30/0.54
% 0.30/0.54 % vebt_buildup.simps(1)
% 0.30/0.54 thf(fact_1253_vebt__buildup_Osimps_I2_J,axiom,
% 0.30/0.54 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 0.30/0.54 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 0.30/0.54
% 0.30/0.54 % vebt_buildup.simps(2)
% 0.30/0.54 thf(fact_1254_mult__less__iff1,axiom,
% 0.30/0.54 ! [Z3: real,X: real,Y: real] :
% 0.30/0.54 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.30/0.54 => ( ( ord_less_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 0.30/0.54 = ( ord_less_real @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_iff1
% 0.30/0.54 thf(fact_1255_mult__less__iff1,axiom,
% 0.30/0.54 ! [Z3: rat,X: rat,Y: rat] :
% 0.30/0.54 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 0.30/0.54 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 0.30/0.54 = ( ord_less_rat @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_iff1
% 0.30/0.54 thf(fact_1256_mult__less__iff1,axiom,
% 0.30/0.54 ! [Z3: int,X: int,Y: int] :
% 0.30/0.54 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 0.30/0.54 => ( ( ord_less_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 0.30/0.54 = ( ord_less_int @ X @ Y ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_less_iff1
% 0.30/0.54 thf(fact_1257_vebt__maxt_Osimps_I3_J,axiom,
% 0.30/0.54 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.30/0.54 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.30/0.54 = ( some_nat @ Ma ) ) ).
% 0.30/0.54
% 0.30/0.54 % vebt_maxt.simps(3)
% 0.30/0.54 thf(fact_1258_vebt__mint_Osimps_I3_J,axiom,
% 0.30/0.54 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 0.30/0.54 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 0.30/0.54 = ( some_nat @ Mi ) ) ).
% 0.30/0.54
% 0.30/0.54 % vebt_mint.simps(3)
% 0.30/0.54 thf(fact_1259_maxt__corr__help,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_maxt @ T )
% 0.30/0.54 = ( some_nat @ Maxi ) )
% 0.30/0.54 => ( ( vEBT_vebt_member @ T @ X )
% 0.30/0.54 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % maxt_corr_help
% 0.30/0.54 thf(fact_1260_mint__corr__help,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_mint @ T )
% 0.30/0.54 = ( some_nat @ Mini ) )
% 0.30/0.54 => ( ( vEBT_vebt_member @ T @ X )
% 0.30/0.54 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mint_corr_help
% 0.30/0.54 thf(fact_1261_buildup__nothing__in__leaf,axiom,
% 0.30/0.54 ! [N: nat,X: nat] :
% 0.30/0.54 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.30/0.54
% 0.30/0.54 % buildup_nothing_in_leaf
% 0.30/0.54 thf(fact_1262_maxt__member,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_maxt @ T )
% 0.30/0.54 = ( some_nat @ Maxi ) )
% 0.30/0.54 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % maxt_member
% 0.30/0.54 thf(fact_1263_mint__member,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_mint @ T )
% 0.30/0.54 = ( some_nat @ Maxi ) )
% 0.30/0.54 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mint_member
% 0.30/0.54 thf(fact_1264_aa,axiom,
% 0.30/0.54 ord_less_eq_set_nat @ ( insert_nat @ mi @ ( insert_nat @ ma @ bot_bot_set_nat ) ) @ ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % aa
% 0.30/0.54 thf(fact_1265_VEBT__internal_Oinsert_H_Ocases,axiom,
% 0.30/0.54 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.54 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.30/0.54 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ X3 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.insert'.cases
% 0.30/0.54 thf(fact_1266_member__correct,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( vEBT_vebt_member @ T @ X )
% 0.30/0.54 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % member_correct
% 0.30/0.54 thf(fact_1267_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.30/0.54 ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 0.30/0.54 ( ( vEBT_V1502963449132264192at_nat @ F2 @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ ( F2 @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_shift.simps(3)
% 0.30/0.54 thf(fact_1268_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.30/0.54 ! [F2: num > num > num,A: num,B: num] :
% 0.30/0.54 ( ( vEBT_V819420779217536731ft_num @ F2 @ ( some_num @ A ) @ ( some_num @ B ) )
% 0.30/0.54 = ( some_num @ ( F2 @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_shift.simps(3)
% 0.30/0.54 thf(fact_1269_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 0.30/0.54 ! [F2: nat > nat > nat,A: nat,B: nat] :
% 0.30/0.54 ( ( vEBT_V4262088993061758097ft_nat @ F2 @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 0.30/0.54 = ( some_nat @ ( F2 @ A @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_shift.simps(3)
% 0.30/0.54 thf(fact_1270_buildup__gives__empty,axiom,
% 0.30/0.54 ! [N: nat] :
% 0.30/0.54 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 0.30/0.54 = bot_bot_set_nat ) ).
% 0.30/0.54
% 0.30/0.54 % buildup_gives_empty
% 0.30/0.54 thf(fact_1271_pred__member,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 0.30/0.54 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 0.30/0.54 = ( ( vEBT_vebt_member @ T @ Y )
% 0.30/0.54 & ( ord_less_nat @ Y @ X )
% 0.30/0.54 & ! [Z4: nat] :
% 0.30/0.54 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 0.30/0.54 & ( ord_less_nat @ Z4 @ X ) )
% 0.30/0.54 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % pred_member
% 0.30/0.54 thf(fact_1272_succ__member,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 0.30/0.54 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 0.30/0.54 = ( ( vEBT_vebt_member @ T @ Y )
% 0.30/0.54 & ( ord_less_nat @ X @ Y )
% 0.30/0.54 & ! [Z4: nat] :
% 0.30/0.54 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 0.30/0.54 & ( ord_less_nat @ X @ Z4 ) )
% 0.30/0.54 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % succ_member
% 0.30/0.54 thf(fact_1273_case4_I6_J,axiom,
% 0.30/0.54 ( deg
% 0.30/0.54 = ( plus_plus_nat @ na @ m ) ) ).
% 0.30/0.54
% 0.30/0.54 % case4(6)
% 0.30/0.54 thf(fact_1274_case4_I1_J,axiom,
% 0.30/0.54 ! [X5: vEBT_VEBT] :
% 0.30/0.54 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 0.30/0.54 => ( ( vEBT_invar_vebt @ X5 @ na )
% 0.30/0.54 & ! [Xa: vEBT_VEBT] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ Xa @ na )
% 0.30/0.54 => ( ( ( vEBT_VEBT_set_vebt @ X5 )
% 0.30/0.54 = ( vEBT_VEBT_set_vebt @ Xa ) )
% 0.30/0.54 => ( Xa = X5 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % case4(1)
% 0.30/0.54 thf(fact_1275_bot_Oextremum__uniqueI,axiom,
% 0.30/0.54 ! [A: set_int] :
% 0.30/0.54 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.30/0.54 => ( A = bot_bot_set_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_uniqueI
% 0.30/0.54 thf(fact_1276_bot_Oextremum__uniqueI,axiom,
% 0.30/0.54 ! [A: set_real] :
% 0.30/0.54 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.30/0.54 => ( A = bot_bot_set_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_uniqueI
% 0.30/0.54 thf(fact_1277_bot_Oextremum__uniqueI,axiom,
% 0.30/0.54 ! [A: set_nat] :
% 0.30/0.54 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.30/0.54 => ( A = bot_bot_set_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_uniqueI
% 0.30/0.54 thf(fact_1278_bot_Oextremum__uniqueI,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.30/0.54 => ( A = bot_bot_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_uniqueI
% 0.30/0.54 thf(fact_1279_bot_Oextremum__unique,axiom,
% 0.30/0.54 ! [A: set_int] :
% 0.30/0.54 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 0.30/0.54 = ( A = bot_bot_set_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_unique
% 0.30/0.54 thf(fact_1280_bot_Oextremum__unique,axiom,
% 0.30/0.54 ! [A: set_real] :
% 0.30/0.54 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 0.30/0.54 = ( A = bot_bot_set_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_unique
% 0.30/0.54 thf(fact_1281_bot_Oextremum__unique,axiom,
% 0.30/0.54 ! [A: set_nat] :
% 0.30/0.54 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 0.30/0.54 = ( A = bot_bot_set_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_unique
% 0.30/0.54 thf(fact_1282_bot_Oextremum__unique,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 0.30/0.54 = ( A = bot_bot_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_unique
% 0.30/0.54 thf(fact_1283_bot_Oextremum,axiom,
% 0.30/0.54 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum
% 0.30/0.54 thf(fact_1284_bot_Oextremum,axiom,
% 0.30/0.54 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum
% 0.30/0.54 thf(fact_1285_bot_Oextremum,axiom,
% 0.30/0.54 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum
% 0.30/0.54 thf(fact_1286_bot_Oextremum,axiom,
% 0.30/0.54 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum
% 0.30/0.54 thf(fact_1287_bot_Oextremum__strict,axiom,
% 0.30/0.54 ! [A: set_nat] :
% 0.30/0.54 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_strict
% 0.30/0.54 thf(fact_1288_bot_Oextremum__strict,axiom,
% 0.30/0.54 ! [A: set_int] :
% 0.30/0.54 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_strict
% 0.30/0.54 thf(fact_1289_bot_Oextremum__strict,axiom,
% 0.30/0.54 ! [A: set_real] :
% 0.30/0.54 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_strict
% 0.30/0.54 thf(fact_1290_bot_Oextremum__strict,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 0.30/0.54
% 0.30/0.54 % bot.extremum_strict
% 0.30/0.54 thf(fact_1291_bot_Onot__eq__extremum,axiom,
% 0.30/0.54 ! [A: set_nat] :
% 0.30/0.54 ( ( A != bot_bot_set_nat )
% 0.30/0.54 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.not_eq_extremum
% 0.30/0.54 thf(fact_1292_bot_Onot__eq__extremum,axiom,
% 0.30/0.54 ! [A: set_int] :
% 0.30/0.54 ( ( A != bot_bot_set_int )
% 0.30/0.54 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.not_eq_extremum
% 0.30/0.54 thf(fact_1293_bot_Onot__eq__extremum,axiom,
% 0.30/0.54 ! [A: set_real] :
% 0.30/0.54 ( ( A != bot_bot_set_real )
% 0.30/0.54 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.not_eq_extremum
% 0.30/0.54 thf(fact_1294_bot_Onot__eq__extremum,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ( ( A != bot_bot_nat )
% 0.30/0.54 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % bot.not_eq_extremum
% 0.30/0.54 thf(fact_1295_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 0.30/0.54 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 0.30/0.54 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw2 ) @ Ux2 ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.naive_member.simps(2)
% 0.30/0.54 thf(fact_1296_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 0.30/0.54 ! [A: $o,B: $o,X: nat] :
% 0.30/0.54 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.30/0.54 = ( ( ( X = zero_zero_nat )
% 0.30/0.54 => A )
% 0.30/0.54 & ( ( X != zero_zero_nat )
% 0.30/0.54 => ( ( ( X = one_one_nat )
% 0.30/0.54 => B )
% 0.30/0.54 & ( X = one_one_nat ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.naive_member.simps(1)
% 0.30/0.54 thf(fact_1297_member__valid__both__member__options,axiom,
% 0.30/0.54 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ Tree @ N )
% 0.30/0.54 => ( ( vEBT_vebt_member @ Tree @ X )
% 0.30/0.54 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 0.30/0.54 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % member_valid_both_member_options
% 0.30/0.54 thf(fact_1298_vebt__member_Osimps_I4_J,axiom,
% 0.30/0.54 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.30/0.54 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 0.30/0.54
% 0.30/0.54 % vebt_member.simps(4)
% 0.30/0.54 thf(fact_1299_vebt__member_Osimps_I1_J,axiom,
% 0.30/0.54 ! [A: $o,B: $o,X: nat] :
% 0.30/0.54 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.30/0.54 = ( ( ( X = zero_zero_nat )
% 0.30/0.54 => A )
% 0.30/0.54 & ( ( X != zero_zero_nat )
% 0.30/0.54 => ( ( ( X = one_one_nat )
% 0.30/0.54 => B )
% 0.30/0.54 & ( X = one_one_nat ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % vebt_member.simps(1)
% 0.30/0.54 thf(fact_1300_vebt__member_Osimps_I3_J,axiom,
% 0.30/0.54 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 0.30/0.54 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X ) ).
% 0.30/0.54
% 0.30/0.54 % vebt_member.simps(3)
% 0.30/0.54 thf(fact_1301_maxt__corr__help__empty,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_maxt @ T )
% 0.30/0.54 = none_nat )
% 0.30/0.54 => ( ( vEBT_VEBT_set_vebt @ T )
% 0.30/0.54 = bot_bot_set_nat ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % maxt_corr_help_empty
% 0.30/0.54 thf(fact_1302_mint__corr__help__empty,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( ( vEBT_vebt_mint @ T )
% 0.30/0.54 = none_nat )
% 0.30/0.54 => ( ( vEBT_VEBT_set_vebt @ T )
% 0.30/0.54 = bot_bot_set_nat ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mint_corr_help_empty
% 0.30/0.54 thf(fact_1303_buildup__nothing__in__min__max,axiom,
% 0.30/0.54 ! [N: nat,X: nat] :
% 0.30/0.54 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 0.30/0.54
% 0.30/0.54 % buildup_nothing_in_min_max
% 0.30/0.54 thf(fact_1304_dele__member__cont__corr,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 0.30/0.54 = ( ( X != Y )
% 0.30/0.54 & ( vEBT_vebt_member @ T @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % dele_member_cont_corr
% 0.30/0.54 thf(fact_1305_VEBT__internal_Omembermima_Ocases,axiom,
% 0.30/0.54 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.54 ( ! [Uu2: $o,Uv2: $o,Uw: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw ) )
% 0.30/0.54 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz2: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz2 ) )
% 0.30/0.54 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 ) )
% 0.30/0.54 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ X3 ) )
% 0.30/0.54 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X3 ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.membermima.cases
% 0.30/0.54 thf(fact_1306_case4_I8_J,axiom,
% 0.30/0.54 ( ( mi = ma )
% 0.30/0.54 => ! [X5: vEBT_VEBT] :
% 0.30/0.54 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 0.30/0.54 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % case4(8)
% 0.30/0.54 thf(fact_1307_even__odd__cases,axiom,
% 0.30/0.54 ! [X: nat] :
% 0.30/0.54 ( ! [N3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( plus_plus_nat @ N3 @ N3 ) )
% 0.30/0.54 => ~ ! [N3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % even_odd_cases
% 0.30/0.54 thf(fact_1308_delete__pres__valid,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % delete_pres_valid
% 0.30/0.54 thf(fact_1309_maxbmo,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,X: nat] :
% 0.30/0.54 ( ( ( vEBT_vebt_maxt @ T )
% 0.30/0.54 = ( some_nat @ X ) )
% 0.30/0.54 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 0.30/0.54
% 0.30/0.54 % maxbmo
% 0.30/0.54 thf(fact_1310_dele__bmo__cont__corr,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 0.30/0.54 = ( ( X != Y )
% 0.30/0.54 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % dele_bmo_cont_corr
% 0.30/0.54 thf(fact_1311_both__member__options__equiv__member,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.30/0.54 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % both_member_options_equiv_member
% 0.30/0.54 thf(fact_1312_valid__member__both__member__options,axiom,
% 0.30/0.54 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.54 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.30/0.54 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % valid_member_both_member_options
% 0.30/0.54 thf(fact_1313_both__member__options__def,axiom,
% 0.30/0.54 ( vEBT_V8194947554948674370ptions
% 0.30/0.54 = ( ^ [T2: vEBT_VEBT,X4: nat] :
% 0.30/0.54 ( ( vEBT_V5719532721284313246member @ T2 @ X4 )
% 0.30/0.54 | ( vEBT_VEBT_membermima @ T2 @ X4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % both_member_options_def
% 0.30/0.54 thf(fact_1314_add__right__cancel,axiom,
% 0.30/0.54 ! [B: real,A: real,C2: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ B @ A )
% 0.30/0.54 = ( plus_plus_real @ C2 @ A ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_cancel
% 0.30/0.54 thf(fact_1315_add__right__cancel,axiom,
% 0.30/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.54 = ( plus_plus_rat @ C2 @ A ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_cancel
% 0.30/0.54 thf(fact_1316_add__right__cancel,axiom,
% 0.30/0.54 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ B @ A )
% 0.30/0.54 = ( plus_plus_nat @ C2 @ A ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_cancel
% 0.30/0.54 thf(fact_1317_add__right__cancel,axiom,
% 0.30/0.54 ! [B: int,A: int,C2: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ B @ A )
% 0.30/0.54 = ( plus_plus_int @ C2 @ A ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_cancel
% 0.30/0.54 thf(fact_1318_add__left__cancel,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ A @ B )
% 0.30/0.54 = ( plus_plus_real @ A @ C2 ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_cancel
% 0.30/0.54 thf(fact_1319_add__left__cancel,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.54 = ( plus_plus_rat @ A @ C2 ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_cancel
% 0.30/0.54 thf(fact_1320_add__left__cancel,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ A @ B )
% 0.30/0.54 = ( plus_plus_nat @ A @ C2 ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_cancel
% 0.30/0.54 thf(fact_1321_add__left__cancel,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ A @ B )
% 0.30/0.54 = ( plus_plus_int @ A @ C2 ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_cancel
% 0.30/0.54 thf(fact_1322_mi__eq__ma__no__ch,axiom,
% 0.30/0.54 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.30/0.54 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 0.30/0.54 => ( ( Mi = Ma )
% 0.30/0.54 => ( ! [X5: vEBT_VEBT] :
% 0.30/0.54 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.30/0.54 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 0.30/0.54 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mi_eq_ma_no_ch
% 0.30/0.54 thf(fact_1323_add__le__cancel__left,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_left
% 0.30/0.54 thf(fact_1324_add__le__cancel__left,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_left
% 0.30/0.54 thf(fact_1325_add__le__cancel__left,axiom,
% 0.30/0.54 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_left
% 0.30/0.54 thf(fact_1326_add__le__cancel__left,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_left
% 0.30/0.54 thf(fact_1327_add__le__cancel__right,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_right
% 0.30/0.54 thf(fact_1328_add__le__cancel__right,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_right
% 0.30/0.54 thf(fact_1329_add__le__cancel__right,axiom,
% 0.30/0.54 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_right
% 0.30/0.54 thf(fact_1330_add__le__cancel__right,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_cancel_right
% 0.30/0.54 thf(fact_1331_add_Oright__neutral,axiom,
% 0.30/0.54 ! [A: complex] :
% 0.30/0.54 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_neutral
% 0.30/0.54 thf(fact_1332_add_Oright__neutral,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_neutral
% 0.30/0.54 thf(fact_1333_add_Oright__neutral,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_neutral
% 0.30/0.54 thf(fact_1334_add_Oright__neutral,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_neutral
% 0.30/0.54 thf(fact_1335_add_Oright__neutral,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_neutral
% 0.30/0.54 thf(fact_1336_double__zero__sym,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( zero_zero_real
% 0.30/0.54 = ( plus_plus_real @ A @ A ) )
% 0.30/0.54 = ( A = zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_zero_sym
% 0.30/0.54 thf(fact_1337_double__zero__sym,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( zero_zero_rat
% 0.30/0.54 = ( plus_plus_rat @ A @ A ) )
% 0.30/0.54 = ( A = zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_zero_sym
% 0.30/0.54 thf(fact_1338_double__zero__sym,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( zero_zero_int
% 0.30/0.54 = ( plus_plus_int @ A @ A ) )
% 0.30/0.54 = ( A = zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_zero_sym
% 0.30/0.54 thf(fact_1339_add__cancel__left__left,axiom,
% 0.30/0.54 ! [B: complex,A: complex] :
% 0.30/0.54 ( ( ( plus_plus_complex @ B @ A )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_complex ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_left
% 0.30/0.54 thf(fact_1340_add__cancel__left__left,axiom,
% 0.30/0.54 ! [B: real,A: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ B @ A )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_left
% 0.30/0.54 thf(fact_1341_add__cancel__left__left,axiom,
% 0.30/0.54 ! [B: rat,A: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_left
% 0.30/0.54 thf(fact_1342_add__cancel__left__left,axiom,
% 0.30/0.54 ! [B: nat,A: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ B @ A )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_left
% 0.30/0.54 thf(fact_1343_add__cancel__left__left,axiom,
% 0.30/0.54 ! [B: int,A: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ B @ A )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_left
% 0.30/0.54 thf(fact_1344_add__cancel__left__right,axiom,
% 0.30/0.54 ! [A: complex,B: complex] :
% 0.30/0.54 ( ( ( plus_plus_complex @ A @ B )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_complex ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_right
% 0.30/0.54 thf(fact_1345_add__cancel__left__right,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ A @ B )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_right
% 0.30/0.54 thf(fact_1346_add__cancel__left__right,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_right
% 0.30/0.54 thf(fact_1347_add__cancel__left__right,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ A @ B )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_right
% 0.30/0.54 thf(fact_1348_add__cancel__left__right,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ A @ B )
% 0.30/0.54 = A )
% 0.30/0.54 = ( B = zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_left_right
% 0.30/0.54 thf(fact_1349_add__cancel__right__left,axiom,
% 0.30/0.54 ! [A: complex,B: complex] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_complex @ B @ A ) )
% 0.30/0.54 = ( B = zero_zero_complex ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_left
% 0.30/0.54 thf(fact_1350_add__cancel__right__left,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_real @ B @ A ) )
% 0.30/0.54 = ( B = zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_left
% 0.30/0.54 thf(fact_1351_add__cancel__right__left,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_rat @ B @ A ) )
% 0.30/0.54 = ( B = zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_left
% 0.30/0.54 thf(fact_1352_add__cancel__right__left,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_nat @ B @ A ) )
% 0.30/0.54 = ( B = zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_left
% 0.30/0.54 thf(fact_1353_add__cancel__right__left,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_int @ B @ A ) )
% 0.30/0.54 = ( B = zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_left
% 0.30/0.54 thf(fact_1354_add__cancel__right__right,axiom,
% 0.30/0.54 ! [A: complex,B: complex] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_complex @ A @ B ) )
% 0.30/0.54 = ( B = zero_zero_complex ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_right
% 0.30/0.54 thf(fact_1355_add__cancel__right__right,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_real @ A @ B ) )
% 0.30/0.54 = ( B = zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_right
% 0.30/0.54 thf(fact_1356_add__cancel__right__right,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_rat @ A @ B ) )
% 0.30/0.54 = ( B = zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_right
% 0.30/0.54 thf(fact_1357_add__cancel__right__right,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_nat @ A @ B ) )
% 0.30/0.54 = ( B = zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_right
% 0.30/0.54 thf(fact_1358_add__cancel__right__right,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( A
% 0.30/0.54 = ( plus_plus_int @ A @ B ) )
% 0.30/0.54 = ( B = zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_cancel_right_right
% 0.30/0.54 thf(fact_1359_add__eq__0__iff__both__eq__0,axiom,
% 0.30/0.54 ! [X: nat,Y: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ X @ Y )
% 0.30/0.54 = zero_zero_nat )
% 0.30/0.54 = ( ( X = zero_zero_nat )
% 0.30/0.54 & ( Y = zero_zero_nat ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_eq_0_iff_both_eq_0
% 0.30/0.54 thf(fact_1360_zero__eq__add__iff__both__eq__0,axiom,
% 0.30/0.54 ! [X: nat,Y: nat] :
% 0.30/0.54 ( ( zero_zero_nat
% 0.30/0.54 = ( plus_plus_nat @ X @ Y ) )
% 0.30/0.54 = ( ( X = zero_zero_nat )
% 0.30/0.54 & ( Y = zero_zero_nat ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % zero_eq_add_iff_both_eq_0
% 0.30/0.54 thf(fact_1361_add__0,axiom,
% 0.30/0.54 ! [A: complex] :
% 0.30/0.54 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add_0
% 0.30/0.54 thf(fact_1362_add__0,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add_0
% 0.30/0.54 thf(fact_1363_add__0,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add_0
% 0.30/0.54 thf(fact_1364_add__0,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add_0
% 0.30/0.54 thf(fact_1365_add__0,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add_0
% 0.30/0.54 thf(fact_1366_add__less__cancel__right,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_right
% 0.30/0.54 thf(fact_1367_add__less__cancel__right,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_right
% 0.30/0.54 thf(fact_1368_add__less__cancel__right,axiom,
% 0.30/0.54 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_right
% 0.30/0.54 thf(fact_1369_add__less__cancel__right,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.54 = ( ord_less_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_right
% 0.30/0.54 thf(fact_1370_add__less__cancel__left,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_left
% 0.30/0.54 thf(fact_1371_add__less__cancel__left,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_left
% 0.30/0.54 thf(fact_1372_add__less__cancel__left,axiom,
% 0.30/0.54 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_left
% 0.30/0.54 thf(fact_1373_add__less__cancel__left,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.30/0.54 = ( ord_less_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_cancel_left
% 0.30/0.54 thf(fact_1374_add__Suc__right,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ M2 @ ( suc @ N ) )
% 0.30/0.54 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_Suc_right
% 0.30/0.54 thf(fact_1375_Nat_Oadd__0__right,axiom,
% 0.30/0.54 ! [M2: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 0.30/0.54 = M2 ) ).
% 0.30/0.54
% 0.30/0.54 % Nat.add_0_right
% 0.30/0.54 thf(fact_1376_add__is__0,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ M2 @ N )
% 0.30/0.54 = zero_zero_nat )
% 0.30/0.54 = ( ( M2 = zero_zero_nat )
% 0.30/0.54 & ( N = zero_zero_nat ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_is_0
% 0.30/0.54 thf(fact_1377_nat__add__left__cancel__less,axiom,
% 0.30/0.54 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 0.30/0.54 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % nat_add_left_cancel_less
% 0.30/0.54 thf(fact_1378_nat__add__left__cancel__le,axiom,
% 0.30/0.54 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 0.30/0.54 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.54
% 0.30/0.54 % nat_add_left_cancel_le
% 0.30/0.54 thf(fact_1379_not__Some__eq,axiom,
% 0.30/0.54 ! [X: option4927543243414619207at_nat] :
% 0.30/0.54 ( ( ! [Y4: product_prod_nat_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( some_P7363390416028606310at_nat @ Y4 ) ) )
% 0.30/0.54 = ( X = none_P5556105721700978146at_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % not_Some_eq
% 0.30/0.54 thf(fact_1380_not__Some__eq,axiom,
% 0.30/0.54 ! [X: option_nat] :
% 0.30/0.54 ( ( ! [Y4: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( some_nat @ Y4 ) ) )
% 0.30/0.54 = ( X = none_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % not_Some_eq
% 0.30/0.54 thf(fact_1381_not__Some__eq,axiom,
% 0.30/0.54 ! [X: option_num] :
% 0.30/0.54 ( ( ! [Y4: num] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( some_num @ Y4 ) ) )
% 0.30/0.54 = ( X = none_num ) ) ).
% 0.30/0.54
% 0.30/0.54 % not_Some_eq
% 0.30/0.54 thf(fact_1382_not__None__eq,axiom,
% 0.30/0.54 ! [X: option4927543243414619207at_nat] :
% 0.30/0.54 ( ( X != none_P5556105721700978146at_nat )
% 0.30/0.54 = ( ? [Y4: product_prod_nat_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ Y4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % not_None_eq
% 0.30/0.54 thf(fact_1383_not__None__eq,axiom,
% 0.30/0.54 ! [X: option_nat] :
% 0.30/0.54 ( ( X != none_nat )
% 0.30/0.54 = ( ? [Y4: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 = ( some_nat @ Y4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % not_None_eq
% 0.30/0.54 thf(fact_1384_not__None__eq,axiom,
% 0.30/0.54 ! [X: option_num] :
% 0.30/0.54 ( ( X != none_num )
% 0.30/0.54 = ( ? [Y4: num] :
% 0.30/0.54 ( X
% 0.30/0.54 = ( some_num @ Y4 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % not_None_eq
% 0.30/0.54 thf(fact_1385_add__le__same__cancel1,axiom,
% 0.30/0.54 ! [B: real,A: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel1
% 0.30/0.54 thf(fact_1386_add__le__same__cancel1,axiom,
% 0.30/0.54 ! [B: rat,A: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel1
% 0.30/0.54 thf(fact_1387_add__le__same__cancel1,axiom,
% 0.30/0.54 ! [B: nat,A: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel1
% 0.30/0.54 thf(fact_1388_add__le__same__cancel1,axiom,
% 0.30/0.54 ! [B: int,A: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel1
% 0.30/0.54 thf(fact_1389_add__le__same__cancel2,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel2
% 0.30/0.54 thf(fact_1390_add__le__same__cancel2,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel2
% 0.30/0.54 thf(fact_1391_add__le__same__cancel2,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel2
% 0.30/0.54 thf(fact_1392_add__le__same__cancel2,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_same_cancel2
% 0.30/0.54 thf(fact_1393_le__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.30/0.54 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel1
% 0.30/0.54 thf(fact_1394_le__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.54 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel1
% 0.30/0.54 thf(fact_1395_le__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.30/0.54 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel1
% 0.30/0.54 thf(fact_1396_le__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.30/0.54 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel1
% 0.30/0.54 thf(fact_1397_le__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.30/0.54 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel2
% 0.30/0.54 thf(fact_1398_le__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.30/0.54 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel2
% 0.30/0.54 thf(fact_1399_le__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.30/0.54 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel2
% 0.30/0.54 thf(fact_1400_le__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.30/0.54 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_add_same_cancel2
% 0.30/0.54 thf(fact_1401_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.30/0.54 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_add_le_zero_iff_single_add_le_zero
% 0.30/0.54 thf(fact_1402_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.30/0.54 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_add_le_zero_iff_single_add_le_zero
% 0.30/0.54 thf(fact_1403_double__add__le__zero__iff__single__add__le__zero,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.30/0.54 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_add_le_zero_iff_single_add_le_zero
% 0.30/0.54 thf(fact_1404_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.30/0.54 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % zero_le_double_add_iff_zero_le_single_add
% 0.30/0.54 thf(fact_1405_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.30/0.54 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % zero_le_double_add_iff_zero_le_single_add
% 0.30/0.54 thf(fact_1406_zero__le__double__add__iff__zero__le__single__add,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.30/0.54 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % zero_le_double_add_iff_zero_le_single_add
% 0.30/0.54 thf(fact_1407_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 0.30/0.54 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % zero_less_double_add_iff_zero_less_single_add
% 0.30/0.54 thf(fact_1408_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 0.30/0.54 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % zero_less_double_add_iff_zero_less_single_add
% 0.30/0.54 thf(fact_1409_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 0.30/0.54 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.30/0.54
% 0.30/0.54 % zero_less_double_add_iff_zero_less_single_add
% 0.30/0.54 thf(fact_1410_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 0.30/0.54 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_add_less_zero_iff_single_add_less_zero
% 0.30/0.54 thf(fact_1411_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 0.30/0.54 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_add_less_zero_iff_single_add_less_zero
% 0.30/0.54 thf(fact_1412_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 0.30/0.54 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % double_add_less_zero_iff_single_add_less_zero
% 0.30/0.54 thf(fact_1413_less__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.30/0.54 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel2
% 0.30/0.54 thf(fact_1414_less__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.30/0.54 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel2
% 0.30/0.54 thf(fact_1415_less__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.30/0.54 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel2
% 0.30/0.54 thf(fact_1416_less__add__same__cancel2,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.30/0.54 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel2
% 0.30/0.54 thf(fact_1417_less__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.30/0.54 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel1
% 0.30/0.54 thf(fact_1418_less__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.30/0.54 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel1
% 0.30/0.54 thf(fact_1419_less__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.30/0.54 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel1
% 0.30/0.54 thf(fact_1420_less__add__same__cancel1,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.30/0.54 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_add_same_cancel1
% 0.30/0.54 thf(fact_1421_add__less__same__cancel2,axiom,
% 0.30/0.54 ! [A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel2
% 0.30/0.54 thf(fact_1422_add__less__same__cancel2,axiom,
% 0.30/0.54 ! [A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel2
% 0.30/0.54 thf(fact_1423_add__less__same__cancel2,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel2
% 0.30/0.54 thf(fact_1424_add__less__same__cancel2,axiom,
% 0.30/0.54 ! [A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.54 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel2
% 0.30/0.54 thf(fact_1425_add__less__same__cancel1,axiom,
% 0.30/0.54 ! [B: real,A: real] :
% 0.30/0.54 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel1
% 0.30/0.54 thf(fact_1426_add__less__same__cancel1,axiom,
% 0.30/0.54 ! [B: rat,A: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel1
% 0.30/0.54 thf(fact_1427_add__less__same__cancel1,axiom,
% 0.30/0.54 ! [B: nat,A: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel1
% 0.30/0.54 thf(fact_1428_add__less__same__cancel1,axiom,
% 0.30/0.54 ! [B: int,A: int] :
% 0.30/0.54 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.30/0.54 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_same_cancel1
% 0.30/0.54 thf(fact_1429_add__gr__0,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.54 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.30/0.54 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_gr_0
% 0.30/0.54 thf(fact_1430_mult__Suc__right,axiom,
% 0.30/0.54 ! [M2: nat,N: nat] :
% 0.30/0.54 ( ( times_times_nat @ M2 @ ( suc @ N ) )
% 0.30/0.54 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % mult_Suc_right
% 0.30/0.54 thf(fact_1431_add__right__imp__eq,axiom,
% 0.30/0.54 ! [B: real,A: real,C2: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ B @ A )
% 0.30/0.54 = ( plus_plus_real @ C2 @ A ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_imp_eq
% 0.30/0.54 thf(fact_1432_add__right__imp__eq,axiom,
% 0.30/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.54 = ( plus_plus_rat @ C2 @ A ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_imp_eq
% 0.30/0.54 thf(fact_1433_add__right__imp__eq,axiom,
% 0.30/0.54 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ B @ A )
% 0.30/0.54 = ( plus_plus_nat @ C2 @ A ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_imp_eq
% 0.30/0.54 thf(fact_1434_add__right__imp__eq,axiom,
% 0.30/0.54 ! [B: int,A: int,C2: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ B @ A )
% 0.30/0.54 = ( plus_plus_int @ C2 @ A ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_imp_eq
% 0.30/0.54 thf(fact_1435_add__left__imp__eq,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ A @ B )
% 0.30/0.54 = ( plus_plus_real @ A @ C2 ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_imp_eq
% 0.30/0.54 thf(fact_1436_add__left__imp__eq,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.54 = ( plus_plus_rat @ A @ C2 ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_imp_eq
% 0.30/0.54 thf(fact_1437_add__left__imp__eq,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ( plus_plus_nat @ A @ B )
% 0.30/0.54 = ( plus_plus_nat @ A @ C2 ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_imp_eq
% 0.30/0.54 thf(fact_1438_add__left__imp__eq,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ A @ B )
% 0.30/0.54 = ( plus_plus_int @ A @ C2 ) )
% 0.30/0.54 => ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_imp_eq
% 0.30/0.54 thf(fact_1439_add_Oleft__commute,axiom,
% 0.30/0.54 ! [B: real,A: real,C2: real] :
% 0.30/0.54 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C2 ) )
% 0.30/0.54 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.left_commute
% 0.30/0.54 thf(fact_1440_add_Oleft__commute,axiom,
% 0.30/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C2 ) )
% 0.30/0.54 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.left_commute
% 0.30/0.54 thf(fact_1441_add_Oleft__commute,axiom,
% 0.30/0.54 ! [B: nat,A: nat,C2: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 0.30/0.54 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.left_commute
% 0.30/0.54 thf(fact_1442_add_Oleft__commute,axiom,
% 0.30/0.54 ! [B: int,A: int,C2: int] :
% 0.30/0.54 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C2 ) )
% 0.30/0.54 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.left_commute
% 0.30/0.54 thf(fact_1443_add_Ocommute,axiom,
% 0.30/0.54 ( plus_plus_real
% 0.30/0.54 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ B4 @ A5 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.commute
% 0.30/0.54 thf(fact_1444_add_Ocommute,axiom,
% 0.30/0.54 ( plus_plus_rat
% 0.30/0.54 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ B4 @ A5 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.commute
% 0.30/0.54 thf(fact_1445_add_Ocommute,axiom,
% 0.30/0.54 ( plus_plus_nat
% 0.30/0.54 = ( ^ [A5: nat,B4: nat] : ( plus_plus_nat @ B4 @ A5 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.commute
% 0.30/0.54 thf(fact_1446_add_Ocommute,axiom,
% 0.30/0.54 ( plus_plus_int
% 0.30/0.54 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ B4 @ A5 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.commute
% 0.30/0.54 thf(fact_1447_add_Oright__cancel,axiom,
% 0.30/0.54 ! [B: real,A: real,C2: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ B @ A )
% 0.30/0.54 = ( plus_plus_real @ C2 @ A ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_cancel
% 0.30/0.54 thf(fact_1448_add_Oright__cancel,axiom,
% 0.30/0.54 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ B @ A )
% 0.30/0.54 = ( plus_plus_rat @ C2 @ A ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_cancel
% 0.30/0.54 thf(fact_1449_add_Oright__cancel,axiom,
% 0.30/0.54 ! [B: int,A: int,C2: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ B @ A )
% 0.30/0.54 = ( plus_plus_int @ C2 @ A ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.right_cancel
% 0.30/0.54 thf(fact_1450_add_Oleft__cancel,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ( plus_plus_real @ A @ B )
% 0.30/0.54 = ( plus_plus_real @ A @ C2 ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.left_cancel
% 0.30/0.54 thf(fact_1451_add_Oleft__cancel,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ( plus_plus_rat @ A @ B )
% 0.30/0.54 = ( plus_plus_rat @ A @ C2 ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.left_cancel
% 0.30/0.54 thf(fact_1452_add_Oleft__cancel,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ( plus_plus_int @ A @ B )
% 0.30/0.54 = ( plus_plus_int @ A @ C2 ) )
% 0.30/0.54 = ( B = C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.left_cancel
% 0.30/0.54 thf(fact_1453_add_Oassoc,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.assoc
% 0.30/0.54 thf(fact_1454_add_Oassoc,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.assoc
% 0.30/0.54 thf(fact_1455_add_Oassoc,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.assoc
% 0.30/0.54 thf(fact_1456_add_Oassoc,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add.assoc
% 0.30/0.54 thf(fact_1457_group__cancel_Oadd2,axiom,
% 0.30/0.54 ! [B5: real,K2: real,B: real,A: real] :
% 0.30/0.54 ( ( B5
% 0.30/0.54 = ( plus_plus_real @ K2 @ B ) )
% 0.30/0.54 => ( ( plus_plus_real @ A @ B5 )
% 0.30/0.54 = ( plus_plus_real @ K2 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add2
% 0.30/0.54 thf(fact_1458_group__cancel_Oadd2,axiom,
% 0.30/0.54 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 0.30/0.54 ( ( B5
% 0.30/0.54 = ( plus_plus_rat @ K2 @ B ) )
% 0.30/0.54 => ( ( plus_plus_rat @ A @ B5 )
% 0.30/0.54 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add2
% 0.30/0.54 thf(fact_1459_group__cancel_Oadd2,axiom,
% 0.30/0.54 ! [B5: nat,K2: nat,B: nat,A: nat] :
% 0.30/0.54 ( ( B5
% 0.30/0.54 = ( plus_plus_nat @ K2 @ B ) )
% 0.30/0.54 => ( ( plus_plus_nat @ A @ B5 )
% 0.30/0.54 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add2
% 0.30/0.54 thf(fact_1460_group__cancel_Oadd2,axiom,
% 0.30/0.54 ! [B5: int,K2: int,B: int,A: int] :
% 0.30/0.54 ( ( B5
% 0.30/0.54 = ( plus_plus_int @ K2 @ B ) )
% 0.30/0.54 => ( ( plus_plus_int @ A @ B5 )
% 0.30/0.54 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add2
% 0.30/0.54 thf(fact_1461_group__cancel_Oadd1,axiom,
% 0.30/0.54 ! [A4: real,K2: real,A: real,B: real] :
% 0.30/0.54 ( ( A4
% 0.30/0.54 = ( plus_plus_real @ K2 @ A ) )
% 0.30/0.54 => ( ( plus_plus_real @ A4 @ B )
% 0.30/0.54 = ( plus_plus_real @ K2 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add1
% 0.30/0.54 thf(fact_1462_group__cancel_Oadd1,axiom,
% 0.30/0.54 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( A4
% 0.30/0.54 = ( plus_plus_rat @ K2 @ A ) )
% 0.30/0.54 => ( ( plus_plus_rat @ A4 @ B )
% 0.30/0.54 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add1
% 0.30/0.54 thf(fact_1463_group__cancel_Oadd1,axiom,
% 0.30/0.54 ! [A4: nat,K2: nat,A: nat,B: nat] :
% 0.30/0.54 ( ( A4
% 0.30/0.54 = ( plus_plus_nat @ K2 @ A ) )
% 0.30/0.54 => ( ( plus_plus_nat @ A4 @ B )
% 0.30/0.54 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add1
% 0.30/0.54 thf(fact_1464_group__cancel_Oadd1,axiom,
% 0.30/0.54 ! [A4: int,K2: int,A: int,B: int] :
% 0.30/0.54 ( ( A4
% 0.30/0.54 = ( plus_plus_int @ K2 @ A ) )
% 0.30/0.54 => ( ( plus_plus_int @ A4 @ B )
% 0.30/0.54 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % group_cancel.add1
% 0.30/0.54 thf(fact_1465_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.54 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ( plus_plus_real @ I2 @ K2 )
% 0.30/0.54 = ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(4)
% 0.30/0.54 thf(fact_1466_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.54 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ( plus_plus_rat @ I2 @ K2 )
% 0.30/0.54 = ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(4)
% 0.30/0.54 thf(fact_1467_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ( plus_plus_nat @ I2 @ K2 )
% 0.30/0.54 = ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(4)
% 0.30/0.54 thf(fact_1468_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.30/0.54 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ( plus_plus_int @ I2 @ K2 )
% 0.30/0.54 = ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(4)
% 0.30/0.54 thf(fact_1469_is__num__normalize_I1_J,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % is_num_normalize(1)
% 0.30/0.54 thf(fact_1470_is__num__normalize_I1_J,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % is_num_normalize(1)
% 0.30/0.54 thf(fact_1471_is__num__normalize_I1_J,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % is_num_normalize(1)
% 0.30/0.54 thf(fact_1472_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ab_semigroup_add_class.add_ac(1)
% 0.30/0.54 thf(fact_1473_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ab_semigroup_add_class.add_ac(1)
% 0.30/0.54 thf(fact_1474_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ab_semigroup_add_class.add_ac(1)
% 0.30/0.54 thf(fact_1475_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ab_semigroup_add_class.add_ac(1)
% 0.30/0.54 thf(fact_1476_bot__nat__def,axiom,
% 0.30/0.54 bot_bot_nat = zero_zero_nat ).
% 0.30/0.54
% 0.30/0.54 % bot_nat_def
% 0.30/0.54 thf(fact_1477_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 0.30/0.54 ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz: nat] :
% 0.30/0.54 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.membermima.simps(2)
% 0.30/0.54 thf(fact_1478_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.54 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.54 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(3)
% 0.30/0.54 thf(fact_1479_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.54 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.54 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(3)
% 0.30/0.54 thf(fact_1480_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.54 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(3)
% 0.30/0.54 thf(fact_1481_add__mono__thms__linordered__semiring_I3_J,axiom,
% 0.30/0.54 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.54 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(3)
% 0.30/0.54 thf(fact_1482_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.54 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_eq_real @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(2)
% 0.30/0.54 thf(fact_1483_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.54 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_eq_rat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(2)
% 0.30/0.54 thf(fact_1484_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_eq_nat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(2)
% 0.30/0.54 thf(fact_1485_add__mono__thms__linordered__semiring_I2_J,axiom,
% 0.30/0.54 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_eq_int @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(2)
% 0.30/0.54 thf(fact_1486_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.54 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.54 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_eq_real @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(1)
% 0.30/0.54 thf(fact_1487_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.54 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.54 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_eq_rat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(1)
% 0.30/0.54 thf(fact_1488_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.54 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_eq_nat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(1)
% 0.30/0.54 thf(fact_1489_add__mono__thms__linordered__semiring_I1_J,axiom,
% 0.30/0.54 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.54 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_eq_int @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_semiring(1)
% 0.30/0.54 thf(fact_1490_add__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_real @ C2 @ D )
% 0.30/0.54 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono
% 0.30/0.54 thf(fact_1491_add__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.30/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono
% 0.30/0.54 thf(fact_1492_add__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.30/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono
% 0.30/0.54 thf(fact_1493_add__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_eq_int @ C2 @ D )
% 0.30/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono
% 0.30/0.54 thf(fact_1494_add__left__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.54 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_mono
% 0.30/0.54 thf(fact_1495_add__left__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_mono
% 0.30/0.54 thf(fact_1496_add__left__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_mono
% 0.30/0.54 thf(fact_1497_add__left__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_left_mono
% 0.30/0.54 thf(fact_1498_less__eqE,axiom,
% 0.30/0.54 ! [A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.54 => ~ ! [C: nat] :
% 0.30/0.54 ( B
% 0.30/0.54 != ( plus_plus_nat @ A @ C ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % less_eqE
% 0.30/0.54 thf(fact_1499_add__right__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.54 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_mono
% 0.30/0.54 thf(fact_1500_add__right__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.54 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_mono
% 0.30/0.54 thf(fact_1501_add__right__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.54 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_mono
% 0.30/0.54 thf(fact_1502_add__right__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.54 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_right_mono
% 0.30/0.54 thf(fact_1503_le__iff__add,axiom,
% 0.30/0.54 ( ord_less_eq_nat
% 0.30/0.54 = ( ^ [A5: nat,B4: nat] :
% 0.30/0.54 ? [C3: nat] :
% 0.30/0.54 ( B4
% 0.30/0.54 = ( plus_plus_nat @ A5 @ C3 ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % le_iff_add
% 0.30/0.54 thf(fact_1504_add__le__imp__le__left,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_left
% 0.30/0.54 thf(fact_1505_add__le__imp__le__left,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_left
% 0.30/0.54 thf(fact_1506_add__le__imp__le__left,axiom,
% 0.30/0.54 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_left
% 0.30/0.54 thf(fact_1507_add__le__imp__le__left,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_left
% 0.30/0.54 thf(fact_1508_add__le__imp__le__right,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_right
% 0.30/0.54 thf(fact_1509_add__le__imp__le__right,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_right
% 0.30/0.54 thf(fact_1510_add__le__imp__le__right,axiom,
% 0.30/0.54 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_right
% 0.30/0.54 thf(fact_1511_add__le__imp__le__right,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_le_imp_le_right
% 0.30/0.54 thf(fact_1512_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.54 ! [A: complex] :
% 0.30/0.54 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % comm_monoid_add_class.add_0
% 0.30/0.54 thf(fact_1513_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % comm_monoid_add_class.add_0
% 0.30/0.54 thf(fact_1514_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % comm_monoid_add_class.add_0
% 0.30/0.54 thf(fact_1515_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % comm_monoid_add_class.add_0
% 0.30/0.54 thf(fact_1516_comm__monoid__add__class_Oadd__0,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % comm_monoid_add_class.add_0
% 0.30/0.54 thf(fact_1517_add_Ocomm__neutral,axiom,
% 0.30/0.54 ! [A: complex] :
% 0.30/0.54 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.comm_neutral
% 0.30/0.54 thf(fact_1518_add_Ocomm__neutral,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.comm_neutral
% 0.30/0.54 thf(fact_1519_add_Ocomm__neutral,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.comm_neutral
% 0.30/0.54 thf(fact_1520_add_Ocomm__neutral,axiom,
% 0.30/0.54 ! [A: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.comm_neutral
% 0.30/0.54 thf(fact_1521_add_Ocomm__neutral,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.comm_neutral
% 0.30/0.54 thf(fact_1522_add_Ogroup__left__neutral,axiom,
% 0.30/0.54 ! [A: complex] :
% 0.30/0.54 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.group_left_neutral
% 0.30/0.54 thf(fact_1523_add_Ogroup__left__neutral,axiom,
% 0.30/0.54 ! [A: real] :
% 0.30/0.54 ( ( plus_plus_real @ zero_zero_real @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.group_left_neutral
% 0.30/0.54 thf(fact_1524_add_Ogroup__left__neutral,axiom,
% 0.30/0.54 ! [A: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.group_left_neutral
% 0.30/0.54 thf(fact_1525_add_Ogroup__left__neutral,axiom,
% 0.30/0.54 ! [A: int] :
% 0.30/0.54 ( ( plus_plus_int @ zero_zero_int @ A )
% 0.30/0.54 = A ) ).
% 0.30/0.54
% 0.30/0.54 % add.group_left_neutral
% 0.30/0.54 thf(fact_1526_add__less__imp__less__right,axiom,
% 0.30/0.54 ! [A: real,C2: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_right
% 0.30/0.54 thf(fact_1527_add__less__imp__less__right,axiom,
% 0.30/0.54 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_right
% 0.30/0.54 thf(fact_1528_add__less__imp__less__right,axiom,
% 0.30/0.54 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_right
% 0.30/0.54 thf(fact_1529_add__less__imp__less__right,axiom,
% 0.30/0.54 ! [A: int,C2: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.54 => ( ord_less_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_right
% 0.30/0.54 thf(fact_1530_add__less__imp__less__left,axiom,
% 0.30/0.54 ! [C2: real,A: real,B: real] :
% 0.30/0.54 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_real @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_left
% 0.30/0.54 thf(fact_1531_add__less__imp__less__left,axiom,
% 0.30/0.54 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.54 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_rat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_left
% 0.30/0.54 thf(fact_1532_add__less__imp__less__left,axiom,
% 0.30/0.54 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.54 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_nat @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_left
% 0.30/0.54 thf(fact_1533_add__less__imp__less__left,axiom,
% 0.30/0.54 ! [C2: int,A: int,B: int] :
% 0.30/0.54 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.30/0.54 => ( ord_less_int @ A @ B ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_less_imp_less_left
% 0.30/0.54 thf(fact_1534_add__strict__right__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_right_mono
% 0.30/0.54 thf(fact_1535_add__strict__right__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_right_mono
% 0.30/0.54 thf(fact_1536_add__strict__right__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_right_mono
% 0.30/0.54 thf(fact_1537_add__strict__right__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_right_mono
% 0.30/0.54 thf(fact_1538_add__strict__left__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_left_mono
% 0.30/0.54 thf(fact_1539_add__strict__left__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_left_mono
% 0.30/0.54 thf(fact_1540_add__strict__left__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_left_mono
% 0.30/0.54 thf(fact_1541_add__strict__left__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_left_mono
% 0.30/0.54 thf(fact_1542_add__strict__mono,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.54 ( ( ord_less_real @ A @ B )
% 0.30/0.54 => ( ( ord_less_real @ C2 @ D )
% 0.30/0.54 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_mono
% 0.30/0.54 thf(fact_1543_add__strict__mono,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.54 ( ( ord_less_rat @ A @ B )
% 0.30/0.54 => ( ( ord_less_rat @ C2 @ D )
% 0.30/0.54 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_mono
% 0.30/0.54 thf(fact_1544_add__strict__mono,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.54 ( ( ord_less_nat @ A @ B )
% 0.30/0.54 => ( ( ord_less_nat @ C2 @ D )
% 0.30/0.54 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_mono
% 0.30/0.54 thf(fact_1545_add__strict__mono,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.54 ( ( ord_less_int @ A @ B )
% 0.30/0.54 => ( ( ord_less_int @ C2 @ D )
% 0.30/0.54 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_strict_mono
% 0.30/0.54 thf(fact_1546_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.54 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.54 ( ( ( ord_less_real @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(1)
% 0.30/0.54 thf(fact_1547_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.54 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.54 ( ( ( ord_less_rat @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(1)
% 0.30/0.54 thf(fact_1548_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.54 ( ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(1)
% 0.30/0.54 thf(fact_1549_add__mono__thms__linordered__field_I1_J,axiom,
% 0.30/0.54 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.54 ( ( ( ord_less_int @ I2 @ J2 )
% 0.30/0.54 & ( K2 = L ) )
% 0.30/0.54 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(1)
% 0.30/0.54 thf(fact_1550_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.54 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_real @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(2)
% 0.30/0.54 thf(fact_1551_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.54 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_rat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(2)
% 0.30/0.54 thf(fact_1552_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_nat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(2)
% 0.30/0.54 thf(fact_1553_add__mono__thms__linordered__field_I2_J,axiom,
% 0.30/0.54 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.54 ( ( ( I2 = J2 )
% 0.30/0.54 & ( ord_less_int @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(2)
% 0.30/0.54 thf(fact_1554_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.54 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.54 ( ( ( ord_less_real @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_real @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(5)
% 0.30/0.54 thf(fact_1555_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.54 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.54 ( ( ( ord_less_rat @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_rat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(5)
% 0.30/0.54 thf(fact_1556_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.54 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.54 ( ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_nat @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(5)
% 0.30/0.54 thf(fact_1557_add__mono__thms__linordered__field_I5_J,axiom,
% 0.30/0.54 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.54 ( ( ( ord_less_int @ I2 @ J2 )
% 0.30/0.54 & ( ord_less_int @ K2 @ L ) )
% 0.30/0.54 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % add_mono_thms_linordered_field(5)
% 0.30/0.54 thf(fact_1558_ring__class_Oring__distribs_I2_J,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ring_class.ring_distribs(2)
% 0.30/0.54 thf(fact_1559_ring__class_Oring__distribs_I2_J,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ring_class.ring_distribs(2)
% 0.30/0.54 thf(fact_1560_ring__class_Oring__distribs_I2_J,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ring_class.ring_distribs(2)
% 0.30/0.54 thf(fact_1561_ring__class_Oring__distribs_I1_J,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.54 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ring_class.ring_distribs(1)
% 0.30/0.54 thf(fact_1562_ring__class_Oring__distribs_I1_J,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ring_class.ring_distribs(1)
% 0.30/0.54 thf(fact_1563_ring__class_Oring__distribs_I1_J,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.54 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % ring_class.ring_distribs(1)
% 0.30/0.54 thf(fact_1564_comm__semiring__class_Odistrib,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % comm_semiring_class.distrib
% 0.30/0.54 thf(fact_1565_comm__semiring__class_Odistrib,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % comm_semiring_class.distrib
% 0.30/0.54 thf(fact_1566_comm__semiring__class_Odistrib,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % comm_semiring_class.distrib
% 0.30/0.54 thf(fact_1567_comm__semiring__class_Odistrib,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % comm_semiring_class.distrib
% 0.30/0.54 thf(fact_1568_distrib__left,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.54 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_left
% 0.30/0.54 thf(fact_1569_distrib__left,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_left
% 0.30/0.54 thf(fact_1570_distrib__left,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 0.30/0.54 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_left
% 0.30/0.54 thf(fact_1571_distrib__left,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.54 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_left
% 0.30/0.54 thf(fact_1572_distrib__right,axiom,
% 0.30/0.54 ! [A: real,B: real,C2: real] :
% 0.30/0.54 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_right
% 0.30/0.54 thf(fact_1573_distrib__right,axiom,
% 0.30/0.54 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_right
% 0.30/0.54 thf(fact_1574_distrib__right,axiom,
% 0.30/0.54 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_right
% 0.30/0.54 thf(fact_1575_distrib__right,axiom,
% 0.30/0.54 ! [A: int,B: int,C2: int] :
% 0.30/0.54 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.30/0.54 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % distrib_right
% 0.30/0.54 thf(fact_1576_combine__common__factor,axiom,
% 0.30/0.54 ! [A: real,E: real,B: real,C2: real] :
% 0.30/0.54 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C2 ) )
% 0.30/0.54 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_common_factor
% 0.30/0.54 thf(fact_1577_combine__common__factor,axiom,
% 0.30/0.54 ! [A: rat,E: rat,B: rat,C2: rat] :
% 0.30/0.54 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C2 ) )
% 0.30/0.54 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_common_factor
% 0.30/0.54 thf(fact_1578_combine__common__factor,axiom,
% 0.30/0.54 ! [A: nat,E: nat,B: nat,C2: nat] :
% 0.30/0.54 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C2 ) )
% 0.30/0.54 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_common_factor
% 0.30/0.54 thf(fact_1579_combine__common__factor,axiom,
% 0.30/0.54 ! [A: int,E: int,B: int,C2: int] :
% 0.30/0.54 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C2 ) )
% 0.30/0.54 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_common_factor
% 0.30/0.54 thf(fact_1580_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.30/0.54 ( ( ( X = none_P5556105721700978146at_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1581_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 0.30/0.54 ( ( ( X = none_P5556105721700978146at_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: product_prod_nat_nat,B3: nat] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_nat @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1582_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 0.30/0.54 ( ( ( X = none_P5556105721700978146at_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_num )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: product_prod_nat_nat,B3: num] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_num @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1583_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option_nat,P2: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.30/0.54 ( ( ( X = none_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: nat,B3: product_prod_nat_nat] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_nat @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1584_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option_nat,P2: option_nat > option_nat > $o,Y: option_nat] :
% 0.30/0.54 ( ( ( X = none_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: nat,B3: nat] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_nat @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_nat @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1585_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option_nat,P2: option_nat > option_num > $o,Y: option_num] :
% 0.30/0.54 ( ( ( X = none_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_num )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: nat,B3: num] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_nat @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_num @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1586_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option_num,P2: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 0.30/0.54 ( ( ( X = none_num )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_P5556105721700978146at_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: num,B3: product_prod_nat_nat] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_num @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1587_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option_num,P2: option_num > option_nat > $o,Y: option_nat] :
% 0.30/0.54 ( ( ( X = none_num )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_nat )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: num,B3: nat] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_num @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_nat @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1588_combine__options__cases,axiom,
% 0.30/0.54 ! [X: option_num,P2: option_num > option_num > $o,Y: option_num] :
% 0.30/0.54 ( ( ( X = none_num )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ( ( Y = none_num )
% 0.30/0.54 => ( P2 @ X @ Y ) )
% 0.30/0.54 => ( ! [A3: num,B3: num] :
% 0.30/0.54 ( ( X
% 0.30/0.54 = ( some_num @ A3 ) )
% 0.30/0.54 => ( ( Y
% 0.30/0.54 = ( some_num @ B3 ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) )
% 0.30/0.54 => ( P2 @ X @ Y ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % combine_options_cases
% 0.30/0.54 thf(fact_1589_split__option__all,axiom,
% 0.30/0.54 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.30/0.54 ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 0.30/0.54 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 0.30/0.54 ( ( P4 @ none_P5556105721700978146at_nat )
% 0.30/0.54 & ! [X4: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X4 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % split_option_all
% 0.30/0.54 thf(fact_1590_split__option__all,axiom,
% 0.30/0.54 ( ( ^ [P3: option_nat > $o] :
% 0.30/0.54 ! [X6: option_nat] : ( P3 @ X6 ) )
% 0.30/0.54 = ( ^ [P4: option_nat > $o] :
% 0.30/0.54 ( ( P4 @ none_nat )
% 0.30/0.54 & ! [X4: nat] : ( P4 @ ( some_nat @ X4 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % split_option_all
% 0.30/0.54 thf(fact_1591_split__option__all,axiom,
% 0.30/0.54 ( ( ^ [P3: option_num > $o] :
% 0.30/0.54 ! [X6: option_num] : ( P3 @ X6 ) )
% 0.30/0.54 = ( ^ [P4: option_num > $o] :
% 0.30/0.54 ( ( P4 @ none_num )
% 0.30/0.54 & ! [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % split_option_all
% 0.30/0.54 thf(fact_1592_split__option__ex,axiom,
% 0.30/0.54 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 0.30/0.54 ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 0.30/0.54 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 0.30/0.54 ( ( P4 @ none_P5556105721700978146at_nat )
% 0.30/0.54 | ? [X4: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X4 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % split_option_ex
% 0.30/0.54 thf(fact_1593_split__option__ex,axiom,
% 0.30/0.54 ( ( ^ [P3: option_nat > $o] :
% 0.30/0.54 ? [X6: option_nat] : ( P3 @ X6 ) )
% 0.30/0.54 = ( ^ [P4: option_nat > $o] :
% 0.30/0.54 ( ( P4 @ none_nat )
% 0.30/0.54 | ? [X4: nat] : ( P4 @ ( some_nat @ X4 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % split_option_ex
% 0.30/0.54 thf(fact_1594_split__option__ex,axiom,
% 0.30/0.54 ( ( ^ [P3: option_num > $o] :
% 0.30/0.54 ? [X6: option_num] : ( P3 @ X6 ) )
% 0.30/0.54 = ( ^ [P4: option_num > $o] :
% 0.30/0.54 ( ( P4 @ none_num )
% 0.30/0.54 | ? [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % split_option_ex
% 0.30/0.54 thf(fact_1595_option_Oexhaust,axiom,
% 0.30/0.54 ! [Y: option4927543243414619207at_nat] :
% 0.30/0.54 ( ( Y != none_P5556105721700978146at_nat )
% 0.30/0.54 => ~ ! [X23: product_prod_nat_nat] :
% 0.30/0.54 ( Y
% 0.30/0.54 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.exhaust
% 0.30/0.54 thf(fact_1596_option_Oexhaust,axiom,
% 0.30/0.54 ! [Y: option_nat] :
% 0.30/0.54 ( ( Y != none_nat )
% 0.30/0.54 => ~ ! [X23: nat] :
% 0.30/0.54 ( Y
% 0.30/0.54 != ( some_nat @ X23 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.exhaust
% 0.30/0.54 thf(fact_1597_option_Oexhaust,axiom,
% 0.30/0.54 ! [Y: option_num] :
% 0.30/0.54 ( ( Y != none_num )
% 0.30/0.54 => ~ ! [X23: num] :
% 0.30/0.54 ( Y
% 0.30/0.54 != ( some_num @ X23 ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.exhaust
% 0.30/0.54 thf(fact_1598_option_OdiscI,axiom,
% 0.30/0.54 ! [Option: option4927543243414619207at_nat,X2: product_prod_nat_nat] :
% 0.30/0.54 ( ( Option
% 0.30/0.54 = ( some_P7363390416028606310at_nat @ X2 ) )
% 0.30/0.54 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.discI
% 0.30/0.54 thf(fact_1599_option_OdiscI,axiom,
% 0.30/0.54 ! [Option: option_nat,X2: nat] :
% 0.30/0.54 ( ( Option
% 0.30/0.54 = ( some_nat @ X2 ) )
% 0.30/0.54 => ( Option != none_nat ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.discI
% 0.30/0.54 thf(fact_1600_option_OdiscI,axiom,
% 0.30/0.54 ! [Option: option_num,X2: num] :
% 0.30/0.54 ( ( Option
% 0.30/0.54 = ( some_num @ X2 ) )
% 0.30/0.54 => ( Option != none_num ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.discI
% 0.30/0.54 thf(fact_1601_option_Odistinct_I1_J,axiom,
% 0.30/0.54 ! [X2: product_prod_nat_nat] :
% 0.30/0.54 ( none_P5556105721700978146at_nat
% 0.30/0.54 != ( some_P7363390416028606310at_nat @ X2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.distinct(1)
% 0.30/0.54 thf(fact_1602_option_Odistinct_I1_J,axiom,
% 0.30/0.54 ! [X2: nat] :
% 0.30/0.54 ( none_nat
% 0.30/0.54 != ( some_nat @ X2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.distinct(1)
% 0.30/0.54 thf(fact_1603_option_Odistinct_I1_J,axiom,
% 0.30/0.54 ! [X2: num] :
% 0.30/0.54 ( none_num
% 0.30/0.54 != ( some_num @ X2 ) ) ).
% 0.30/0.54
% 0.30/0.54 % option.distinct(1)
% 0.30/0.54 thf(fact_1604_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.30/0.54 ! [X: produc5542196010084753463at_nat] :
% 0.30/0.54 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 0.30/0.54 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc2899441246263362727at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat ) ) )
% 0.30/0.54 => ~ ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc2899441246263362727at_nat @ F @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B3 ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_shift.cases
% 0.30/0.54 thf(fact_1605_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.30/0.54 ! [X: produc8306885398267862888on_nat] :
% 0.30/0.54 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 0.30/0.54 => ( ! [Uw: nat > nat > nat,V: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc8929957630744042906on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V ) @ none_nat ) ) )
% 0.30/0.54 => ~ ! [F: nat > nat > nat,A3: nat,B3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc8929957630744042906on_nat @ F @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B3 ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_shift.cases
% 0.30/0.54 thf(fact_1606_VEBT__internal_Ooption__shift_Ocases,axiom,
% 0.30/0.54 ! [X: produc1193250871479095198on_num] :
% 0.30/0.54 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 0.30/0.54 => ( ! [Uw: num > num > num,V: num] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc5778274026573060048on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V ) @ none_num ) ) )
% 0.30/0.54 => ~ ! [F: num > num > num,A3: num,B3: num] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc5778274026573060048on_num @ F @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B3 ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_shift.cases
% 0.30/0.54 thf(fact_1607_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.30/0.54 ! [X: produc5491161045314408544at_nat] :
% 0.30/0.54 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 0.30/0.54 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > $o,V: product_prod_nat_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc3994169339658061776at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat ) ) )
% 0.30/0.54 => ~ ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc3994169339658061776at_nat @ F @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_comp_shift.cases
% 0.30/0.54 thf(fact_1608_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.30/0.54 ! [X: produc2233624965454879586on_nat] :
% 0.30/0.54 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 0.30/0.54 => ( ! [Uw: nat > nat > $o,V: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc4035269172776083154on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V ) @ none_nat ) ) )
% 0.30/0.54 => ~ ! [F: nat > nat > $o,X3: nat,Y3: nat] :
% 0.30/0.54 ( X
% 0.30/0.54 != ( produc4035269172776083154on_nat @ F @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 0.30/0.54
% 0.30/0.54 % VEBT_internal.option_comp_shift.cases
% 0.30/0.54 thf(fact_1609_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 0.30/0.54 ! [X: produc7036089656553540234on_num] :
% 0.30/0.54 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 0.30/0.55 => ( ! [Uw: num > num > $o,V: num] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc3576312749637752826on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V ) @ none_num ) ) )
% 0.30/0.55 => ~ ! [F: num > num > $o,X3: num,Y3: num] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc3576312749637752826on_num @ F @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.option_comp_shift.cases
% 0.30/0.55 thf(fact_1610_nat__arith_Osuc1,axiom,
% 0.30/0.55 ! [A4: nat,K2: nat,A: nat] :
% 0.30/0.55 ( ( A4
% 0.30/0.55 = ( plus_plus_nat @ K2 @ A ) )
% 0.30/0.55 => ( ( suc @ A4 )
% 0.30/0.55 = ( plus_plus_nat @ K2 @ ( suc @ A ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % nat_arith.suc1
% 0.30/0.55 thf(fact_1611_add__Suc,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 0.30/0.55 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_Suc
% 0.30/0.55 thf(fact_1612_add__Suc__shift,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 0.30/0.55 = ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_Suc_shift
% 0.30/0.55 thf(fact_1613_add__eq__self__zero,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( ( plus_plus_nat @ M2 @ N )
% 0.30/0.55 = M2 )
% 0.30/0.55 => ( N = zero_zero_nat ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_eq_self_zero
% 0.30/0.55 thf(fact_1614_plus__nat_Oadd__0,axiom,
% 0.30/0.55 ! [N: nat] :
% 0.30/0.55 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.30/0.55 = N ) ).
% 0.30/0.55
% 0.30/0.55 % plus_nat.add_0
% 0.30/0.55 thf(fact_1615_less__add__eq__less,axiom,
% 0.30/0.55 ! [K2: nat,L: nat,M2: nat,N: nat] :
% 0.30/0.55 ( ( ord_less_nat @ K2 @ L )
% 0.30/0.55 => ( ( ( plus_plus_nat @ M2 @ L )
% 0.30/0.55 = ( plus_plus_nat @ K2 @ N ) )
% 0.30/0.55 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_eq_less
% 0.30/0.55 thf(fact_1616_trans__less__add2,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,M2: nat] :
% 0.30/0.55 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.55 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % trans_less_add2
% 0.30/0.55 thf(fact_1617_trans__less__add1,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,M2: nat] :
% 0.30/0.55 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.55 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % trans_less_add1
% 0.30/0.55 thf(fact_1618_add__less__mono1,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.55 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_mono1
% 0.30/0.55 thf(fact_1619_not__add__less2,axiom,
% 0.30/0.55 ! [J2: nat,I2: nat] :
% 0.30/0.55 ~ ( ord_less_nat @ ( plus_plus_nat @ J2 @ I2 ) @ I2 ) ).
% 0.30/0.55
% 0.30/0.55 % not_add_less2
% 0.30/0.55 thf(fact_1620_not__add__less1,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat] :
% 0.30/0.55 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ I2 ) ).
% 0.30/0.55
% 0.30/0.55 % not_add_less1
% 0.30/0.55 thf(fact_1621_add__less__mono,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.55 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.55 => ( ( ord_less_nat @ K2 @ L )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_mono
% 0.30/0.55 thf(fact_1622_add__lessD1,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.55 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 0.30/0.55 => ( ord_less_nat @ I2 @ K2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_lessD1
% 0.30/0.55 thf(fact_1623_add__leE,axiom,
% 0.30/0.55 ! [M2: nat,K2: nat,N: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 0.30/0.55 => ~ ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.55 => ~ ( ord_less_eq_nat @ K2 @ N ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_leE
% 0.30/0.55 thf(fact_1624_le__add1,axiom,
% 0.30/0.55 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add1
% 0.30/0.55 thf(fact_1625_le__add2,axiom,
% 0.30/0.55 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M2 @ N ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add2
% 0.30/0.55 thf(fact_1626_add__leD1,axiom,
% 0.30/0.55 ! [M2: nat,K2: nat,N: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 0.30/0.55 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_leD1
% 0.30/0.55 thf(fact_1627_add__leD2,axiom,
% 0.30/0.55 ! [M2: nat,K2: nat,N: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 0.30/0.55 => ( ord_less_eq_nat @ K2 @ N ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_leD2
% 0.30/0.55 thf(fact_1628_le__Suc__ex,axiom,
% 0.30/0.55 ! [K2: nat,L: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ K2 @ L )
% 0.30/0.55 => ? [N3: nat] :
% 0.30/0.55 ( L
% 0.30/0.55 = ( plus_plus_nat @ K2 @ N3 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_Suc_ex
% 0.30/0.55 thf(fact_1629_add__le__mono,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.55 => ( ( ord_less_eq_nat @ K2 @ L )
% 0.30/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_mono
% 0.30/0.55 thf(fact_1630_add__le__mono1,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_mono1
% 0.30/0.55 thf(fact_1631_trans__le__add1,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,M2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.55 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % trans_le_add1
% 0.30/0.55 thf(fact_1632_trans__le__add2,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,M2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.55 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % trans_le_add2
% 0.30/0.55 thf(fact_1633_nat__le__iff__add,axiom,
% 0.30/0.55 ( ord_less_eq_nat
% 0.30/0.55 = ( ^ [M6: nat,N4: nat] :
% 0.30/0.55 ? [K3: nat] :
% 0.30/0.55 ( N4
% 0.30/0.55 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % nat_le_iff_add
% 0.30/0.55 thf(fact_1634_add__mult__distrib2,axiom,
% 0.30/0.55 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.55 ( ( times_times_nat @ K2 @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.55 = ( plus_plus_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mult_distrib2
% 0.30/0.55 thf(fact_1635_add__mult__distrib,axiom,
% 0.30/0.55 ! [M2: nat,N: nat,K2: nat] :
% 0.30/0.55 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N ) @ K2 )
% 0.30/0.55 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mult_distrib
% 0.30/0.55 thf(fact_1636_left__add__mult__distrib,axiom,
% 0.30/0.55 ! [I2: nat,U: nat,J2: nat,K2: nat] :
% 0.30/0.55 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ K2 ) )
% 0.30/0.55 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J2 ) @ U ) @ K2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_add_mult_distrib
% 0.30/0.55 thf(fact_1637_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 0.30/0.55 ! [Uu: $o,Uv: $o,Uw2: nat] :
% 0.30/0.55 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw2 ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.membermima.simps(1)
% 0.30/0.55 thf(fact_1638_add__decreasing,axiom,
% 0.30/0.55 ! [A: real,C2: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_eq_real @ C2 @ B )
% 0.30/0.55 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing
% 0.30/0.55 thf(fact_1639_add__decreasing,axiom,
% 0.30/0.55 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_eq_rat @ C2 @ B )
% 0.30/0.55 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing
% 0.30/0.55 thf(fact_1640_add__decreasing,axiom,
% 0.30/0.55 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.55 => ( ( ord_less_eq_nat @ C2 @ B )
% 0.30/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing
% 0.30/0.55 thf(fact_1641_add__decreasing,axiom,
% 0.30/0.55 ! [A: int,C2: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_eq_int @ C2 @ B )
% 0.30/0.55 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing
% 0.30/0.55 thf(fact_1642_add__increasing,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_eq_real @ B @ C2 )
% 0.30/0.55 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing
% 0.30/0.55 thf(fact_1643_add__increasing,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.55 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing
% 0.30/0.55 thf(fact_1644_add__increasing,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.55 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing
% 0.30/0.55 thf(fact_1645_add__increasing,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_eq_int @ B @ C2 )
% 0.30/0.55 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing
% 0.30/0.55 thf(fact_1646_add__decreasing2,axiom,
% 0.30/0.55 ! [C2: real,A: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_eq_real @ A @ B )
% 0.30/0.55 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing2
% 0.30/0.55 thf(fact_1647_add__decreasing2,axiom,
% 0.30/0.55 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.55 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing2
% 0.30/0.55 thf(fact_1648_add__decreasing2,axiom,
% 0.30/0.55 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ C2 @ zero_zero_nat )
% 0.30/0.55 => ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing2
% 0.30/0.55 thf(fact_1649_add__decreasing2,axiom,
% 0.30/0.55 ! [C2: int,A: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_eq_int @ A @ B )
% 0.30/0.55 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_decreasing2
% 0.30/0.55 thf(fact_1650_add__increasing2,axiom,
% 0.30/0.55 ! [C2: real,B: real,A: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.30/0.55 => ( ( ord_less_eq_real @ B @ A )
% 0.30/0.55 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing2
% 0.30/0.55 thf(fact_1651_add__increasing2,axiom,
% 0.30/0.55 ! [C2: rat,B: rat,A: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.30/0.55 => ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.55 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing2
% 0.30/0.55 thf(fact_1652_add__increasing2,axiom,
% 0.30/0.55 ! [C2: nat,B: nat,A: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.30/0.55 => ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.55 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing2
% 0.30/0.55 thf(fact_1653_add__increasing2,axiom,
% 0.30/0.55 ! [C2: int,B: int,A: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.30/0.55 => ( ( ord_less_eq_int @ B @ A )
% 0.30/0.55 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_increasing2
% 0.30/0.55 thf(fact_1654_add__nonneg__nonneg,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.55 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_nonneg
% 0.30/0.55 thf(fact_1655_add__nonneg__nonneg,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.55 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_nonneg
% 0.30/0.55 thf(fact_1656_add__nonneg__nonneg,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.55 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_nonneg
% 0.30/0.55 thf(fact_1657_add__nonneg__nonneg,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.55 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_nonneg
% 0.30/0.55 thf(fact_1658_add__nonpos__nonpos,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.30/0.55 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_nonpos
% 0.30/0.55 thf(fact_1659_add__nonpos__nonpos,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.55 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_nonpos
% 0.30/0.55 thf(fact_1660_add__nonpos__nonpos,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.55 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_nonpos
% 0.30/0.55 thf(fact_1661_add__nonpos__nonpos,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.55 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_nonpos
% 0.30/0.55 thf(fact_1662_add__nonneg__eq__0__iff,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.30/0.55 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.30/0.55 => ( ( ( plus_plus_real @ X @ Y )
% 0.30/0.55 = zero_zero_real )
% 0.30/0.55 = ( ( X = zero_zero_real )
% 0.30/0.55 & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_eq_0_iff
% 0.30/0.55 thf(fact_1663_add__nonneg__eq__0__iff,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.30/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.30/0.55 => ( ( ( plus_plus_rat @ X @ Y )
% 0.30/0.55 = zero_zero_rat )
% 0.30/0.55 = ( ( X = zero_zero_rat )
% 0.30/0.55 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_eq_0_iff
% 0.30/0.55 thf(fact_1664_add__nonneg__eq__0__iff,axiom,
% 0.30/0.55 ! [X: nat,Y: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.30/0.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.30/0.55 => ( ( ( plus_plus_nat @ X @ Y )
% 0.30/0.55 = zero_zero_nat )
% 0.30/0.55 = ( ( X = zero_zero_nat )
% 0.30/0.55 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_eq_0_iff
% 0.30/0.55 thf(fact_1665_add__nonneg__eq__0__iff,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.30/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.30/0.55 => ( ( ( plus_plus_int @ X @ Y )
% 0.30/0.55 = zero_zero_int )
% 0.30/0.55 = ( ( X = zero_zero_int )
% 0.30/0.55 & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_eq_0_iff
% 0.30/0.55 thf(fact_1666_add__nonpos__eq__0__iff,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.30/0.55 => ( ( ( plus_plus_real @ X @ Y )
% 0.30/0.55 = zero_zero_real )
% 0.30/0.55 = ( ( X = zero_zero_real )
% 0.30/0.55 & ( Y = zero_zero_real ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_eq_0_iff
% 0.30/0.55 thf(fact_1667_add__nonpos__eq__0__iff,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.30/0.55 => ( ( ( plus_plus_rat @ X @ Y )
% 0.30/0.55 = zero_zero_rat )
% 0.30/0.55 = ( ( X = zero_zero_rat )
% 0.30/0.55 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_eq_0_iff
% 0.30/0.55 thf(fact_1668_add__nonpos__eq__0__iff,axiom,
% 0.30/0.55 ! [X: nat,Y: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 0.30/0.55 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 0.30/0.55 => ( ( ( plus_plus_nat @ X @ Y )
% 0.30/0.55 = zero_zero_nat )
% 0.30/0.55 = ( ( X = zero_zero_nat )
% 0.30/0.55 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_eq_0_iff
% 0.30/0.55 thf(fact_1669_add__nonpos__eq__0__iff,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 0.30/0.55 => ( ( ( plus_plus_int @ X @ Y )
% 0.30/0.55 = zero_zero_int )
% 0.30/0.55 = ( ( X = zero_zero_int )
% 0.30/0.55 & ( Y = zero_zero_int ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_eq_0_iff
% 0.30/0.55 thf(fact_1670_add__less__le__mono,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.55 ( ( ord_less_real @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_real @ C2 @ D )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_le_mono
% 0.30/0.55 thf(fact_1671_add__less__le__mono,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.55 ( ( ord_less_rat @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_rat @ C2 @ D )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_le_mono
% 0.30/0.55 thf(fact_1672_add__less__le__mono,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.55 ( ( ord_less_nat @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_nat @ C2 @ D )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_le_mono
% 0.30/0.55 thf(fact_1673_add__less__le__mono,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.55 ( ( ord_less_int @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_int @ C2 @ D )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_le_mono
% 0.30/0.55 thf(fact_1674_add__le__less__mono,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.55 => ( ( ord_less_real @ C2 @ D )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_less_mono
% 0.30/0.55 thf(fact_1675_add__le__less__mono,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.55 => ( ( ord_less_rat @ C2 @ D )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_less_mono
% 0.30/0.55 thf(fact_1676_add__le__less__mono,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( ord_less_nat @ C2 @ D )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_less_mono
% 0.30/0.55 thf(fact_1677_add__le__less__mono,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.55 => ( ( ord_less_int @ C2 @ D )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_less_mono
% 0.30/0.55 thf(fact_1678_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.55 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.55 ( ( ( ord_less_real @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_eq_real @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(3)
% 0.30/0.55 thf(fact_1679_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.55 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.55 ( ( ( ord_less_rat @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_eq_rat @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(3)
% 0.30/0.55 thf(fact_1680_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.55 ( ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_eq_nat @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(3)
% 0.30/0.55 thf(fact_1681_add__mono__thms__linordered__field_I3_J,axiom,
% 0.30/0.55 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.55 ( ( ( ord_less_int @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_eq_int @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(3)
% 0.30/0.55 thf(fact_1682_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.55 ! [I2: real,J2: real,K2: real,L: real] :
% 0.30/0.55 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_real @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(4)
% 0.30/0.55 thf(fact_1683_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.55 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 0.30/0.55 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_rat @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(4)
% 0.30/0.55 thf(fact_1684_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 0.30/0.55 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_nat @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(4)
% 0.30/0.55 thf(fact_1685_add__mono__thms__linordered__field_I4_J,axiom,
% 0.30/0.55 ! [I2: int,J2: int,K2: int,L: int] :
% 0.30/0.55 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 0.30/0.55 & ( ord_less_int @ K2 @ L ) )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono_thms_linordered_field(4)
% 0.30/0.55 thf(fact_1686_add__less__zeroD,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.30/0.55 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_zeroD
% 0.30/0.55 thf(fact_1687_add__less__zeroD,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.30/0.55 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_zeroD
% 0.30/0.55 thf(fact_1688_add__less__zeroD,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_int @ X @ zero_zero_int )
% 0.30/0.55 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_less_zeroD
% 0.30/0.55 thf(fact_1689_pos__add__strict,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.55 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % pos_add_strict
% 0.30/0.55 thf(fact_1690_pos__add__strict,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.55 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % pos_add_strict
% 0.30/0.55 thf(fact_1691_pos__add__strict,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.55 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % pos_add_strict
% 0.30/0.55 thf(fact_1692_pos__add__strict,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.55 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % pos_add_strict
% 0.30/0.55 thf(fact_1693_canonically__ordered__monoid__add__class_OlessE,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_nat @ A @ B )
% 0.30/0.55 => ~ ! [C: nat] :
% 0.30/0.55 ( ( B
% 0.30/0.55 = ( plus_plus_nat @ A @ C ) )
% 0.30/0.55 => ( C = zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % canonically_ordered_monoid_add_class.lessE
% 0.30/0.55 thf(fact_1694_add__pos__pos,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.30/0.55 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_pos
% 0.30/0.55 thf(fact_1695_add__pos__pos,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.55 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_pos
% 0.30/0.55 thf(fact_1696_add__pos__pos,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_pos
% 0.30/0.55 thf(fact_1697_add__pos__pos,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.55 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_pos
% 0.30/0.55 thf(fact_1698_add__neg__neg,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_real @ A @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_neg
% 0.30/0.55 thf(fact_1699_add__neg__neg,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_neg
% 0.30/0.55 thf(fact_1700_add__neg__neg,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.30/0.55 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_neg
% 0.30/0.55 thf(fact_1701_add__neg__neg,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_neg
% 0.30/0.55 thf(fact_1702_add__mono1,axiom,
% 0.30/0.55 ! [A: code_integer,B: code_integer] :
% 0.30/0.55 ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.30/0.55 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono1
% 0.30/0.55 thf(fact_1703_add__mono1,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_real @ A @ B )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono1
% 0.30/0.55 thf(fact_1704_add__mono1,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_rat @ A @ B )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono1
% 0.30/0.55 thf(fact_1705_add__mono1,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_nat @ A @ B )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono1
% 0.30/0.55 thf(fact_1706_add__mono1,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_int @ A @ B )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_mono1
% 0.30/0.55 thf(fact_1707_less__add__one,axiom,
% 0.30/0.55 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_one
% 0.30/0.55 thf(fact_1708_less__add__one,axiom,
% 0.30/0.55 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_one
% 0.30/0.55 thf(fact_1709_less__add__one,axiom,
% 0.30/0.55 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_one
% 0.30/0.55 thf(fact_1710_less__add__one,axiom,
% 0.30/0.55 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_one
% 0.30/0.55 thf(fact_1711_less__add__one,axiom,
% 0.30/0.55 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_one
% 0.30/0.55 thf(fact_1712_add__is__1,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( ( plus_plus_nat @ M2 @ N )
% 0.30/0.55 = ( suc @ zero_zero_nat ) )
% 0.30/0.55 = ( ( ( M2
% 0.30/0.55 = ( suc @ zero_zero_nat ) )
% 0.30/0.55 & ( N = zero_zero_nat ) )
% 0.30/0.55 | ( ( M2 = zero_zero_nat )
% 0.30/0.55 & ( N
% 0.30/0.55 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_is_1
% 0.30/0.55 thf(fact_1713_one__is__add,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( ( suc @ zero_zero_nat )
% 0.30/0.55 = ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.55 = ( ( ( M2
% 0.30/0.55 = ( suc @ zero_zero_nat ) )
% 0.30/0.55 & ( N = zero_zero_nat ) )
% 0.30/0.55 | ( ( M2 = zero_zero_nat )
% 0.30/0.55 & ( N
% 0.30/0.55 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % one_is_add
% 0.30/0.55 thf(fact_1714_less__natE,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.55 => ~ ! [Q3: nat] :
% 0.30/0.55 ( N
% 0.30/0.55 != ( suc @ ( plus_plus_nat @ M2 @ Q3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_natE
% 0.30/0.55 thf(fact_1715_less__add__Suc1,axiom,
% 0.30/0.55 ! [I2: nat,M2: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_Suc1
% 0.30/0.55 thf(fact_1716_less__add__Suc2,axiom,
% 0.30/0.55 ! [I2: nat,M2: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M2 @ I2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_Suc2
% 0.30/0.55 thf(fact_1717_less__iff__Suc__add,axiom,
% 0.30/0.55 ( ord_less_nat
% 0.30/0.55 = ( ^ [M6: nat,N4: nat] :
% 0.30/0.55 ? [K3: nat] :
% 0.30/0.55 ( N4
% 0.30/0.55 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_iff_Suc_add
% 0.30/0.55 thf(fact_1718_less__imp__Suc__add,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.55 => ? [K: nat] :
% 0.30/0.55 ( N
% 0.30/0.55 = ( suc @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_imp_Suc_add
% 0.30/0.55 thf(fact_1719_less__imp__add__positive,axiom,
% 0.30/0.55 ! [I2: nat,J2: nat] :
% 0.30/0.55 ( ( ord_less_nat @ I2 @ J2 )
% 0.30/0.55 => ? [K: nat] :
% 0.30/0.55 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.30/0.55 & ( ( plus_plus_nat @ I2 @ K )
% 0.30/0.55 = J2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_imp_add_positive
% 0.30/0.55 thf(fact_1720_mono__nat__linear__lb,axiom,
% 0.30/0.55 ! [F2: nat > nat,M2: nat,K2: nat] :
% 0.30/0.55 ( ! [M: nat,N3: nat] :
% 0.30/0.55 ( ( ord_less_nat @ M @ N3 )
% 0.30/0.55 => ( ord_less_nat @ ( F2 @ M ) @ ( F2 @ N3 ) ) )
% 0.30/0.55 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F2 @ M2 ) @ K2 ) @ ( F2 @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % mono_nat_linear_lb
% 0.30/0.55 thf(fact_1721_mult__Suc,axiom,
% 0.30/0.55 ! [M2: nat,N: nat] :
% 0.30/0.55 ( ( times_times_nat @ ( suc @ M2 ) @ N )
% 0.30/0.55 = ( plus_plus_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % mult_Suc
% 0.30/0.55 thf(fact_1722_Suc__eq__plus1,axiom,
% 0.30/0.55 ( suc
% 0.30/0.55 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % Suc_eq_plus1
% 0.30/0.55 thf(fact_1723_plus__1__eq__Suc,axiom,
% 0.30/0.55 ( ( plus_plus_nat @ one_one_nat )
% 0.30/0.55 = suc ) ).
% 0.30/0.55
% 0.30/0.55 % plus_1_eq_Suc
% 0.30/0.55 thf(fact_1724_Suc__eq__plus1__left,axiom,
% 0.30/0.55 ( suc
% 0.30/0.55 = ( plus_plus_nat @ one_one_nat ) ) ).
% 0.30/0.55
% 0.30/0.55 % Suc_eq_plus1_left
% 0.30/0.55 thf(fact_1725_VEBT__internal_OminNull_Ocases,axiom,
% 0.30/0.55 ! [X: vEBT_VEBT] :
% 0.30/0.55 ( ( X
% 0.30/0.55 != ( vEBT_Leaf @ $false @ $false ) )
% 0.30/0.55 => ( ! [Uv2: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.30/0.55 => ( ! [Uu2: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.30/0.55 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.30/0.55 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.minNull.cases
% 0.30/0.55 thf(fact_1726_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.30/0.55 ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 0.30/0.55 ( ( vEBT_V1502963449132264192at_nat @ Uw2 @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat )
% 0.30/0.55 = none_P5556105721700978146at_nat ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.option_shift.simps(2)
% 0.30/0.55 thf(fact_1727_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.30/0.55 ! [Uw2: num > num > num,V2: num] :
% 0.30/0.55 ( ( vEBT_V819420779217536731ft_num @ Uw2 @ ( some_num @ V2 ) @ none_num )
% 0.30/0.55 = none_num ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.option_shift.simps(2)
% 0.30/0.55 thf(fact_1728_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 0.30/0.55 ! [Uw2: nat > nat > nat,V2: nat] :
% 0.30/0.55 ( ( vEBT_V4262088993061758097ft_nat @ Uw2 @ ( some_nat @ V2 ) @ none_nat )
% 0.30/0.55 = none_nat ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.option_shift.simps(2)
% 0.30/0.55 thf(fact_1729_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.30/0.55 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 0.30/0.55 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 0.30/0.55 = Y )
% 0.30/0.55 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 0.30/0.55 => ( Y != none_P5556105721700978146at_nat ) )
% 0.30/0.55 => ( ( ? [V: product_prod_nat_nat] :
% 0.30/0.55 ( Xa2
% 0.30/0.55 = ( some_P7363390416028606310at_nat @ V ) )
% 0.30/0.55 => ( ( Xb = none_P5556105721700978146at_nat )
% 0.30/0.55 => ( Y != none_P5556105721700978146at_nat ) ) )
% 0.30/0.55 => ~ ! [A3: product_prod_nat_nat] :
% 0.30/0.55 ( ( Xa2
% 0.30/0.55 = ( some_P7363390416028606310at_nat @ A3 ) )
% 0.30/0.55 => ! [B3: product_prod_nat_nat] :
% 0.30/0.55 ( ( Xb
% 0.30/0.55 = ( some_P7363390416028606310at_nat @ B3 ) )
% 0.30/0.55 => ( Y
% 0.30/0.55 != ( some_P7363390416028606310at_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.option_shift.elims
% 0.30/0.55 thf(fact_1730_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.30/0.55 ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y: option_num] :
% 0.30/0.55 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 0.30/0.55 = Y )
% 0.30/0.55 => ( ( ( Xa2 = none_num )
% 0.30/0.55 => ( Y != none_num ) )
% 0.30/0.55 => ( ( ? [V: num] :
% 0.30/0.55 ( Xa2
% 0.30/0.55 = ( some_num @ V ) )
% 0.30/0.55 => ( ( Xb = none_num )
% 0.30/0.55 => ( Y != none_num ) ) )
% 0.30/0.55 => ~ ! [A3: num] :
% 0.30/0.55 ( ( Xa2
% 0.30/0.55 = ( some_num @ A3 ) )
% 0.30/0.55 => ! [B3: num] :
% 0.30/0.55 ( ( Xb
% 0.30/0.55 = ( some_num @ B3 ) )
% 0.30/0.55 => ( Y
% 0.30/0.55 != ( some_num @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.option_shift.elims
% 0.30/0.55 thf(fact_1731_VEBT__internal_Ooption__shift_Oelims,axiom,
% 0.30/0.55 ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y: option_nat] :
% 0.30/0.55 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 0.30/0.55 = Y )
% 0.30/0.55 => ( ( ( Xa2 = none_nat )
% 0.30/0.55 => ( Y != none_nat ) )
% 0.30/0.55 => ( ( ? [V: nat] :
% 0.30/0.55 ( Xa2
% 0.30/0.55 = ( some_nat @ V ) )
% 0.30/0.55 => ( ( Xb = none_nat )
% 0.30/0.55 => ( Y != none_nat ) ) )
% 0.30/0.55 => ~ ! [A3: nat] :
% 0.30/0.55 ( ( Xa2
% 0.30/0.55 = ( some_nat @ A3 ) )
% 0.30/0.55 => ! [B3: nat] :
% 0.30/0.55 ( ( Xb
% 0.30/0.55 = ( some_nat @ B3 ) )
% 0.30/0.55 => ( Y
% 0.30/0.55 != ( some_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.option_shift.elims
% 0.30/0.55 thf(fact_1732_field__le__epsilon,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ! [E2: real] :
% 0.30/0.55 ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.30/0.55 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 0.30/0.55 => ( ord_less_eq_real @ X @ Y ) ) ).
% 0.30/0.55
% 0.30/0.55 % field_le_epsilon
% 0.30/0.55 thf(fact_1733_field__le__epsilon,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ! [E2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.30/0.55 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 0.30/0.55 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.30/0.55
% 0.30/0.55 % field_le_epsilon
% 0.30/0.55 thf(fact_1734_add__neg__nonpos,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_real @ A @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_nonpos
% 0.30/0.55 thf(fact_1735_add__neg__nonpos,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_nonpos
% 0.30/0.55 thf(fact_1736_add__neg__nonpos,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_nat @ A @ zero_zero_nat )
% 0.30/0.55 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_nonpos
% 0.30/0.55 thf(fact_1737_add__neg__nonpos,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_int @ A @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_neg_nonpos
% 0.30/0.55 thf(fact_1738_add__nonneg__pos,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.30/0.55 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_pos
% 0.30/0.55 thf(fact_1739_add__nonneg__pos,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.55 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_pos
% 0.30/0.55 thf(fact_1740_add__nonneg__pos,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_pos
% 0.30/0.55 thf(fact_1741_add__nonneg__pos,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.55 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonneg_pos
% 0.30/0.55 thf(fact_1742_add__nonpos__neg,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.30/0.55 => ( ( ord_less_real @ B @ zero_zero_real )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_neg
% 0.30/0.55 thf(fact_1743_add__nonpos__neg,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.30/0.55 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_neg
% 0.30/0.55 thf(fact_1744_add__nonpos__neg,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 0.30/0.55 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 0.30/0.55 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_neg
% 0.30/0.55 thf(fact_1745_add__nonpos__neg,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.30/0.55 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_nonpos_neg
% 0.30/0.55 thf(fact_1746_add__pos__nonneg,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.55 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_nonneg
% 0.30/0.55 thf(fact_1747_add__pos__nonneg,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.55 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_nonneg
% 0.30/0.55 thf(fact_1748_add__pos__nonneg,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_nonneg
% 0.30/0.55 thf(fact_1749_add__pos__nonneg,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.55 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_pos_nonneg
% 0.30/0.55 thf(fact_1750_add__strict__increasing,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_eq_real @ B @ C2 )
% 0.30/0.55 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing
% 0.30/0.55 thf(fact_1751_add__strict__increasing,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_eq_rat @ B @ C2 )
% 0.30/0.55 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing
% 0.30/0.55 thf(fact_1752_add__strict__increasing,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.55 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing
% 0.30/0.55 thf(fact_1753_add__strict__increasing,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_eq_int @ B @ C2 )
% 0.30/0.55 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing
% 0.30/0.55 thf(fact_1754_add__strict__increasing2,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.55 => ( ( ord_less_real @ B @ C2 )
% 0.30/0.55 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing2
% 0.30/0.55 thf(fact_1755_add__strict__increasing2,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.55 => ( ( ord_less_rat @ B @ C2 )
% 0.30/0.55 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing2
% 0.30/0.55 thf(fact_1756_add__strict__increasing2,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.55 => ( ( ord_less_nat @ B @ C2 )
% 0.30/0.55 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing2
% 0.30/0.55 thf(fact_1757_add__strict__increasing2,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.55 => ( ( ord_less_int @ B @ C2 )
% 0.30/0.55 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_strict_increasing2
% 0.30/0.55 thf(fact_1758_sum__squares__ge__zero,axiom,
% 0.30/0.55 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_ge_zero
% 0.30/0.55 thf(fact_1759_sum__squares__ge__zero,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_ge_zero
% 0.30/0.55 thf(fact_1760_sum__squares__ge__zero,axiom,
% 0.30/0.55 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_ge_zero
% 0.30/0.55 thf(fact_1761_not__sum__squares__lt__zero,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 0.30/0.55
% 0.30/0.55 % not_sum_squares_lt_zero
% 0.30/0.55 thf(fact_1762_not__sum__squares__lt__zero,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 0.30/0.55
% 0.30/0.55 % not_sum_squares_lt_zero
% 0.30/0.55 thf(fact_1763_not__sum__squares__lt__zero,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 0.30/0.55
% 0.30/0.55 % not_sum_squares_lt_zero
% 0.30/0.55 thf(fact_1764_discrete,axiom,
% 0.30/0.55 ( ord_le6747313008572928689nteger
% 0.30/0.55 = ( ^ [A5: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % discrete
% 0.30/0.55 thf(fact_1765_discrete,axiom,
% 0.30/0.55 ( ord_less_nat
% 0.30/0.55 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % discrete
% 0.30/0.55 thf(fact_1766_discrete,axiom,
% 0.30/0.55 ( ord_less_int
% 0.30/0.55 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % discrete
% 0.30/0.55 thf(fact_1767_zero__less__two,axiom,
% 0.30/0.55 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 0.30/0.55
% 0.30/0.55 % zero_less_two
% 0.30/0.55 thf(fact_1768_zero__less__two,axiom,
% 0.30/0.55 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.30/0.55
% 0.30/0.55 % zero_less_two
% 0.30/0.55 thf(fact_1769_zero__less__two,axiom,
% 0.30/0.55 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 0.30/0.55
% 0.30/0.55 % zero_less_two
% 0.30/0.55 thf(fact_1770_zero__less__two,axiom,
% 0.30/0.55 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.30/0.55
% 0.30/0.55 % zero_less_two
% 0.30/0.55 thf(fact_1771_zero__less__two,axiom,
% 0.30/0.55 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.30/0.55
% 0.30/0.55 % zero_less_two
% 0.30/0.55 thf(fact_1772_option_Osize_I3_J,axiom,
% 0.30/0.55 ( ( size_size_option_nat @ none_nat )
% 0.30/0.55 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.55
% 0.30/0.55 % option.size(3)
% 0.30/0.55 thf(fact_1773_option_Osize_I3_J,axiom,
% 0.30/0.55 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 0.30/0.55 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.55
% 0.30/0.55 % option.size(3)
% 0.30/0.55 thf(fact_1774_option_Osize_I3_J,axiom,
% 0.30/0.55 ( ( size_size_option_num @ none_num )
% 0.30/0.55 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.55
% 0.30/0.55 % option.size(3)
% 0.30/0.55 thf(fact_1775_convex__bound__le,axiom,
% 0.30/0.55 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 0.30/0.55 ( ( ord_le3102999989581377725nteger @ X @ A )
% 0.30/0.55 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 0.30/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.30/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 0.30/0.55 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 0.30/0.55 = one_one_Code_integer )
% 0.30/0.55 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_le
% 0.30/0.55 thf(fact_1776_convex__bound__le,axiom,
% 0.30/0.55 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ X @ A )
% 0.30/0.55 => ( ( ord_less_eq_real @ Y @ A )
% 0.30/0.55 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.30/0.55 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 0.30/0.55 => ( ( ( plus_plus_real @ U @ V2 )
% 0.30/0.55 = one_one_real )
% 0.30/0.55 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_le
% 0.30/0.55 thf(fact_1777_convex__bound__le,axiom,
% 0.30/0.55 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ X @ A )
% 0.30/0.55 => ( ( ord_less_eq_rat @ Y @ A )
% 0.30/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.30/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 0.30/0.55 => ( ( ( plus_plus_rat @ U @ V2 )
% 0.30/0.55 = one_one_rat )
% 0.30/0.55 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_le
% 0.30/0.55 thf(fact_1778_convex__bound__le,axiom,
% 0.30/0.55 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ X @ A )
% 0.30/0.55 => ( ( ord_less_eq_int @ Y @ A )
% 0.30/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.30/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 0.30/0.55 => ( ( ( plus_plus_int @ U @ V2 )
% 0.30/0.55 = one_one_int )
% 0.30/0.55 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_le
% 0.30/0.55 thf(fact_1779_vebt__mint_Oelims,axiom,
% 0.30/0.55 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.30/0.55 ( ( ( vEBT_vebt_mint @ X )
% 0.30/0.55 = Y )
% 0.30/0.55 => ( ! [A3: $o,B3: $o] :
% 0.30/0.55 ( ( X
% 0.30/0.55 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.30/0.55 => ~ ( ( A3
% 0.30/0.55 => ( Y
% 0.30/0.55 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.55 & ( ~ A3
% 0.30/0.55 => ( ( B3
% 0.30/0.55 => ( Y
% 0.30/0.55 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.55 & ( ~ B3
% 0.30/0.55 => ( Y = none_nat ) ) ) ) ) )
% 0.30/0.55 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.30/0.55 => ( Y != none_nat ) )
% 0.30/0.55 => ~ ! [Mi2: nat] :
% 0.30/0.55 ( ? [Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.30/0.55 => ( Y
% 0.30/0.55 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_mint.elims
% 0.30/0.55 thf(fact_1780_vebt__maxt_Oelims,axiom,
% 0.30/0.55 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.30/0.55 ( ( ( vEBT_vebt_maxt @ X )
% 0.30/0.55 = Y )
% 0.30/0.55 => ( ! [A3: $o,B3: $o] :
% 0.30/0.55 ( ( X
% 0.30/0.55 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.30/0.55 => ~ ( ( B3
% 0.30/0.55 => ( Y
% 0.30/0.55 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.55 & ( ~ B3
% 0.30/0.55 => ( ( A3
% 0.30/0.55 => ( Y
% 0.30/0.55 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.55 & ( ~ A3
% 0.30/0.55 => ( Y = none_nat ) ) ) ) ) )
% 0.30/0.55 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.30/0.55 => ( Y != none_nat ) )
% 0.30/0.55 => ~ ! [Mi2: nat,Ma2: nat] :
% 0.30/0.55 ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.30/0.55 => ( Y
% 0.30/0.55 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_maxt.elims
% 0.30/0.55 thf(fact_1781_vebt__mint_Ocases,axiom,
% 0.30/0.55 ! [X: vEBT_VEBT] :
% 0.30/0.55 ( ! [A3: $o,B3: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( vEBT_Leaf @ A3 @ B3 ) )
% 0.30/0.55 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.30/0.55 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_mint.cases
% 0.30/0.55 thf(fact_1782_convex__bound__lt,axiom,
% 0.30/0.55 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 0.30/0.55 ( ( ord_le6747313008572928689nteger @ X @ A )
% 0.30/0.55 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 0.30/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 0.30/0.55 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 0.30/0.55 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 0.30/0.55 = one_one_Code_integer )
% 0.30/0.55 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_lt
% 0.30/0.55 thf(fact_1783_convex__bound__lt,axiom,
% 0.30/0.55 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 0.30/0.55 ( ( ord_less_real @ X @ A )
% 0.30/0.55 => ( ( ord_less_real @ Y @ A )
% 0.30/0.55 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 0.30/0.55 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 0.30/0.55 => ( ( ( plus_plus_real @ U @ V2 )
% 0.30/0.55 = one_one_real )
% 0.30/0.55 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_lt
% 0.30/0.55 thf(fact_1784_convex__bound__lt,axiom,
% 0.30/0.55 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ X @ A )
% 0.30/0.55 => ( ( ord_less_rat @ Y @ A )
% 0.30/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 0.30/0.55 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 0.30/0.55 => ( ( ( plus_plus_rat @ U @ V2 )
% 0.30/0.55 = one_one_rat )
% 0.30/0.55 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_lt
% 0.30/0.55 thf(fact_1785_convex__bound__lt,axiom,
% 0.30/0.55 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 0.30/0.55 ( ( ord_less_int @ X @ A )
% 0.30/0.55 => ( ( ord_less_int @ Y @ A )
% 0.30/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.30/0.55 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 0.30/0.55 => ( ( ( plus_plus_int @ U @ V2 )
% 0.30/0.55 = one_one_int )
% 0.30/0.55 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % convex_bound_lt
% 0.30/0.55 thf(fact_1786_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 0.30/0.55 ! [Mi: nat,Ma: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 0.30/0.55 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va3 @ Vb ) @ X )
% 0.30/0.55 = ( ( X = Mi )
% 0.30/0.55 | ( X = Ma ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % VEBT_internal.membermima.simps(3)
% 0.30/0.55 thf(fact_1787_vebt__member_Ocases,axiom,
% 0.30/0.55 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.55 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.30/0.55 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ X3 ) )
% 0.30/0.55 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ X3 ) )
% 0.30/0.55 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 0.30/0.55 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_member.cases
% 0.30/0.55 thf(fact_1788_vebt__mint_Osimps_I1_J,axiom,
% 0.30/0.55 ! [A: $o,B: $o] :
% 0.30/0.55 ( ( A
% 0.30/0.55 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.30/0.55 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.55 & ( ~ A
% 0.30/0.55 => ( ( B
% 0.30/0.55 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.30/0.55 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.55 & ( ~ B
% 0.30/0.55 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 0.30/0.55 = none_nat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_mint.simps(1)
% 0.30/0.55 thf(fact_1789_vebt__maxt_Osimps_I1_J,axiom,
% 0.30/0.55 ! [B: $o,A: $o] :
% 0.30/0.55 ( ( B
% 0.30/0.55 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.30/0.55 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.55 & ( ~ B
% 0.30/0.55 => ( ( A
% 0.30/0.55 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.30/0.55 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.55 & ( ~ A
% 0.30/0.55 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 0.30/0.55 = none_nat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_maxt.simps(1)
% 0.30/0.55 thf(fact_1790_geqmaxNone,axiom,
% 0.30/0.55 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_nat @ Ma @ X )
% 0.30/0.55 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.30/0.55 = none_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % geqmaxNone
% 0.30/0.55 thf(fact_1791_vebt__pred_Ocases,axiom,
% 0.30/0.55 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.55 ( ! [Uu2: $o,Uv2: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 0.30/0.55 => ( ! [A3: $o,Uw: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 0.30/0.55 => ( ! [A3: $o,B3: $o,Va: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) )
% 0.30/0.55 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) @ Vb2 ) )
% 0.30/0.55 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf ) )
% 0.30/0.55 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 0.30/0.55 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_pred.cases
% 0.30/0.55 thf(fact_1792_vebt__succ_Ocases,axiom,
% 0.30/0.55 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.55 ( ! [Uu2: $o,B3: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) )
% 0.30/0.55 => ( ! [Uv2: $o,Uw: $o,N3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw ) @ ( suc @ N3 ) ) )
% 0.30/0.55 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Va2 ) )
% 0.30/0.55 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve ) )
% 0.30/0.55 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 0.30/0.55 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_succ.cases
% 0.30/0.55 thf(fact_1793_vebt__delete_Ocases,axiom,
% 0.30/0.55 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.55 ( ! [A3: $o,B3: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) )
% 0.30/0.55 => ( ! [A3: $o,B3: $o] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 0.30/0.55 => ( ! [A3: $o,B3: $o,N3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 0.30/0.55 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Uu2 ) )
% 0.30/0.55 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X3 ) )
% 0.30/0.55 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X3 ) )
% 0.30/0.55 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_delete.cases
% 0.30/0.55 thf(fact_1794_vebt__insert_Ocases,axiom,
% 0.30/0.55 ! [X: produc9072475918466114483BT_nat] :
% 0.30/0.55 ( ! [A3: $o,B3: $o,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 0.30/0.55 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X3 ) )
% 0.30/0.55 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 ) )
% 0.30/0.55 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) @ X3 ) )
% 0.30/0.55 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 0.30/0.55 ( X
% 0.30/0.55 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_insert.cases
% 0.30/0.55 thf(fact_1795_succ__correct,axiom,
% 0.30/0.55 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.55 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.30/0.55 = ( some_nat @ Sx ) )
% 0.30/0.55 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % succ_correct
% 0.30/0.55 thf(fact_1796_pred__correct,axiom,
% 0.30/0.55 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.55 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.30/0.55 = ( some_nat @ Sx ) )
% 0.30/0.55 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % pred_correct
% 0.30/0.55 thf(fact_1797_pred__corr,axiom,
% 0.30/0.55 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.55 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.30/0.55 = ( some_nat @ Px ) )
% 0.30/0.55 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % pred_corr
% 0.30/0.55 thf(fact_1798_succ__corr,axiom,
% 0.30/0.55 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.55 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.30/0.55 = ( some_nat @ Sx ) )
% 0.30/0.55 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % succ_corr
% 0.30/0.55 thf(fact_1799_sum__squares__eq__zero__iff,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 0.30/0.55 = zero_zero_real )
% 0.30/0.55 = ( ( X = zero_zero_real )
% 0.30/0.55 & ( Y = zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_eq_zero_iff
% 0.30/0.55 thf(fact_1800_sum__squares__eq__zero__iff,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.30/0.55 = zero_zero_rat )
% 0.30/0.55 = ( ( X = zero_zero_rat )
% 0.30/0.55 & ( Y = zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_eq_zero_iff
% 0.30/0.55 thf(fact_1801_sum__squares__eq__zero__iff,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.30/0.55 = zero_zero_int )
% 0.30/0.55 = ( ( X = zero_zero_int )
% 0.30/0.55 & ( Y = zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_eq_zero_iff
% 0.30/0.55 thf(fact_1802_vebt__succ_Osimps_I2_J,axiom,
% 0.30/0.55 ! [Uv: $o,Uw2: $o,N: nat] :
% 0.30/0.55 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw2 ) @ ( suc @ N ) )
% 0.30/0.55 = none_nat ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_succ.simps(2)
% 0.30/0.55 thf(fact_1803_vebt__pred_Osimps_I1_J,axiom,
% 0.30/0.55 ! [Uu: $o,Uv: $o] :
% 0.30/0.55 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 0.30/0.55 = none_nat ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_pred.simps(1)
% 0.30/0.55 thf(fact_1804_vebt__succ_Osimps_I4_J,axiom,
% 0.30/0.55 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 0.30/0.55 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 0.30/0.55 = none_nat ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_succ.simps(4)
% 0.30/0.55 thf(fact_1805_vebt__pred_Osimps_I5_J,axiom,
% 0.30/0.55 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 0.30/0.55 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 0.30/0.55 = none_nat ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_pred.simps(5)
% 0.30/0.55 thf(fact_1806_vebt__pred_Osimps_I6_J,axiom,
% 0.30/0.55 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 0.30/0.55 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 0.30/0.55 = none_nat ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_pred.simps(6)
% 0.30/0.55 thf(fact_1807_vebt__succ_Osimps_I5_J,axiom,
% 0.30/0.55 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 0.30/0.55 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 0.30/0.55 = none_nat ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_succ.simps(5)
% 0.30/0.55 thf(fact_1808_vebt__pred_Osimps_I2_J,axiom,
% 0.30/0.55 ! [A: $o,Uw2: $o] :
% 0.30/0.55 ( ( A
% 0.30/0.55 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.55 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.55 & ( ~ A
% 0.30/0.55 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.55 = none_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_pred.simps(2)
% 0.30/0.55 thf(fact_1809_vebt__succ_Osimps_I1_J,axiom,
% 0.30/0.55 ! [B: $o,Uu: $o] :
% 0.30/0.55 ( ( B
% 0.30/0.55 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.30/0.55 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.55 & ( ~ B
% 0.30/0.55 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 0.30/0.55 = none_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_succ.simps(1)
% 0.30/0.55 thf(fact_1810_vebt__pred_Osimps_I3_J,axiom,
% 0.30/0.55 ! [B: $o,A: $o,Va3: nat] :
% 0.30/0.55 ( ( B
% 0.30/0.55 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 0.30/0.55 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.55 & ( ~ B
% 0.30/0.55 => ( ( A
% 0.30/0.55 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 0.30/0.55 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.55 & ( ~ A
% 0.30/0.55 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 0.30/0.55 = none_nat ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_pred.simps(3)
% 0.30/0.55 thf(fact_1811_vebt__delete_Osimps_I3_J,axiom,
% 0.30/0.55 ! [A: $o,B: $o,N: nat] :
% 0.30/0.55 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 0.30/0.55 = ( vEBT_Leaf @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_delete.simps(3)
% 0.30/0.55 thf(fact_1812_vebt__delete_Osimps_I1_J,axiom,
% 0.30/0.55 ! [A: $o,B: $o] :
% 0.30/0.55 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 0.30/0.55 = ( vEBT_Leaf @ $false @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_delete.simps(1)
% 0.30/0.55 thf(fact_1813_is__pred__in__set__def,axiom,
% 0.30/0.55 ( vEBT_is_pred_in_set
% 0.30/0.55 = ( ^ [Xs: set_nat,X4: nat,Y4: nat] :
% 0.30/0.55 ( ( member_nat @ Y4 @ Xs )
% 0.30/0.55 & ( ord_less_nat @ Y4 @ X4 )
% 0.30/0.55 & ! [Z4: nat] :
% 0.30/0.55 ( ( member_nat @ Z4 @ Xs )
% 0.30/0.55 => ( ( ord_less_nat @ Z4 @ X4 )
% 0.30/0.55 => ( ord_less_eq_nat @ Z4 @ Y4 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % is_pred_in_set_def
% 0.30/0.55 thf(fact_1814_is__succ__in__set__def,axiom,
% 0.30/0.55 ( vEBT_is_succ_in_set
% 0.30/0.55 = ( ^ [Xs: set_nat,X4: nat,Y4: nat] :
% 0.30/0.55 ( ( member_nat @ Y4 @ Xs )
% 0.30/0.55 & ( ord_less_nat @ X4 @ Y4 )
% 0.30/0.55 & ! [Z4: nat] :
% 0.30/0.55 ( ( member_nat @ Z4 @ Xs )
% 0.30/0.55 => ( ( ord_less_nat @ X4 @ Z4 )
% 0.30/0.55 => ( ord_less_eq_nat @ Y4 @ Z4 ) ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % is_succ_in_set_def
% 0.30/0.55 thf(fact_1815_sum__squares__le__zero__iff,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 0.30/0.55 = ( ( X = zero_zero_real )
% 0.30/0.55 & ( Y = zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_le_zero_iff
% 0.30/0.55 thf(fact_1816_sum__squares__le__zero__iff,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 0.30/0.55 = ( ( X = zero_zero_rat )
% 0.30/0.55 & ( Y = zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_le_zero_iff
% 0.30/0.55 thf(fact_1817_sum__squares__le__zero__iff,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 0.30/0.55 = ( ( X = zero_zero_int )
% 0.30/0.55 & ( Y = zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_le_zero_iff
% 0.30/0.55 thf(fact_1818_sum__squares__gt__zero__iff,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 0.30/0.55 = ( ( X != zero_zero_real )
% 0.30/0.55 | ( Y != zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_gt_zero_iff
% 0.30/0.55 thf(fact_1819_sum__squares__gt__zero__iff,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 0.30/0.55 = ( ( X != zero_zero_rat )
% 0.30/0.55 | ( Y != zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_gt_zero_iff
% 0.30/0.55 thf(fact_1820_sum__squares__gt__zero__iff,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 0.30/0.55 = ( ( X != zero_zero_int )
% 0.30/0.55 | ( Y != zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % sum_squares_gt_zero_iff
% 0.30/0.55 thf(fact_1821_vebt__delete_Osimps_I2_J,axiom,
% 0.30/0.55 ! [A: $o,B: $o] :
% 0.30/0.55 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.55 = ( vEBT_Leaf @ A @ $false ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_delete.simps(2)
% 0.30/0.55 thf(fact_1822_vebt__delete_Osimps_I5_J,axiom,
% 0.30/0.55 ! [Mi: nat,Ma: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X: nat] :
% 0.30/0.55 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X )
% 0.30/0.55 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_delete.simps(5)
% 0.30/0.55 thf(fact_1823_vebt__delete_Osimps_I6_J,axiom,
% 0.30/0.55 ! [Mi: nat,Ma: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X: nat] :
% 0.30/0.55 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X )
% 0.30/0.55 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % vebt_delete.simps(6)
% 0.30/0.55 thf(fact_1824_add__def,axiom,
% 0.30/0.55 ( vEBT_VEBT_add
% 0.30/0.55 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_def
% 0.30/0.55 thf(fact_1825_delete__correct,axiom,
% 0.30/0.55 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.55 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 0.30/0.55 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % delete_correct
% 0.30/0.55 thf(fact_1826_double__eq__0__iff,axiom,
% 0.30/0.55 ! [A: real] :
% 0.30/0.55 ( ( ( plus_plus_real @ A @ A )
% 0.30/0.55 = zero_zero_real )
% 0.30/0.55 = ( A = zero_zero_real ) ) ).
% 0.30/0.55
% 0.30/0.55 % double_eq_0_iff
% 0.30/0.55 thf(fact_1827_double__eq__0__iff,axiom,
% 0.30/0.55 ! [A: rat] :
% 0.30/0.55 ( ( ( plus_plus_rat @ A @ A )
% 0.30/0.55 = zero_zero_rat )
% 0.30/0.55 = ( A = zero_zero_rat ) ) ).
% 0.30/0.55
% 0.30/0.55 % double_eq_0_iff
% 0.30/0.55 thf(fact_1828_double__eq__0__iff,axiom,
% 0.30/0.55 ! [A: int] :
% 0.30/0.55 ( ( ( plus_plus_int @ A @ A )
% 0.30/0.55 = zero_zero_int )
% 0.30/0.55 = ( A = zero_zero_int ) ) ).
% 0.30/0.55
% 0.30/0.55 % double_eq_0_iff
% 0.30/0.55 thf(fact_1829_add__shift,axiom,
% 0.30/0.55 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.55 ( ( ( plus_plus_nat @ X @ Y )
% 0.30/0.55 = Z3 )
% 0.30/0.55 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.30/0.55 = ( some_nat @ Z3 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_shift
% 0.30/0.55 thf(fact_1830_delete__correct_H,axiom,
% 0.30/0.55 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.55 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 0.30/0.55 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % delete_correct'
% 0.30/0.55 thf(fact_1831_obtain__set__succ,axiom,
% 0.30/0.55 ! [X: nat,Z3: nat,A4: set_nat,B5: set_nat] :
% 0.30/0.55 ( ( ord_less_nat @ X @ Z3 )
% 0.30/0.55 => ( ( vEBT_VEBT_max_in_set @ A4 @ Z3 )
% 0.30/0.55 => ( ( finite_finite_nat @ B5 )
% 0.30/0.55 => ( ( A4 = B5 )
% 0.30/0.55 => ? [X_12: nat] : ( vEBT_is_succ_in_set @ A4 @ X @ X_12 ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % obtain_set_succ
% 0.30/0.55 thf(fact_1832_obtain__set__pred,axiom,
% 0.30/0.55 ! [Z3: nat,X: nat,A4: set_nat] :
% 0.30/0.55 ( ( ord_less_nat @ Z3 @ X )
% 0.30/0.55 => ( ( vEBT_VEBT_min_in_set @ A4 @ Z3 )
% 0.30/0.55 => ( ( finite_finite_nat @ A4 )
% 0.30/0.55 => ? [X_12: nat] : ( vEBT_is_pred_in_set @ A4 @ X @ X_12 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % obtain_set_pred
% 0.30/0.55 thf(fact_1833_length__pos__if__in__set,axiom,
% 0.30/0.55 ! [X: complex,Xs2: list_complex] :
% 0.30/0.55 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_pos_if_in_set
% 0.30/0.55 thf(fact_1834_length__pos__if__in__set,axiom,
% 0.30/0.55 ! [X: real,Xs2: list_real] :
% 0.30/0.55 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_pos_if_in_set
% 0.30/0.55 thf(fact_1835_length__pos__if__in__set,axiom,
% 0.30/0.55 ! [X: set_nat,Xs2: list_set_nat] :
% 0.30/0.55 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_pos_if_in_set
% 0.30/0.55 thf(fact_1836_length__pos__if__in__set,axiom,
% 0.30/0.55 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.55 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_pos_if_in_set
% 0.30/0.55 thf(fact_1837_length__pos__if__in__set,axiom,
% 0.30/0.55 ! [X: $o,Xs2: list_o] :
% 0.30/0.55 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_pos_if_in_set
% 0.30/0.55 thf(fact_1838_length__pos__if__in__set,axiom,
% 0.30/0.55 ! [X: nat,Xs2: list_nat] :
% 0.30/0.55 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_pos_if_in_set
% 0.30/0.55 thf(fact_1839_length__pos__if__in__set,axiom,
% 0.30/0.55 ! [X: int,Xs2: list_int] :
% 0.30/0.55 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.30/0.55 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_pos_if_in_set
% 0.30/0.55 thf(fact_1840_option_Osize__gen_I2_J,axiom,
% 0.30/0.55 ! [X: product_prod_nat_nat > nat,X2: product_prod_nat_nat] :
% 0.30/0.55 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X2 ) )
% 0.30/0.55 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % option.size_gen(2)
% 0.30/0.55 thf(fact_1841_option_Osize__gen_I2_J,axiom,
% 0.30/0.55 ! [X: nat > nat,X2: nat] :
% 0.30/0.55 ( ( size_option_nat @ X @ ( some_nat @ X2 ) )
% 0.30/0.55 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % option.size_gen(2)
% 0.30/0.55 thf(fact_1842_option_Osize__gen_I2_J,axiom,
% 0.30/0.55 ! [X: num > nat,X2: num] :
% 0.30/0.55 ( ( size_option_num @ X @ ( some_num @ X2 ) )
% 0.30/0.55 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % option.size_gen(2)
% 0.30/0.55 thf(fact_1843_add__scale__eq__noteq,axiom,
% 0.30/0.55 ! [R3: complex,A: complex,B: complex,C2: complex,D: complex] :
% 0.30/0.55 ( ( R3 != zero_zero_complex )
% 0.30/0.55 => ( ( ( A = B )
% 0.30/0.55 & ( C2 != D ) )
% 0.30/0.55 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R3 @ C2 ) )
% 0.30/0.55 != ( plus_plus_complex @ B @ ( times_times_complex @ R3 @ D ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_scale_eq_noteq
% 0.30/0.55 thf(fact_1844_add__scale__eq__noteq,axiom,
% 0.30/0.55 ! [R3: real,A: real,B: real,C2: real,D: real] :
% 0.30/0.55 ( ( R3 != zero_zero_real )
% 0.30/0.55 => ( ( ( A = B )
% 0.30/0.55 & ( C2 != D ) )
% 0.30/0.55 => ( ( plus_plus_real @ A @ ( times_times_real @ R3 @ C2 ) )
% 0.30/0.55 != ( plus_plus_real @ B @ ( times_times_real @ R3 @ D ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_scale_eq_noteq
% 0.30/0.55 thf(fact_1845_add__scale__eq__noteq,axiom,
% 0.30/0.55 ! [R3: rat,A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.55 ( ( R3 != zero_zero_rat )
% 0.30/0.55 => ( ( ( A = B )
% 0.30/0.55 & ( C2 != D ) )
% 0.30/0.55 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C2 ) )
% 0.30/0.55 != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_scale_eq_noteq
% 0.30/0.55 thf(fact_1846_add__scale__eq__noteq,axiom,
% 0.30/0.55 ! [R3: nat,A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.55 ( ( R3 != zero_zero_nat )
% 0.30/0.55 => ( ( ( A = B )
% 0.30/0.55 & ( C2 != D ) )
% 0.30/0.55 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C2 ) )
% 0.30/0.55 != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_scale_eq_noteq
% 0.30/0.55 thf(fact_1847_add__scale__eq__noteq,axiom,
% 0.30/0.55 ! [R3: int,A: int,B: int,C2: int,D: int] :
% 0.30/0.55 ( ( R3 != zero_zero_int )
% 0.30/0.55 => ( ( ( A = B )
% 0.30/0.55 & ( C2 != D ) )
% 0.30/0.55 => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C2 ) )
% 0.30/0.55 != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_scale_eq_noteq
% 0.30/0.55 thf(fact_1848_set__vebt__finite,axiom,
% 0.30/0.55 ! [T: vEBT_VEBT,N: nat] :
% 0.30/0.55 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.55 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % set_vebt_finite
% 0.30/0.55 thf(fact_1849_pred__none__empty,axiom,
% 0.30/0.55 ! [Xs2: set_nat,A: nat] :
% 0.30/0.55 ( ~ ? [X_12: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_12 )
% 0.30/0.55 => ( ( finite_finite_nat @ Xs2 )
% 0.30/0.55 => ~ ? [X5: nat] :
% 0.30/0.55 ( ( member_nat @ X5 @ Xs2 )
% 0.30/0.55 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % pred_none_empty
% 0.30/0.55 thf(fact_1850_succ__none__empty,axiom,
% 0.30/0.55 ! [Xs2: set_nat,A: nat] :
% 0.30/0.55 ( ~ ? [X_12: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_12 )
% 0.30/0.55 => ( ( finite_finite_nat @ Xs2 )
% 0.30/0.55 => ~ ? [X5: nat] :
% 0.30/0.55 ( ( member_nat @ X5 @ Xs2 )
% 0.30/0.55 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % succ_none_empty
% 0.30/0.55 thf(fact_1851_diff__self,axiom,
% 0.30/0.55 ! [A: complex] :
% 0.30/0.55 ( ( minus_minus_complex @ A @ A )
% 0.30/0.55 = zero_zero_complex ) ).
% 0.30/0.55
% 0.30/0.55 % diff_self
% 0.30/0.55 thf(fact_1852_diff__self,axiom,
% 0.30/0.55 ! [A: real] :
% 0.30/0.55 ( ( minus_minus_real @ A @ A )
% 0.30/0.55 = zero_zero_real ) ).
% 0.30/0.55
% 0.30/0.55 % diff_self
% 0.30/0.55 thf(fact_1853_diff__self,axiom,
% 0.30/0.55 ! [A: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ A @ A )
% 0.30/0.55 = zero_zero_rat ) ).
% 0.30/0.55
% 0.30/0.55 % diff_self
% 0.30/0.55 thf(fact_1854_diff__self,axiom,
% 0.30/0.55 ! [A: int] :
% 0.30/0.55 ( ( minus_minus_int @ A @ A )
% 0.30/0.55 = zero_zero_int ) ).
% 0.30/0.55
% 0.30/0.55 % diff_self
% 0.30/0.55 thf(fact_1855_diff__0__right,axiom,
% 0.30/0.55 ! [A: complex] :
% 0.30/0.55 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_0_right
% 0.30/0.55 thf(fact_1856_diff__0__right,axiom,
% 0.30/0.55 ! [A: real] :
% 0.30/0.55 ( ( minus_minus_real @ A @ zero_zero_real )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_0_right
% 0.30/0.55 thf(fact_1857_diff__0__right,axiom,
% 0.30/0.55 ! [A: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_0_right
% 0.30/0.55 thf(fact_1858_diff__0__right,axiom,
% 0.30/0.55 ! [A: int] :
% 0.30/0.55 ( ( minus_minus_int @ A @ zero_zero_int )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_0_right
% 0.30/0.55 thf(fact_1859_zero__diff,axiom,
% 0.30/0.55 ! [A: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 0.30/0.55 = zero_zero_nat ) ).
% 0.30/0.55
% 0.30/0.55 % zero_diff
% 0.30/0.55 thf(fact_1860_diff__zero,axiom,
% 0.30/0.55 ! [A: complex] :
% 0.30/0.55 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_zero
% 0.30/0.55 thf(fact_1861_diff__zero,axiom,
% 0.30/0.55 ! [A: real] :
% 0.30/0.55 ( ( minus_minus_real @ A @ zero_zero_real )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_zero
% 0.30/0.55 thf(fact_1862_diff__zero,axiom,
% 0.30/0.55 ! [A: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_zero
% 0.30/0.55 thf(fact_1863_diff__zero,axiom,
% 0.30/0.55 ! [A: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_zero
% 0.30/0.55 thf(fact_1864_diff__zero,axiom,
% 0.30/0.55 ! [A: int] :
% 0.30/0.55 ( ( minus_minus_int @ A @ zero_zero_int )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_zero
% 0.30/0.55 thf(fact_1865_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.30/0.55 ! [A: complex] :
% 0.30/0.55 ( ( minus_minus_complex @ A @ A )
% 0.30/0.55 = zero_zero_complex ) ).
% 0.30/0.55
% 0.30/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.30/0.55 thf(fact_1866_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.30/0.55 ! [A: real] :
% 0.30/0.55 ( ( minus_minus_real @ A @ A )
% 0.30/0.55 = zero_zero_real ) ).
% 0.30/0.55
% 0.30/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.30/0.55 thf(fact_1867_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.30/0.55 ! [A: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ A @ A )
% 0.30/0.55 = zero_zero_rat ) ).
% 0.30/0.55
% 0.30/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.30/0.55 thf(fact_1868_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.30/0.55 ! [A: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ A @ A )
% 0.30/0.55 = zero_zero_nat ) ).
% 0.30/0.55
% 0.30/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.30/0.55 thf(fact_1869_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 0.30/0.55 ! [A: int] :
% 0.30/0.55 ( ( minus_minus_int @ A @ A )
% 0.30/0.55 = zero_zero_int ) ).
% 0.30/0.55
% 0.30/0.55 % cancel_comm_monoid_add_class.diff_cancel
% 0.30/0.55 thf(fact_1870_add__diff__cancel__right_H,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right'
% 0.30/0.55 thf(fact_1871_add__diff__cancel__right_H,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right'
% 0.30/0.55 thf(fact_1872_add__diff__cancel__right_H,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right'
% 0.30/0.55 thf(fact_1873_add__diff__cancel__right_H,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right'
% 0.30/0.55 thf(fact_1874_add__diff__cancel__right,axiom,
% 0.30/0.55 ! [A: real,C2: real,B: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_real @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right
% 0.30/0.55 thf(fact_1875_add__diff__cancel__right,axiom,
% 0.30/0.55 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_rat @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right
% 0.30/0.55 thf(fact_1876_add__diff__cancel__right,axiom,
% 0.30/0.55 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_nat @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right
% 0.30/0.55 thf(fact_1877_add__diff__cancel__right,axiom,
% 0.30/0.55 ! [A: int,C2: int,B: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_int @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_right
% 0.30/0.55 thf(fact_1878_add__diff__cancel__left_H,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 0.30/0.55 = B ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left'
% 0.30/0.55 thf(fact_1879_add__diff__cancel__left_H,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 0.30/0.55 = B ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left'
% 0.30/0.55 thf(fact_1880_add__diff__cancel__left_H,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 0.30/0.55 = B ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left'
% 0.30/0.55 thf(fact_1881_add__diff__cancel__left_H,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 0.30/0.55 = B ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left'
% 0.30/0.55 thf(fact_1882_add__diff__cancel__left,axiom,
% 0.30/0.55 ! [C2: real,A: real,B: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 0.30/0.55 = ( minus_minus_real @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left
% 0.30/0.55 thf(fact_1883_add__diff__cancel__left,axiom,
% 0.30/0.55 ! [C2: rat,A: rat,B: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 0.30/0.55 = ( minus_minus_rat @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left
% 0.30/0.55 thf(fact_1884_add__diff__cancel__left,axiom,
% 0.30/0.55 ! [C2: nat,A: nat,B: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 0.30/0.55 = ( minus_minus_nat @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left
% 0.30/0.55 thf(fact_1885_add__diff__cancel__left,axiom,
% 0.30/0.55 ! [C2: int,A: int,B: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 0.30/0.55 = ( minus_minus_int @ A @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel_left
% 0.30/0.55 thf(fact_1886_diff__add__cancel,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_cancel
% 0.30/0.55 thf(fact_1887_diff__add__cancel,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_cancel
% 0.30/0.55 thf(fact_1888_diff__add__cancel,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_cancel
% 0.30/0.55 thf(fact_1889_add__diff__cancel,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel
% 0.30/0.55 thf(fact_1890_add__diff__cancel,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel
% 0.30/0.55 thf(fact_1891_add__diff__cancel,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.30/0.55 = A ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_cancel
% 0.30/0.55 thf(fact_1892_diff__ge__0__iff__ge,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.30/0.55 = ( ord_less_eq_real @ B @ A ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_ge_0_iff_ge
% 0.30/0.55 thf(fact_1893_diff__ge__0__iff__ge,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.30/0.55 = ( ord_less_eq_rat @ B @ A ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_ge_0_iff_ge
% 0.30/0.55 thf(fact_1894_diff__ge__0__iff__ge,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.30/0.55 = ( ord_less_eq_int @ B @ A ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_ge_0_iff_ge
% 0.30/0.55 thf(fact_1895_diff__gt__0__iff__gt,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 0.30/0.55 = ( ord_less_real @ B @ A ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_gt_0_iff_gt
% 0.30/0.55 thf(fact_1896_diff__gt__0__iff__gt,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 0.30/0.55 = ( ord_less_rat @ B @ A ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_gt_0_iff_gt
% 0.30/0.55 thf(fact_1897_diff__gt__0__iff__gt,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 0.30/0.55 = ( ord_less_int @ B @ A ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_gt_0_iff_gt
% 0.30/0.55 thf(fact_1898_le__add__diff__inverse2,axiom,
% 0.30/0.55 ! [B: real,A: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ B @ A )
% 0.30/0.55 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse2
% 0.30/0.55 thf(fact_1899_le__add__diff__inverse2,axiom,
% 0.30/0.55 ! [B: rat,A: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.55 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse2
% 0.30/0.55 thf(fact_1900_le__add__diff__inverse2,axiom,
% 0.30/0.55 ! [B: nat,A: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.55 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse2
% 0.30/0.55 thf(fact_1901_le__add__diff__inverse2,axiom,
% 0.30/0.55 ! [B: int,A: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.55 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse2
% 0.30/0.55 thf(fact_1902_le__add__diff__inverse,axiom,
% 0.30/0.55 ! [B: real,A: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ B @ A )
% 0.30/0.55 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse
% 0.30/0.55 thf(fact_1903_le__add__diff__inverse,axiom,
% 0.30/0.55 ! [B: rat,A: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.55 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse
% 0.30/0.55 thf(fact_1904_le__add__diff__inverse,axiom,
% 0.30/0.55 ! [B: nat,A: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ B @ A )
% 0.30/0.55 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse
% 0.30/0.55 thf(fact_1905_le__add__diff__inverse,axiom,
% 0.30/0.55 ! [B: int,A: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.55 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff_inverse
% 0.30/0.55 thf(fact_1906_diff__add__zero,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.30/0.55 = zero_zero_nat ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_zero
% 0.30/0.55 thf(fact_1907_diff__numeral__special_I9_J,axiom,
% 0.30/0.55 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.30/0.55 = zero_z3403309356797280102nteger ) ).
% 0.30/0.55
% 0.30/0.55 % diff_numeral_special(9)
% 0.30/0.55 thf(fact_1908_diff__numeral__special_I9_J,axiom,
% 0.30/0.55 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 0.30/0.55 = zero_zero_complex ) ).
% 0.30/0.55
% 0.30/0.55 % diff_numeral_special(9)
% 0.30/0.55 thf(fact_1909_diff__numeral__special_I9_J,axiom,
% 0.30/0.55 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 0.30/0.55 = zero_zero_real ) ).
% 0.30/0.55
% 0.30/0.55 % diff_numeral_special(9)
% 0.30/0.55 thf(fact_1910_diff__numeral__special_I9_J,axiom,
% 0.30/0.55 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 0.30/0.55 = zero_zero_rat ) ).
% 0.30/0.55
% 0.30/0.55 % diff_numeral_special(9)
% 0.30/0.55 thf(fact_1911_diff__numeral__special_I9_J,axiom,
% 0.30/0.55 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 0.30/0.55 = zero_zero_int ) ).
% 0.30/0.55
% 0.30/0.55 % diff_numeral_special(9)
% 0.30/0.55 thf(fact_1912_neq__if__length__neq,axiom,
% 0.30/0.55 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.30/0.55 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.55 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.55 => ( Xs2 != Ys ) ) ).
% 0.30/0.55
% 0.30/0.55 % neq_if_length_neq
% 0.30/0.55 thf(fact_1913_neq__if__length__neq,axiom,
% 0.30/0.55 ! [Xs2: list_o,Ys: list_o] :
% 0.30/0.55 ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.55 != ( size_size_list_o @ Ys ) )
% 0.30/0.55 => ( Xs2 != Ys ) ) ).
% 0.30/0.55
% 0.30/0.55 % neq_if_length_neq
% 0.30/0.55 thf(fact_1914_neq__if__length__neq,axiom,
% 0.30/0.55 ! [Xs2: list_nat,Ys: list_nat] :
% 0.30/0.55 ( ( ( size_size_list_nat @ Xs2 )
% 0.30/0.55 != ( size_size_list_nat @ Ys ) )
% 0.30/0.55 => ( Xs2 != Ys ) ) ).
% 0.30/0.55
% 0.30/0.55 % neq_if_length_neq
% 0.30/0.55 thf(fact_1915_neq__if__length__neq,axiom,
% 0.30/0.55 ! [Xs2: list_int,Ys: list_int] :
% 0.30/0.55 ( ( ( size_size_list_int @ Xs2 )
% 0.30/0.55 != ( size_size_list_int @ Ys ) )
% 0.30/0.55 => ( Xs2 != Ys ) ) ).
% 0.30/0.55
% 0.30/0.55 % neq_if_length_neq
% 0.30/0.55 thf(fact_1916_Ex__list__of__length,axiom,
% 0.30/0.55 ! [N: nat] :
% 0.30/0.55 ? [Xs3: list_VEBT_VEBT] :
% 0.30/0.55 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 0.30/0.55 = N ) ).
% 0.30/0.55
% 0.30/0.55 % Ex_list_of_length
% 0.30/0.55 thf(fact_1917_Ex__list__of__length,axiom,
% 0.30/0.55 ! [N: nat] :
% 0.30/0.55 ? [Xs3: list_o] :
% 0.30/0.55 ( ( size_size_list_o @ Xs3 )
% 0.30/0.55 = N ) ).
% 0.30/0.55
% 0.30/0.55 % Ex_list_of_length
% 0.30/0.55 thf(fact_1918_Ex__list__of__length,axiom,
% 0.30/0.55 ! [N: nat] :
% 0.30/0.55 ? [Xs3: list_nat] :
% 0.30/0.55 ( ( size_size_list_nat @ Xs3 )
% 0.30/0.55 = N ) ).
% 0.30/0.55
% 0.30/0.55 % Ex_list_of_length
% 0.30/0.55 thf(fact_1919_Ex__list__of__length,axiom,
% 0.30/0.55 ! [N: nat] :
% 0.30/0.55 ? [Xs3: list_int] :
% 0.30/0.55 ( ( size_size_list_int @ Xs3 )
% 0.30/0.55 = N ) ).
% 0.30/0.55
% 0.30/0.55 % Ex_list_of_length
% 0.30/0.55 thf(fact_1920_diff__right__commute,axiom,
% 0.30/0.55 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B )
% 0.30/0.55 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_right_commute
% 0.30/0.55 thf(fact_1921_diff__right__commute,axiom,
% 0.30/0.55 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B )
% 0.30/0.55 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_right_commute
% 0.30/0.55 thf(fact_1922_diff__right__commute,axiom,
% 0.30/0.55 ! [A: int,C2: int,B: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B )
% 0.30/0.55 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_right_commute
% 0.30/0.55 thf(fact_1923_diff__eq__diff__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.55 ( ( ( minus_minus_rat @ A @ B )
% 0.30/0.55 = ( minus_minus_rat @ C2 @ D ) )
% 0.30/0.55 => ( ( A = B )
% 0.30/0.55 = ( C2 = D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_diff_eq
% 0.30/0.55 thf(fact_1924_diff__eq__diff__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.55 ( ( ( minus_minus_int @ A @ B )
% 0.30/0.55 = ( minus_minus_int @ C2 @ D ) )
% 0.30/0.55 => ( ( A = B )
% 0.30/0.55 = ( C2 = D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_diff_eq
% 0.30/0.55 thf(fact_1925_diff__mono,axiom,
% 0.30/0.55 ! [A: rat,B: rat,D: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_rat @ D @ C2 )
% 0.30/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_mono
% 0.30/0.55 thf(fact_1926_diff__mono,axiom,
% 0.30/0.55 ! [A: int,B: int,D: int,C2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_int @ D @ C2 )
% 0.30/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_mono
% 0.30/0.55 thf(fact_1927_diff__left__mono,axiom,
% 0.30/0.55 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ B @ A )
% 0.30/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_left_mono
% 0.30/0.55 thf(fact_1928_diff__left__mono,axiom,
% 0.30/0.55 ! [B: int,A: int,C2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ B @ A )
% 0.30/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_left_mono
% 0.30/0.55 thf(fact_1929_diff__right__mono,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_right_mono
% 0.30/0.55 thf(fact_1930_diff__right__mono,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_right_mono
% 0.30/0.55 thf(fact_1931_diff__eq__diff__less__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.55 ( ( ( minus_minus_rat @ A @ B )
% 0.30/0.55 = ( minus_minus_rat @ C2 @ D ) )
% 0.30/0.55 => ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.55 = ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_diff_less_eq
% 0.30/0.55 thf(fact_1932_diff__eq__diff__less__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.55 ( ( ( minus_minus_int @ A @ B )
% 0.30/0.55 = ( minus_minus_int @ C2 @ D ) )
% 0.30/0.55 => ( ( ord_less_eq_int @ A @ B )
% 0.30/0.55 = ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_diff_less_eq
% 0.30/0.55 thf(fact_1933_eq__iff__diff__eq__0,axiom,
% 0.30/0.55 ( ( ^ [Y5: complex,Z2: complex] : ( Y5 = Z2 ) )
% 0.30/0.55 = ( ^ [A5: complex,B4: complex] :
% 0.30/0.55 ( ( minus_minus_complex @ A5 @ B4 )
% 0.30/0.55 = zero_zero_complex ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_iff_diff_eq_0
% 0.30/0.55 thf(fact_1934_eq__iff__diff__eq__0,axiom,
% 0.30/0.55 ( ( ^ [Y5: real,Z2: real] : ( Y5 = Z2 ) )
% 0.30/0.55 = ( ^ [A5: real,B4: real] :
% 0.30/0.55 ( ( minus_minus_real @ A5 @ B4 )
% 0.30/0.55 = zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_iff_diff_eq_0
% 0.30/0.55 thf(fact_1935_eq__iff__diff__eq__0,axiom,
% 0.30/0.55 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 0.30/0.55 = ( ^ [A5: rat,B4: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ A5 @ B4 )
% 0.30/0.55 = zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_iff_diff_eq_0
% 0.30/0.55 thf(fact_1936_eq__iff__diff__eq__0,axiom,
% 0.30/0.55 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.30/0.55 = ( ^ [A5: int,B4: int] :
% 0.30/0.55 ( ( minus_minus_int @ A5 @ B4 )
% 0.30/0.55 = zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_iff_diff_eq_0
% 0.30/0.55 thf(fact_1937_diff__strict__right__mono,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ord_less_real @ A @ B )
% 0.30/0.55 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_right_mono
% 0.30/0.55 thf(fact_1938_diff__strict__right__mono,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ A @ B )
% 0.30/0.55 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_right_mono
% 0.30/0.55 thf(fact_1939_diff__strict__right__mono,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_int @ A @ B )
% 0.30/0.55 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_right_mono
% 0.30/0.55 thf(fact_1940_diff__strict__left__mono,axiom,
% 0.30/0.55 ! [B: real,A: real,C2: real] :
% 0.30/0.55 ( ( ord_less_real @ B @ A )
% 0.30/0.55 => ( ord_less_real @ ( minus_minus_real @ C2 @ A ) @ ( minus_minus_real @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_left_mono
% 0.30/0.55 thf(fact_1941_diff__strict__left__mono,axiom,
% 0.30/0.55 ! [B: rat,A: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ B @ A )
% 0.30/0.55 => ( ord_less_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_left_mono
% 0.30/0.55 thf(fact_1942_diff__strict__left__mono,axiom,
% 0.30/0.55 ! [B: int,A: int,C2: int] :
% 0.30/0.55 ( ( ord_less_int @ B @ A )
% 0.30/0.55 => ( ord_less_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_left_mono
% 0.30/0.55 thf(fact_1943_diff__eq__diff__less,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.55 ( ( ( minus_minus_real @ A @ B )
% 0.30/0.55 = ( minus_minus_real @ C2 @ D ) )
% 0.30/0.55 => ( ( ord_less_real @ A @ B )
% 0.30/0.55 = ( ord_less_real @ C2 @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_diff_less
% 0.30/0.55 thf(fact_1944_diff__eq__diff__less,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.55 ( ( ( minus_minus_rat @ A @ B )
% 0.30/0.55 = ( minus_minus_rat @ C2 @ D ) )
% 0.30/0.55 => ( ( ord_less_rat @ A @ B )
% 0.30/0.55 = ( ord_less_rat @ C2 @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_diff_less
% 0.30/0.55 thf(fact_1945_diff__eq__diff__less,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.55 ( ( ( minus_minus_int @ A @ B )
% 0.30/0.55 = ( minus_minus_int @ C2 @ D ) )
% 0.30/0.55 => ( ( ord_less_int @ A @ B )
% 0.30/0.55 = ( ord_less_int @ C2 @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_diff_less
% 0.30/0.55 thf(fact_1946_diff__strict__mono,axiom,
% 0.30/0.55 ! [A: real,B: real,D: real,C2: real] :
% 0.30/0.55 ( ( ord_less_real @ A @ B )
% 0.30/0.55 => ( ( ord_less_real @ D @ C2 )
% 0.30/0.55 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_mono
% 0.30/0.55 thf(fact_1947_diff__strict__mono,axiom,
% 0.30/0.55 ! [A: rat,B: rat,D: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ A @ B )
% 0.30/0.55 => ( ( ord_less_rat @ D @ C2 )
% 0.30/0.55 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_mono
% 0.30/0.55 thf(fact_1948_diff__strict__mono,axiom,
% 0.30/0.55 ! [A: int,B: int,D: int,C2: int] :
% 0.30/0.55 ( ( ord_less_int @ A @ B )
% 0.30/0.55 => ( ( ord_less_int @ D @ C2 )
% 0.30/0.55 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_strict_mono
% 0.30/0.55 thf(fact_1949_left__diff__distrib,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_diff_distrib
% 0.30/0.55 thf(fact_1950_left__diff__distrib,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_diff_distrib
% 0.30/0.55 thf(fact_1951_left__diff__distrib,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_diff_distrib
% 0.30/0.55 thf(fact_1952_right__diff__distrib,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % right_diff_distrib
% 0.30/0.55 thf(fact_1953_right__diff__distrib,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % right_diff_distrib
% 0.30/0.55 thf(fact_1954_right__diff__distrib,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % right_diff_distrib
% 0.30/0.55 thf(fact_1955_left__diff__distrib_H,axiom,
% 0.30/0.55 ! [B: real,C2: real,A: real] :
% 0.30/0.55 ( ( times_times_real @ ( minus_minus_real @ B @ C2 ) @ A )
% 0.30/0.55 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C2 @ A ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_diff_distrib'
% 0.30/0.55 thf(fact_1956_left__diff__distrib_H,axiom,
% 0.30/0.55 ! [B: rat,C2: rat,A: rat] :
% 0.30/0.55 ( ( times_times_rat @ ( minus_minus_rat @ B @ C2 ) @ A )
% 0.30/0.55 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C2 @ A ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_diff_distrib'
% 0.30/0.55 thf(fact_1957_left__diff__distrib_H,axiom,
% 0.30/0.55 ! [B: nat,C2: nat,A: nat] :
% 0.30/0.55 ( ( times_times_nat @ ( minus_minus_nat @ B @ C2 ) @ A )
% 0.30/0.55 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C2 @ A ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_diff_distrib'
% 0.30/0.55 thf(fact_1958_left__diff__distrib_H,axiom,
% 0.30/0.55 ! [B: int,C2: int,A: int] :
% 0.30/0.55 ( ( times_times_int @ ( minus_minus_int @ B @ C2 ) @ A )
% 0.30/0.55 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C2 @ A ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % left_diff_distrib'
% 0.30/0.55 thf(fact_1959_right__diff__distrib_H,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % right_diff_distrib'
% 0.30/0.55 thf(fact_1960_right__diff__distrib_H,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % right_diff_distrib'
% 0.30/0.55 thf(fact_1961_right__diff__distrib_H,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % right_diff_distrib'
% 0.30/0.55 thf(fact_1962_right__diff__distrib_H,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % right_diff_distrib'
% 0.30/0.55 thf(fact_1963_diff__diff__eq,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_diff_eq
% 0.30/0.55 thf(fact_1964_diff__diff__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_diff_eq
% 0.30/0.55 thf(fact_1965_diff__diff__eq,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_diff_eq
% 0.30/0.55 thf(fact_1966_diff__diff__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_diff_eq
% 0.30/0.55 thf(fact_1967_add__implies__diff,axiom,
% 0.30/0.55 ! [C2: real,B: real,A: real] :
% 0.30/0.55 ( ( ( plus_plus_real @ C2 @ B )
% 0.30/0.55 = A )
% 0.30/0.55 => ( C2
% 0.30/0.55 = ( minus_minus_real @ A @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_implies_diff
% 0.30/0.55 thf(fact_1968_add__implies__diff,axiom,
% 0.30/0.55 ! [C2: rat,B: rat,A: rat] :
% 0.30/0.55 ( ( ( plus_plus_rat @ C2 @ B )
% 0.30/0.55 = A )
% 0.30/0.55 => ( C2
% 0.30/0.55 = ( minus_minus_rat @ A @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_implies_diff
% 0.30/0.55 thf(fact_1969_add__implies__diff,axiom,
% 0.30/0.55 ! [C2: nat,B: nat,A: nat] :
% 0.30/0.55 ( ( ( plus_plus_nat @ C2 @ B )
% 0.30/0.55 = A )
% 0.30/0.55 => ( C2
% 0.30/0.55 = ( minus_minus_nat @ A @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_implies_diff
% 0.30/0.55 thf(fact_1970_add__implies__diff,axiom,
% 0.30/0.55 ! [C2: int,B: int,A: int] :
% 0.30/0.55 ( ( ( plus_plus_int @ C2 @ B )
% 0.30/0.55 = A )
% 0.30/0.55 => ( C2
% 0.30/0.55 = ( minus_minus_int @ A @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_implies_diff
% 0.30/0.55 thf(fact_1971_diff__add__eq__diff__diff__swap,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_real @ ( minus_minus_real @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_eq_diff_diff_swap
% 0.30/0.55 thf(fact_1972_diff__add__eq__diff__diff__swap,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_eq_diff_diff_swap
% 0.30/0.55 thf(fact_1973_diff__add__eq__diff__diff__swap,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_eq_diff_diff_swap
% 0.30/0.55 thf(fact_1974_diff__add__eq,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_eq
% 0.30/0.55 thf(fact_1975_diff__add__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_eq
% 0.30/0.55 thf(fact_1976_diff__add__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.30/0.55 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add_eq
% 0.30/0.55 thf(fact_1977_diff__diff__eq2,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_diff_eq2
% 0.30/0.55 thf(fact_1978_diff__diff__eq2,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_diff_eq2
% 0.30/0.55 thf(fact_1979_diff__diff__eq2,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_diff_eq2
% 0.30/0.55 thf(fact_1980_add__diff__eq,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_eq
% 0.30/0.55 thf(fact_1981_add__diff__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_eq
% 0.30/0.55 thf(fact_1982_add__diff__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 0.30/0.55 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_diff_eq
% 0.30/0.55 thf(fact_1983_eq__diff__eq,axiom,
% 0.30/0.55 ! [A: real,C2: real,B: real] :
% 0.30/0.55 ( ( A
% 0.30/0.55 = ( minus_minus_real @ C2 @ B ) )
% 0.30/0.55 = ( ( plus_plus_real @ A @ B )
% 0.30/0.55 = C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_diff_eq
% 0.30/0.55 thf(fact_1984_eq__diff__eq,axiom,
% 0.30/0.55 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.55 ( ( A
% 0.30/0.55 = ( minus_minus_rat @ C2 @ B ) )
% 0.30/0.55 = ( ( plus_plus_rat @ A @ B )
% 0.30/0.55 = C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_diff_eq
% 0.30/0.55 thf(fact_1985_eq__diff__eq,axiom,
% 0.30/0.55 ! [A: int,C2: int,B: int] :
% 0.30/0.55 ( ( A
% 0.30/0.55 = ( minus_minus_int @ C2 @ B ) )
% 0.30/0.55 = ( ( plus_plus_int @ A @ B )
% 0.30/0.55 = C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_diff_eq
% 0.30/0.55 thf(fact_1986_diff__eq__eq,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ( minus_minus_real @ A @ B )
% 0.30/0.55 = C2 )
% 0.30/0.55 = ( A
% 0.30/0.55 = ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_eq
% 0.30/0.55 thf(fact_1987_diff__eq__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ( minus_minus_rat @ A @ B )
% 0.30/0.55 = C2 )
% 0.30/0.55 = ( A
% 0.30/0.55 = ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_eq
% 0.30/0.55 thf(fact_1988_diff__eq__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ( minus_minus_int @ A @ B )
% 0.30/0.55 = C2 )
% 0.30/0.55 = ( A
% 0.30/0.55 = ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_eq_eq
% 0.30/0.55 thf(fact_1989_group__cancel_Osub1,axiom,
% 0.30/0.55 ! [A4: real,K2: real,A: real,B: real] :
% 0.30/0.55 ( ( A4
% 0.30/0.55 = ( plus_plus_real @ K2 @ A ) )
% 0.30/0.55 => ( ( minus_minus_real @ A4 @ B )
% 0.30/0.55 = ( plus_plus_real @ K2 @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % group_cancel.sub1
% 0.30/0.55 thf(fact_1990_group__cancel_Osub1,axiom,
% 0.30/0.55 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 0.30/0.55 ( ( A4
% 0.30/0.55 = ( plus_plus_rat @ K2 @ A ) )
% 0.30/0.55 => ( ( minus_minus_rat @ A4 @ B )
% 0.30/0.55 = ( plus_plus_rat @ K2 @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % group_cancel.sub1
% 0.30/0.55 thf(fact_1991_group__cancel_Osub1,axiom,
% 0.30/0.55 ! [A4: int,K2: int,A: int,B: int] :
% 0.30/0.55 ( ( A4
% 0.30/0.55 = ( plus_plus_int @ K2 @ A ) )
% 0.30/0.55 => ( ( minus_minus_int @ A4 @ B )
% 0.30/0.55 = ( plus_plus_int @ K2 @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % group_cancel.sub1
% 0.30/0.55 thf(fact_1992_finite__nat__set__iff__bounded,axiom,
% 0.30/0.55 ( finite_finite_nat
% 0.30/0.55 = ( ^ [N5: set_nat] :
% 0.30/0.55 ? [M6: nat] :
% 0.30/0.55 ! [X4: nat] :
% 0.30/0.55 ( ( member_nat @ X4 @ N5 )
% 0.30/0.55 => ( ord_less_nat @ X4 @ M6 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_nat_set_iff_bounded
% 0.30/0.55 thf(fact_1993_bounded__nat__set__is__finite,axiom,
% 0.30/0.55 ! [N6: set_nat,N: nat] :
% 0.30/0.55 ( ! [X3: nat] :
% 0.30/0.55 ( ( member_nat @ X3 @ N6 )
% 0.30/0.55 => ( ord_less_nat @ X3 @ N ) )
% 0.30/0.55 => ( finite_finite_nat @ N6 ) ) ).
% 0.30/0.55
% 0.30/0.55 % bounded_nat_set_is_finite
% 0.30/0.55 thf(fact_1994_finite__nat__set__iff__bounded__le,axiom,
% 0.30/0.55 ( finite_finite_nat
% 0.30/0.55 = ( ^ [N5: set_nat] :
% 0.30/0.55 ? [M6: nat] :
% 0.30/0.55 ! [X4: nat] :
% 0.30/0.55 ( ( member_nat @ X4 @ N5 )
% 0.30/0.55 => ( ord_less_eq_nat @ X4 @ M6 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_nat_set_iff_bounded_le
% 0.30/0.55 thf(fact_1995_le__iff__diff__le__0,axiom,
% 0.30/0.55 ( ord_less_eq_real
% 0.30/0.55 = ( ^ [A5: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A5 @ B4 ) @ zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_iff_diff_le_0
% 0.30/0.55 thf(fact_1996_le__iff__diff__le__0,axiom,
% 0.30/0.55 ( ord_less_eq_rat
% 0.30/0.55 = ( ^ [A5: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_iff_diff_le_0
% 0.30/0.55 thf(fact_1997_le__iff__diff__le__0,axiom,
% 0.30/0.55 ( ord_less_eq_int
% 0.30/0.55 = ( ^ [A5: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_iff_diff_le_0
% 0.30/0.55 thf(fact_1998_less__iff__diff__less__0,axiom,
% 0.30/0.55 ( ord_less_real
% 0.30/0.55 = ( ^ [A5: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A5 @ B4 ) @ zero_zero_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_iff_diff_less_0
% 0.30/0.55 thf(fact_1999_less__iff__diff__less__0,axiom,
% 0.30/0.55 ( ord_less_rat
% 0.30/0.55 = ( ^ [A5: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_iff_diff_less_0
% 0.30/0.55 thf(fact_2000_less__iff__diff__less__0,axiom,
% 0.30/0.55 ( ord_less_int
% 0.30/0.55 = ( ^ [A5: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_iff_diff_less_0
% 0.30/0.55 thf(fact_2001_add__le__add__imp__diff__le,axiom,
% 0.30/0.55 ! [I2: real,K2: real,N: real,J2: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K2 ) )
% 0.30/0.55 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K2 ) )
% 0.30/0.55 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_add_imp_diff_le
% 0.30/0.55 thf(fact_2002_add__le__add__imp__diff__le,axiom,
% 0.30/0.55 ! [I2: rat,K2: rat,N: rat,J2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K2 ) )
% 0.30/0.55 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K2 ) )
% 0.30/0.55 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_add_imp_diff_le
% 0.30/0.55 thf(fact_2003_add__le__add__imp__diff__le,axiom,
% 0.30/0.55 ! [I2: nat,K2: nat,N: nat,J2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K2 ) )
% 0.30/0.55 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K2 ) )
% 0.30/0.55 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_add_imp_diff_le
% 0.30/0.55 thf(fact_2004_add__le__add__imp__diff__le,axiom,
% 0.30/0.55 ! [I2: int,K2: int,N: int,J2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K2 ) )
% 0.30/0.55 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K2 ) )
% 0.30/0.55 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_add_imp_diff_le
% 0.30/0.55 thf(fact_2005_add__le__imp__le__diff,axiom,
% 0.30/0.55 ! [I2: real,K2: real,N: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_imp_le_diff
% 0.30/0.55 thf(fact_2006_add__le__imp__le__diff,axiom,
% 0.30/0.55 ! [I2: rat,K2: rat,N: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_imp_le_diff
% 0.30/0.55 thf(fact_2007_add__le__imp__le__diff,axiom,
% 0.30/0.55 ! [I2: nat,K2: nat,N: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_imp_le_diff
% 0.30/0.55 thf(fact_2008_add__le__imp__le__diff,axiom,
% 0.30/0.55 ! [I2: int,K2: int,N: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 0.30/0.55 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_le_imp_le_diff
% 0.30/0.55 thf(fact_2009_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( ( minus_minus_nat @ B @ A )
% 0.30/0.55 = C2 )
% 0.30/0.55 = ( B
% 0.30/0.55 = ( plus_plus_nat @ C2 @ A ) ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 0.30/0.55 thf(fact_2010_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.55 = B ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 0.30/0.55 thf(fact_2011_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( minus_minus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.55 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 0.30/0.55 thf(fact_2012_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A )
% 0.30/0.55 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 0.30/0.55 thf(fact_2013_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 )
% 0.30/0.55 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 0.30/0.55 thf(fact_2014_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A )
% 0.30/0.55 = ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 0.30/0.55 thf(fact_2015_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.55 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 0.30/0.55 thf(fact_2016_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 0.30/0.55 = ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 0.30/0.55 thf(fact_2017_le__add__diff,axiom,
% 0.30/0.55 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_add_diff
% 0.30/0.55 thf(fact_2018_diff__add,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.55 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 0.30/0.55 = B ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_add
% 0.30/0.55 thf(fact_2019_le__diff__eq,axiom,
% 0.30/0.55 ! [A: real,C2: real,B: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 0.30/0.55 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_diff_eq
% 0.30/0.55 thf(fact_2020_le__diff__eq,axiom,
% 0.30/0.55 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 0.30/0.55 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_diff_eq
% 0.30/0.55 thf(fact_2021_le__diff__eq,axiom,
% 0.30/0.55 ! [A: int,C2: int,B: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 0.30/0.55 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % le_diff_eq
% 0.30/0.55 thf(fact_2022_diff__le__eq,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.30/0.55 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_le_eq
% 0.30/0.55 thf(fact_2023_diff__le__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.30/0.55 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_le_eq
% 0.30/0.55 thf(fact_2024_diff__le__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.30/0.55 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_le_eq
% 0.30/0.55 thf(fact_2025_less__diff__eq,axiom,
% 0.30/0.55 ! [A: real,C2: real,B: real] :
% 0.30/0.55 ( ( ord_less_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 0.30/0.55 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_diff_eq
% 0.30/0.55 thf(fact_2026_less__diff__eq,axiom,
% 0.30/0.55 ! [A: rat,C2: rat,B: rat] :
% 0.30/0.55 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 0.30/0.55 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_diff_eq
% 0.30/0.55 thf(fact_2027_less__diff__eq,axiom,
% 0.30/0.55 ! [A: int,C2: int,B: int] :
% 0.30/0.55 ( ( ord_less_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 0.30/0.55 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_diff_eq
% 0.30/0.55 thf(fact_2028_diff__less__eq,axiom,
% 0.30/0.55 ! [A: real,B: real,C2: real] :
% 0.30/0.55 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 0.30/0.55 = ( ord_less_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_less_eq
% 0.30/0.55 thf(fact_2029_diff__less__eq,axiom,
% 0.30/0.55 ! [A: rat,B: rat,C2: rat] :
% 0.30/0.55 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 0.30/0.55 = ( ord_less_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_less_eq
% 0.30/0.55 thf(fact_2030_diff__less__eq,axiom,
% 0.30/0.55 ! [A: int,B: int,C2: int] :
% 0.30/0.55 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.30/0.55 = ( ord_less_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % diff_less_eq
% 0.30/0.55 thf(fact_2031_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.30/0.55 ! [A: real,B: real] :
% 0.30/0.55 ( ~ ( ord_less_real @ A @ B )
% 0.30/0.55 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % linordered_semidom_class.add_diff_inverse
% 0.30/0.55 thf(fact_2032_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.30/0.55 ! [A: rat,B: rat] :
% 0.30/0.55 ( ~ ( ord_less_rat @ A @ B )
% 0.30/0.55 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % linordered_semidom_class.add_diff_inverse
% 0.30/0.55 thf(fact_2033_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.30/0.55 ! [A: nat,B: nat] :
% 0.30/0.55 ( ~ ( ord_less_nat @ A @ B )
% 0.30/0.55 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % linordered_semidom_class.add_diff_inverse
% 0.30/0.55 thf(fact_2034_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 0.30/0.55 ! [A: int,B: int] :
% 0.30/0.55 ( ~ ( ord_less_int @ A @ B )
% 0.30/0.55 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 0.30/0.55 = A ) ) ).
% 0.30/0.55
% 0.30/0.55 % linordered_semidom_class.add_diff_inverse
% 0.30/0.55 thf(fact_2035_square__diff__square__factored,axiom,
% 0.30/0.55 ! [X: real,Y: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 0.30/0.55 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_square_factored
% 0.30/0.55 thf(fact_2036_square__diff__square__factored,axiom,
% 0.30/0.55 ! [X: rat,Y: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 0.30/0.55 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_square_factored
% 0.30/0.55 thf(fact_2037_square__diff__square__factored,axiom,
% 0.30/0.55 ! [X: int,Y: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 0.30/0.55 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_square_factored
% 0.30/0.55 thf(fact_2038_eq__add__iff2,axiom,
% 0.30/0.55 ! [A: real,E: real,C2: real,B: real,D: real] :
% 0.30/0.55 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 )
% 0.30/0.55 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.30/0.55 = ( C2
% 0.30/0.55 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_add_iff2
% 0.30/0.55 thf(fact_2039_eq__add__iff2,axiom,
% 0.30/0.55 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 0.30/0.55 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 0.30/0.55 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.30/0.55 = ( C2
% 0.30/0.55 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_add_iff2
% 0.30/0.55 thf(fact_2040_eq__add__iff2,axiom,
% 0.30/0.55 ! [A: int,E: int,C2: int,B: int,D: int] :
% 0.30/0.55 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 0.30/0.55 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.30/0.55 = ( C2
% 0.30/0.55 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_add_iff2
% 0.30/0.55 thf(fact_2041_eq__add__iff1,axiom,
% 0.30/0.55 ! [A: real,E: real,C2: real,B: real,D: real] :
% 0.30/0.55 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 )
% 0.30/0.55 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.30/0.55 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 )
% 0.30/0.55 = D ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_add_iff1
% 0.30/0.55 thf(fact_2042_eq__add__iff1,axiom,
% 0.30/0.55 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 0.30/0.55 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 0.30/0.55 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.30/0.55 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 )
% 0.30/0.55 = D ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_add_iff1
% 0.30/0.55 thf(fact_2043_eq__add__iff1,axiom,
% 0.30/0.55 ! [A: int,E: int,C2: int,B: int,D: int] :
% 0.30/0.55 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 0.30/0.55 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.30/0.55 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 )
% 0.30/0.55 = D ) ) ).
% 0.30/0.55
% 0.30/0.55 % eq_add_iff1
% 0.30/0.55 thf(fact_2044_ordered__ring__class_Ole__add__iff2,axiom,
% 0.30/0.55 ! [A: real,E: real,C2: real,B: real,D: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_eq_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_ring_class.le_add_iff2
% 0.30/0.55 thf(fact_2045_ordered__ring__class_Ole__add__iff2,axiom,
% 0.30/0.55 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_eq_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_ring_class.le_add_iff2
% 0.30/0.55 thf(fact_2046_ordered__ring__class_Ole__add__iff2,axiom,
% 0.30/0.55 ! [A: int,E: int,C2: int,B: int,D: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_eq_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_ring_class.le_add_iff2
% 0.30/0.55 thf(fact_2047_ordered__ring__class_Ole__add__iff1,axiom,
% 0.30/0.55 ! [A: real,E: real,C2: real,B: real,D: real] :
% 0.30/0.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_ring_class.le_add_iff1
% 0.30/0.55 thf(fact_2048_ordered__ring__class_Ole__add__iff1,axiom,
% 0.30/0.55 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 0.30/0.55 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_ring_class.le_add_iff1
% 0.30/0.55 thf(fact_2049_ordered__ring__class_Ole__add__iff1,axiom,
% 0.30/0.55 ! [A: int,E: int,C2: int,B: int,D: int] :
% 0.30/0.55 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 0.30/0.55
% 0.30/0.55 % ordered_ring_class.le_add_iff1
% 0.30/0.55 thf(fact_2050_less__add__iff1,axiom,
% 0.30/0.55 ! [A: real,E: real,C2: real,B: real,D: real] :
% 0.30/0.55 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_iff1
% 0.30/0.55 thf(fact_2051_less__add__iff1,axiom,
% 0.30/0.55 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 0.30/0.55 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_iff1
% 0.30/0.55 thf(fact_2052_less__add__iff1,axiom,
% 0.30/0.55 ! [A: int,E: int,C2: int,B: int,D: int] :
% 0.30/0.55 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_iff1
% 0.30/0.55 thf(fact_2053_less__add__iff2,axiom,
% 0.30/0.55 ! [A: real,E: real,C2: real,B: real,D: real] :
% 0.30/0.55 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_iff2
% 0.30/0.55 thf(fact_2054_less__add__iff2,axiom,
% 0.30/0.55 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 0.30/0.55 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_iff2
% 0.30/0.55 thf(fact_2055_less__add__iff2,axiom,
% 0.30/0.55 ! [A: int,E: int,C2: int,B: int,D: int] :
% 0.30/0.55 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 0.30/0.55 = ( ord_less_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % less_add_iff2
% 0.30/0.55 thf(fact_2056_square__diff__one__factored,axiom,
% 0.30/0.55 ! [X: code_integer] :
% 0.30/0.55 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 0.30/0.55 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_one_factored
% 0.30/0.55 thf(fact_2057_square__diff__one__factored,axiom,
% 0.30/0.55 ! [X: complex] :
% 0.30/0.55 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 0.30/0.55 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_one_factored
% 0.30/0.55 thf(fact_2058_square__diff__one__factored,axiom,
% 0.30/0.55 ! [X: real] :
% 0.30/0.55 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 0.30/0.55 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_one_factored
% 0.30/0.55 thf(fact_2059_square__diff__one__factored,axiom,
% 0.30/0.55 ! [X: rat] :
% 0.30/0.55 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 0.30/0.55 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_one_factored
% 0.30/0.55 thf(fact_2060_square__diff__one__factored,axiom,
% 0.30/0.55 ! [X: int] :
% 0.30/0.55 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 0.30/0.55 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % square_diff_one_factored
% 0.30/0.55 thf(fact_2061_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_complex,P2: set_complex > $o,F2: complex > rat] :
% 0.30/0.55 ( ( finite3207457112153483333omplex @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_complex )
% 0.30/0.55 => ( ! [X3: complex,S4: set_complex] :
% 0.30/0.55 ( ( finite3207457112153483333omplex @ S4 )
% 0.30/0.55 => ( ! [Y6: complex] :
% 0.30/0.55 ( ( member_complex @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2062_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_nat,P2: set_nat > $o,F2: nat > rat] :
% 0.30/0.55 ( ( finite_finite_nat @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_nat )
% 0.30/0.55 => ( ! [X3: nat,S4: set_nat] :
% 0.30/0.55 ( ( finite_finite_nat @ S4 )
% 0.30/0.55 => ( ! [Y6: nat] :
% 0.30/0.55 ( ( member_nat @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2063_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_int,P2: set_int > $o,F2: int > rat] :
% 0.30/0.55 ( ( finite_finite_int @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_int )
% 0.30/0.55 => ( ! [X3: int,S4: set_int] :
% 0.30/0.55 ( ( finite_finite_int @ S4 )
% 0.30/0.55 => ( ! [Y6: int] :
% 0.30/0.55 ( ( member_int @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2064_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_real,P2: set_real > $o,F2: real > rat] :
% 0.30/0.55 ( ( finite_finite_real @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_real )
% 0.30/0.55 => ( ! [X3: real,S4: set_real] :
% 0.30/0.55 ( ( finite_finite_real @ S4 )
% 0.30/0.55 => ( ! [Y6: real] :
% 0.30/0.55 ( ( member_real @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2065_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_complex,P2: set_complex > $o,F2: complex > num] :
% 0.30/0.55 ( ( finite3207457112153483333omplex @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_complex )
% 0.30/0.55 => ( ! [X3: complex,S4: set_complex] :
% 0.30/0.55 ( ( finite3207457112153483333omplex @ S4 )
% 0.30/0.55 => ( ! [Y6: complex] :
% 0.30/0.55 ( ( member_complex @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2066_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_nat,P2: set_nat > $o,F2: nat > num] :
% 0.30/0.55 ( ( finite_finite_nat @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_nat )
% 0.30/0.55 => ( ! [X3: nat,S4: set_nat] :
% 0.30/0.55 ( ( finite_finite_nat @ S4 )
% 0.30/0.55 => ( ! [Y6: nat] :
% 0.30/0.55 ( ( member_nat @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2067_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_int,P2: set_int > $o,F2: int > num] :
% 0.30/0.55 ( ( finite_finite_int @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_int )
% 0.30/0.55 => ( ! [X3: int,S4: set_int] :
% 0.30/0.55 ( ( finite_finite_int @ S4 )
% 0.30/0.55 => ( ! [Y6: int] :
% 0.30/0.55 ( ( member_int @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2068_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_real,P2: set_real > $o,F2: real > num] :
% 0.30/0.55 ( ( finite_finite_real @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_real )
% 0.30/0.55 => ( ! [X3: real,S4: set_real] :
% 0.30/0.55 ( ( finite_finite_real @ S4 )
% 0.30/0.55 => ( ! [Y6: real] :
% 0.30/0.55 ( ( member_real @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2069_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_complex,P2: set_complex > $o,F2: complex > nat] :
% 0.30/0.55 ( ( finite3207457112153483333omplex @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_complex )
% 0.30/0.55 => ( ! [X3: complex,S4: set_complex] :
% 0.30/0.55 ( ( finite3207457112153483333omplex @ S4 )
% 0.30/0.55 => ( ! [Y6: complex] :
% 0.30/0.55 ( ( member_complex @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_nat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2070_finite__ranking__induct,axiom,
% 0.30/0.55 ! [S3: set_nat,P2: set_nat > $o,F2: nat > nat] :
% 0.30/0.55 ( ( finite_finite_nat @ S3 )
% 0.30/0.55 => ( ( P2 @ bot_bot_set_nat )
% 0.30/0.55 => ( ! [X3: nat,S4: set_nat] :
% 0.30/0.55 ( ( finite_finite_nat @ S4 )
% 0.30/0.55 => ( ! [Y6: nat] :
% 0.30/0.55 ( ( member_nat @ Y6 @ S4 )
% 0.30/0.55 => ( ord_less_eq_nat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 0.30/0.55 => ( ( P2 @ S4 )
% 0.30/0.55 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 0.30/0.55 => ( P2 @ S3 ) ) ) ) ).
% 0.30/0.55
% 0.30/0.55 % finite_ranking_induct
% 0.30/0.55 thf(fact_2071_length__induct,axiom,
% 0.30/0.55 ! [P2: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 0.30/0.55 ( ! [Xs3: list_VEBT_VEBT] :
% 0.30/0.55 ( ! [Ys2: list_VEBT_VEBT] :
% 0.30/0.55 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Ys2 ) )
% 0.30/0.55 => ( P2 @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Xs2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_induct
% 0.30/0.55 thf(fact_2072_length__induct,axiom,
% 0.30/0.55 ! [P2: list_o > $o,Xs2: list_o] :
% 0.30/0.55 ( ! [Xs3: list_o] :
% 0.30/0.55 ( ! [Ys2: list_o] :
% 0.30/0.55 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Ys2 ) )
% 0.30/0.55 => ( P2 @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Xs2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_induct
% 0.30/0.55 thf(fact_2073_length__induct,axiom,
% 0.30/0.55 ! [P2: list_nat > $o,Xs2: list_nat] :
% 0.30/0.55 ( ! [Xs3: list_nat] :
% 0.30/0.55 ( ! [Ys2: list_nat] :
% 0.30/0.55 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Ys2 ) )
% 0.30/0.55 => ( P2 @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Xs2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_induct
% 0.30/0.55 thf(fact_2074_length__induct,axiom,
% 0.30/0.55 ! [P2: list_int > $o,Xs2: list_int] :
% 0.30/0.55 ( ! [Xs3: list_int] :
% 0.30/0.55 ( ! [Ys2: list_int] :
% 0.30/0.55 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Ys2 ) )
% 0.30/0.55 => ( P2 @ Xs3 ) )
% 0.30/0.55 => ( P2 @ Xs2 ) ) ).
% 0.30/0.55
% 0.30/0.55 % length_induct
% 0.30/0.55 thf(fact_2075_add__0__iff,axiom,
% 0.30/0.55 ! [B: complex,A: complex] :
% 0.30/0.55 ( ( B
% 0.30/0.55 = ( plus_plus_complex @ B @ A ) )
% 0.30/0.55 = ( A = zero_zero_complex ) ) ).
% 0.30/0.55
% 0.30/0.55 % add_0_iff
% 0.30/0.55 thf(fact_2076_add__0__iff,axiom,
% 0.30/0.55 ! [B: real,A: real] :
% 0.30/0.55 ( ( B
% 0.30/0.55 = ( plus_plus_real @ B @ A ) )
% 0.30/0.55 = ( A = zero_zero_real ) ) ).
% 0.30/0.56
% 0.30/0.56 % add_0_iff
% 0.30/0.56 thf(fact_2077_add__0__iff,axiom,
% 0.30/0.56 ! [B: rat,A: rat] :
% 0.30/0.56 ( ( B
% 0.30/0.56 = ( plus_plus_rat @ B @ A ) )
% 0.30/0.56 = ( A = zero_zero_rat ) ) ).
% 0.30/0.56
% 0.30/0.56 % add_0_iff
% 0.30/0.56 thf(fact_2078_add__0__iff,axiom,
% 0.30/0.56 ! [B: nat,A: nat] :
% 0.30/0.56 ( ( B
% 0.30/0.56 = ( plus_plus_nat @ B @ A ) )
% 0.30/0.56 = ( A = zero_zero_nat ) ) ).
% 0.30/0.56
% 0.30/0.56 % add_0_iff
% 0.30/0.56 thf(fact_2079_add__0__iff,axiom,
% 0.30/0.56 ! [B: int,A: int] :
% 0.30/0.56 ( ( B
% 0.30/0.56 = ( plus_plus_int @ B @ A ) )
% 0.30/0.56 = ( A = zero_zero_int ) ) ).
% 0.30/0.56
% 0.30/0.56 % add_0_iff
% 0.30/0.56 thf(fact_2080_crossproduct__eq,axiom,
% 0.30/0.56 ! [W2: real,Y: real,X: real,Z3: real] :
% 0.30/0.56 ( ( ( plus_plus_real @ ( times_times_real @ W2 @ Y ) @ ( times_times_real @ X @ Z3 ) )
% 0.30/0.56 = ( plus_plus_real @ ( times_times_real @ W2 @ Z3 ) @ ( times_times_real @ X @ Y ) ) )
% 0.30/0.56 = ( ( W2 = X )
% 0.30/0.56 | ( Y = Z3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_eq
% 0.30/0.56 thf(fact_2081_crossproduct__eq,axiom,
% 0.30/0.56 ! [W2: rat,Y: rat,X: rat,Z3: rat] :
% 0.30/0.56 ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X @ Z3 ) )
% 0.30/0.56 = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z3 ) @ ( times_times_rat @ X @ Y ) ) )
% 0.30/0.56 = ( ( W2 = X )
% 0.30/0.56 | ( Y = Z3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_eq
% 0.30/0.56 thf(fact_2082_crossproduct__eq,axiom,
% 0.30/0.56 ! [W2: nat,Y: nat,X: nat,Z3: nat] :
% 0.30/0.56 ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X @ Z3 ) )
% 0.30/0.56 = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z3 ) @ ( times_times_nat @ X @ Y ) ) )
% 0.30/0.56 = ( ( W2 = X )
% 0.30/0.56 | ( Y = Z3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_eq
% 0.30/0.56 thf(fact_2083_crossproduct__eq,axiom,
% 0.30/0.56 ! [W2: int,Y: int,X: int,Z3: int] :
% 0.30/0.56 ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X @ Z3 ) )
% 0.30/0.56 = ( plus_plus_int @ ( times_times_int @ W2 @ Z3 ) @ ( times_times_int @ X @ Y ) ) )
% 0.30/0.56 = ( ( W2 = X )
% 0.30/0.56 | ( Y = Z3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_eq
% 0.30/0.56 thf(fact_2084_crossproduct__noteq,axiom,
% 0.30/0.56 ! [A: real,B: real,C2: real,D: real] :
% 0.30/0.56 ( ( ( A != B )
% 0.30/0.56 & ( C2 != D ) )
% 0.30/0.56 = ( ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) )
% 0.30/0.56 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_noteq
% 0.30/0.56 thf(fact_2085_crossproduct__noteq,axiom,
% 0.30/0.56 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.30/0.56 ( ( ( A != B )
% 0.30/0.56 & ( C2 != D ) )
% 0.30/0.56 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) )
% 0.30/0.56 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_noteq
% 0.30/0.56 thf(fact_2086_crossproduct__noteq,axiom,
% 0.30/0.56 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.30/0.56 ( ( ( A != B )
% 0.30/0.56 & ( C2 != D ) )
% 0.30/0.56 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) )
% 0.30/0.56 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_noteq
% 0.30/0.56 thf(fact_2087_crossproduct__noteq,axiom,
% 0.30/0.56 ! [A: int,B: int,C2: int,D: int] :
% 0.30/0.56 ( ( ( A != B )
% 0.30/0.56 & ( C2 != D ) )
% 0.30/0.56 = ( ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) )
% 0.30/0.56 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % crossproduct_noteq
% 0.30/0.56 thf(fact_2088_option_Osize__gen_I1_J,axiom,
% 0.30/0.56 ! [X: nat > nat] :
% 0.30/0.56 ( ( size_option_nat @ X @ none_nat )
% 0.30/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.56
% 0.30/0.56 % option.size_gen(1)
% 0.30/0.56 thf(fact_2089_option_Osize__gen_I1_J,axiom,
% 0.30/0.56 ! [X: product_prod_nat_nat > nat] :
% 0.30/0.56 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 0.30/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.56
% 0.30/0.56 % option.size_gen(1)
% 0.30/0.56 thf(fact_2090_option_Osize__gen_I1_J,axiom,
% 0.30/0.56 ! [X: num > nat] :
% 0.30/0.56 ( ( size_option_num @ X @ none_num )
% 0.30/0.56 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.56
% 0.30/0.56 % option.size_gen(1)
% 0.30/0.56 thf(fact_2091_finite__has__minimal,axiom,
% 0.30/0.56 ! [A4: set_real] :
% 0.30/0.56 ( ( finite_finite_real @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_real )
% 0.30/0.56 => ? [X3: real] :
% 0.30/0.56 ( ( member_real @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: real] :
% 0.30/0.56 ( ( member_real @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_real @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal
% 0.30/0.56 thf(fact_2092_finite__has__minimal,axiom,
% 0.30/0.56 ! [A4: set_set_nat] :
% 0.30/0.56 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_set_nat )
% 0.30/0.56 => ? [X3: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal
% 0.30/0.56 thf(fact_2093_finite__has__minimal,axiom,
% 0.30/0.56 ! [A4: set_rat] :
% 0.30/0.56 ( ( finite_finite_rat @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_rat )
% 0.30/0.56 => ? [X3: rat] :
% 0.30/0.56 ( ( member_rat @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: rat] :
% 0.30/0.56 ( ( member_rat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal
% 0.30/0.56 thf(fact_2094_finite__has__minimal,axiom,
% 0.30/0.56 ! [A4: set_num] :
% 0.30/0.56 ( ( finite_finite_num @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_num )
% 0.30/0.56 => ? [X3: num] :
% 0.30/0.56 ( ( member_num @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: num] :
% 0.30/0.56 ( ( member_num @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_num @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal
% 0.30/0.56 thf(fact_2095_finite__has__minimal,axiom,
% 0.30/0.56 ! [A4: set_nat] :
% 0.30/0.56 ( ( finite_finite_nat @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_nat )
% 0.30/0.56 => ? [X3: nat] :
% 0.30/0.56 ( ( member_nat @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: nat] :
% 0.30/0.56 ( ( member_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal
% 0.30/0.56 thf(fact_2096_finite__has__minimal,axiom,
% 0.30/0.56 ! [A4: set_int] :
% 0.30/0.56 ( ( finite_finite_int @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_int )
% 0.30/0.56 => ? [X3: int] :
% 0.30/0.56 ( ( member_int @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: int] :
% 0.30/0.56 ( ( member_int @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_int @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal
% 0.30/0.56 thf(fact_2097_finite__has__maximal,axiom,
% 0.30/0.56 ! [A4: set_real] :
% 0.30/0.56 ( ( finite_finite_real @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_real )
% 0.30/0.56 => ? [X3: real] :
% 0.30/0.56 ( ( member_real @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: real] :
% 0.30/0.56 ( ( member_real @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_real @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal
% 0.30/0.56 thf(fact_2098_finite__has__maximal,axiom,
% 0.30/0.56 ! [A4: set_set_nat] :
% 0.30/0.56 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_set_nat )
% 0.30/0.56 => ? [X3: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal
% 0.30/0.56 thf(fact_2099_finite__has__maximal,axiom,
% 0.30/0.56 ! [A4: set_rat] :
% 0.30/0.56 ( ( finite_finite_rat @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_rat )
% 0.30/0.56 => ? [X3: rat] :
% 0.30/0.56 ( ( member_rat @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: rat] :
% 0.30/0.56 ( ( member_rat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal
% 0.30/0.56 thf(fact_2100_finite__has__maximal,axiom,
% 0.30/0.56 ! [A4: set_num] :
% 0.30/0.56 ( ( finite_finite_num @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_num )
% 0.30/0.56 => ? [X3: num] :
% 0.30/0.56 ( ( member_num @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: num] :
% 0.30/0.56 ( ( member_num @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_num @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal
% 0.30/0.56 thf(fact_2101_finite__has__maximal,axiom,
% 0.30/0.56 ! [A4: set_nat] :
% 0.30/0.56 ( ( finite_finite_nat @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_nat )
% 0.30/0.56 => ? [X3: nat] :
% 0.30/0.56 ( ( member_nat @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: nat] :
% 0.30/0.56 ( ( member_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal
% 0.30/0.56 thf(fact_2102_finite__has__maximal,axiom,
% 0.30/0.56 ! [A4: set_int] :
% 0.30/0.56 ( ( finite_finite_int @ A4 )
% 0.30/0.56 => ( ( A4 != bot_bot_set_int )
% 0.30/0.56 => ? [X3: int] :
% 0.30/0.56 ( ( member_int @ X3 @ A4 )
% 0.30/0.56 & ! [Xa: int] :
% 0.30/0.56 ( ( member_int @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_int @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal
% 0.30/0.56 thf(fact_2103_mult__diff__mult,axiom,
% 0.30/0.56 ! [X: real,Y: real,A: real,B: real] :
% 0.30/0.56 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 0.30/0.56 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % mult_diff_mult
% 0.30/0.56 thf(fact_2104_mult__diff__mult,axiom,
% 0.30/0.56 ! [X: rat,Y: rat,A: rat,B: rat] :
% 0.30/0.56 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 0.30/0.56 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % mult_diff_mult
% 0.30/0.56 thf(fact_2105_mult__diff__mult,axiom,
% 0.30/0.56 ! [X: int,Y: int,A: int,B: int] :
% 0.30/0.56 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 0.30/0.56 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % mult_diff_mult
% 0.30/0.56 thf(fact_2106_diff__shunt__var,axiom,
% 0.30/0.56 ! [X: set_int,Y: set_int] :
% 0.30/0.56 ( ( ( minus_minus_set_int @ X @ Y )
% 0.30/0.56 = bot_bot_set_int )
% 0.30/0.56 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_shunt_var
% 0.30/0.56 thf(fact_2107_diff__shunt__var,axiom,
% 0.30/0.56 ! [X: set_real,Y: set_real] :
% 0.30/0.56 ( ( ( minus_minus_set_real @ X @ Y )
% 0.30/0.56 = bot_bot_set_real )
% 0.30/0.56 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_shunt_var
% 0.30/0.56 thf(fact_2108_diff__shunt__var,axiom,
% 0.30/0.56 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.30/0.56 ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 0.30/0.56 = bot_bo2099793752762293965at_nat )
% 0.30/0.56 = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_shunt_var
% 0.30/0.56 thf(fact_2109_diff__shunt__var,axiom,
% 0.30/0.56 ! [X: set_nat,Y: set_nat] :
% 0.30/0.56 ( ( ( minus_minus_set_nat @ X @ Y )
% 0.30/0.56 = bot_bot_set_nat )
% 0.30/0.56 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_shunt_var
% 0.30/0.56 thf(fact_2110_minNullmin,axiom,
% 0.30/0.56 ! [T: vEBT_VEBT] :
% 0.30/0.56 ( ( vEBT_VEBT_minNull @ T )
% 0.30/0.56 => ( ( vEBT_vebt_mint @ T )
% 0.30/0.56 = none_nat ) ) ).
% 0.30/0.56
% 0.30/0.56 % minNullmin
% 0.30/0.56 thf(fact_2111_minminNull,axiom,
% 0.30/0.56 ! [T: vEBT_VEBT] :
% 0.30/0.56 ( ( ( vEBT_vebt_mint @ T )
% 0.30/0.56 = none_nat )
% 0.30/0.56 => ( vEBT_VEBT_minNull @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % minminNull
% 0.30/0.56 thf(fact_2112_vebt__maxt_Opelims,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.30/0.56 ( ( ( vEBT_vebt_maxt @ X )
% 0.30/0.56 = Y )
% 0.30/0.56 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 0.30/0.56 => ( ! [A3: $o,B3: $o] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.30/0.56 => ( ( ( B3
% 0.30/0.56 => ( Y
% 0.30/0.56 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.56 & ( ~ B3
% 0.30/0.56 => ( ( A3
% 0.30/0.56 => ( Y
% 0.30/0.56 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.56 & ( ~ A3
% 0.30/0.56 => ( Y = none_nat ) ) ) ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.30/0.56 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.30/0.56 => ( ( Y = none_nat )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) ) ) )
% 0.30/0.56 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.30/0.56 => ( ( Y
% 0.30/0.56 = ( some_nat @ Ma2 ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % vebt_maxt.pelims
% 0.30/0.56 thf(fact_2113_vebt__mint_Opelims,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,Y: option_nat] :
% 0.30/0.56 ( ( ( vEBT_vebt_mint @ X )
% 0.30/0.56 = Y )
% 0.30/0.56 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 0.30/0.56 => ( ! [A3: $o,B3: $o] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.30/0.56 => ( ( ( A3
% 0.30/0.56 => ( Y
% 0.30/0.56 = ( some_nat @ zero_zero_nat ) ) )
% 0.30/0.56 & ( ~ A3
% 0.30/0.56 => ( ( B3
% 0.30/0.56 => ( Y
% 0.30/0.56 = ( some_nat @ one_one_nat ) ) )
% 0.30/0.56 & ( ~ B3
% 0.30/0.56 => ( Y = none_nat ) ) ) ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.30/0.56 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.30/0.56 => ( ( Y = none_nat )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) ) ) )
% 0.30/0.56 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 0.30/0.56 => ( ( Y
% 0.30/0.56 = ( some_nat @ Mi2 ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % vebt_mint.pelims
% 0.30/0.56 thf(fact_2114_infinite__nat__iff__unbounded__le,axiom,
% 0.30/0.56 ! [S3: set_nat] :
% 0.30/0.56 ( ( ~ ( finite_finite_nat @ S3 ) )
% 0.30/0.56 = ( ! [M6: nat] :
% 0.30/0.56 ? [N4: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ M6 @ N4 )
% 0.30/0.56 & ( member_nat @ N4 @ S3 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % infinite_nat_iff_unbounded_le
% 0.30/0.56 thf(fact_2115_inthall,axiom,
% 0.30/0.56 ! [Xs2: list_complex,P2: complex > $o,N: nat] :
% 0.30/0.56 ( ! [X3: complex] :
% 0.30/0.56 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inthall
% 0.30/0.56 thf(fact_2116_inthall,axiom,
% 0.30/0.56 ! [Xs2: list_real,P2: real > $o,N: nat] :
% 0.30/0.56 ( ! [X3: real] :
% 0.30/0.56 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inthall
% 0.30/0.56 thf(fact_2117_inthall,axiom,
% 0.30/0.56 ! [Xs2: list_set_nat,P2: set_nat > $o,N: nat] :
% 0.30/0.56 ( ! [X3: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_set_nat @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inthall
% 0.30/0.56 thf(fact_2118_inthall,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o,N: nat] :
% 0.30/0.56 ( ! [X3: vEBT_VEBT] :
% 0.30/0.56 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inthall
% 0.30/0.56 thf(fact_2119_inthall,axiom,
% 0.30/0.56 ! [Xs2: list_o,P2: $o > $o,N: nat] :
% 0.30/0.56 ( ! [X3: $o] :
% 0.30/0.56 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inthall
% 0.30/0.56 thf(fact_2120_inthall,axiom,
% 0.30/0.56 ! [Xs2: list_nat,P2: nat > $o,N: nat] :
% 0.30/0.56 ( ! [X3: nat] :
% 0.30/0.56 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inthall
% 0.30/0.56 thf(fact_2121_inthall,axiom,
% 0.30/0.56 ! [Xs2: list_int,P2: int > $o,N: nat] :
% 0.30/0.56 ( ! [X3: int] :
% 0.30/0.56 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inthall
% 0.30/0.56 thf(fact_2122_not__min__Null__member,axiom,
% 0.30/0.56 ! [T: vEBT_VEBT] :
% 0.30/0.56 ( ~ ( vEBT_VEBT_minNull @ T )
% 0.30/0.56 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 0.30/0.56
% 0.30/0.56 % not_min_Null_member
% 0.30/0.56 thf(fact_2123_min__Null__member,axiom,
% 0.30/0.56 ! [T: vEBT_VEBT,X: nat] :
% 0.30/0.56 ( ( vEBT_VEBT_minNull @ T )
% 0.30/0.56 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 0.30/0.56
% 0.30/0.56 % min_Null_member
% 0.30/0.56 thf(fact_2124_Suc__diff__diff,axiom,
% 0.30/0.56 ! [M2: nat,N: nat,K2: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K2 ) )
% 0.30/0.56 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_diff_diff
% 0.30/0.56 thf(fact_2125_diff__Suc__Suc,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.30/0.56 = ( minus_minus_nat @ M2 @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_Suc_Suc
% 0.30/0.56 thf(fact_2126_diff__0__eq__0,axiom,
% 0.30/0.56 ! [N: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.30/0.56 = zero_zero_nat ) ).
% 0.30/0.56
% 0.30/0.56 % diff_0_eq_0
% 0.30/0.56 thf(fact_2127_diff__self__eq__0,axiom,
% 0.30/0.56 ! [M2: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ M2 @ M2 )
% 0.30/0.56 = zero_zero_nat ) ).
% 0.30/0.56
% 0.30/0.56 % diff_self_eq_0
% 0.30/0.56 thf(fact_2128_diff__diff__cancel,axiom,
% 0.30/0.56 ! [I2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ I2 @ N )
% 0.30/0.56 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 0.30/0.56 = I2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_diff_cancel
% 0.30/0.56 thf(fact_2129_diff__diff__left,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 0.30/0.56 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_diff_left
% 0.30/0.56 thf(fact_2130_zero__less__diff,axiom,
% 0.30/0.56 ! [N: nat,M2: nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M2 ) )
% 0.30/0.56 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % zero_less_diff
% 0.30/0.56 thf(fact_2131_diff__is__0__eq_H,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.56 => ( ( minus_minus_nat @ M2 @ N )
% 0.30/0.56 = zero_zero_nat ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_is_0_eq'
% 0.30/0.56 thf(fact_2132_diff__is__0__eq,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] :
% 0.30/0.56 ( ( ( minus_minus_nat @ M2 @ N )
% 0.30/0.56 = zero_zero_nat )
% 0.30/0.56 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_is_0_eq
% 0.30/0.56 thf(fact_2133_Nat_Oadd__diff__assoc,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 0.30/0.56 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.add_diff_assoc
% 0.30/0.56 thf(fact_2134_Nat_Oadd__diff__assoc2,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 0.30/0.56 = ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.add_diff_assoc2
% 0.30/0.56 thf(fact_2135_Nat_Odiff__diff__right,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 0.30/0.56 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.diff_diff_right
% 0.30/0.56 thf(fact_2136_diff__Suc__1,axiom,
% 0.30/0.56 ! [N: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 0.30/0.56 = N ) ).
% 0.30/0.56
% 0.30/0.56 % diff_Suc_1
% 0.30/0.56 thf(fact_2137_Suc__pred,axiom,
% 0.30/0.56 ! [N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.30/0.56 = N ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_pred
% 0.30/0.56 thf(fact_2138_diff__Suc__diff__eq1,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) )
% 0.30/0.56 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( suc @ J2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_Suc_diff_eq1
% 0.30/0.56 thf(fact_2139_diff__Suc__diff__eq2,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) @ I2 )
% 0.30/0.56 = ( minus_minus_nat @ ( suc @ J2 ) @ ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_Suc_diff_eq2
% 0.30/0.56 thf(fact_2140_Suc__diff__1,axiom,
% 0.30/0.56 ! [N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.56 = N ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_diff_1
% 0.30/0.56 thf(fact_2141_zero__induct__lemma,axiom,
% 0.30/0.56 ! [P2: nat > $o,K2: nat,I2: nat] :
% 0.30/0.56 ( ( P2 @ K2 )
% 0.30/0.56 => ( ! [N3: nat] :
% 0.30/0.56 ( ( P2 @ ( suc @ N3 ) )
% 0.30/0.56 => ( P2 @ N3 ) )
% 0.30/0.56 => ( P2 @ ( minus_minus_nat @ K2 @ I2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zero_induct_lemma
% 0.30/0.56 thf(fact_2142_minus__nat_Odiff__0,axiom,
% 0.30/0.56 ! [M2: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 0.30/0.56 = M2 ) ).
% 0.30/0.56
% 0.30/0.56 % minus_nat.diff_0
% 0.30/0.56 thf(fact_2143_diffs0__imp__equal,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] :
% 0.30/0.56 ( ( ( minus_minus_nat @ M2 @ N )
% 0.30/0.56 = zero_zero_nat )
% 0.30/0.56 => ( ( ( minus_minus_nat @ N @ M2 )
% 0.30/0.56 = zero_zero_nat )
% 0.30/0.56 => ( M2 = N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diffs0_imp_equal
% 0.30/0.56 thf(fact_2144_diff__less__mono2,axiom,
% 0.30/0.56 ! [M2: nat,N: nat,L: nat] :
% 0.30/0.56 ( ( ord_less_nat @ M2 @ N )
% 0.30/0.56 => ( ( ord_less_nat @ M2 @ L )
% 0.30/0.56 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_less_mono2
% 0.30/0.56 thf(fact_2145_less__imp__diff__less,axiom,
% 0.30/0.56 ! [J2: nat,K2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J2 @ K2 )
% 0.30/0.56 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % less_imp_diff_less
% 0.30/0.56 thf(fact_2146_diff__le__mono2,axiom,
% 0.30/0.56 ! [M2: nat,N: nat,L: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.56 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_le_mono2
% 0.30/0.56 thf(fact_2147_le__diff__iff_H,axiom,
% 0.30/0.56 ! [A: nat,C2: nat,B: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ A @ C2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ B @ C2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C2 @ A ) @ ( minus_minus_nat @ C2 @ B ) )
% 0.30/0.56 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % le_diff_iff'
% 0.30/0.56 thf(fact_2148_diff__le__self,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ).
% 0.30/0.56
% 0.30/0.56 % diff_le_self
% 0.30/0.56 thf(fact_2149_diff__le__mono,axiom,
% 0.30/0.56 ! [M2: nat,N: nat,L: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ M2 @ N )
% 0.30/0.56 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_le_mono
% 0.30/0.56 thf(fact_2150_Nat_Odiff__diff__eq,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.30/0.56 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 0.30/0.56 = ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.diff_diff_eq
% 0.30/0.56 thf(fact_2151_le__diff__iff,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.30/0.56 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 0.30/0.56 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % le_diff_iff
% 0.30/0.56 thf(fact_2152_eq__diff__iff,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.30/0.56 => ( ( ( minus_minus_nat @ M2 @ K2 )
% 0.30/0.56 = ( minus_minus_nat @ N @ K2 ) )
% 0.30/0.56 = ( M2 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % eq_diff_iff
% 0.30/0.56 thf(fact_2153_Nat_Odiff__cancel,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 0.30/0.56 = ( minus_minus_nat @ M2 @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.diff_cancel
% 0.30/0.56 thf(fact_2154_diff__cancel2,axiom,
% 0.30/0.56 ! [M2: nat,K2: nat,N: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) )
% 0.30/0.56 = ( minus_minus_nat @ M2 @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_cancel2
% 0.30/0.56 thf(fact_2155_diff__add__inverse,axiom,
% 0.30/0.56 ! [N: nat,M2: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M2 ) @ N )
% 0.30/0.56 = M2 ) ).
% 0.30/0.56
% 0.30/0.56 % diff_add_inverse
% 0.30/0.56 thf(fact_2156_diff__add__inverse2,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ N )
% 0.30/0.56 = M2 ) ).
% 0.30/0.56
% 0.30/0.56 % diff_add_inverse2
% 0.30/0.56 thf(fact_2157_diff__mult__distrib,axiom,
% 0.30/0.56 ! [M2: nat,N: nat,K2: nat] :
% 0.30/0.56 ( ( times_times_nat @ ( minus_minus_nat @ M2 @ N ) @ K2 )
% 0.30/0.56 = ( minus_minus_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_mult_distrib
% 0.30/0.56 thf(fact_2158_diff__mult__distrib2,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( times_times_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 0.30/0.56 = ( minus_minus_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_mult_distrib2
% 0.30/0.56 thf(fact_2159_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 0.30/0.56 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.simps(1)
% 0.30/0.56 thf(fact_2160_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 0.30/0.56 ! [Uv: $o] :
% 0.30/0.56 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.simps(2)
% 0.30/0.56 thf(fact_2161_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 0.30/0.56 ! [Uu: $o] :
% 0.30/0.56 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.simps(3)
% 0.30/0.56 thf(fact_2162_list__eq__iff__nth__eq,axiom,
% 0.30/0.56 ( ( ^ [Y5: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y5 = Z2 ) )
% 0.30/0.56 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.30/0.56 => ( ( nth_VEBT_VEBT @ Xs @ I )
% 0.30/0.56 = ( nth_VEBT_VEBT @ Ys3 @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_eq_iff_nth_eq
% 0.30/0.56 thf(fact_2163_list__eq__iff__nth__eq,axiom,
% 0.30/0.56 ( ( ^ [Y5: list_o,Z2: list_o] : ( Y5 = Z2 ) )
% 0.30/0.56 = ( ^ [Xs: list_o,Ys3: list_o] :
% 0.30/0.56 ( ( ( size_size_list_o @ Xs )
% 0.30/0.56 = ( size_size_list_o @ Ys3 ) )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.30/0.56 => ( ( nth_o @ Xs @ I )
% 0.30/0.56 = ( nth_o @ Ys3 @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_eq_iff_nth_eq
% 0.30/0.56 thf(fact_2164_list__eq__iff__nth__eq,axiom,
% 0.30/0.56 ( ( ^ [Y5: list_nat,Z2: list_nat] : ( Y5 = Z2 ) )
% 0.30/0.56 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 0.30/0.56 ( ( ( size_size_list_nat @ Xs )
% 0.30/0.56 = ( size_size_list_nat @ Ys3 ) )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.30/0.56 => ( ( nth_nat @ Xs @ I )
% 0.30/0.56 = ( nth_nat @ Ys3 @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_eq_iff_nth_eq
% 0.30/0.56 thf(fact_2165_list__eq__iff__nth__eq,axiom,
% 0.30/0.56 ( ( ^ [Y5: list_int,Z2: list_int] : ( Y5 = Z2 ) )
% 0.30/0.56 = ( ^ [Xs: list_int,Ys3: list_int] :
% 0.30/0.56 ( ( ( size_size_list_int @ Xs )
% 0.30/0.56 = ( size_size_list_int @ Ys3 ) )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.30/0.56 => ( ( nth_int @ Xs @ I )
% 0.30/0.56 = ( nth_int @ Ys3 @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_eq_iff_nth_eq
% 0.30/0.56 thf(fact_2166_Skolem__list__nth,axiom,
% 0.30/0.56 ! [K2: nat,P2: nat > vEBT_VEBT > $o] :
% 0.30/0.56 ( ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ? [X7: vEBT_VEBT] : ( P2 @ I @ X7 ) ) )
% 0.30/0.56 = ( ? [Xs: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.30/0.56 = K2 )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ( P2 @ I @ ( nth_VEBT_VEBT @ Xs @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Skolem_list_nth
% 0.30/0.56 thf(fact_2167_Skolem__list__nth,axiom,
% 0.30/0.56 ! [K2: nat,P2: nat > $o > $o] :
% 0.30/0.56 ( ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ? [X7: $o] : ( P2 @ I @ X7 ) ) )
% 0.30/0.56 = ( ? [Xs: list_o] :
% 0.30/0.56 ( ( ( size_size_list_o @ Xs )
% 0.30/0.56 = K2 )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ( P2 @ I @ ( nth_o @ Xs @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Skolem_list_nth
% 0.30/0.56 thf(fact_2168_Skolem__list__nth,axiom,
% 0.30/0.56 ! [K2: nat,P2: nat > nat > $o] :
% 0.30/0.56 ( ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ? [X7: nat] : ( P2 @ I @ X7 ) ) )
% 0.30/0.56 = ( ? [Xs: list_nat] :
% 0.30/0.56 ( ( ( size_size_list_nat @ Xs )
% 0.30/0.56 = K2 )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ( P2 @ I @ ( nth_nat @ Xs @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Skolem_list_nth
% 0.30/0.56 thf(fact_2169_Skolem__list__nth,axiom,
% 0.30/0.56 ! [K2: nat,P2: nat > int > $o] :
% 0.30/0.56 ( ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ? [X7: int] : ( P2 @ I @ X7 ) ) )
% 0.30/0.56 = ( ? [Xs: list_int] :
% 0.30/0.56 ( ( ( size_size_list_int @ Xs )
% 0.30/0.56 = K2 )
% 0.30/0.56 & ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ K2 )
% 0.30/0.56 => ( P2 @ I @ ( nth_int @ Xs @ I ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Skolem_list_nth
% 0.30/0.56 thf(fact_2170_nth__equalityI,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 0.30/0.56 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 0.30/0.56 => ( Xs2 = Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_equalityI
% 0.30/0.56 thf(fact_2171_nth__equalityI,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_o] :
% 0.30/0.56 ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.56 = ( size_size_list_o @ Ys ) )
% 0.30/0.56 => ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( ( nth_o @ Xs2 @ I3 )
% 0.30/0.56 = ( nth_o @ Ys @ I3 ) ) )
% 0.30/0.56 => ( Xs2 = Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_equalityI
% 0.30/0.56 thf(fact_2172_nth__equalityI,axiom,
% 0.30/0.56 ! [Xs2: list_nat,Ys: list_nat] :
% 0.30/0.56 ( ( ( size_size_list_nat @ Xs2 )
% 0.30/0.56 = ( size_size_list_nat @ Ys ) )
% 0.30/0.56 => ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( ( nth_nat @ Xs2 @ I3 )
% 0.30/0.56 = ( nth_nat @ Ys @ I3 ) ) )
% 0.30/0.56 => ( Xs2 = Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_equalityI
% 0.30/0.56 thf(fact_2173_nth__equalityI,axiom,
% 0.30/0.56 ! [Xs2: list_int,Ys: list_int] :
% 0.30/0.56 ( ( ( size_size_list_int @ Xs2 )
% 0.30/0.56 = ( size_size_list_int @ Ys ) )
% 0.30/0.56 => ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 => ( ( nth_int @ Xs2 @ I3 )
% 0.30/0.56 = ( nth_int @ Ys @ I3 ) ) )
% 0.30/0.56 => ( Xs2 = Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_equalityI
% 0.30/0.56 thf(fact_2174_diff__less__Suc,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ ( suc @ M2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_less_Suc
% 0.30/0.56 thf(fact_2175_Suc__diff__Suc,axiom,
% 0.30/0.56 ! [N: nat,M2: nat] :
% 0.30/0.56 ( ( ord_less_nat @ N @ M2 )
% 0.30/0.56 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N ) ) )
% 0.30/0.56 = ( minus_minus_nat @ M2 @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_diff_Suc
% 0.30/0.56 thf(fact_2176_diff__less,axiom,
% 0.30/0.56 ! [N: nat,M2: nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.30/0.56 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_less
% 0.30/0.56 thf(fact_2177_Suc__diff__le,axiom,
% 0.30/0.56 ! [N: nat,M2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ N @ M2 )
% 0.30/0.56 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 0.30/0.56 = ( suc @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_diff_le
% 0.30/0.56 thf(fact_2178_less__diff__iff,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.30/0.56 => ( ( ord_less_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 0.30/0.56 = ( ord_less_nat @ M2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % less_diff_iff
% 0.30/0.56 thf(fact_2179_diff__less__mono,axiom,
% 0.30/0.56 ! [A: nat,B: nat,C2: nat] :
% 0.30/0.56 ( ( ord_less_nat @ A @ B )
% 0.30/0.56 => ( ( ord_less_eq_nat @ C2 @ A )
% 0.30/0.56 => ( ord_less_nat @ ( minus_minus_nat @ A @ C2 ) @ ( minus_minus_nat @ B @ C2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_less_mono
% 0.30/0.56 thf(fact_2180_diff__add__0,axiom,
% 0.30/0.56 ! [N: nat,M2: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M2 ) )
% 0.30/0.56 = zero_zero_nat ) ).
% 0.30/0.56
% 0.30/0.56 % diff_add_0
% 0.30/0.56 thf(fact_2181_finite__maxlen,axiom,
% 0.30/0.56 ! [M5: set_list_VEBT_VEBT] :
% 0.30/0.56 ( ( finite3004134309566078307T_VEBT @ M5 )
% 0.30/0.56 => ? [N3: nat] :
% 0.30/0.56 ! [X5: list_VEBT_VEBT] :
% 0.30/0.56 ( ( member2936631157270082147T_VEBT @ X5 @ M5 )
% 0.30/0.56 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_maxlen
% 0.30/0.56 thf(fact_2182_finite__maxlen,axiom,
% 0.30/0.56 ! [M5: set_list_o] :
% 0.30/0.56 ( ( finite_finite_list_o @ M5 )
% 0.30/0.56 => ? [N3: nat] :
% 0.30/0.56 ! [X5: list_o] :
% 0.30/0.56 ( ( member_list_o @ X5 @ M5 )
% 0.30/0.56 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_maxlen
% 0.30/0.56 thf(fact_2183_finite__maxlen,axiom,
% 0.30/0.56 ! [M5: set_list_nat] :
% 0.30/0.56 ( ( finite8100373058378681591st_nat @ M5 )
% 0.30/0.56 => ? [N3: nat] :
% 0.30/0.56 ! [X5: list_nat] :
% 0.30/0.56 ( ( member_list_nat @ X5 @ M5 )
% 0.30/0.56 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_maxlen
% 0.30/0.56 thf(fact_2184_finite__maxlen,axiom,
% 0.30/0.56 ! [M5: set_list_int] :
% 0.30/0.56 ( ( finite3922522038869484883st_int @ M5 )
% 0.30/0.56 => ? [N3: nat] :
% 0.30/0.56 ! [X5: list_int] :
% 0.30/0.56 ( ( member_list_int @ X5 @ M5 )
% 0.30/0.56 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_maxlen
% 0.30/0.56 thf(fact_2185_less__diff__conv,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 0.30/0.56 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % less_diff_conv
% 0.30/0.56 thf(fact_2186_add__diff__inverse__nat,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] :
% 0.30/0.56 ( ~ ( ord_less_nat @ M2 @ N )
% 0.30/0.56 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M2 @ N ) )
% 0.30/0.56 = M2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % add_diff_inverse_nat
% 0.30/0.56 thf(fact_2187_le__diff__conv,axiom,
% 0.30/0.56 ! [J2: nat,K2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 0.30/0.56 = ( ord_less_eq_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % le_diff_conv
% 0.30/0.56 thf(fact_2188_Nat_Ole__diff__conv2,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 0.30/0.56 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.le_diff_conv2
% 0.30/0.56 thf(fact_2189_Nat_Odiff__add__assoc,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 0.30/0.56 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.diff_add_assoc
% 0.30/0.56 thf(fact_2190_Nat_Odiff__add__assoc2,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 )
% 0.30/0.56 = ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.diff_add_assoc2
% 0.30/0.56 thf(fact_2191_Nat_Ole__imp__diff__is__add,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.56 => ( ( ( minus_minus_nat @ J2 @ I2 )
% 0.30/0.56 = K2 )
% 0.30/0.56 = ( J2
% 0.30/0.56 = ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Nat.le_imp_diff_is_add
% 0.30/0.56 thf(fact_2192_diff__Suc__eq__diff__pred,axiom,
% 0.30/0.56 ! [M2: nat,N: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 0.30/0.56 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_Suc_eq_diff_pred
% 0.30/0.56 thf(fact_2193_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 0.30/0.56 ! [Uz: product_prod_nat_nat,Va3: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 0.30/0.56 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va3 @ Vb @ Vc ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.simps(5)
% 0.30/0.56 thf(fact_2194_nth__mem,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_complex] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.30/0.56 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_mem
% 0.30/0.56 thf(fact_2195_nth__mem,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_real] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.30/0.56 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_mem
% 0.30/0.56 thf(fact_2196_nth__mem,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_set_nat] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.30/0.56 => ( member_set_nat @ ( nth_set_nat @ Xs2 @ N ) @ ( set_set_nat2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_mem
% 0.30/0.56 thf(fact_2197_nth__mem,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_mem
% 0.30/0.56 thf(fact_2198_nth__mem,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_o] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_mem
% 0.30/0.56 thf(fact_2199_nth__mem,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_mem
% 0.30/0.56 thf(fact_2200_nth__mem,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_int] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_mem
% 0.30/0.56 thf(fact_2201_list__ball__nth,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( ! [X3: vEBT_VEBT] :
% 0.30/0.56 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_ball_nth
% 0.30/0.56 thf(fact_2202_list__ball__nth,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_o,P2: $o > $o] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( ! [X3: $o] :
% 0.30/0.56 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( P2 @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_ball_nth
% 0.30/0.56 thf(fact_2203_list__ball__nth,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_nat,P2: nat > $o] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( ! [X3: nat] :
% 0.30/0.56 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( P2 @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_ball_nth
% 0.30/0.56 thf(fact_2204_list__ball__nth,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_int,P2: int > $o] :
% 0.30/0.56 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 => ( ! [X3: int] :
% 0.30/0.56 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( P2 @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % list_ball_nth
% 0.30/0.56 thf(fact_2205_in__set__conv__nth,axiom,
% 0.30/0.56 ! [X: complex,Xs2: list_complex] :
% 0.30/0.56 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.30/0.56 & ( ( nth_complex @ Xs2 @ I )
% 0.30/0.56 = X ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_conv_nth
% 0.30/0.56 thf(fact_2206_in__set__conv__nth,axiom,
% 0.30/0.56 ! [X: real,Xs2: list_real] :
% 0.30/0.56 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs2 ) )
% 0.30/0.56 & ( ( nth_real @ Xs2 @ I )
% 0.30/0.56 = X ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_conv_nth
% 0.30/0.56 thf(fact_2207_in__set__conv__nth,axiom,
% 0.30/0.56 ! [X: set_nat,Xs2: list_set_nat] :
% 0.30/0.56 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.30/0.56 & ( ( nth_set_nat @ Xs2 @ I )
% 0.30/0.56 = X ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_conv_nth
% 0.30/0.56 thf(fact_2208_in__set__conv__nth,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 & ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 0.30/0.56 = X ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_conv_nth
% 0.30/0.56 thf(fact_2209_in__set__conv__nth,axiom,
% 0.30/0.56 ! [X: $o,Xs2: list_o] :
% 0.30/0.56 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 & ( ( nth_o @ Xs2 @ I )
% 0.30/0.56 = X ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_conv_nth
% 0.30/0.56 thf(fact_2210_in__set__conv__nth,axiom,
% 0.30/0.56 ! [X: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 & ( ( nth_nat @ Xs2 @ I )
% 0.30/0.56 = X ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_conv_nth
% 0.30/0.56 thf(fact_2211_in__set__conv__nth,axiom,
% 0.30/0.56 ! [X: int,Xs2: list_int] :
% 0.30/0.56 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 & ( ( nth_int @ Xs2 @ I )
% 0.30/0.56 = X ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_conv_nth
% 0.30/0.56 thf(fact_2212_all__nth__imp__all__set,axiom,
% 0.30/0.56 ! [Xs2: list_complex,P2: complex > $o,X: complex] :
% 0.30/0.56 ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_complex @ Xs2 @ I3 ) ) )
% 0.30/0.56 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_nth_imp_all_set
% 0.30/0.56 thf(fact_2213_all__nth__imp__all__set,axiom,
% 0.30/0.56 ! [Xs2: list_real,P2: real > $o,X: real] :
% 0.30/0.56 ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_real @ Xs2 @ I3 ) ) )
% 0.30/0.56 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_nth_imp_all_set
% 0.30/0.56 thf(fact_2214_all__nth__imp__all__set,axiom,
% 0.30/0.56 ! [Xs2: list_set_nat,P2: set_nat > $o,X: set_nat] :
% 0.30/0.56 ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_set_nat @ Xs2 @ I3 ) ) )
% 0.30/0.56 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_nth_imp_all_set
% 0.30/0.56 thf(fact_2215_all__nth__imp__all__set,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 0.30/0.56 ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 0.30/0.56 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_nth_imp_all_set
% 0.30/0.56 thf(fact_2216_all__nth__imp__all__set,axiom,
% 0.30/0.56 ! [Xs2: list_o,P2: $o > $o,X: $o] :
% 0.30/0.56 ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_o @ Xs2 @ I3 ) ) )
% 0.30/0.56 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_nth_imp_all_set
% 0.30/0.56 thf(fact_2217_all__nth__imp__all__set,axiom,
% 0.30/0.56 ! [Xs2: list_nat,P2: nat > $o,X: nat] :
% 0.30/0.56 ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_nat @ Xs2 @ I3 ) ) )
% 0.30/0.56 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_nth_imp_all_set
% 0.30/0.56 thf(fact_2218_all__nth__imp__all__set,axiom,
% 0.30/0.56 ! [Xs2: list_int,P2: int > $o,X: int] :
% 0.30/0.56 ( ! [I3: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_int @ Xs2 @ I3 ) ) )
% 0.30/0.56 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_nth_imp_all_set
% 0.30/0.56 thf(fact_2219_all__set__conv__all__nth,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.30/0.56 ( ( ! [X4: vEBT_VEBT] :
% 0.30/0.56 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X4 ) ) )
% 0.30/0.56 = ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_set_conv_all_nth
% 0.30/0.56 thf(fact_2220_all__set__conv__all__nth,axiom,
% 0.30/0.56 ! [Xs2: list_o,P2: $o > $o] :
% 0.30/0.56 ( ( ! [X4: $o] :
% 0.30/0.56 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X4 ) ) )
% 0.30/0.56 = ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_o @ Xs2 @ I ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_set_conv_all_nth
% 0.30/0.56 thf(fact_2221_all__set__conv__all__nth,axiom,
% 0.30/0.56 ! [Xs2: list_nat,P2: nat > $o] :
% 0.30/0.56 ( ( ! [X4: nat] :
% 0.30/0.56 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X4 ) ) )
% 0.30/0.56 = ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_nat @ Xs2 @ I ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_set_conv_all_nth
% 0.30/0.56 thf(fact_2222_all__set__conv__all__nth,axiom,
% 0.30/0.56 ! [Xs2: list_int,P2: int > $o] :
% 0.30/0.56 ( ( ! [X4: int] :
% 0.30/0.56 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 => ( P2 @ X4 ) ) )
% 0.30/0.56 = ( ! [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 => ( P2 @ ( nth_int @ Xs2 @ I ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % all_set_conv_all_nth
% 0.30/0.56 thf(fact_2223_diff__Suc__less,axiom,
% 0.30/0.56 ! [N: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_Suc_less
% 0.30/0.56 thf(fact_2224_nat__diff__split,axiom,
% 0.30/0.56 ! [P2: nat > $o,A: nat,B: nat] :
% 0.30/0.56 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 0.30/0.56 = ( ( ( ord_less_nat @ A @ B )
% 0.30/0.56 => ( P2 @ zero_zero_nat ) )
% 0.30/0.56 & ! [D2: nat] :
% 0.30/0.56 ( ( A
% 0.30/0.56 = ( plus_plus_nat @ B @ D2 ) )
% 0.30/0.56 => ( P2 @ D2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_diff_split
% 0.30/0.56 thf(fact_2225_nat__diff__split__asm,axiom,
% 0.30/0.56 ! [P2: nat > $o,A: nat,B: nat] :
% 0.30/0.56 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 0.30/0.56 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 0.30/0.56 & ~ ( P2 @ zero_zero_nat ) )
% 0.30/0.56 | ? [D2: nat] :
% 0.30/0.56 ( ( A
% 0.30/0.56 = ( plus_plus_nat @ B @ D2 ) )
% 0.30/0.56 & ~ ( P2 @ D2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_diff_split_asm
% 0.30/0.56 thf(fact_2226_less__diff__conv2,axiom,
% 0.30/0.56 ! [K2: nat,J2: nat,I2: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K2 @ J2 )
% 0.30/0.56 => ( ( ord_less_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 0.30/0.56 = ( ord_less_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % less_diff_conv2
% 0.30/0.56 thf(fact_2227_nat__eq__add__iff1,axiom,
% 0.30/0.56 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ J2 @ I2 )
% 0.30/0.56 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 )
% 0.30/0.56 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 )
% 0.30/0.56 = N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_eq_add_iff1
% 0.30/0.56 thf(fact_2228_nat__eq__add__iff2,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.56 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 )
% 0.30/0.56 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( M2
% 0.30/0.56 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_eq_add_iff2
% 0.30/0.56 thf(fact_2229_nat__le__add__iff1,axiom,
% 0.30/0.56 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ J2 @ I2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_le_add_iff1
% 0.30/0.56 thf(fact_2230_nat__le__add__iff2,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_le_add_iff2
% 0.30/0.56 thf(fact_2231_nat__diff__add__eq1,axiom,
% 0.30/0.56 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ J2 @ I2 )
% 0.30/0.56 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_diff_add_eq1
% 0.30/0.56 thf(fact_2232_nat__diff__add__eq2,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.56 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_diff_add_eq2
% 0.30/0.56 thf(fact_2233_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT] :
% 0.30/0.56 ( ~ ( vEBT_VEBT_minNull @ X )
% 0.30/0.56 => ( ! [Uv2: $o] :
% 0.30/0.56 ( X
% 0.30/0.56 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.30/0.56 => ( ! [Uu2: $o] :
% 0.30/0.56 ( X
% 0.30/0.56 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.30/0.56 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.30/0.56 ( X
% 0.30/0.56 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.elims(3)
% 0.30/0.56 thf(fact_2234_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT] :
% 0.30/0.56 ( ( vEBT_VEBT_minNull @ X )
% 0.30/0.56 => ( ( X
% 0.30/0.56 != ( vEBT_Leaf @ $false @ $false ) )
% 0.30/0.56 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.30/0.56 ( X
% 0.30/0.56 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.elims(2)
% 0.30/0.56 thf(fact_2235_Suc__pred_H,axiom,
% 0.30/0.56 ! [N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( N
% 0.30/0.56 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_pred'
% 0.30/0.56 thf(fact_2236_Suc__diff__eq__diff__pred,axiom,
% 0.30/0.56 ! [N: nat,M2: nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 0.30/0.56 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_diff_eq_diff_pred
% 0.30/0.56 thf(fact_2237_add__eq__if,axiom,
% 0.30/0.56 ( plus_plus_nat
% 0.30/0.56 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % add_eq_if
% 0.30/0.56 thf(fact_2238_nat__less__add__iff1,axiom,
% 0.30/0.56 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ J2 @ I2 )
% 0.30/0.56 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_less_add_iff1
% 0.30/0.56 thf(fact_2239_nat__less__add__iff2,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.30/0.56 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 0.30/0.56 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_less_add_iff2
% 0.30/0.56 thf(fact_2240_mult__eq__if,axiom,
% 0.30/0.56 ( times_times_nat
% 0.30/0.56 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % mult_eq_if
% 0.30/0.56 thf(fact_2241_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,Y: $o] :
% 0.30/0.56 ( ( ( vEBT_VEBT_minNull @ X )
% 0.30/0.56 = Y )
% 0.30/0.56 => ( ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ $false @ $false ) )
% 0.30/0.56 => ~ Y )
% 0.30/0.56 => ( ( ? [Uv2: $o] :
% 0.30/0.56 ( X
% 0.30/0.56 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.30/0.56 => Y )
% 0.30/0.56 => ( ( ? [Uu2: $o] :
% 0.30/0.56 ( X
% 0.30/0.56 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.30/0.56 => Y )
% 0.30/0.56 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.30/0.56 ( X
% 0.30/0.56 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.30/0.56 => ~ Y )
% 0.30/0.56 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.30/0.56 ( X
% 0.30/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 0.30/0.56 => Y ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.elims(1)
% 0.30/0.56 thf(fact_2242_field__lbound__gt__zero,axiom,
% 0.30/0.56 ! [D1: real,D22: real] :
% 0.30/0.56 ( ( ord_less_real @ zero_zero_real @ D1 )
% 0.30/0.56 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 0.30/0.56 => ? [E2: real] :
% 0.30/0.56 ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.30/0.56 & ( ord_less_real @ E2 @ D1 )
% 0.30/0.56 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % field_lbound_gt_zero
% 0.30/0.56 thf(fact_2243_field__lbound__gt__zero,axiom,
% 0.30/0.56 ! [D1: rat,D22: rat] :
% 0.30/0.56 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 0.30/0.56 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 0.30/0.56 => ? [E2: rat] :
% 0.30/0.56 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.30/0.56 & ( ord_less_rat @ E2 @ D1 )
% 0.30/0.56 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % field_lbound_gt_zero
% 0.30/0.56 thf(fact_2244_finite__has__minimal2,axiom,
% 0.30/0.56 ! [A4: set_real,A: real] :
% 0.30/0.56 ( ( finite_finite_real @ A4 )
% 0.30/0.56 => ( ( member_real @ A @ A4 )
% 0.30/0.56 => ? [X3: real] :
% 0.30/0.56 ( ( member_real @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_real @ X3 @ A )
% 0.30/0.56 & ! [Xa: real] :
% 0.30/0.56 ( ( member_real @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_real @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal2
% 0.30/0.56 thf(fact_2245_finite__has__minimal2,axiom,
% 0.30/0.56 ! [A4: set_set_nat,A: set_nat] :
% 0.30/0.56 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.56 => ( ( member_set_nat @ A @ A4 )
% 0.30/0.56 => ? [X3: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_set_nat @ X3 @ A )
% 0.30/0.56 & ! [Xa: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal2
% 0.30/0.56 thf(fact_2246_finite__has__minimal2,axiom,
% 0.30/0.56 ! [A4: set_rat,A: rat] :
% 0.30/0.56 ( ( finite_finite_rat @ A4 )
% 0.30/0.56 => ( ( member_rat @ A @ A4 )
% 0.30/0.56 => ? [X3: rat] :
% 0.30/0.56 ( ( member_rat @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_rat @ X3 @ A )
% 0.30/0.56 & ! [Xa: rat] :
% 0.30/0.56 ( ( member_rat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal2
% 0.30/0.56 thf(fact_2247_finite__has__minimal2,axiom,
% 0.30/0.56 ! [A4: set_num,A: num] :
% 0.30/0.56 ( ( finite_finite_num @ A4 )
% 0.30/0.56 => ( ( member_num @ A @ A4 )
% 0.30/0.56 => ? [X3: num] :
% 0.30/0.56 ( ( member_num @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_num @ X3 @ A )
% 0.30/0.56 & ! [Xa: num] :
% 0.30/0.56 ( ( member_num @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_num @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal2
% 0.30/0.56 thf(fact_2248_finite__has__minimal2,axiom,
% 0.30/0.56 ! [A4: set_nat,A: nat] :
% 0.30/0.56 ( ( finite_finite_nat @ A4 )
% 0.30/0.56 => ( ( member_nat @ A @ A4 )
% 0.30/0.56 => ? [X3: nat] :
% 0.30/0.56 ( ( member_nat @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_nat @ X3 @ A )
% 0.30/0.56 & ! [Xa: nat] :
% 0.30/0.56 ( ( member_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal2
% 0.30/0.56 thf(fact_2249_finite__has__minimal2,axiom,
% 0.30/0.56 ! [A4: set_int,A: int] :
% 0.30/0.56 ( ( finite_finite_int @ A4 )
% 0.30/0.56 => ( ( member_int @ A @ A4 )
% 0.30/0.56 => ? [X3: int] :
% 0.30/0.56 ( ( member_int @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_int @ X3 @ A )
% 0.30/0.56 & ! [Xa: int] :
% 0.30/0.56 ( ( member_int @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_int @ Xa @ X3 )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_minimal2
% 0.30/0.56 thf(fact_2250_finite__has__maximal2,axiom,
% 0.30/0.56 ! [A4: set_real,A: real] :
% 0.30/0.56 ( ( finite_finite_real @ A4 )
% 0.30/0.56 => ( ( member_real @ A @ A4 )
% 0.30/0.56 => ? [X3: real] :
% 0.30/0.56 ( ( member_real @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_real @ A @ X3 )
% 0.30/0.56 & ! [Xa: real] :
% 0.30/0.56 ( ( member_real @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_real @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal2
% 0.30/0.56 thf(fact_2251_finite__has__maximal2,axiom,
% 0.30/0.56 ! [A4: set_set_nat,A: set_nat] :
% 0.30/0.56 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.56 => ( ( member_set_nat @ A @ A4 )
% 0.30/0.56 => ? [X3: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_set_nat @ A @ X3 )
% 0.30/0.56 & ! [Xa: set_nat] :
% 0.30/0.56 ( ( member_set_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal2
% 0.30/0.56 thf(fact_2252_finite__has__maximal2,axiom,
% 0.30/0.56 ! [A4: set_rat,A: rat] :
% 0.30/0.56 ( ( finite_finite_rat @ A4 )
% 0.30/0.56 => ( ( member_rat @ A @ A4 )
% 0.30/0.56 => ? [X3: rat] :
% 0.30/0.56 ( ( member_rat @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_rat @ A @ X3 )
% 0.30/0.56 & ! [Xa: rat] :
% 0.30/0.56 ( ( member_rat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal2
% 0.30/0.56 thf(fact_2253_finite__has__maximal2,axiom,
% 0.30/0.56 ! [A4: set_num,A: num] :
% 0.30/0.56 ( ( finite_finite_num @ A4 )
% 0.30/0.56 => ( ( member_num @ A @ A4 )
% 0.30/0.56 => ? [X3: num] :
% 0.30/0.56 ( ( member_num @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_num @ A @ X3 )
% 0.30/0.56 & ! [Xa: num] :
% 0.30/0.56 ( ( member_num @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_num @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal2
% 0.30/0.56 thf(fact_2254_finite__has__maximal2,axiom,
% 0.30/0.56 ! [A4: set_nat,A: nat] :
% 0.30/0.56 ( ( finite_finite_nat @ A4 )
% 0.30/0.56 => ( ( member_nat @ A @ A4 )
% 0.30/0.56 => ? [X3: nat] :
% 0.30/0.56 ( ( member_nat @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_nat @ A @ X3 )
% 0.30/0.56 & ! [Xa: nat] :
% 0.30/0.56 ( ( member_nat @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal2
% 0.30/0.56 thf(fact_2255_finite__has__maximal2,axiom,
% 0.30/0.56 ! [A4: set_int,A: int] :
% 0.30/0.56 ( ( finite_finite_int @ A4 )
% 0.30/0.56 => ( ( member_int @ A @ A4 )
% 0.30/0.56 => ? [X3: int] :
% 0.30/0.56 ( ( member_int @ X3 @ A4 )
% 0.30/0.56 & ( ord_less_eq_int @ A @ X3 )
% 0.30/0.56 & ! [Xa: int] :
% 0.30/0.56 ( ( member_int @ Xa @ A4 )
% 0.30/0.56 => ( ( ord_less_eq_int @ X3 @ Xa )
% 0.30/0.56 => ( X3 = Xa ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % finite_has_maximal2
% 0.30/0.56 thf(fact_2256_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,Y: $o] :
% 0.30/0.56 ( ( ( vEBT_VEBT_minNull @ X )
% 0.30/0.56 = Y )
% 0.30/0.56 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.30/0.56 => ( ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ $false @ $false ) )
% 0.30/0.56 => ( Y
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 0.30/0.56 => ( ! [Uv2: $o] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.30/0.56 => ( ~ Y
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 0.30/0.56 => ( ! [Uu2: $o] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.30/0.56 => ( ~ Y
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 0.30/0.56 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.30/0.56 => ( Y
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) )
% 0.30/0.56 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 0.30/0.56 => ( ~ Y
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.pelims(1)
% 0.30/0.56 thf(fact_2257_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT] :
% 0.30/0.56 ( ( vEBT_VEBT_minNull @ X )
% 0.30/0.56 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.30/0.56 => ( ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ $false @ $false ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 0.30/0.56 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.pelims(2)
% 0.30/0.56 thf(fact_2258_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT] :
% 0.30/0.56 ( ~ ( vEBT_VEBT_minNull @ X )
% 0.30/0.56 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 0.30/0.56 => ( ! [Uv2: $o] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 0.30/0.56 => ( ! [Uu2: $o] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 0.30/0.56 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.30/0.56 ( ( X
% 0.30/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 0.30/0.56 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % VEBT_internal.minNull.pelims(3)
% 0.30/0.56 thf(fact_2259_nth__enumerate__eq,axiom,
% 0.30/0.56 ! [M2: nat,Xs2: list_VEBT_VEBT,N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ M2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs2 ) @ M2 )
% 0.30/0.56 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N @ M2 ) @ ( nth_VEBT_VEBT @ Xs2 @ M2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_enumerate_eq
% 0.30/0.56 thf(fact_2260_nth__enumerate__eq,axiom,
% 0.30/0.56 ! [M2: nat,Xs2: list_o,N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ M2 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N @ Xs2 ) @ M2 )
% 0.30/0.56 = ( product_Pair_nat_o @ ( plus_plus_nat @ N @ M2 ) @ ( nth_o @ Xs2 @ M2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_enumerate_eq
% 0.30/0.56 thf(fact_2261_nth__enumerate__eq,axiom,
% 0.30/0.56 ! [M2: nat,Xs2: list_nat,N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ M2 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs2 ) @ M2 )
% 0.30/0.56 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M2 ) @ ( nth_nat @ Xs2 @ M2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_enumerate_eq
% 0.30/0.56 thf(fact_2262_nth__enumerate__eq,axiom,
% 0.30/0.56 ! [M2: nat,Xs2: list_int,N: nat] :
% 0.30/0.56 ( ( ord_less_nat @ M2 @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs2 ) @ M2 )
% 0.30/0.56 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M2 ) @ ( nth_int @ Xs2 @ M2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_enumerate_eq
% 0.30/0.56 thf(fact_2263_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_complex,Y: complex,F2: complex > rat] :
% 0.30/0.56 ( ( finite3207457112153483333omplex @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_complex )
% 0.30/0.56 => ( ( member_complex @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_rat @ ( F2 @ ( lattic4729654577720512673ex_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2264_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_nat,Y: nat,F2: nat > rat] :
% 0.30/0.56 ( ( finite_finite_nat @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_nat )
% 0.30/0.56 => ( ( member_nat @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_rat @ ( F2 @ ( lattic6811802900495863747at_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2265_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_int,Y: int,F2: int > rat] :
% 0.30/0.56 ( ( finite_finite_int @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_int )
% 0.30/0.56 => ( ( member_int @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_rat @ ( F2 @ ( lattic7811156612396918303nt_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2266_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_real,Y: real,F2: real > rat] :
% 0.30/0.56 ( ( finite_finite_real @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_real )
% 0.30/0.56 => ( ( member_real @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_rat @ ( F2 @ ( lattic4420706379359479199al_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2267_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_complex,Y: complex,F2: complex > num] :
% 0.30/0.56 ( ( finite3207457112153483333omplex @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_complex )
% 0.30/0.56 => ( ( member_complex @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_num @ ( F2 @ ( lattic1922116423962787043ex_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2268_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_nat,Y: nat,F2: nat > num] :
% 0.30/0.56 ( ( finite_finite_nat @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_nat )
% 0.30/0.56 => ( ( member_nat @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_num @ ( F2 @ ( lattic4004264746738138117at_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2269_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_int,Y: int,F2: int > num] :
% 0.30/0.56 ( ( finite_finite_int @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_int )
% 0.30/0.56 => ( ( member_int @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_num @ ( F2 @ ( lattic5003618458639192673nt_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2270_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_real,Y: real,F2: real > num] :
% 0.30/0.56 ( ( finite_finite_real @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_real )
% 0.30/0.56 => ( ( member_real @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_num @ ( F2 @ ( lattic1613168225601753569al_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2271_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_complex,Y: complex,F2: complex > nat] :
% 0.30/0.56 ( ( finite3207457112153483333omplex @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_complex )
% 0.30/0.56 => ( ( member_complex @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_nat @ ( F2 @ ( lattic5364784637807008409ex_nat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2272_arg__min__least,axiom,
% 0.30/0.56 ! [S3: set_nat,Y: nat,F2: nat > nat] :
% 0.30/0.56 ( ( finite_finite_nat @ S3 )
% 0.30/0.56 => ( ( S3 != bot_bot_set_nat )
% 0.30/0.56 => ( ( member_nat @ Y @ S3 )
% 0.30/0.56 => ( ord_less_eq_nat @ ( F2 @ ( lattic7446932960582359483at_nat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % arg_min_least
% 0.30/0.56 thf(fact_2273_Euclid__induct,axiom,
% 0.30/0.56 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 0.30/0.56 ( ! [A3: nat,B3: nat] :
% 0.30/0.56 ( ( P2 @ A3 @ B3 )
% 0.30/0.56 = ( P2 @ B3 @ A3 ) )
% 0.30/0.56 => ( ! [A3: nat] : ( P2 @ A3 @ zero_zero_nat )
% 0.30/0.56 => ( ! [A3: nat,B3: nat] :
% 0.30/0.56 ( ( P2 @ A3 @ B3 )
% 0.30/0.56 => ( P2 @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 0.30/0.56 => ( P2 @ A @ B ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Euclid_induct
% 0.30/0.56 thf(fact_2274_nat__descend__induct,axiom,
% 0.30/0.56 ! [N: nat,P2: nat > $o,M2: nat] :
% 0.30/0.56 ( ! [K: nat] :
% 0.30/0.56 ( ( ord_less_nat @ N @ K )
% 0.30/0.56 => ( P2 @ K ) )
% 0.30/0.56 => ( ! [K: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ K @ N )
% 0.30/0.56 => ( ! [I4: nat] :
% 0.30/0.56 ( ( ord_less_nat @ K @ I4 )
% 0.30/0.56 => ( P2 @ I4 ) )
% 0.30/0.56 => ( P2 @ K ) ) )
% 0.30/0.56 => ( P2 @ M2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nat_descend_induct
% 0.30/0.56 thf(fact_2275_length__mul__elem,axiom,
% 0.30/0.56 ! [Xs2: list_list_VEBT_VEBT,N: nat] :
% 0.30/0.56 ( ! [X3: list_VEBT_VEBT] :
% 0.30/0.56 ( ( member2936631157270082147T_VEBT @ X3 @ ( set_list_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 => ( ( size_s6755466524823107622T_VEBT @ X3 )
% 0.30/0.56 = N ) )
% 0.30/0.56 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs2 ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs2 ) @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_mul_elem
% 0.30/0.56 thf(fact_2276_length__mul__elem,axiom,
% 0.30/0.56 ! [Xs2: list_list_o,N: nat] :
% 0.30/0.56 ( ! [X3: list_o] :
% 0.30/0.56 ( ( member_list_o @ X3 @ ( set_list_o2 @ Xs2 ) )
% 0.30/0.56 => ( ( size_size_list_o @ X3 )
% 0.30/0.56 = N ) )
% 0.30/0.56 => ( ( size_size_list_o @ ( concat_o @ Xs2 ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs2 ) @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_mul_elem
% 0.30/0.56 thf(fact_2277_length__mul__elem,axiom,
% 0.30/0.56 ! [Xs2: list_list_nat,N: nat] :
% 0.30/0.56 ( ! [X3: list_nat] :
% 0.30/0.56 ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xs2 ) )
% 0.30/0.56 => ( ( size_size_list_nat @ X3 )
% 0.30/0.56 = N ) )
% 0.30/0.56 => ( ( size_size_list_nat @ ( concat_nat @ Xs2 ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs2 ) @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_mul_elem
% 0.30/0.56 thf(fact_2278_length__mul__elem,axiom,
% 0.30/0.56 ! [Xs2: list_list_int,N: nat] :
% 0.30/0.56 ( ! [X3: list_int] :
% 0.30/0.56 ( ( member_list_int @ X3 @ ( set_list_int2 @ Xs2 ) )
% 0.30/0.56 => ( ( size_size_list_int @ X3 )
% 0.30/0.56 = N ) )
% 0.30/0.56 => ( ( size_size_list_int @ ( concat_int @ Xs2 ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs2 ) @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_mul_elem
% 0.30/0.56 thf(fact_2279_triangle__Suc,axiom,
% 0.30/0.56 ! [N: nat] :
% 0.30/0.56 ( ( nat_triangle @ ( suc @ N ) )
% 0.30/0.56 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % triangle_Suc
% 0.30/0.56 thf(fact_2280_length__enumerate,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( size_s4762443039079500285T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs2 ) )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_enumerate
% 0.30/0.56 thf(fact_2281_length__enumerate,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_o] :
% 0.30/0.56 ( ( size_s6491369823275344609_nat_o @ ( enumerate_o @ N @ Xs2 ) )
% 0.30/0.56 = ( size_size_list_o @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_enumerate
% 0.30/0.56 thf(fact_2282_length__enumerate,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( size_s5460976970255530739at_nat @ ( enumerate_nat @ N @ Xs2 ) )
% 0.30/0.56 = ( size_size_list_nat @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_enumerate
% 0.30/0.56 thf(fact_2283_length__enumerate,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_int] :
% 0.30/0.56 ( ( size_s2970893825323803983at_int @ ( enumerate_int @ N @ Xs2 ) )
% 0.30/0.56 = ( size_size_list_int @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_enumerate
% 0.30/0.56 thf(fact_2284_triangle__0,axiom,
% 0.30/0.56 ( ( nat_triangle @ zero_zero_nat )
% 0.30/0.56 = zero_zero_nat ) ).
% 0.30/0.56
% 0.30/0.56 % triangle_0
% 0.30/0.56 thf(fact_2285_diff__commute,axiom,
% 0.30/0.56 ! [I2: nat,J2: nat,K2: nat] :
% 0.30/0.56 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 0.30/0.56 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % diff_commute
% 0.30/0.56 thf(fact_2286_prod__decode__aux_Oelims,axiom,
% 0.30/0.56 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 0.30/0.56 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.30/0.56 = Y )
% 0.30/0.56 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.30/0.56 => ( Y
% 0.30/0.56 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.30/0.56 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.30/0.56 => ( Y
% 0.30/0.56 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % prod_decode_aux.elims
% 0.30/0.56 thf(fact_2287_prod__decode__aux_Osimps,axiom,
% 0.30/0.56 ( nat_prod_decode_aux
% 0.30/0.56 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % prod_decode_aux.simps
% 0.30/0.56 thf(fact_2288_prod__encode__prod__decode__aux,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat] :
% 0.30/0.56 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K2 @ M2 ) )
% 0.30/0.56 = ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % prod_encode_prod_decode_aux
% 0.30/0.56 thf(fact_2289_prod__decode__triangle__add,axiom,
% 0.30/0.56 ! [K2: nat,M2: nat] :
% 0.30/0.56 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M2 ) )
% 0.30/0.56 = ( nat_prod_decode_aux @ K2 @ M2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % prod_decode_triangle_add
% 0.30/0.56 thf(fact_2290_in__set__product__lists__length,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Xss: list_list_VEBT_VEBT] :
% 0.30/0.56 ( ( member2936631157270082147T_VEBT @ Xs2 @ ( set_list_VEBT_VEBT2 @ ( produc3021084454716106787T_VEBT @ Xss ) ) )
% 0.30/0.56 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_s8217280938318005548T_VEBT @ Xss ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_product_lists_length
% 0.30/0.56 thf(fact_2291_in__set__product__lists__length,axiom,
% 0.30/0.56 ! [Xs2: list_o,Xss: list_list_o] :
% 0.30/0.56 ( ( member_list_o @ Xs2 @ ( set_list_o2 @ ( product_lists_o @ Xss ) ) )
% 0.30/0.56 => ( ( size_size_list_o @ Xs2 )
% 0.30/0.56 = ( size_s2710708370519433104list_o @ Xss ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_product_lists_length
% 0.30/0.56 thf(fact_2292_in__set__product__lists__length,axiom,
% 0.30/0.56 ! [Xs2: list_nat,Xss: list_list_nat] :
% 0.30/0.56 ( ( member_list_nat @ Xs2 @ ( set_list_nat2 @ ( product_lists_nat @ Xss ) ) )
% 0.30/0.56 => ( ( size_size_list_nat @ Xs2 )
% 0.30/0.56 = ( size_s3023201423986296836st_nat @ Xss ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_product_lists_length
% 0.30/0.56 thf(fact_2293_in__set__product__lists__length,axiom,
% 0.30/0.56 ! [Xs2: list_int,Xss: list_list_int] :
% 0.30/0.56 ( ( member_list_int @ Xs2 @ ( set_list_int2 @ ( product_lists_int @ Xss ) ) )
% 0.30/0.56 => ( ( size_size_list_int @ Xs2 )
% 0.30/0.56 = ( size_s533118279054570080st_int @ Xss ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_product_lists_length
% 0.30/0.56 thf(fact_2294_Gcd__remove0__nat,axiom,
% 0.30/0.56 ! [M5: set_nat] :
% 0.30/0.56 ( ( finite_finite_nat @ M5 )
% 0.30/0.56 => ( ( gcd_Gcd_nat @ M5 )
% 0.30/0.56 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Gcd_remove0_nat
% 0.30/0.56 thf(fact_2295_inf__period_I2_J,axiom,
% 0.30/0.56 ! [P2: real > $o,D3: real,Q: real > $o] :
% 0.30/0.56 ( ! [X3: real,K: real] :
% 0.30/0.56 ( ( P2 @ X3 )
% 0.30/0.56 = ( P2 @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 0.30/0.56 => ( ! [X3: real,K: real] :
% 0.30/0.56 ( ( Q @ X3 )
% 0.30/0.56 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 0.30/0.56 => ! [X5: real,K4: real] :
% 0.30/0.56 ( ( ( P2 @ X5 )
% 0.30/0.56 | ( Q @ X5 ) )
% 0.30/0.56 = ( ( P2 @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 0.30/0.56 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inf_period(2)
% 0.30/0.56 thf(fact_2296_inf__period_I2_J,axiom,
% 0.30/0.56 ! [P2: rat > $o,D3: rat,Q: rat > $o] :
% 0.30/0.56 ( ! [X3: rat,K: rat] :
% 0.30/0.56 ( ( P2 @ X3 )
% 0.30/0.56 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 0.30/0.56 => ( ! [X3: rat,K: rat] :
% 0.30/0.56 ( ( Q @ X3 )
% 0.30/0.56 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 0.30/0.56 => ! [X5: rat,K4: rat] :
% 0.30/0.56 ( ( ( P2 @ X5 )
% 0.30/0.56 | ( Q @ X5 ) )
% 0.30/0.56 = ( ( P2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 0.30/0.56 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inf_period(2)
% 0.30/0.56 thf(fact_2297_inf__period_I2_J,axiom,
% 0.30/0.56 ! [P2: int > $o,D3: int,Q: int > $o] :
% 0.30/0.56 ( ! [X3: int,K: int] :
% 0.30/0.56 ( ( P2 @ X3 )
% 0.30/0.56 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 0.30/0.56 => ( ! [X3: int,K: int] :
% 0.30/0.56 ( ( Q @ X3 )
% 0.30/0.56 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 0.30/0.56 => ! [X5: int,K4: int] :
% 0.30/0.56 ( ( ( P2 @ X5 )
% 0.30/0.56 | ( Q @ X5 ) )
% 0.30/0.56 = ( ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 0.30/0.56 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inf_period(2)
% 0.30/0.56 thf(fact_2298_inf__period_I1_J,axiom,
% 0.30/0.56 ! [P2: real > $o,D3: real,Q: real > $o] :
% 0.30/0.56 ( ! [X3: real,K: real] :
% 0.30/0.56 ( ( P2 @ X3 )
% 0.30/0.56 = ( P2 @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 0.30/0.56 => ( ! [X3: real,K: real] :
% 0.30/0.56 ( ( Q @ X3 )
% 0.30/0.56 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 0.30/0.56 => ! [X5: real,K4: real] :
% 0.30/0.56 ( ( ( P2 @ X5 )
% 0.30/0.56 & ( Q @ X5 ) )
% 0.30/0.56 = ( ( P2 @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 0.30/0.56 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inf_period(1)
% 0.30/0.56 thf(fact_2299_inf__period_I1_J,axiom,
% 0.30/0.56 ! [P2: rat > $o,D3: rat,Q: rat > $o] :
% 0.30/0.56 ( ! [X3: rat,K: rat] :
% 0.30/0.56 ( ( P2 @ X3 )
% 0.30/0.56 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 0.30/0.56 => ( ! [X3: rat,K: rat] :
% 0.30/0.56 ( ( Q @ X3 )
% 0.30/0.56 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 0.30/0.56 => ! [X5: rat,K4: rat] :
% 0.30/0.56 ( ( ( P2 @ X5 )
% 0.30/0.56 & ( Q @ X5 ) )
% 0.30/0.56 = ( ( P2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 0.30/0.56 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inf_period(1)
% 0.30/0.56 thf(fact_2300_inf__period_I1_J,axiom,
% 0.30/0.56 ! [P2: int > $o,D3: int,Q: int > $o] :
% 0.30/0.56 ( ! [X3: int,K: int] :
% 0.30/0.56 ( ( P2 @ X3 )
% 0.30/0.56 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 0.30/0.56 => ( ! [X3: int,K: int] :
% 0.30/0.56 ( ( Q @ X3 )
% 0.30/0.56 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 0.30/0.56 => ! [X5: int,K4: int] :
% 0.30/0.56 ( ( ( P2 @ X5 )
% 0.30/0.56 & ( Q @ X5 ) )
% 0.30/0.56 = ( ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 0.30/0.56 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % inf_period(1)
% 0.30/0.56 thf(fact_2301_verit__sum__simplify,axiom,
% 0.30/0.56 ! [A: complex] :
% 0.30/0.56 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 0.30/0.56 = A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_sum_simplify
% 0.30/0.56 thf(fact_2302_verit__sum__simplify,axiom,
% 0.30/0.56 ! [A: real] :
% 0.30/0.56 ( ( plus_plus_real @ A @ zero_zero_real )
% 0.30/0.56 = A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_sum_simplify
% 0.30/0.56 thf(fact_2303_verit__sum__simplify,axiom,
% 0.30/0.56 ! [A: rat] :
% 0.30/0.56 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 0.30/0.56 = A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_sum_simplify
% 0.30/0.56 thf(fact_2304_verit__sum__simplify,axiom,
% 0.30/0.56 ! [A: nat] :
% 0.30/0.56 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 0.30/0.56 = A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_sum_simplify
% 0.30/0.56 thf(fact_2305_verit__sum__simplify,axiom,
% 0.30/0.56 ! [A: int] :
% 0.30/0.56 ( ( plus_plus_int @ A @ zero_zero_int )
% 0.30/0.56 = A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_sum_simplify
% 0.30/0.56 thf(fact_2306_Gcd__empty,axiom,
% 0.30/0.56 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 0.30/0.56 = zero_zero_nat ) ).
% 0.30/0.56
% 0.30/0.56 % Gcd_empty
% 0.30/0.56 thf(fact_2307_Gcd__empty,axiom,
% 0.30/0.56 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 0.30/0.56 = zero_zero_int ) ).
% 0.30/0.56
% 0.30/0.56 % Gcd_empty
% 0.30/0.56 thf(fact_2308_Gcd__0__iff,axiom,
% 0.30/0.56 ! [A4: set_int] :
% 0.30/0.56 ( ( ( gcd_Gcd_int @ A4 )
% 0.30/0.56 = zero_zero_int )
% 0.30/0.56 = ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Gcd_0_iff
% 0.30/0.56 thf(fact_2309_Gcd__0__iff,axiom,
% 0.30/0.56 ! [A4: set_nat] :
% 0.30/0.56 ( ( ( gcd_Gcd_nat @ A4 )
% 0.30/0.56 = zero_zero_nat )
% 0.30/0.56 = ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Gcd_0_iff
% 0.30/0.56 thf(fact_2310_verit__la__disequality,axiom,
% 0.30/0.56 ! [A: rat,B: rat] :
% 0.30/0.56 ( ( A = B )
% 0.30/0.56 | ~ ( ord_less_eq_rat @ A @ B )
% 0.30/0.56 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_la_disequality
% 0.30/0.56 thf(fact_2311_verit__la__disequality,axiom,
% 0.30/0.56 ! [A: num,B: num] :
% 0.30/0.56 ( ( A = B )
% 0.30/0.56 | ~ ( ord_less_eq_num @ A @ B )
% 0.30/0.56 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_la_disequality
% 0.30/0.56 thf(fact_2312_verit__la__disequality,axiom,
% 0.30/0.56 ! [A: nat,B: nat] :
% 0.30/0.56 ( ( A = B )
% 0.30/0.56 | ~ ( ord_less_eq_nat @ A @ B )
% 0.30/0.56 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_la_disequality
% 0.30/0.56 thf(fact_2313_verit__la__disequality,axiom,
% 0.30/0.56 ! [A: int,B: int] :
% 0.30/0.56 ( ( A = B )
% 0.30/0.56 | ~ ( ord_less_eq_int @ A @ B )
% 0.30/0.56 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_la_disequality
% 0.30/0.56 thf(fact_2314_verit__comp__simplify1_I2_J,axiom,
% 0.30/0.56 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(2)
% 0.30/0.56 thf(fact_2315_verit__comp__simplify1_I2_J,axiom,
% 0.30/0.56 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(2)
% 0.30/0.56 thf(fact_2316_verit__comp__simplify1_I2_J,axiom,
% 0.30/0.56 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(2)
% 0.30/0.56 thf(fact_2317_verit__comp__simplify1_I2_J,axiom,
% 0.30/0.56 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(2)
% 0.30/0.56 thf(fact_2318_verit__comp__simplify1_I2_J,axiom,
% 0.30/0.56 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(2)
% 0.30/0.56 thf(fact_2319_prod__decode__def,axiom,
% 0.30/0.56 ( nat_prod_decode
% 0.30/0.56 = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 0.30/0.56
% 0.30/0.56 % prod_decode_def
% 0.30/0.56 thf(fact_2320_verit__comp__simplify1_I3_J,axiom,
% 0.30/0.56 ! [B2: real,A2: real] :
% 0.30/0.56 ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 0.30/0.56 = ( ord_less_real @ A2 @ B2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(3)
% 0.30/0.56 thf(fact_2321_verit__comp__simplify1_I3_J,axiom,
% 0.30/0.56 ! [B2: rat,A2: rat] :
% 0.30/0.56 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 0.30/0.56 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(3)
% 0.30/0.56 thf(fact_2322_verit__comp__simplify1_I3_J,axiom,
% 0.30/0.56 ! [B2: num,A2: num] :
% 0.30/0.56 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 0.30/0.56 = ( ord_less_num @ A2 @ B2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(3)
% 0.30/0.56 thf(fact_2323_verit__comp__simplify1_I3_J,axiom,
% 0.30/0.56 ! [B2: nat,A2: nat] :
% 0.30/0.56 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 0.30/0.56 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(3)
% 0.30/0.56 thf(fact_2324_verit__comp__simplify1_I3_J,axiom,
% 0.30/0.56 ! [B2: int,A2: int] :
% 0.30/0.56 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 0.30/0.56 = ( ord_less_int @ A2 @ B2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % verit_comp_simplify1(3)
% 0.30/0.56 thf(fact_2325_pinf_I6_J,axiom,
% 0.30/0.56 ! [T: real] :
% 0.30/0.56 ? [Z: real] :
% 0.30/0.56 ! [X5: real] :
% 0.30/0.56 ( ( ord_less_real @ Z @ X5 )
% 0.30/0.56 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(6)
% 0.30/0.56 thf(fact_2326_pinf_I6_J,axiom,
% 0.30/0.56 ! [T: rat] :
% 0.30/0.56 ? [Z: rat] :
% 0.30/0.56 ! [X5: rat] :
% 0.30/0.56 ( ( ord_less_rat @ Z @ X5 )
% 0.30/0.56 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(6)
% 0.30/0.56 thf(fact_2327_pinf_I6_J,axiom,
% 0.30/0.56 ! [T: num] :
% 0.30/0.56 ? [Z: num] :
% 0.30/0.56 ! [X5: num] :
% 0.30/0.56 ( ( ord_less_num @ Z @ X5 )
% 0.30/0.56 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(6)
% 0.30/0.56 thf(fact_2328_pinf_I6_J,axiom,
% 0.30/0.56 ! [T: nat] :
% 0.30/0.56 ? [Z: nat] :
% 0.30/0.56 ! [X5: nat] :
% 0.30/0.56 ( ( ord_less_nat @ Z @ X5 )
% 0.30/0.56 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(6)
% 0.30/0.56 thf(fact_2329_pinf_I6_J,axiom,
% 0.30/0.56 ! [T: int] :
% 0.30/0.56 ? [Z: int] :
% 0.30/0.56 ! [X5: int] :
% 0.30/0.56 ( ( ord_less_int @ Z @ X5 )
% 0.30/0.56 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(6)
% 0.30/0.56 thf(fact_2330_pinf_I8_J,axiom,
% 0.30/0.56 ! [T: real] :
% 0.30/0.56 ? [Z: real] :
% 0.30/0.56 ! [X5: real] :
% 0.30/0.56 ( ( ord_less_real @ Z @ X5 )
% 0.30/0.56 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(8)
% 0.30/0.56 thf(fact_2331_pinf_I8_J,axiom,
% 0.30/0.56 ! [T: rat] :
% 0.30/0.56 ? [Z: rat] :
% 0.30/0.56 ! [X5: rat] :
% 0.30/0.56 ( ( ord_less_rat @ Z @ X5 )
% 0.30/0.56 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(8)
% 0.30/0.56 thf(fact_2332_pinf_I8_J,axiom,
% 0.30/0.56 ! [T: num] :
% 0.30/0.56 ? [Z: num] :
% 0.30/0.56 ! [X5: num] :
% 0.30/0.56 ( ( ord_less_num @ Z @ X5 )
% 0.30/0.56 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(8)
% 0.30/0.56 thf(fact_2333_pinf_I8_J,axiom,
% 0.30/0.56 ! [T: nat] :
% 0.30/0.56 ? [Z: nat] :
% 0.30/0.56 ! [X5: nat] :
% 0.30/0.56 ( ( ord_less_nat @ Z @ X5 )
% 0.30/0.56 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(8)
% 0.30/0.56 thf(fact_2334_pinf_I8_J,axiom,
% 0.30/0.56 ! [T: int] :
% 0.30/0.56 ? [Z: int] :
% 0.30/0.56 ! [X5: int] :
% 0.30/0.56 ( ( ord_less_int @ Z @ X5 )
% 0.30/0.56 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % pinf(8)
% 0.30/0.56 thf(fact_2335_minf_I6_J,axiom,
% 0.30/0.56 ! [T: real] :
% 0.30/0.56 ? [Z: real] :
% 0.30/0.56 ! [X5: real] :
% 0.30/0.56 ( ( ord_less_real @ X5 @ Z )
% 0.30/0.56 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(6)
% 0.30/0.56 thf(fact_2336_minf_I6_J,axiom,
% 0.30/0.56 ! [T: rat] :
% 0.30/0.56 ? [Z: rat] :
% 0.30/0.56 ! [X5: rat] :
% 0.30/0.56 ( ( ord_less_rat @ X5 @ Z )
% 0.30/0.56 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(6)
% 0.30/0.56 thf(fact_2337_minf_I6_J,axiom,
% 0.30/0.56 ! [T: num] :
% 0.30/0.56 ? [Z: num] :
% 0.30/0.56 ! [X5: num] :
% 0.30/0.56 ( ( ord_less_num @ X5 @ Z )
% 0.30/0.56 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(6)
% 0.30/0.56 thf(fact_2338_minf_I6_J,axiom,
% 0.30/0.56 ! [T: nat] :
% 0.30/0.56 ? [Z: nat] :
% 0.30/0.56 ! [X5: nat] :
% 0.30/0.56 ( ( ord_less_nat @ X5 @ Z )
% 0.30/0.56 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(6)
% 0.30/0.56 thf(fact_2339_minf_I6_J,axiom,
% 0.30/0.56 ! [T: int] :
% 0.30/0.56 ? [Z: int] :
% 0.30/0.56 ! [X5: int] :
% 0.30/0.56 ( ( ord_less_int @ X5 @ Z )
% 0.30/0.56 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(6)
% 0.30/0.56 thf(fact_2340_minf_I8_J,axiom,
% 0.30/0.56 ! [T: real] :
% 0.30/0.56 ? [Z: real] :
% 0.30/0.56 ! [X5: real] :
% 0.30/0.56 ( ( ord_less_real @ X5 @ Z )
% 0.30/0.56 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(8)
% 0.30/0.56 thf(fact_2341_minf_I8_J,axiom,
% 0.30/0.56 ! [T: rat] :
% 0.30/0.56 ? [Z: rat] :
% 0.30/0.56 ! [X5: rat] :
% 0.30/0.56 ( ( ord_less_rat @ X5 @ Z )
% 0.30/0.56 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(8)
% 0.30/0.56 thf(fact_2342_minf_I8_J,axiom,
% 0.30/0.56 ! [T: num] :
% 0.30/0.56 ? [Z: num] :
% 0.30/0.56 ! [X5: num] :
% 0.30/0.56 ( ( ord_less_num @ X5 @ Z )
% 0.30/0.56 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(8)
% 0.30/0.56 thf(fact_2343_minf_I8_J,axiom,
% 0.30/0.56 ! [T: nat] :
% 0.30/0.56 ? [Z: nat] :
% 0.30/0.56 ! [X5: nat] :
% 0.30/0.56 ( ( ord_less_nat @ X5 @ Z )
% 0.30/0.56 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(8)
% 0.30/0.56 thf(fact_2344_minf_I8_J,axiom,
% 0.30/0.56 ! [T: int] :
% 0.30/0.56 ? [Z: int] :
% 0.30/0.56 ! [X5: int] :
% 0.30/0.56 ( ( ord_less_int @ X5 @ Z )
% 0.30/0.56 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 0.30/0.56
% 0.30/0.56 % minf(8)
% 0.30/0.56 thf(fact_2345_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2346_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 0.30/0.56 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2347_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 0.30/0.56 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2348_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 0.30/0.56 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2349_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2350_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_o] :
% 0.30/0.56 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2351_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_nat] :
% 0.30/0.56 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2352_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_int] :
% 0.30/0.56 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2353_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2354_length__product,axiom,
% 0.30/0.56 ! [Xs2: list_nat,Ys: list_o] :
% 0.30/0.56 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 0.30/0.56 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_product
% 0.30/0.56 thf(fact_2355_complete__interval,axiom,
% 0.30/0.56 ! [A: real,B: real,P2: real > $o] :
% 0.30/0.56 ( ( ord_less_real @ A @ B )
% 0.30/0.56 => ( ( P2 @ A )
% 0.30/0.56 => ( ~ ( P2 @ B )
% 0.30/0.56 => ? [C: real] :
% 0.30/0.56 ( ( ord_less_eq_real @ A @ C )
% 0.30/0.56 & ( ord_less_eq_real @ C @ B )
% 0.30/0.56 & ! [X5: real] :
% 0.30/0.56 ( ( ( ord_less_eq_real @ A @ X5 )
% 0.30/0.56 & ( ord_less_real @ X5 @ C ) )
% 0.30/0.56 => ( P2 @ X5 ) )
% 0.30/0.56 & ! [D4: real] :
% 0.30/0.56 ( ! [X3: real] :
% 0.30/0.56 ( ( ( ord_less_eq_real @ A @ X3 )
% 0.30/0.56 & ( ord_less_real @ X3 @ D4 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ord_less_eq_real @ D4 @ C ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % complete_interval
% 0.30/0.56 thf(fact_2356_complete__interval,axiom,
% 0.30/0.56 ! [A: nat,B: nat,P2: nat > $o] :
% 0.30/0.56 ( ( ord_less_nat @ A @ B )
% 0.30/0.56 => ( ( P2 @ A )
% 0.30/0.56 => ( ~ ( P2 @ B )
% 0.30/0.56 => ? [C: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ A @ C )
% 0.30/0.56 & ( ord_less_eq_nat @ C @ B )
% 0.30/0.56 & ! [X5: nat] :
% 0.30/0.56 ( ( ( ord_less_eq_nat @ A @ X5 )
% 0.30/0.56 & ( ord_less_nat @ X5 @ C ) )
% 0.30/0.56 => ( P2 @ X5 ) )
% 0.30/0.56 & ! [D4: nat] :
% 0.30/0.56 ( ! [X3: nat] :
% 0.30/0.56 ( ( ( ord_less_eq_nat @ A @ X3 )
% 0.30/0.56 & ( ord_less_nat @ X3 @ D4 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ord_less_eq_nat @ D4 @ C ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % complete_interval
% 0.30/0.56 thf(fact_2357_complete__interval,axiom,
% 0.30/0.56 ! [A: int,B: int,P2: int > $o] :
% 0.30/0.56 ( ( ord_less_int @ A @ B )
% 0.30/0.56 => ( ( P2 @ A )
% 0.30/0.56 => ( ~ ( P2 @ B )
% 0.30/0.56 => ? [C: int] :
% 0.30/0.56 ( ( ord_less_eq_int @ A @ C )
% 0.30/0.56 & ( ord_less_eq_int @ C @ B )
% 0.30/0.56 & ! [X5: int] :
% 0.30/0.56 ( ( ( ord_less_eq_int @ A @ X5 )
% 0.30/0.56 & ( ord_less_int @ X5 @ C ) )
% 0.30/0.56 => ( P2 @ X5 ) )
% 0.30/0.56 & ! [D4: int] :
% 0.30/0.56 ( ! [X3: int] :
% 0.30/0.56 ( ( ( ord_less_eq_int @ A @ X3 )
% 0.30/0.56 & ( ord_less_int @ X3 @ D4 ) )
% 0.30/0.56 => ( P2 @ X3 ) )
% 0.30/0.56 => ( ord_less_eq_int @ D4 @ C ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % complete_interval
% 0.30/0.56 thf(fact_2358_vebt__insert_Osimps_I4_J,axiom,
% 0.30/0.56 ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.30/0.56 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary ) @ X )
% 0.30/0.56 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary ) ) ).
% 0.30/0.56
% 0.30/0.56 % vebt_insert.simps(4)
% 0.30/0.56 thf(fact_2359_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_s3445333598471063425nteger @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_s3445333598471063425nteger @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr2304437835452373666nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ I2 ) @ ( nth_Code_integer @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2360_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr4953567300277697838T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2361_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr4606735188037164562VEBT_o @ ( zip_VEBT_VEBT_o @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_o @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2362_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr1791586995822124652BT_nat @ ( zip_VEBT_VEBT_nat @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2363_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr6837108013167703752BT_int @ ( zip_VEBT_VEBT_int @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2364_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr6777367263587873994T_VEBT @ ( zip_o_VEBT_VEBT @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2365_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_o,Ys: list_o] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 0.30/0.56 => ( ( nth_Product_prod_o_o @ ( zip_o_o @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ I2 ) @ ( nth_o @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2366_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_o,Ys: list_nat] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr5826913651314560976_o_nat @ ( zip_o_nat @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2367_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_o,Ys: list_int] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr1649062631805364268_o_int @ ( zip_o_int @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2368_nth__zip,axiom,
% 0.30/0.56 ! [I2: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ( nth_Pr744662078594809490T_VEBT @ ( zip_nat_VEBT_VEBT @ Xs2 @ Ys ) @ I2 )
% 0.30/0.56 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_zip
% 0.30/0.56 thf(fact_2369_find__Some__iff2,axiom,
% 0.30/0.56 ! [X: product_prod_nat_nat,P2: product_prod_nat_nat > $o,Xs2: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( ( some_P7363390416028606310at_nat @ X )
% 0.30/0.56 = ( find_P8199882355184865565at_nat @ P2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff2
% 0.30/0.56 thf(fact_2370_find__Some__iff2,axiom,
% 0.30/0.56 ! [X: num,P2: num > $o,Xs2: list_num] :
% 0.30/0.56 ( ( ( some_num @ X )
% 0.30/0.56 = ( find_num @ P2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_num @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_num @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_num @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff2
% 0.30/0.56 thf(fact_2371_find__Some__iff2,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,P2: vEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ( some_VEBT_VEBT @ X )
% 0.30/0.56 = ( find_VEBT_VEBT @ P2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff2
% 0.30/0.56 thf(fact_2372_find__Some__iff2,axiom,
% 0.30/0.56 ! [X: $o,P2: $o > $o,Xs2: list_o] :
% 0.30/0.56 ( ( ( some_o @ X )
% 0.30/0.56 = ( find_o @ P2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_o @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_o @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_o @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff2
% 0.30/0.56 thf(fact_2373_find__Some__iff2,axiom,
% 0.30/0.56 ! [X: nat,P2: nat > $o,Xs2: list_nat] :
% 0.30/0.56 ( ( ( some_nat @ X )
% 0.30/0.56 = ( find_nat @ P2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_nat @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_nat @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff2
% 0.30/0.56 thf(fact_2374_find__Some__iff2,axiom,
% 0.30/0.56 ! [X: int,P2: int > $o,Xs2: list_int] :
% 0.30/0.56 ( ( ( some_int @ X )
% 0.30/0.56 = ( find_int @ P2 @ Xs2 ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_int @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_int @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_int @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff2
% 0.30/0.56 thf(fact_2375_find__Some__iff,axiom,
% 0.30/0.56 ! [P2: product_prod_nat_nat > $o,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 0.30/0.56 ( ( ( find_P8199882355184865565at_nat @ P2 @ Xs2 )
% 0.30/0.56 = ( some_P7363390416028606310at_nat @ X ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff
% 0.30/0.56 thf(fact_2376_find__Some__iff,axiom,
% 0.30/0.56 ! [P2: num > $o,Xs2: list_num,X: num] :
% 0.30/0.56 ( ( ( find_num @ P2 @ Xs2 )
% 0.30/0.56 = ( some_num @ X ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_num @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_num @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_num @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff
% 0.30/0.56 thf(fact_2377_find__Some__iff,axiom,
% 0.30/0.56 ! [P2: vEBT_VEBT > $o,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.30/0.56 ( ( ( find_VEBT_VEBT @ P2 @ Xs2 )
% 0.30/0.56 = ( some_VEBT_VEBT @ X ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff
% 0.30/0.56 thf(fact_2378_find__Some__iff,axiom,
% 0.30/0.56 ! [P2: $o > $o,Xs2: list_o,X: $o] :
% 0.30/0.56 ( ( ( find_o @ P2 @ Xs2 )
% 0.30/0.56 = ( some_o @ X ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_o @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_o @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_o @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff
% 0.30/0.56 thf(fact_2379_find__Some__iff,axiom,
% 0.30/0.56 ! [P2: nat > $o,Xs2: list_nat,X: nat] :
% 0.30/0.56 ( ( ( find_nat @ P2 @ Xs2 )
% 0.30/0.56 = ( some_nat @ X ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_nat @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_nat @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff
% 0.30/0.56 thf(fact_2380_find__Some__iff,axiom,
% 0.30/0.56 ! [P2: int > $o,Xs2: list_int,X: int] :
% 0.30/0.56 ( ( ( find_int @ P2 @ Xs2 )
% 0.30/0.56 = ( some_int @ X ) )
% 0.30/0.56 = ( ? [I: nat] :
% 0.30/0.56 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 & ( P2 @ ( nth_int @ Xs2 @ I ) )
% 0.30/0.56 & ( X
% 0.30/0.56 = ( nth_int @ Xs2 @ I ) )
% 0.30/0.56 & ! [J: nat] :
% 0.30/0.56 ( ( ord_less_nat @ J @ I )
% 0.30/0.56 => ~ ( P2 @ ( nth_int @ Xs2 @ J ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find_Some_iff
% 0.30/0.56 thf(fact_2381_nth__Cons__pos,axiom,
% 0.30/0.56 ! [N: nat,X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 0.30/0.56 = ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_Cons_pos
% 0.30/0.56 thf(fact_2382_nth__Cons__pos,axiom,
% 0.30/0.56 ! [N: nat,X: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.56 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 0.30/0.56 = ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_Cons_pos
% 0.30/0.56 thf(fact_2383_rotate1__length01,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ one_one_nat )
% 0.30/0.56 => ( ( rotate1_VEBT_VEBT @ Xs2 )
% 0.30/0.56 = Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % rotate1_length01
% 0.30/0.56 thf(fact_2384_rotate1__length01,axiom,
% 0.30/0.56 ! [Xs2: list_o] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ one_one_nat )
% 0.30/0.56 => ( ( rotate1_o @ Xs2 )
% 0.30/0.56 = Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % rotate1_length01
% 0.30/0.56 thf(fact_2385_rotate1__length01,axiom,
% 0.30/0.56 ! [Xs2: list_nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ one_one_nat )
% 0.30/0.56 => ( ( rotate1_nat @ Xs2 )
% 0.30/0.56 = Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % rotate1_length01
% 0.30/0.56 thf(fact_2386_rotate1__length01,axiom,
% 0.30/0.56 ! [Xs2: list_int] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ one_one_nat )
% 0.30/0.56 => ( ( rotate1_int @ Xs2 )
% 0.30/0.56 = Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % rotate1_length01
% 0.30/0.56 thf(fact_2387_length__rotate1,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( size_s6755466524823107622T_VEBT @ ( rotate1_VEBT_VEBT @ Xs2 ) )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_rotate1
% 0.30/0.56 thf(fact_2388_length__rotate1,axiom,
% 0.30/0.56 ! [Xs2: list_o] :
% 0.30/0.56 ( ( size_size_list_o @ ( rotate1_o @ Xs2 ) )
% 0.30/0.56 = ( size_size_list_o @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_rotate1
% 0.30/0.56 thf(fact_2389_length__rotate1,axiom,
% 0.30/0.56 ! [Xs2: list_nat] :
% 0.30/0.56 ( ( size_size_list_nat @ ( rotate1_nat @ Xs2 ) )
% 0.30/0.56 = ( size_size_list_nat @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_rotate1
% 0.30/0.56 thf(fact_2390_length__rotate1,axiom,
% 0.30/0.56 ! [Xs2: list_int] :
% 0.30/0.56 ( ( size_size_list_int @ ( rotate1_int @ Xs2 ) )
% 0.30/0.56 = ( size_size_list_int @ Xs2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_rotate1
% 0.30/0.56 thf(fact_2391_nth__Cons__Suc,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 0.30/0.56 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( suc @ N ) )
% 0.30/0.56 = ( nth_VEBT_VEBT @ Xs2 @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_Cons_Suc
% 0.30/0.56 thf(fact_2392_nth__Cons__Suc,axiom,
% 0.30/0.56 ! [X: nat,Xs2: list_nat,N: nat] :
% 0.30/0.56 ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ ( suc @ N ) )
% 0.30/0.56 = ( nth_nat @ Xs2 @ N ) ) ).
% 0.30/0.56
% 0.30/0.56 % nth_Cons_Suc
% 0.30/0.56 thf(fact_2393_nth__Cons__0,axiom,
% 0.30/0.56 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ zero_zero_nat )
% 0.30/0.56 = X ) ).
% 0.30/0.56
% 0.30/0.56 % nth_Cons_0
% 0.30/0.56 thf(fact_2394_nth__Cons__0,axiom,
% 0.30/0.56 ! [X: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ zero_zero_nat )
% 0.30/0.56 = X ) ).
% 0.30/0.56
% 0.30/0.56 % nth_Cons_0
% 0.30/0.56 thf(fact_2395_zip__Cons__Cons,axiom,
% 0.30/0.56 ! [X: code_integer,Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer] :
% 0.30/0.56 ( ( zip_Co3543743374963494515nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) )
% 0.30/0.56 = ( cons_P9044669534377732177nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_Cons_Cons
% 0.30/0.56 thf(fact_2396_zip__Cons__Cons,axiom,
% 0.30/0.56 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( zip_Pr4664179122662387191at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) )
% 0.30/0.56 = ( cons_P8732206157123786781at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_Cons_Cons
% 0.30/0.56 thf(fact_2397_zip__Cons__Cons,axiom,
% 0.30/0.56 ! [X: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat] :
% 0.30/0.56 ( ( zip_se5600341670672612855at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) )
% 0.30/0.56 = ( cons_P3940603068885512221at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_Cons_Cons
% 0.30/0.56 thf(fact_2398_zip__Cons__Cons,axiom,
% 0.30/0.56 ! [X: nat,Xs2: list_nat,Y: nat,Ys: list_nat] :
% 0.30/0.56 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) )
% 0.30/0.56 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_Cons_Cons
% 0.30/0.56 thf(fact_2399_zip__Cons__Cons,axiom,
% 0.30/0.56 ! [X: int,Xs2: list_int,Y: int,Ys: list_int] :
% 0.30/0.56 ( ( zip_int_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) )
% 0.30/0.56 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_Cons_Cons
% 0.30/0.56 thf(fact_2400_enumerate__simps_I2_J,axiom,
% 0.30/0.56 ! [N: nat,X: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( enumerate_nat @ N @ ( cons_nat @ X @ Xs2 ) )
% 0.30/0.56 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ N @ X ) @ ( enumerate_nat @ ( suc @ N ) @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % enumerate_simps(2)
% 0.30/0.56 thf(fact_2401_zip__eq__ConsE,axiom,
% 0.30/0.56 ! [Xs2: list_Code_integer,Ys: list_Code_integer,Xy: produc8923325533196201883nteger,Xys: list_P5578671422887162913nteger] :
% 0.30/0.56 ( ( ( zip_Co3543743374963494515nteger @ Xs2 @ Ys )
% 0.30/0.56 = ( cons_P9044669534377732177nteger @ Xy @ Xys ) )
% 0.30/0.56 => ~ ! [X3: code_integer,Xs4: list_Code_integer] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_Code_integer @ X3 @ Xs4 ) )
% 0.30/0.56 => ! [Y3: code_integer,Ys4: list_Code_integer] :
% 0.30/0.56 ( ( Ys
% 0.30/0.56 = ( cons_Code_integer @ Y3 @ Ys4 ) )
% 0.30/0.56 => ( ( Xy
% 0.30/0.56 = ( produc1086072967326762835nteger @ X3 @ Y3 ) )
% 0.30/0.56 => ( Xys
% 0.30/0.56 != ( zip_Co3543743374963494515nteger @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_eq_ConsE
% 0.30/0.56 thf(fact_2402_zip__eq__ConsE,axiom,
% 0.30/0.56 ! [Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat,Xy: produc859450856879609959at_nat,Xys: list_P8469869581646625389at_nat] :
% 0.30/0.56 ( ( ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys )
% 0.30/0.56 = ( cons_P8732206157123786781at_nat @ Xy @ Xys ) )
% 0.30/0.56 => ~ ! [X3: product_prod_nat_nat,Xs4: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_P6512896166579812791at_nat @ X3 @ Xs4 ) )
% 0.30/0.56 => ! [Y3: product_prod_nat_nat,Ys4: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( Ys
% 0.30/0.56 = ( cons_P6512896166579812791at_nat @ Y3 @ Ys4 ) )
% 0.30/0.56 => ( ( Xy
% 0.30/0.56 = ( produc6161850002892822231at_nat @ X3 @ Y3 ) )
% 0.30/0.56 => ( Xys
% 0.30/0.56 != ( zip_Pr4664179122662387191at_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_eq_ConsE
% 0.30/0.56 thf(fact_2403_zip__eq__ConsE,axiom,
% 0.30/0.56 ! [Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat,Xy: produc3843707927480180839at_nat,Xys: list_P5464809261938338413at_nat] :
% 0.30/0.56 ( ( ( zip_se5600341670672612855at_nat @ Xs2 @ Ys )
% 0.30/0.56 = ( cons_P3940603068885512221at_nat @ Xy @ Xys ) )
% 0.30/0.56 => ~ ! [X3: set_Pr1261947904930325089at_nat,Xs4: list_s1210847774152347623at_nat] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_s6881495754146722583at_nat @ X3 @ Xs4 ) )
% 0.30/0.56 => ! [Y3: set_Pr1261947904930325089at_nat,Ys4: list_s1210847774152347623at_nat] :
% 0.30/0.56 ( ( Ys
% 0.30/0.56 = ( cons_s6881495754146722583at_nat @ Y3 @ Ys4 ) )
% 0.30/0.56 => ( ( Xy
% 0.30/0.56 = ( produc2922128104949294807at_nat @ X3 @ Y3 ) )
% 0.30/0.56 => ( Xys
% 0.30/0.56 != ( zip_se5600341670672612855at_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_eq_ConsE
% 0.30/0.56 thf(fact_2404_zip__eq__ConsE,axiom,
% 0.30/0.56 ! [Xs2: list_nat,Ys: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( ( zip_nat_nat @ Xs2 @ Ys )
% 0.30/0.56 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 0.30/0.56 => ~ ! [X3: nat,Xs4: list_nat] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_nat @ X3 @ Xs4 ) )
% 0.30/0.56 => ! [Y3: nat,Ys4: list_nat] :
% 0.30/0.56 ( ( Ys
% 0.30/0.56 = ( cons_nat @ Y3 @ Ys4 ) )
% 0.30/0.56 => ( ( Xy
% 0.30/0.56 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 0.30/0.56 => ( Xys
% 0.30/0.56 != ( zip_nat_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_eq_ConsE
% 0.30/0.56 thf(fact_2405_zip__eq__ConsE,axiom,
% 0.30/0.56 ! [Xs2: list_int,Ys: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 0.30/0.56 ( ( ( zip_int_int @ Xs2 @ Ys )
% 0.30/0.56 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 0.30/0.56 => ~ ! [X3: int,Xs4: list_int] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_int @ X3 @ Xs4 ) )
% 0.30/0.56 => ! [Y3: int,Ys4: list_int] :
% 0.30/0.56 ( ( Ys
% 0.30/0.56 = ( cons_int @ Y3 @ Ys4 ) )
% 0.30/0.56 => ( ( Xy
% 0.30/0.56 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 0.30/0.56 => ( Xys
% 0.30/0.56 != ( zip_int_int @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_eq_ConsE
% 0.30/0.56 thf(fact_2406_find_Osimps_I2_J,axiom,
% 0.30/0.56 ! [P2: product_prod_nat_nat > $o,X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( ( P2 @ X )
% 0.30/0.56 => ( ( find_P8199882355184865565at_nat @ P2 @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) )
% 0.30/0.56 = ( some_P7363390416028606310at_nat @ X ) ) )
% 0.30/0.56 & ( ~ ( P2 @ X )
% 0.30/0.56 => ( ( find_P8199882355184865565at_nat @ P2 @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) )
% 0.30/0.56 = ( find_P8199882355184865565at_nat @ P2 @ Xs2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find.simps(2)
% 0.30/0.56 thf(fact_2407_find_Osimps_I2_J,axiom,
% 0.30/0.56 ! [P2: nat > $o,X: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( ( P2 @ X )
% 0.30/0.56 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs2 ) )
% 0.30/0.56 = ( some_nat @ X ) ) )
% 0.30/0.56 & ( ~ ( P2 @ X )
% 0.30/0.56 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs2 ) )
% 0.30/0.56 = ( find_nat @ P2 @ Xs2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find.simps(2)
% 0.30/0.56 thf(fact_2408_find_Osimps_I2_J,axiom,
% 0.30/0.56 ! [P2: num > $o,X: num,Xs2: list_num] :
% 0.30/0.56 ( ( ( P2 @ X )
% 0.30/0.56 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs2 ) )
% 0.30/0.56 = ( some_num @ X ) ) )
% 0.30/0.56 & ( ~ ( P2 @ X )
% 0.30/0.56 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs2 ) )
% 0.30/0.56 = ( find_num @ P2 @ Xs2 ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % find.simps(2)
% 0.30/0.56 thf(fact_2409_set__zip__rightD,axiom,
% 0.30/0.56 ! [X: code_integer,Y: code_integer,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 0.30/0.56 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member_Code_integer @ Y @ ( set_Code_integer2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_rightD
% 0.30/0.56 thf(fact_2410_set__zip__rightD,axiom,
% 0.30/0.56 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_rightD
% 0.30/0.56 thf(fact_2411_set__zip__rightD,axiom,
% 0.30/0.56 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 0.30/0.56 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member2643936169264416010at_nat @ Y @ ( set_se5049602875457034614at_nat @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_rightD
% 0.30/0.56 thf(fact_2412_set__zip__rightD,axiom,
% 0.30/0.56 ! [X: nat,Y: nat,Xs2: list_nat,Ys: list_nat] :
% 0.30/0.56 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_rightD
% 0.30/0.56 thf(fact_2413_set__zip__rightD,axiom,
% 0.30/0.56 ! [X: int,Y: int,Xs2: list_int,Ys: list_int] :
% 0.30/0.56 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_rightD
% 0.30/0.56 thf(fact_2414_set__zip__leftD,axiom,
% 0.30/0.56 ! [X: code_integer,Y: code_integer,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 0.30/0.56 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member_Code_integer @ X @ ( set_Code_integer2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_leftD
% 0.30/0.56 thf(fact_2415_set__zip__leftD,axiom,
% 0.30/0.56 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_leftD
% 0.30/0.56 thf(fact_2416_set__zip__leftD,axiom,
% 0.30/0.56 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 0.30/0.56 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member2643936169264416010at_nat @ X @ ( set_se5049602875457034614at_nat @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_leftD
% 0.30/0.56 thf(fact_2417_set__zip__leftD,axiom,
% 0.30/0.56 ! [X: nat,Y: nat,Xs2: list_nat,Ys: list_nat] :
% 0.30/0.56 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member_nat @ X @ ( set_nat2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_leftD
% 0.30/0.56 thf(fact_2418_set__zip__leftD,axiom,
% 0.30/0.56 ! [X: int,Y: int,Xs2: list_int,Ys: list_int] :
% 0.30/0.56 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ( member_int @ X @ ( set_int2 @ Xs2 ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % set_zip_leftD
% 0.30/0.56 thf(fact_2419_in__set__zipE,axiom,
% 0.30/0.56 ! [X: complex,Y: complex,Xs2: list_complex,Ys: list_complex] :
% 0.30/0.56 ( ( member5793383173714906214omplex @ ( produc101793102246108661omplex @ X @ Y ) @ ( set_Pr8199049879907524818omplex @ ( zip_complex_complex @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2420_in__set__zipE,axiom,
% 0.30/0.56 ! [X: complex,Y: real,Xs2: list_complex,Ys: list_real] :
% 0.30/0.56 ( ( member47443559803733732x_real @ ( produc1746590499379883635x_real @ X @ Y ) @ ( set_Pr1225976482156248400x_real @ ( zip_complex_real @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2421_in__set__zipE,axiom,
% 0.30/0.56 ! [X: complex,Y: int,Xs2: list_complex,Ys: list_int] :
% 0.30/0.56 ( ( member595073364599660772ex_int @ ( produc1367138851071493491ex_int @ X @ Y ) @ ( set_Pr4995810437751016784ex_int @ ( zip_complex_int @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2422_in__set__zipE,axiom,
% 0.30/0.56 ! [X: real,Y: complex,Xs2: list_real,Ys: list_complex] :
% 0.30/0.56 ( ( member7358116576843751780omplex @ ( produc1693001998875562995omplex @ X @ Y ) @ ( set_Pr8536649499196266448omplex @ ( zip_real_complex @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2423_in__set__zipE,axiom,
% 0.30/0.56 ! [X: real,Y: real,Xs2: list_real,Ys: list_real] :
% 0.30/0.56 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X @ Y ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2424_in__set__zipE,axiom,
% 0.30/0.56 ! [X: real,Y: int,Xs2: list_real,Ys: list_int] :
% 0.30/0.56 ( ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X @ Y ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2425_in__set__zipE,axiom,
% 0.30/0.56 ! [X: int,Y: complex,Xs2: list_int,Ys: list_complex] :
% 0.30/0.56 ( ( member8811922270175639012omplex @ ( produc7948753499206759283omplex @ X @ Y ) @ ( set_Pr3989287306472219216omplex @ ( zip_int_complex @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2426_in__set__zipE,axiom,
% 0.30/0.56 ! [X: int,Y: real,Xs2: list_int,Ys: list_real] :
% 0.30/0.56 ( ( member2744130022092475746t_real @ ( produc801115645435158769t_real @ X @ Y ) @ ( set_Pr112895574167722958t_real @ ( zip_int_real @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2427_in__set__zipE,axiom,
% 0.30/0.56 ! [X: complex,Y: vEBT_VEBT,Xs2: list_complex,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( member1978952105866562066T_VEBT @ ( produc2757191886755552429T_VEBT @ X @ Y ) @ ( set_Pr5158653123227461798T_VEBT @ ( zip_co9157518722488180109T_VEBT @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2428_in__set__zipE,axiom,
% 0.30/0.56 ! [X: real,Y: vEBT_VEBT,Xs2: list_real,Ys: list_VEBT_VEBT] :
% 0.30/0.56 ( ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X @ Y ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs2 @ Ys ) ) )
% 0.30/0.56 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_zipE
% 0.30/0.56 thf(fact_2429_zip__same,axiom,
% 0.30/0.56 ! [A: complex,B: complex,Xs2: list_complex] :
% 0.30/0.56 ( ( member5793383173714906214omplex @ ( produc101793102246108661omplex @ A @ B ) @ ( set_Pr8199049879907524818omplex @ ( zip_complex_complex @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member_complex @ A @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2430_zip__same,axiom,
% 0.30/0.56 ! [A: real,B: real,Xs2: list_real] :
% 0.30/0.56 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ A @ B ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member_real @ A @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2431_zip__same,axiom,
% 0.30/0.56 ! [A: set_nat,B: set_nat,Xs2: list_set_nat] :
% 0.30/0.56 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ B ) @ ( set_Pr9040384385603167362et_nat @ ( zip_set_nat_set_nat @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member_set_nat @ A @ ( set_set_nat2 @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2432_zip__same,axiom,
% 0.30/0.56 ! [A: vEBT_VEBT,B: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ A @ B ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2433_zip__same,axiom,
% 0.30/0.56 ! [A: code_integer,B: code_integer,Xs2: list_Code_integer] :
% 0.30/0.56 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A @ B ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member_Code_integer @ A @ ( set_Code_integer2 @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2434_zip__same,axiom,
% 0.30/0.56 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 0.30/0.56 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member8440522571783428010at_nat @ A @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2435_zip__same,axiom,
% 0.30/0.56 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat] :
% 0.30/0.56 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member2643936169264416010at_nat @ A @ ( set_se5049602875457034614at_nat @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2436_zip__same,axiom,
% 0.30/0.56 ! [A: nat,B: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member_nat @ A @ ( set_nat2 @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2437_zip__same,axiom,
% 0.30/0.56 ! [A: int,B: int,Xs2: list_int] :
% 0.30/0.56 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Xs2 ) ) )
% 0.30/0.56 = ( ( member_int @ A @ ( set_int2 @ Xs2 ) )
% 0.30/0.56 & ( A = B ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % zip_same
% 0.30/0.56 thf(fact_2438_Suc__length__conv,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 0.30/0.56 ( ( ( suc @ N )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.56 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_length_conv
% 0.30/0.56 thf(fact_2439_Suc__length__conv,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_o] :
% 0.30/0.56 ( ( ( suc @ N )
% 0.30/0.56 = ( size_size_list_o @ Xs2 ) )
% 0.30/0.56 = ( ? [Y4: $o,Ys3: list_o] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_o @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_size_list_o @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_length_conv
% 0.30/0.56 thf(fact_2440_Suc__length__conv,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_nat] :
% 0.30/0.56 ( ( ( suc @ N )
% 0.30/0.56 = ( size_size_list_nat @ Xs2 ) )
% 0.30/0.56 = ( ? [Y4: nat,Ys3: list_nat] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_nat @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_size_list_nat @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_length_conv
% 0.30/0.56 thf(fact_2441_Suc__length__conv,axiom,
% 0.30/0.56 ! [N: nat,Xs2: list_int] :
% 0.30/0.56 ( ( ( suc @ N )
% 0.30/0.56 = ( size_size_list_int @ Xs2 ) )
% 0.30/0.56 = ( ? [Y4: int,Ys3: list_int] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_int @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_size_list_int @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % Suc_length_conv
% 0.30/0.56 thf(fact_2442_length__Suc__conv,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,N: nat] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( suc @ N ) )
% 0.30/0.56 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_Suc_conv
% 0.30/0.56 thf(fact_2443_length__Suc__conv,axiom,
% 0.30/0.56 ! [Xs2: list_o,N: nat] :
% 0.30/0.56 ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.56 = ( suc @ N ) )
% 0.30/0.56 = ( ? [Y4: $o,Ys3: list_o] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_o @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_size_list_o @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_Suc_conv
% 0.30/0.56 thf(fact_2444_length__Suc__conv,axiom,
% 0.30/0.56 ! [Xs2: list_nat,N: nat] :
% 0.30/0.56 ( ( ( size_size_list_nat @ Xs2 )
% 0.30/0.56 = ( suc @ N ) )
% 0.30/0.56 = ( ? [Y4: nat,Ys3: list_nat] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_nat @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_size_list_nat @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_Suc_conv
% 0.30/0.56 thf(fact_2445_length__Suc__conv,axiom,
% 0.30/0.56 ! [Xs2: list_int,N: nat] :
% 0.30/0.56 ( ( ( size_size_list_int @ Xs2 )
% 0.30/0.56 = ( suc @ N ) )
% 0.30/0.56 = ( ? [Y4: int,Ys3: list_int] :
% 0.30/0.56 ( ( Xs2
% 0.30/0.56 = ( cons_int @ Y4 @ Ys3 ) )
% 0.30/0.56 & ( ( size_size_list_int @ Ys3 )
% 0.30/0.56 = N ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % length_Suc_conv
% 0.30/0.56 thf(fact_2446_impossible__Cons,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( Xs2
% 0.30/0.56 != ( cons_VEBT_VEBT @ X @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % impossible_Cons
% 0.30/0.56 thf(fact_2447_impossible__Cons,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_o,X: $o] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) )
% 0.30/0.56 => ( Xs2
% 0.30/0.56 != ( cons_o @ X @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % impossible_Cons
% 0.30/0.56 thf(fact_2448_impossible__Cons,axiom,
% 0.30/0.56 ! [Xs2: list_nat,Ys: list_nat,X: nat] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_nat @ Ys ) )
% 0.30/0.56 => ( Xs2
% 0.30/0.56 != ( cons_nat @ X @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % impossible_Cons
% 0.30/0.56 thf(fact_2449_impossible__Cons,axiom,
% 0.30/0.56 ! [Xs2: list_int,Ys: list_int,X: int] :
% 0.30/0.56 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_int @ Ys ) )
% 0.30/0.56 => ( Xs2
% 0.30/0.56 != ( cons_int @ X @ Ys ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % impossible_Cons
% 0.30/0.56 thf(fact_2450_vebt__insert_Osimps_I2_J,axiom,
% 0.30/0.56 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 0.30/0.56 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X )
% 0.30/0.56 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) ).
% 0.30/0.56
% 0.30/0.56 % vebt_insert.simps(2)
% 0.30/0.56 thf(fact_2451_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_Code_integer,Ys: list_Code_integer,X: code_integer] :
% 0.30/0.56 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 0.30/0.56 = ( size_s3445333598471063425nteger @ Ys ) )
% 0.30/0.56 => ( ( member_Code_integer @ X @ ( set_Code_integer2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: code_integer] :
% 0.30/0.56 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y3 ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2452_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_complex,Ys: list_VEBT_VEBT,X: complex] :
% 0.30/0.56 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member1978952105866562066T_VEBT @ ( produc2757191886755552429T_VEBT @ X @ Y3 ) @ ( set_Pr5158653123227461798T_VEBT @ ( zip_co9157518722488180109T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2453_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_real,Ys: list_VEBT_VEBT,X: real] :
% 0.30/0.56 ( ( ( size_size_list_real @ Xs2 )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X @ Y3 ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2454_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_complex,Ys: list_o,X: complex] :
% 0.30/0.56 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.30/0.56 = ( size_size_list_o @ Ys ) )
% 0.30/0.56 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: $o] :
% 0.30/0.56 ~ ( member6487239523555734774plex_o @ ( produc2908979694703026321plex_o @ X @ Y3 ) @ ( set_Pr6829704231520703882plex_o @ ( zip_complex_o @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2455_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_real,Ys: list_o,X: real] :
% 0.30/0.56 ( ( ( size_size_list_real @ Xs2 )
% 0.30/0.56 = ( size_size_list_o @ Ys ) )
% 0.30/0.56 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: $o] :
% 0.30/0.56 ~ ( member772602641336174712real_o @ ( product_Pair_real_o @ X @ Y3 ) @ ( set_Pr5196769464307566348real_o @ ( zip_real_o @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2456_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_complex,Ys: list_nat,X: complex] :
% 0.30/0.56 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.30/0.56 = ( size_size_list_nat @ Ys ) )
% 0.30/0.56 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: nat] :
% 0.30/0.56 ~ ( member4772924384108857480ex_nat @ ( produc1369629321580543767ex_nat @ X @ Y3 ) @ ( set_Pr9173661457260213492ex_nat @ ( zip_complex_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2457_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_real,Ys: list_nat,X: real] :
% 0.30/0.56 ( ( ( size_size_list_real @ Xs2 )
% 0.30/0.56 = ( size_size_list_nat @ Ys ) )
% 0.30/0.56 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: nat] :
% 0.30/0.56 ~ ( member5805532792777349510al_nat @ ( produc3181502643871035669al_nat @ X @ Y3 ) @ ( set_Pr3174298344852596722al_nat @ ( zip_real_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2458_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_complex,Ys: list_int,X: complex] :
% 0.30/0.56 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.30/0.56 = ( size_size_list_int @ Ys ) )
% 0.30/0.56 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: int] :
% 0.30/0.56 ~ ( member595073364599660772ex_int @ ( produc1367138851071493491ex_int @ X @ Y3 ) @ ( set_Pr4995810437751016784ex_int @ ( zip_complex_int @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2459_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_real,Ys: list_int,X: real] :
% 0.30/0.56 ( ( ( size_size_list_real @ Xs2 )
% 0.30/0.56 = ( size_size_list_int @ Ys ) )
% 0.30/0.56 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: int] :
% 0.30/0.56 ~ ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X @ Y3 ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2460_in__set__impl__in__set__zip1,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.56 => ~ ! [Y3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y3 ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip1
% 0.30/0.56 thf(fact_2461_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_Code_integer,Ys: list_Code_integer,Y: code_integer] :
% 0.30/0.56 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 0.30/0.56 = ( size_s3445333598471063425nteger @ Ys ) )
% 0.30/0.56 => ( ( member_Code_integer @ Y @ ( set_Code_integer2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: code_integer] :
% 0.30/0.56 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2462_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_complex,Y: complex] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_s3451745648224563538omplex @ Ys ) )
% 0.30/0.56 => ( ( member_complex @ Y @ ( set_complex2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member3207599676835851048omplex @ ( produc5617778602380981643omplex @ X3 @ Y ) @ ( set_Pr6387300694196750780omplex @ ( zip_VE2794733401258833515omplex @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2463_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_real,Y: real] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_size_list_real @ Ys ) )
% 0.30/0.56 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X3 @ Y ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2464_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.56 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X3 @ Y ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2465_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_o,Y: $o] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_size_list_o @ Ys ) )
% 0.30/0.56 => ( ( member_o @ Y @ ( set_o2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X3 @ Y ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2466_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,Y: nat] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_size_list_nat @ Ys ) )
% 0.30/0.56 => ( ( member_nat @ Y @ ( set_nat2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X3 @ Y ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2467_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_VEBT_VEBT,Ys: list_int,Y: int] :
% 0.30/0.56 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.56 = ( size_size_list_int @ Ys ) )
% 0.30/0.56 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: vEBT_VEBT] :
% 0.30/0.56 ~ ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ X3 @ Y ) @ ( set_Pr2853735649769556538BT_int @ ( zip_VEBT_VEBT_int @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2468_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_complex,Y: complex] :
% 0.30/0.56 ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.56 = ( size_s3451745648224563538omplex @ Ys ) )
% 0.30/0.56 => ( ( member_complex @ Y @ ( set_complex2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: $o] :
% 0.30/0.56 ~ ( member1046615901120239500omplex @ ( produc414345526774272751omplex @ X3 @ Y ) @ ( set_Pr1389080609085208608omplex @ ( zip_o_complex @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2469_in__set__impl__in__set__zip2,axiom,
% 0.30/0.56 ! [Xs2: list_o,Ys: list_real,Y: real] :
% 0.30/0.56 ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.56 = ( size_size_list_real @ Ys ) )
% 0.30/0.56 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 0.30/0.56 => ~ ! [X3: $o] :
% 0.30/0.56 ~ ( member7400031367953476362o_real @ ( product_Pair_o_real @ X3 @ Y ) @ ( set_Pr2600826154070092190o_real @ ( zip_o_real @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.56
% 0.30/0.56 % in_set_impl_in_set_zip2
% 0.30/0.56 thf(fact_2470_in__set__impl__in__set__zip2,axiom,
% 0.30/0.57 ! [Xs2: list_o,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.30/0.57 ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.57 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.57 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 0.30/0.57 => ~ ! [X3: $o] :
% 0.30/0.57 ~ ( member5477980866518848620T_VEBT @ ( produc2982872950893828659T_VEBT @ X3 @ Y ) @ ( set_Pr655345902815428824T_VEBT @ ( zip_o_VEBT_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % in_set_impl_in_set_zip2
% 0.30/0.57 thf(fact_2471_Suc__le__length__iff,axiom,
% 0.30/0.57 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.57 = ( ? [X4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 0.30/0.57 ( ( Xs2
% 0.30/0.57 = ( cons_VEBT_VEBT @ X4 @ Ys3 ) )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Suc_le_length_iff
% 0.30/0.57 thf(fact_2472_Suc__le__length__iff,axiom,
% 0.30/0.57 ! [N: nat,Xs2: list_o] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.57 = ( ? [X4: $o,Ys3: list_o] :
% 0.30/0.57 ( ( Xs2
% 0.30/0.57 = ( cons_o @ X4 @ Ys3 ) )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( size_size_list_o @ Ys3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Suc_le_length_iff
% 0.30/0.57 thf(fact_2473_Suc__le__length__iff,axiom,
% 0.30/0.57 ! [N: nat,Xs2: list_nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.57 = ( ? [X4: nat,Ys3: list_nat] :
% 0.30/0.57 ( ( Xs2
% 0.30/0.57 = ( cons_nat @ X4 @ Ys3 ) )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Suc_le_length_iff
% 0.30/0.57 thf(fact_2474_Suc__le__length__iff,axiom,
% 0.30/0.57 ! [N: nat,Xs2: list_int] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.57 = ( ? [X4: int,Ys3: list_int] :
% 0.30/0.57 ( ( Xs2
% 0.30/0.57 = ( cons_int @ X4 @ Ys3 ) )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Suc_le_length_iff
% 0.30/0.57 thf(fact_2475_VEBT__internal_Oinsert_H_Osimps_I1_J,axiom,
% 0.30/0.57 ! [A: $o,B: $o,X: nat] :
% 0.30/0.57 ( ( vEBT_VEBT_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.30/0.57 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X ) ) ).
% 0.30/0.57
% 0.30/0.57 % VEBT_internal.insert'.simps(1)
% 0.30/0.57 thf(fact_2476_vebt__insert_Osimps_I3_J,axiom,
% 0.30/0.57 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 0.30/0.57 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X )
% 0.30/0.57 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % vebt_insert.simps(3)
% 0.30/0.57 thf(fact_2477_vebt__insert_Osimps_I1_J,axiom,
% 0.30/0.57 ! [X: nat,A: $o,B: $o] :
% 0.30/0.57 ( ( ( X = zero_zero_nat )
% 0.30/0.57 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.30/0.57 = ( vEBT_Leaf @ $true @ B ) ) )
% 0.30/0.57 & ( ( X != zero_zero_nat )
% 0.30/0.57 => ( ( ( X = one_one_nat )
% 0.30/0.57 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.30/0.57 = ( vEBT_Leaf @ A @ $true ) ) )
% 0.30/0.57 & ( ( X != one_one_nat )
% 0.30/0.57 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 0.30/0.57 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % vebt_insert.simps(1)
% 0.30/0.57 thf(fact_2478_list_Osize_I4_J,axiom,
% 0.30/0.57 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 0.30/0.57 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X21 @ X22 ) )
% 0.30/0.57 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % list.size(4)
% 0.30/0.57 thf(fact_2479_list_Osize_I4_J,axiom,
% 0.30/0.57 ! [X21: $o,X22: list_o] :
% 0.30/0.57 ( ( size_size_list_o @ ( cons_o @ X21 @ X22 ) )
% 0.30/0.57 = ( plus_plus_nat @ ( size_size_list_o @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % list.size(4)
% 0.30/0.57 thf(fact_2480_list_Osize_I4_J,axiom,
% 0.30/0.57 ! [X21: nat,X22: list_nat] :
% 0.30/0.57 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X22 ) )
% 0.30/0.57 = ( plus_plus_nat @ ( size_size_list_nat @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % list.size(4)
% 0.30/0.57 thf(fact_2481_list_Osize_I4_J,axiom,
% 0.30/0.57 ! [X21: int,X22: list_int] :
% 0.30/0.57 ( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
% 0.30/0.57 = ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % list.size(4)
% 0.30/0.57 thf(fact_2482_nth__Cons_H,axiom,
% 0.30/0.57 ! [N: nat,X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 0.30/0.57 = X ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 0.30/0.57 = ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_Cons'
% 0.30/0.57 thf(fact_2483_nth__Cons_H,axiom,
% 0.30/0.57 ! [N: nat,X: nat,Xs2: list_nat] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 0.30/0.57 = X ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 0.30/0.57 = ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_Cons'
% 0.30/0.57 thf(fact_2484_nth__equal__first__eq,axiom,
% 0.30/0.57 ! [X: complex,Xs2: list_complex,N: nat] :
% 0.30/0.57 ( ~ ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.30/0.57 => ( ( ( nth_complex @ ( cons_complex @ X @ Xs2 ) @ N )
% 0.30/0.57 = X )
% 0.30/0.57 = ( N = zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_equal_first_eq
% 0.30/0.57 thf(fact_2485_nth__equal__first__eq,axiom,
% 0.30/0.57 ! [X: real,Xs2: list_real,N: nat] :
% 0.30/0.57 ( ~ ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.30/0.57 => ( ( ( nth_real @ ( cons_real @ X @ Xs2 ) @ N )
% 0.30/0.57 = X )
% 0.30/0.57 = ( N = zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_equal_first_eq
% 0.30/0.57 thf(fact_2486_nth__equal__first__eq,axiom,
% 0.30/0.57 ! [X: set_nat,Xs2: list_set_nat,N: nat] :
% 0.30/0.57 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.30/0.57 => ( ( ( nth_set_nat @ ( cons_set_nat @ X @ Xs2 ) @ N )
% 0.30/0.57 = X )
% 0.30/0.57 = ( N = zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_equal_first_eq
% 0.30/0.57 thf(fact_2487_nth__equal__first__eq,axiom,
% 0.30/0.57 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 0.30/0.57 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.57 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 0.30/0.57 = X )
% 0.30/0.57 = ( N = zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_equal_first_eq
% 0.30/0.57 thf(fact_2488_nth__equal__first__eq,axiom,
% 0.30/0.57 ! [X: $o,Xs2: list_o,N: nat] :
% 0.30/0.57 ( ~ ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.57 => ( ( ( nth_o @ ( cons_o @ X @ Xs2 ) @ N )
% 0.30/0.57 = X )
% 0.30/0.57 = ( N = zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_equal_first_eq
% 0.30/0.57 thf(fact_2489_nth__equal__first__eq,axiom,
% 0.30/0.57 ! [X: nat,Xs2: list_nat,N: nat] :
% 0.30/0.57 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.57 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 0.30/0.57 = X )
% 0.30/0.57 = ( N = zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_equal_first_eq
% 0.30/0.57 thf(fact_2490_nth__equal__first__eq,axiom,
% 0.30/0.57 ! [X: int,Xs2: list_int,N: nat] :
% 0.30/0.57 ( ~ ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.30/0.57 => ( ( ( nth_int @ ( cons_int @ X @ Xs2 ) @ N )
% 0.30/0.57 = X )
% 0.30/0.57 = ( N = zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_equal_first_eq
% 0.30/0.57 thf(fact_2491_nth__non__equal__first__eq,axiom,
% 0.30/0.57 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 0.30/0.57 ( ( X != Y )
% 0.30/0.57 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 0.30/0.57 = Y )
% 0.30/0.57 = ( ( ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 = Y )
% 0.30/0.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_non_equal_first_eq
% 0.30/0.57 thf(fact_2492_nth__non__equal__first__eq,axiom,
% 0.30/0.57 ! [X: nat,Y: nat,Xs2: list_nat,N: nat] :
% 0.30/0.57 ( ( X != Y )
% 0.30/0.57 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 0.30/0.57 = Y )
% 0.30/0.57 = ( ( ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 = Y )
% 0.30/0.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nth_non_equal_first_eq
% 0.30/0.57 thf(fact_2493_length__Cons,axiom,
% 0.30/0.57 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.57 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) )
% 0.30/0.57 = ( suc @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % length_Cons
% 0.30/0.57 thf(fact_2494_length__Cons,axiom,
% 0.30/0.57 ! [X: $o,Xs2: list_o] :
% 0.30/0.57 ( ( size_size_list_o @ ( cons_o @ X @ Xs2 ) )
% 0.30/0.57 = ( suc @ ( size_size_list_o @ Xs2 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % length_Cons
% 0.30/0.57 thf(fact_2495_length__Cons,axiom,
% 0.30/0.57 ! [X: nat,Xs2: list_nat] :
% 0.30/0.57 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs2 ) )
% 0.30/0.57 = ( suc @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % length_Cons
% 0.30/0.57 thf(fact_2496_length__Cons,axiom,
% 0.30/0.57 ! [X: int,Xs2: list_int] :
% 0.30/0.57 ( ( size_size_list_int @ ( cons_int @ X @ Xs2 ) )
% 0.30/0.57 = ( suc @ ( size_size_list_int @ Xs2 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % length_Cons
% 0.30/0.57 thf(fact_2497_dbl__inc__simps_I2_J,axiom,
% 0.30/0.57 ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 0.30/0.57 = one_one_Code_integer ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_simps(2)
% 0.30/0.57 thf(fact_2498_dbl__inc__simps_I2_J,axiom,
% 0.30/0.57 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 0.30/0.57 = one_one_complex ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_simps(2)
% 0.30/0.57 thf(fact_2499_dbl__inc__simps_I2_J,axiom,
% 0.30/0.57 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 0.30/0.57 = one_one_real ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_simps(2)
% 0.30/0.57 thf(fact_2500_dbl__inc__simps_I2_J,axiom,
% 0.30/0.57 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 0.30/0.57 = one_one_rat ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_simps(2)
% 0.30/0.57 thf(fact_2501_dbl__inc__simps_I2_J,axiom,
% 0.30/0.57 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 0.30/0.57 = one_one_int ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_simps(2)
% 0.30/0.57 thf(fact_2502_enumerate__Suc_H,axiom,
% 0.30/0.57 ! [S3: set_nat,N: nat] :
% 0.30/0.57 ( ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) )
% 0.30/0.57 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ ( infini8530281810654367211te_nat @ S3 @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N ) ) ).
% 0.30/0.57
% 0.30/0.57 % enumerate_Suc'
% 0.30/0.57 thf(fact_2503_dbl__dec__def,axiom,
% 0.30/0.57 ( neg_nu7757733837767384882nteger
% 0.30/0.57 = ( ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X4 @ X4 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_def
% 0.30/0.57 thf(fact_2504_dbl__dec__def,axiom,
% 0.30/0.57 ( neg_nu6511756317524482435omplex
% 0.30/0.57 = ( ^ [X4: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X4 @ X4 ) @ one_one_complex ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_def
% 0.30/0.57 thf(fact_2505_dbl__dec__def,axiom,
% 0.30/0.57 ( neg_nu6075765906172075777c_real
% 0.30/0.57 = ( ^ [X4: real] : ( minus_minus_real @ ( plus_plus_real @ X4 @ X4 ) @ one_one_real ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_def
% 0.30/0.57 thf(fact_2506_dbl__dec__def,axiom,
% 0.30/0.57 ( neg_nu3179335615603231917ec_rat
% 0.30/0.57 = ( ^ [X4: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X4 @ X4 ) @ one_one_rat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_def
% 0.30/0.57 thf(fact_2507_dbl__dec__def,axiom,
% 0.30/0.57 ( neg_nu3811975205180677377ec_int
% 0.30/0.57 = ( ^ [X4: int] : ( minus_minus_int @ ( plus_plus_int @ X4 @ X4 ) @ one_one_int ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_def
% 0.30/0.57 thf(fact_2508_Gcd__fin__0__iff,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ( ( semiri4256215615220890538in_int @ A4 )
% 0.30/0.57 = zero_zero_int )
% 0.30/0.57 = ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) )
% 0.30/0.57 & ( finite_finite_int @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Gcd_fin_0_iff
% 0.30/0.57 thf(fact_2509_Gcd__fin__0__iff,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ( ( semiri4258706085729940814in_nat @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 0.30/0.57 & ( finite_finite_nat @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Gcd_fin_0_iff
% 0.30/0.57 thf(fact_2510_power__decreasing__iff,axiom,
% 0.30/0.57 ! [B: code_integer,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.57 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing_iff
% 0.30/0.57 thf(fact_2511_power__decreasing__iff,axiom,
% 0.30/0.57 ! [B: real,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ zero_zero_real @ B )
% 0.30/0.57 => ( ( ord_less_real @ B @ one_one_real )
% 0.30/0.57 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing_iff
% 0.30/0.57 thf(fact_2512_power__decreasing__iff,axiom,
% 0.30/0.57 ! [B: rat,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( ( ord_less_rat @ B @ one_one_rat )
% 0.30/0.57 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing_iff
% 0.30/0.57 thf(fact_2513_power__decreasing__iff,axiom,
% 0.30/0.57 ! [B: nat,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( ( ord_less_nat @ B @ one_one_nat )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing_iff
% 0.30/0.57 thf(fact_2514_power__decreasing__iff,axiom,
% 0.30/0.57 ! [B: int,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.57 => ( ( ord_less_int @ B @ one_one_int )
% 0.30/0.57 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing_iff
% 0.30/0.57 thf(fact_2515_card__insert__le__m1,axiom,
% 0.30/0.57 ! [N: nat,Y: set_real,X: real] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_real @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_real @ ( insert_real @ X @ Y ) ) @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le_m1
% 0.30/0.57 thf(fact_2516_card__insert__le__m1,axiom,
% 0.30/0.57 ! [N: nat,Y: set_nat,X: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le_m1
% 0.30/0.57 thf(fact_2517_card__insert__le__m1,axiom,
% 0.30/0.57 ! [N: nat,Y: set_complex,X: complex] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_complex @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_complex @ ( insert_complex @ X @ Y ) ) @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le_m1
% 0.30/0.57 thf(fact_2518_card__insert__le__m1,axiom,
% 0.30/0.57 ! [N: nat,Y: set_int,X: int] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le_m1
% 0.30/0.57 thf(fact_2519_card__insert__le__m1,axiom,
% 0.30/0.57 ! [N: nat,Y: set_list_nat,X: list_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le_m1
% 0.30/0.57 thf(fact_2520_card__insert__le__m1,axiom,
% 0.30/0.57 ! [N: nat,Y: set_set_nat,X: set_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ Y ) ) @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le_m1
% 0.30/0.57 thf(fact_2521_count__notin,axiom,
% 0.30/0.57 ! [X: complex,Xs2: list_complex] :
% 0.30/0.57 ( ~ ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.30/0.57 => ( ( count_list_complex @ Xs2 @ X )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_notin
% 0.30/0.57 thf(fact_2522_count__notin,axiom,
% 0.30/0.57 ! [X: real,Xs2: list_real] :
% 0.30/0.57 ( ~ ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.30/0.57 => ( ( count_list_real @ Xs2 @ X )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_notin
% 0.30/0.57 thf(fact_2523_count__notin,axiom,
% 0.30/0.57 ! [X: set_nat,Xs2: list_set_nat] :
% 0.30/0.57 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 0.30/0.57 => ( ( count_list_set_nat @ Xs2 @ X )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_notin
% 0.30/0.57 thf(fact_2524_count__notin,axiom,
% 0.30/0.57 ! [X: int,Xs2: list_int] :
% 0.30/0.57 ( ~ ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.30/0.57 => ( ( count_list_int @ Xs2 @ X )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_notin
% 0.30/0.57 thf(fact_2525_count__notin,axiom,
% 0.30/0.57 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 0.30/0.57 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.30/0.57 => ( ( count_list_VEBT_VEBT @ Xs2 @ X )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_notin
% 0.30/0.57 thf(fact_2526_count__notin,axiom,
% 0.30/0.57 ! [X: nat,Xs2: list_nat] :
% 0.30/0.57 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.30/0.57 => ( ( count_list_nat @ Xs2 @ X )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_notin
% 0.30/0.57 thf(fact_2527_Cons__lenlex__iff,axiom,
% 0.30/0.57 ! [M2: code_integer,Ms: list_Code_integer,N: code_integer,Ns: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 0.30/0.57 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ M2 @ Ms ) @ ( cons_Code_integer @ N @ Ns ) ) @ ( lenlex_Code_integer @ R3 ) )
% 0.30/0.57 = ( ( ord_less_nat @ ( size_s3445333598471063425nteger @ Ms ) @ ( size_s3445333598471063425nteger @ Ns ) )
% 0.30/0.57 | ( ( ( size_s3445333598471063425nteger @ Ms )
% 0.30/0.57 = ( size_s3445333598471063425nteger @ Ns ) )
% 0.30/0.57 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ M2 @ N ) @ R3 ) )
% 0.30/0.57 | ( ( M2 = N )
% 0.30/0.57 & ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Ms @ Ns ) @ ( lenlex_Code_integer @ R3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Cons_lenlex_iff
% 0.30/0.57 thf(fact_2528_Cons__lenlex__iff,axiom,
% 0.30/0.57 ! [M2: product_prod_nat_nat,Ms: list_P6011104703257516679at_nat,N: product_prod_nat_nat,Ns: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 0.30/0.57 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ M2 @ Ms ) @ ( cons_P6512896166579812791at_nat @ N @ Ns ) ) @ ( lenlex325483962726685836at_nat @ R3 ) )
% 0.30/0.57 = ( ( ord_less_nat @ ( size_s5460976970255530739at_nat @ Ms ) @ ( size_s5460976970255530739at_nat @ Ns ) )
% 0.30/0.57 | ( ( ( size_s5460976970255530739at_nat @ Ms )
% 0.30/0.57 = ( size_s5460976970255530739at_nat @ Ns ) )
% 0.30/0.57 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ M2 @ N ) @ R3 ) )
% 0.30/0.57 | ( ( M2 = N )
% 0.30/0.57 & ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Ms @ Ns ) @ ( lenlex325483962726685836at_nat @ R3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Cons_lenlex_iff
% 0.30/0.57 thf(fact_2529_Cons__lenlex__iff,axiom,
% 0.30/0.57 ! [M2: set_Pr1261947904930325089at_nat,Ms: list_s1210847774152347623at_nat,N: set_Pr1261947904930325089at_nat,Ns: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.30/0.57 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ M2 @ Ms ) @ ( cons_s6881495754146722583at_nat @ N @ Ns ) ) @ ( lenlex1357538814655152620at_nat @ R3 ) )
% 0.30/0.57 = ( ( ord_less_nat @ ( size_s8736152011456118867at_nat @ Ms ) @ ( size_s8736152011456118867at_nat @ Ns ) )
% 0.30/0.57 | ( ( ( size_s8736152011456118867at_nat @ Ms )
% 0.30/0.57 = ( size_s8736152011456118867at_nat @ Ns ) )
% 0.30/0.57 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ M2 @ N ) @ R3 ) )
% 0.30/0.57 | ( ( M2 = N )
% 0.30/0.57 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ms @ Ns ) @ ( lenlex1357538814655152620at_nat @ R3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Cons_lenlex_iff
% 0.30/0.57 thf(fact_2530_Cons__lenlex__iff,axiom,
% 0.30/0.57 ! [M2: vEBT_VEBT,Ms: list_VEBT_VEBT,N: vEBT_VEBT,Ns: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 0.30/0.57 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ M2 @ Ms ) @ ( cons_VEBT_VEBT @ N @ Ns ) ) @ ( lenlex_VEBT_VEBT @ R3 ) )
% 0.30/0.57 = ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) )
% 0.30/0.57 | ( ( ( size_s6755466524823107622T_VEBT @ Ms )
% 0.30/0.57 = ( size_s6755466524823107622T_VEBT @ Ns ) )
% 0.30/0.57 & ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ M2 @ N ) @ R3 ) )
% 0.30/0.57 | ( ( M2 = N )
% 0.30/0.57 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Cons_lenlex_iff
% 0.30/0.57 thf(fact_2531_Cons__lenlex__iff,axiom,
% 0.30/0.57 ! [M2: $o,Ms: list_o,N: $o,Ns: list_o,R3: set_Product_prod_o_o] :
% 0.30/0.57 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ M2 @ Ms ) @ ( cons_o @ N @ Ns ) ) @ ( lenlex_o @ R3 ) )
% 0.30/0.57 = ( ( ord_less_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) )
% 0.30/0.57 | ( ( ( size_size_list_o @ Ms )
% 0.30/0.57 = ( size_size_list_o @ Ns ) )
% 0.30/0.57 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ M2 @ N ) @ R3 ) )
% 0.30/0.57 | ( ( M2 = N )
% 0.30/0.57 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Cons_lenlex_iff
% 0.30/0.57 thf(fact_2532_Cons__lenlex__iff,axiom,
% 0.30/0.57 ! [M2: nat,Ms: list_nat,N: nat,Ns: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.30/0.57 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ M2 @ Ms ) @ ( cons_nat @ N @ Ns ) ) @ ( lenlex_nat @ R3 ) )
% 0.30/0.57 = ( ( ord_less_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) )
% 0.30/0.57 | ( ( ( size_size_list_nat @ Ms )
% 0.30/0.57 = ( size_size_list_nat @ Ns ) )
% 0.30/0.57 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ R3 ) )
% 0.30/0.57 | ( ( M2 = N )
% 0.30/0.57 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Cons_lenlex_iff
% 0.30/0.57 thf(fact_2533_Cons__lenlex__iff,axiom,
% 0.30/0.57 ! [M2: int,Ms: list_int,N: int,Ns: list_int,R3: set_Pr958786334691620121nt_int] :
% 0.30/0.57 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ M2 @ Ms ) @ ( cons_int @ N @ Ns ) ) @ ( lenlex_int @ R3 ) )
% 0.30/0.57 = ( ( ord_less_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) )
% 0.30/0.57 | ( ( ( size_size_list_int @ Ms )
% 0.30/0.57 = ( size_size_list_int @ Ns ) )
% 0.30/0.57 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ M2 @ N ) @ R3 ) )
% 0.30/0.57 | ( ( M2 = N )
% 0.30/0.57 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R3 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % Cons_lenlex_iff
% 0.30/0.57 thf(fact_2534_power__shift,axiom,
% 0.30/0.57 ! [X: nat,Y: nat,Z3: nat] :
% 0.30/0.57 ( ( ( power_power_nat @ X @ Y )
% 0.30/0.57 = Z3 )
% 0.30/0.57 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 0.30/0.57 = ( some_nat @ Z3 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_shift
% 0.30/0.57 thf(fact_2535_local_Opower__def,axiom,
% 0.30/0.57 ( vEBT_VEBT_power
% 0.30/0.57 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % local.power_def
% 0.30/0.57 thf(fact_2536_nat__power__eq__Suc__0__iff,axiom,
% 0.30/0.57 ! [X: nat,M2: nat] :
% 0.30/0.57 ( ( ( power_power_nat @ X @ M2 )
% 0.30/0.57 = ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ( M2 = zero_zero_nat )
% 0.30/0.57 | ( X
% 0.30/0.57 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nat_power_eq_Suc_0_iff
% 0.30/0.57 thf(fact_2537_power__Suc__0,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.30/0.57 = ( suc @ zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_0
% 0.30/0.57 thf(fact_2538_nat__zero__less__power__iff,axiom,
% 0.30/0.57 ! [X: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 0.30/0.57 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.30/0.57 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nat_zero_less_power_iff
% 0.30/0.57 thf(fact_2539_dbl__dec__simps_I3_J,axiom,
% 0.30/0.57 ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 0.30/0.57 = one_one_Code_integer ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_simps(3)
% 0.30/0.57 thf(fact_2540_dbl__dec__simps_I3_J,axiom,
% 0.30/0.57 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 0.30/0.57 = one_one_complex ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_simps(3)
% 0.30/0.57 thf(fact_2541_dbl__dec__simps_I3_J,axiom,
% 0.30/0.57 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 0.30/0.57 = one_one_real ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_simps(3)
% 0.30/0.57 thf(fact_2542_dbl__dec__simps_I3_J,axiom,
% 0.30/0.57 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 0.30/0.57 = one_one_int ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_dec_simps(3)
% 0.30/0.57 thf(fact_2543_power__0__Suc,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 0.30/0.57 = zero_zero_rat ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_Suc
% 0.30/0.57 thf(fact_2544_power__0__Suc,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_Suc
% 0.30/0.57 thf(fact_2545_power__0__Suc,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 0.30/0.57 = zero_zero_real ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_Suc
% 0.30/0.57 thf(fact_2546_power__0__Suc,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 0.30/0.57 = zero_zero_int ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_Suc
% 0.30/0.57 thf(fact_2547_power__0__Suc,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 0.30/0.57 = zero_zero_complex ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_Suc
% 0.30/0.57 thf(fact_2548_power__Suc0__right,axiom,
% 0.30/0.57 ! [A: nat] :
% 0.30/0.57 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = A ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc0_right
% 0.30/0.57 thf(fact_2549_power__Suc0__right,axiom,
% 0.30/0.57 ! [A: real] :
% 0.30/0.57 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = A ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc0_right
% 0.30/0.57 thf(fact_2550_power__Suc0__right,axiom,
% 0.30/0.57 ! [A: int] :
% 0.30/0.57 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = A ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc0_right
% 0.30/0.57 thf(fact_2551_power__Suc0__right,axiom,
% 0.30/0.57 ! [A: complex] :
% 0.30/0.57 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = A ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc0_right
% 0.30/0.57 thf(fact_2552_card_Oempty,axiom,
% 0.30/0.57 ( ( finite_card_complex @ bot_bot_set_complex )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % card.empty
% 0.30/0.57 thf(fact_2553_card_Oempty,axiom,
% 0.30/0.57 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % card.empty
% 0.30/0.57 thf(fact_2554_card_Oempty,axiom,
% 0.30/0.57 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % card.empty
% 0.30/0.57 thf(fact_2555_card_Oempty,axiom,
% 0.30/0.57 ( ( finite_card_nat @ bot_bot_set_nat )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % card.empty
% 0.30/0.57 thf(fact_2556_card_Oempty,axiom,
% 0.30/0.57 ( ( finite_card_int @ bot_bot_set_int )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % card.empty
% 0.30/0.57 thf(fact_2557_card_Oempty,axiom,
% 0.30/0.57 ( ( finite_card_real @ bot_bot_set_real )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % card.empty
% 0.30/0.57 thf(fact_2558_card_Oinfinite,axiom,
% 0.30/0.57 ! [A4: set_list_nat] :
% 0.30/0.57 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.infinite
% 0.30/0.57 thf(fact_2559_card_Oinfinite,axiom,
% 0.30/0.57 ! [A4: set_set_nat] :
% 0.30/0.57 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.infinite
% 0.30/0.57 thf(fact_2560_card_Oinfinite,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ~ ( finite_finite_nat @ A4 )
% 0.30/0.57 => ( ( finite_card_nat @ A4 )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.infinite
% 0.30/0.57 thf(fact_2561_card_Oinfinite,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ~ ( finite_finite_int @ A4 )
% 0.30/0.57 => ( ( finite_card_int @ A4 )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.infinite
% 0.30/0.57 thf(fact_2562_card_Oinfinite,axiom,
% 0.30/0.57 ! [A4: set_complex] :
% 0.30/0.57 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ( finite_card_complex @ A4 )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.infinite
% 0.30/0.57 thf(fact_2563_Gcd__fin_Oempty,axiom,
% 0.30/0.57 ( ( semiri4258706085729940814in_nat @ bot_bot_set_nat )
% 0.30/0.57 = zero_zero_nat ) ).
% 0.30/0.57
% 0.30/0.57 % Gcd_fin.empty
% 0.30/0.57 thf(fact_2564_Gcd__fin_Oempty,axiom,
% 0.30/0.57 ( ( semiri4256215615220890538in_int @ bot_bot_set_int )
% 0.30/0.57 = zero_zero_int ) ).
% 0.30/0.57
% 0.30/0.57 % Gcd_fin.empty
% 0.30/0.57 thf(fact_2565_power__eq__0__iff,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ( power_power_rat @ A @ N )
% 0.30/0.57 = zero_zero_rat )
% 0.30/0.57 = ( ( A = zero_zero_rat )
% 0.30/0.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_0_iff
% 0.30/0.57 thf(fact_2566_power__eq__0__iff,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ( power_power_nat @ A @ N )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( A = zero_zero_nat )
% 0.30/0.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_0_iff
% 0.30/0.57 thf(fact_2567_power__eq__0__iff,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ( power_power_real @ A @ N )
% 0.30/0.57 = zero_zero_real )
% 0.30/0.57 = ( ( A = zero_zero_real )
% 0.30/0.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_0_iff
% 0.30/0.57 thf(fact_2568_power__eq__0__iff,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ( power_power_int @ A @ N )
% 0.30/0.57 = zero_zero_int )
% 0.30/0.57 = ( ( A = zero_zero_int )
% 0.30/0.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_0_iff
% 0.30/0.57 thf(fact_2569_power__eq__0__iff,axiom,
% 0.30/0.57 ! [A: complex,N: nat] :
% 0.30/0.57 ( ( ( power_power_complex @ A @ N )
% 0.30/0.57 = zero_zero_complex )
% 0.30/0.57 = ( ( A = zero_zero_complex )
% 0.30/0.57 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_0_iff
% 0.30/0.57 thf(fact_2570_card__0__eq,axiom,
% 0.30/0.57 ! [A4: set_list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( A4 = bot_bot_set_list_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_0_eq
% 0.30/0.57 thf(fact_2571_card__0__eq,axiom,
% 0.30/0.57 ! [A4: set_set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( A4 = bot_bot_set_set_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_0_eq
% 0.30/0.57 thf(fact_2572_card__0__eq,axiom,
% 0.30/0.57 ! [A4: set_complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ( ( finite_card_complex @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( A4 = bot_bot_set_complex ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_0_eq
% 0.30/0.57 thf(fact_2573_card__0__eq,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ( finite_finite_nat @ A4 )
% 0.30/0.57 => ( ( ( finite_card_nat @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( A4 = bot_bot_set_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_0_eq
% 0.30/0.57 thf(fact_2574_card__0__eq,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ( finite_finite_int @ A4 )
% 0.30/0.57 => ( ( ( finite_card_int @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( A4 = bot_bot_set_int ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_0_eq
% 0.30/0.57 thf(fact_2575_card__0__eq,axiom,
% 0.30/0.57 ! [A4: set_real] :
% 0.30/0.57 ( ( finite_finite_real @ A4 )
% 0.30/0.57 => ( ( ( finite_card_real @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( A4 = bot_bot_set_real ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_0_eq
% 0.30/0.57 thf(fact_2576_card__insert__disjoint,axiom,
% 0.30/0.57 ! [A4: set_real,X: real] :
% 0.30/0.57 ( ( finite_finite_real @ A4 )
% 0.30/0.57 => ( ~ ( member_real @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_disjoint
% 0.30/0.57 thf(fact_2577_card__insert__disjoint,axiom,
% 0.30/0.57 ! [A4: set_list_nat,X: list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ~ ( member_list_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_disjoint
% 0.30/0.57 thf(fact_2578_card__insert__disjoint,axiom,
% 0.30/0.57 ! [A4: set_set_nat,X: set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ~ ( member_set_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_disjoint
% 0.30/0.57 thf(fact_2579_card__insert__disjoint,axiom,
% 0.30/0.57 ! [A4: set_nat,X: nat] :
% 0.30/0.57 ( ( finite_finite_nat @ A4 )
% 0.30/0.57 => ( ~ ( member_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_disjoint
% 0.30/0.57 thf(fact_2580_card__insert__disjoint,axiom,
% 0.30/0.57 ! [A4: set_int,X: int] :
% 0.30/0.57 ( ( finite_finite_int @ A4 )
% 0.30/0.57 => ( ~ ( member_int @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_disjoint
% 0.30/0.57 thf(fact_2581_card__insert__disjoint,axiom,
% 0.30/0.57 ! [A4: set_complex,X: complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ~ ( member_complex @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_disjoint
% 0.30/0.57 thf(fact_2582_power__strict__decreasing__iff,axiom,
% 0.30/0.57 ! [B: code_integer,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.30/0.57 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 0.30/0.57 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 0.30/0.57 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing_iff
% 0.30/0.57 thf(fact_2583_power__strict__decreasing__iff,axiom,
% 0.30/0.57 ! [B: real,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ zero_zero_real @ B )
% 0.30/0.57 => ( ( ord_less_real @ B @ one_one_real )
% 0.30/0.57 => ( ( ord_less_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 0.30/0.57 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing_iff
% 0.30/0.57 thf(fact_2584_power__strict__decreasing__iff,axiom,
% 0.30/0.57 ! [B: rat,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( ( ord_less_rat @ B @ one_one_rat )
% 0.30/0.57 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 0.30/0.57 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing_iff
% 0.30/0.57 thf(fact_2585_power__strict__decreasing__iff,axiom,
% 0.30/0.57 ! [B: nat,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( ( ord_less_nat @ B @ one_one_nat )
% 0.30/0.57 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 0.30/0.57 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing_iff
% 0.30/0.57 thf(fact_2586_power__strict__decreasing__iff,axiom,
% 0.30/0.57 ! [B: int,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ zero_zero_int @ B )
% 0.30/0.57 => ( ( ord_less_int @ B @ one_one_int )
% 0.30/0.57 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 0.30/0.57 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing_iff
% 0.30/0.57 thf(fact_2587_power__increasing__iff,axiom,
% 0.30/0.57 ! [B: code_integer,X: nat,Y: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 0.30/0.57 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing_iff
% 0.30/0.57 thf(fact_2588_power__increasing__iff,axiom,
% 0.30/0.57 ! [B: real,X: nat,Y: nat] :
% 0.30/0.57 ( ( ord_less_real @ one_one_real @ B )
% 0.30/0.57 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 0.30/0.57 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing_iff
% 0.30/0.57 thf(fact_2589_power__increasing__iff,axiom,
% 0.30/0.57 ! [B: rat,X: nat,Y: nat] :
% 0.30/0.57 ( ( ord_less_rat @ one_one_rat @ B )
% 0.30/0.57 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 0.30/0.57 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing_iff
% 0.30/0.57 thf(fact_2590_power__increasing__iff,axiom,
% 0.30/0.57 ! [B: nat,X: nat,Y: nat] :
% 0.30/0.57 ( ( ord_less_nat @ one_one_nat @ B )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 0.30/0.57 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing_iff
% 0.30/0.57 thf(fact_2591_power__increasing__iff,axiom,
% 0.30/0.57 ! [B: int,X: nat,Y: nat] :
% 0.30/0.57 ( ( ord_less_int @ one_one_int @ B )
% 0.30/0.57 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 0.30/0.57 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing_iff
% 0.30/0.57 thf(fact_2592_power__mono__iff,axiom,
% 0.30/0.57 ! [A: real,B: real,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono_iff
% 0.30/0.57 thf(fact_2593_power__mono__iff,axiom,
% 0.30/0.57 ! [A: rat,B: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono_iff
% 0.30/0.57 thf(fact_2594_power__mono__iff,axiom,
% 0.30/0.57 ! [A: nat,B: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono_iff
% 0.30/0.57 thf(fact_2595_power__mono__iff,axiom,
% 0.30/0.57 ! [A: int,B: int,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.30/0.57 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono_iff
% 0.30/0.57 thf(fact_2596_power__not__zero,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( A != zero_zero_rat )
% 0.30/0.57 => ( ( power_power_rat @ A @ N )
% 0.30/0.57 != zero_zero_rat ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_not_zero
% 0.30/0.57 thf(fact_2597_power__not__zero,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( A != zero_zero_nat )
% 0.30/0.57 => ( ( power_power_nat @ A @ N )
% 0.30/0.57 != zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_not_zero
% 0.30/0.57 thf(fact_2598_power__not__zero,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( A != zero_zero_real )
% 0.30/0.57 => ( ( power_power_real @ A @ N )
% 0.30/0.57 != zero_zero_real ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_not_zero
% 0.30/0.57 thf(fact_2599_power__not__zero,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( A != zero_zero_int )
% 0.30/0.57 => ( ( power_power_int @ A @ N )
% 0.30/0.57 != zero_zero_int ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_not_zero
% 0.30/0.57 thf(fact_2600_power__not__zero,axiom,
% 0.30/0.57 ! [A: complex,N: nat] :
% 0.30/0.57 ( ( A != zero_zero_complex )
% 0.30/0.57 => ( ( power_power_complex @ A @ N )
% 0.30/0.57 != zero_zero_complex ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_not_zero
% 0.30/0.57 thf(fact_2601_power__commuting__commutes,axiom,
% 0.30/0.57 ! [X: complex,Y: complex,N: nat] :
% 0.30/0.57 ( ( ( times_times_complex @ X @ Y )
% 0.30/0.57 = ( times_times_complex @ Y @ X ) )
% 0.30/0.57 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y )
% 0.30/0.57 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commuting_commutes
% 0.30/0.57 thf(fact_2602_power__commuting__commutes,axiom,
% 0.30/0.57 ! [X: real,Y: real,N: nat] :
% 0.30/0.57 ( ( ( times_times_real @ X @ Y )
% 0.30/0.57 = ( times_times_real @ Y @ X ) )
% 0.30/0.57 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y )
% 0.30/0.57 = ( times_times_real @ Y @ ( power_power_real @ X @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commuting_commutes
% 0.30/0.57 thf(fact_2603_power__commuting__commutes,axiom,
% 0.30/0.57 ! [X: rat,Y: rat,N: nat] :
% 0.30/0.57 ( ( ( times_times_rat @ X @ Y )
% 0.30/0.57 = ( times_times_rat @ Y @ X ) )
% 0.30/0.57 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 0.30/0.57 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commuting_commutes
% 0.30/0.57 thf(fact_2604_power__commuting__commutes,axiom,
% 0.30/0.57 ! [X: nat,Y: nat,N: nat] :
% 0.30/0.57 ( ( ( times_times_nat @ X @ Y )
% 0.30/0.57 = ( times_times_nat @ Y @ X ) )
% 0.30/0.57 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 0.30/0.57 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commuting_commutes
% 0.30/0.57 thf(fact_2605_power__commuting__commutes,axiom,
% 0.30/0.57 ! [X: int,Y: int,N: nat] :
% 0.30/0.57 ( ( ( times_times_int @ X @ Y )
% 0.30/0.57 = ( times_times_int @ Y @ X ) )
% 0.30/0.57 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 0.30/0.57 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commuting_commutes
% 0.30/0.57 thf(fact_2606_power__mult__distrib,axiom,
% 0.30/0.57 ! [A: complex,B: complex,N: nat] :
% 0.30/0.57 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 0.30/0.57 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult_distrib
% 0.30/0.57 thf(fact_2607_power__mult__distrib,axiom,
% 0.30/0.57 ! [A: real,B: real,N: nat] :
% 0.30/0.57 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 0.30/0.57 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult_distrib
% 0.30/0.57 thf(fact_2608_power__mult__distrib,axiom,
% 0.30/0.57 ! [A: rat,B: rat,N: nat] :
% 0.30/0.57 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 0.30/0.57 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult_distrib
% 0.30/0.57 thf(fact_2609_power__mult__distrib,axiom,
% 0.30/0.57 ! [A: nat,B: nat,N: nat] :
% 0.30/0.57 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 0.30/0.57 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult_distrib
% 0.30/0.57 thf(fact_2610_power__mult__distrib,axiom,
% 0.30/0.57 ! [A: int,B: int,N: nat] :
% 0.30/0.57 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 0.30/0.57 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult_distrib
% 0.30/0.57 thf(fact_2611_power__commutes,axiom,
% 0.30/0.57 ! [A: complex,N: nat] :
% 0.30/0.57 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 0.30/0.57 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commutes
% 0.30/0.57 thf(fact_2612_power__commutes,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 0.30/0.57 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commutes
% 0.30/0.57 thf(fact_2613_power__commutes,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 0.30/0.57 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commutes
% 0.30/0.57 thf(fact_2614_power__commutes,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 0.30/0.57 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commutes
% 0.30/0.57 thf(fact_2615_power__commutes,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 0.30/0.57 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_commutes
% 0.30/0.57 thf(fact_2616_power__mult,axiom,
% 0.30/0.57 ! [A: nat,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_nat @ A @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.57 = ( power_power_nat @ ( power_power_nat @ A @ M2 ) @ N ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult
% 0.30/0.57 thf(fact_2617_power__mult,axiom,
% 0.30/0.57 ! [A: real,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_real @ A @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.57 = ( power_power_real @ ( power_power_real @ A @ M2 ) @ N ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult
% 0.30/0.57 thf(fact_2618_power__mult,axiom,
% 0.30/0.57 ! [A: int,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_int @ A @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.57 = ( power_power_int @ ( power_power_int @ A @ M2 ) @ N ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult
% 0.30/0.57 thf(fact_2619_power__mult,axiom,
% 0.30/0.57 ! [A: complex,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_complex @ A @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.57 = ( power_power_complex @ ( power_power_complex @ A @ M2 ) @ N ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mult
% 0.30/0.57 thf(fact_2620_finite__le__enumerate,axiom,
% 0.30/0.57 ! [S3: set_nat,N: nat] :
% 0.30/0.57 ( ( finite_finite_nat @ S3 )
% 0.30/0.57 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_le_enumerate
% 0.30/0.57 thf(fact_2621_lenlex__irreflexive,axiom,
% 0.30/0.57 ! [R3: set_Pr4811707699266497531nteger,Xs2: list_Code_integer] :
% 0.30/0.57 ( ! [X3: code_integer] :
% 0.30/0.57 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ X3 ) @ R3 )
% 0.30/0.57 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Xs2 ) @ ( lenlex_Code_integer @ R3 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_irreflexive
% 0.30/0.57 thf(fact_2622_lenlex__irreflexive,axiom,
% 0.30/0.57 ! [R3: set_Pr8693737435421807431at_nat,Xs2: list_P6011104703257516679at_nat] :
% 0.30/0.57 ( ! [X3: product_prod_nat_nat] :
% 0.30/0.57 ~ ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ X3 ) @ R3 )
% 0.30/0.57 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Xs2 ) @ ( lenlex325483962726685836at_nat @ R3 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_irreflexive
% 0.30/0.57 thf(fact_2623_lenlex__irreflexive,axiom,
% 0.30/0.57 ! [R3: set_Pr4329608150637261639at_nat,Xs2: list_s1210847774152347623at_nat] :
% 0.30/0.57 ( ! [X3: set_Pr1261947904930325089at_nat] :
% 0.30/0.57 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ X3 ) @ R3 )
% 0.30/0.57 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Xs2 ) @ ( lenlex1357538814655152620at_nat @ R3 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_irreflexive
% 0.30/0.57 thf(fact_2624_lenlex__irreflexive,axiom,
% 0.30/0.57 ! [R3: set_Pr1261947904930325089at_nat,Xs2: list_nat] :
% 0.30/0.57 ( ! [X3: nat] :
% 0.30/0.57 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R3 )
% 0.30/0.57 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Xs2 ) @ ( lenlex_nat @ R3 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_irreflexive
% 0.30/0.57 thf(fact_2625_lenlex__irreflexive,axiom,
% 0.30/0.57 ! [R3: set_Pr958786334691620121nt_int,Xs2: list_int] :
% 0.30/0.57 ( ! [X3: int] :
% 0.30/0.57 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ R3 )
% 0.30/0.57 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Xs2 ) @ ( lenlex_int @ R3 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_irreflexive
% 0.30/0.57 thf(fact_2626_zero__le__power,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_le_power
% 0.30/0.57 thf(fact_2627_zero__le__power,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_le_power
% 0.30/0.57 thf(fact_2628_zero__le__power,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_le_power
% 0.30/0.57 thf(fact_2629_zero__le__power,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_le_power
% 0.30/0.57 thf(fact_2630_power__mono,axiom,
% 0.30/0.57 ! [A: real,B: real,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_real @ A @ B )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono
% 0.30/0.57 thf(fact_2631_power__mono,axiom,
% 0.30/0.57 ! [A: rat,B: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ A @ B )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono
% 0.30/0.57 thf(fact_2632_power__mono,axiom,
% 0.30/0.57 ! [A: nat,B: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ A @ B )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono
% 0.30/0.57 thf(fact_2633_power__mono,axiom,
% 0.30/0.57 ! [A: int,B: int,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_int @ A @ B )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_mono
% 0.30/0.57 thf(fact_2634_finite__enumerate__step,axiom,
% 0.30/0.57 ! [S3: set_nat,N: nat] :
% 0.30/0.57 ( ( finite_finite_nat @ S3 )
% 0.30/0.57 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite_card_nat @ S3 ) )
% 0.30/0.57 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_enumerate_step
% 0.30/0.57 thf(fact_2635_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_real,A4: set_real,R3: real > real > $o] :
% 0.30/0.57 ( ( finite_finite_real @ B5 )
% 0.30/0.57 => ( ! [A3: real] :
% 0.30/0.57 ( ( member_real @ A3 @ A4 )
% 0.30/0.57 => ? [B6: real] :
% 0.30/0.57 ( ( member_real @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: real,A22: real,B3: real] :
% 0.30/0.57 ( ( member_real @ A1 @ A4 )
% 0.30/0.57 => ( ( member_real @ A22 @ A4 )
% 0.30/0.57 => ( ( member_real @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2636_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_real,A4: set_nat,R3: nat > real > $o] :
% 0.30/0.57 ( ( finite_finite_real @ B5 )
% 0.30/0.57 => ( ! [A3: nat] :
% 0.30/0.57 ( ( member_nat @ A3 @ A4 )
% 0.30/0.57 => ? [B6: real] :
% 0.30/0.57 ( ( member_real @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: nat,A22: nat,B3: real] :
% 0.30/0.57 ( ( member_nat @ A1 @ A4 )
% 0.30/0.57 => ( ( member_nat @ A22 @ A4 )
% 0.30/0.57 => ( ( member_real @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2637_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_real,A4: set_complex,R3: complex > real > $o] :
% 0.30/0.57 ( ( finite_finite_real @ B5 )
% 0.30/0.57 => ( ! [A3: complex] :
% 0.30/0.57 ( ( member_complex @ A3 @ A4 )
% 0.30/0.57 => ? [B6: real] :
% 0.30/0.57 ( ( member_real @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: complex,A22: complex,B3: real] :
% 0.30/0.57 ( ( member_complex @ A1 @ A4 )
% 0.30/0.57 => ( ( member_complex @ A22 @ A4 )
% 0.30/0.57 => ( ( member_real @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2638_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_real,A4: set_int,R3: int > real > $o] :
% 0.30/0.57 ( ( finite_finite_real @ B5 )
% 0.30/0.57 => ( ! [A3: int] :
% 0.30/0.57 ( ( member_int @ A3 @ A4 )
% 0.30/0.57 => ? [B6: real] :
% 0.30/0.57 ( ( member_real @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: int,A22: int,B3: real] :
% 0.30/0.57 ( ( member_int @ A1 @ A4 )
% 0.30/0.57 => ( ( member_int @ A22 @ A4 )
% 0.30/0.57 => ( ( member_real @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2639_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_nat,A4: set_real,R3: real > nat > $o] :
% 0.30/0.57 ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ! [A3: real] :
% 0.30/0.57 ( ( member_real @ A3 @ A4 )
% 0.30/0.57 => ? [B6: nat] :
% 0.30/0.57 ( ( member_nat @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: real,A22: real,B3: nat] :
% 0.30/0.57 ( ( member_real @ A1 @ A4 )
% 0.30/0.57 => ( ( member_real @ A22 @ A4 )
% 0.30/0.57 => ( ( member_nat @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2640_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_nat,A4: set_nat,R3: nat > nat > $o] :
% 0.30/0.57 ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ! [A3: nat] :
% 0.30/0.57 ( ( member_nat @ A3 @ A4 )
% 0.30/0.57 => ? [B6: nat] :
% 0.30/0.57 ( ( member_nat @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: nat,A22: nat,B3: nat] :
% 0.30/0.57 ( ( member_nat @ A1 @ A4 )
% 0.30/0.57 => ( ( member_nat @ A22 @ A4 )
% 0.30/0.57 => ( ( member_nat @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2641_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_nat,A4: set_complex,R3: complex > nat > $o] :
% 0.30/0.57 ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ! [A3: complex] :
% 0.30/0.57 ( ( member_complex @ A3 @ A4 )
% 0.30/0.57 => ? [B6: nat] :
% 0.30/0.57 ( ( member_nat @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: complex,A22: complex,B3: nat] :
% 0.30/0.57 ( ( member_complex @ A1 @ A4 )
% 0.30/0.57 => ( ( member_complex @ A22 @ A4 )
% 0.30/0.57 => ( ( member_nat @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2642_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_nat,A4: set_int,R3: int > nat > $o] :
% 0.30/0.57 ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ! [A3: int] :
% 0.30/0.57 ( ( member_int @ A3 @ A4 )
% 0.30/0.57 => ? [B6: nat] :
% 0.30/0.57 ( ( member_nat @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: int,A22: int,B3: nat] :
% 0.30/0.57 ( ( member_int @ A1 @ A4 )
% 0.30/0.57 => ( ( member_int @ A22 @ A4 )
% 0.30/0.57 => ( ( member_nat @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2643_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_int,A4: set_real,R3: real > int > $o] :
% 0.30/0.57 ( ( finite_finite_int @ B5 )
% 0.30/0.57 => ( ! [A3: real] :
% 0.30/0.57 ( ( member_real @ A3 @ A4 )
% 0.30/0.57 => ? [B6: int] :
% 0.30/0.57 ( ( member_int @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: real,A22: real,B3: int] :
% 0.30/0.57 ( ( member_real @ A1 @ A4 )
% 0.30/0.57 => ( ( member_real @ A22 @ A4 )
% 0.30/0.57 => ( ( member_int @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2644_card__le__if__inj__on__rel,axiom,
% 0.30/0.57 ! [B5: set_int,A4: set_nat,R3: nat > int > $o] :
% 0.30/0.57 ( ( finite_finite_int @ B5 )
% 0.30/0.57 => ( ! [A3: nat] :
% 0.30/0.57 ( ( member_nat @ A3 @ A4 )
% 0.30/0.57 => ? [B6: int] :
% 0.30/0.57 ( ( member_int @ B6 @ B5 )
% 0.30/0.57 & ( R3 @ A3 @ B6 ) ) )
% 0.30/0.57 => ( ! [A1: nat,A22: nat,B3: int] :
% 0.30/0.57 ( ( member_nat @ A1 @ A4 )
% 0.30/0.57 => ( ( member_nat @ A22 @ A4 )
% 0.30/0.57 => ( ( member_int @ B3 @ B5 )
% 0.30/0.57 => ( ( R3 @ A1 @ B3 )
% 0.30/0.57 => ( ( R3 @ A22 @ B3 )
% 0.30/0.57 => ( A1 = A22 ) ) ) ) ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_if_inj_on_rel
% 0.30/0.57 thf(fact_2645_zero__less__power,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_less_power
% 0.30/0.57 thf(fact_2646_zero__less__power,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_less_power
% 0.30/0.57 thf(fact_2647_zero__less__power,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_less_power
% 0.30/0.57 thf(fact_2648_zero__less__power,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_less_power
% 0.30/0.57 thf(fact_2649_card__insert__le,axiom,
% 0.30/0.57 ! [A4: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ ( insert_real @ X @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le
% 0.30/0.57 thf(fact_2650_card__insert__le,axiom,
% 0.30/0.57 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le
% 0.30/0.57 thf(fact_2651_card__insert__le,axiom,
% 0.30/0.57 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ ( insert_complex @ X @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le
% 0.30/0.57 thf(fact_2652_card__insert__le,axiom,
% 0.30/0.57 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le
% 0.30/0.57 thf(fact_2653_card__insert__le,axiom,
% 0.30/0.57 ! [A4: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le
% 0.30/0.57 thf(fact_2654_card__insert__le,axiom,
% 0.30/0.57 ! [A4: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_le
% 0.30/0.57 thf(fact_2655_one__le__power,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_le_power
% 0.30/0.57 thf(fact_2656_one__le__power,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_real @ one_one_real @ A )
% 0.30/0.57 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_le_power
% 0.30/0.57 thf(fact_2657_one__le__power,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_le_power
% 0.30/0.57 thf(fact_2658_one__le__power,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_le_power
% 0.30/0.57 thf(fact_2659_one__le__power,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_int @ one_one_int @ A )
% 0.30/0.57 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_le_power
% 0.30/0.57 thf(fact_2660_left__right__inverse__power,axiom,
% 0.30/0.57 ! [X: code_integer,Y: code_integer,N: nat] :
% 0.30/0.57 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 0.30/0.57 = one_one_Code_integer )
% 0.30/0.57 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 0.30/0.57 = one_one_Code_integer ) ) ).
% 0.30/0.57
% 0.30/0.57 % left_right_inverse_power
% 0.30/0.57 thf(fact_2661_left__right__inverse__power,axiom,
% 0.30/0.57 ! [X: complex,Y: complex,N: nat] :
% 0.30/0.57 ( ( ( times_times_complex @ X @ Y )
% 0.30/0.57 = one_one_complex )
% 0.30/0.57 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 0.30/0.57 = one_one_complex ) ) ).
% 0.30/0.57
% 0.30/0.57 % left_right_inverse_power
% 0.30/0.57 thf(fact_2662_left__right__inverse__power,axiom,
% 0.30/0.57 ! [X: real,Y: real,N: nat] :
% 0.30/0.57 ( ( ( times_times_real @ X @ Y )
% 0.30/0.57 = one_one_real )
% 0.30/0.57 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 0.30/0.57 = one_one_real ) ) ).
% 0.30/0.57
% 0.30/0.57 % left_right_inverse_power
% 0.30/0.57 thf(fact_2663_left__right__inverse__power,axiom,
% 0.30/0.57 ! [X: rat,Y: rat,N: nat] :
% 0.30/0.57 ( ( ( times_times_rat @ X @ Y )
% 0.30/0.57 = one_one_rat )
% 0.30/0.57 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 0.30/0.57 = one_one_rat ) ) ).
% 0.30/0.57
% 0.30/0.57 % left_right_inverse_power
% 0.30/0.57 thf(fact_2664_left__right__inverse__power,axiom,
% 0.30/0.57 ! [X: nat,Y: nat,N: nat] :
% 0.30/0.57 ( ( ( times_times_nat @ X @ Y )
% 0.30/0.57 = one_one_nat )
% 0.30/0.57 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 0.30/0.57 = one_one_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % left_right_inverse_power
% 0.30/0.57 thf(fact_2665_left__right__inverse__power,axiom,
% 0.30/0.57 ! [X: int,Y: int,N: nat] :
% 0.30/0.57 ( ( ( times_times_int @ X @ Y )
% 0.30/0.57 = one_one_int )
% 0.30/0.57 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.30/0.57 = one_one_int ) ) ).
% 0.30/0.57
% 0.30/0.57 % left_right_inverse_power
% 0.30/0.57 thf(fact_2666_finite__enum__subset,axiom,
% 0.30/0.57 ! [X8: set_nat,Y7: set_nat] :
% 0.30/0.57 ( ! [I3: nat] :
% 0.30/0.57 ( ( ord_less_nat @ I3 @ ( finite_card_nat @ X8 ) )
% 0.30/0.57 => ( ( infini8530281810654367211te_nat @ X8 @ I3 )
% 0.30/0.57 = ( infini8530281810654367211te_nat @ Y7 @ I3 ) ) )
% 0.30/0.57 => ( ( finite_finite_nat @ X8 )
% 0.30/0.57 => ( ( finite_finite_nat @ Y7 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ X8 ) @ ( finite_card_nat @ Y7 ) )
% 0.30/0.57 => ( ord_less_eq_set_nat @ X8 @ Y7 ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_enum_subset
% 0.30/0.57 thf(fact_2667_power__Suc,axiom,
% 0.30/0.57 ! [A: complex,N: nat] :
% 0.30/0.57 ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc
% 0.30/0.57 thf(fact_2668_power__Suc,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( power_power_real @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc
% 0.30/0.57 thf(fact_2669_power__Suc,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc
% 0.30/0.57 thf(fact_2670_power__Suc,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc
% 0.30/0.57 thf(fact_2671_power__Suc,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( power_power_int @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc
% 0.30/0.57 thf(fact_2672_power__Suc2,axiom,
% 0.30/0.57 ! [A: complex,N: nat] :
% 0.30/0.57 ( ( power_power_complex @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc2
% 0.30/0.57 thf(fact_2673_power__Suc2,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( power_power_real @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc2
% 0.30/0.57 thf(fact_2674_power__Suc2,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc2
% 0.30/0.57 thf(fact_2675_power__Suc2,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc2
% 0.30/0.57 thf(fact_2676_power__Suc2,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( power_power_int @ A @ ( suc @ N ) )
% 0.30/0.57 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc2
% 0.30/0.57 thf(fact_2677_power__0,axiom,
% 0.30/0.57 ! [A: code_integer] :
% 0.30/0.57 ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 0.30/0.57 = one_one_Code_integer ) ).
% 0.30/0.57
% 0.30/0.57 % power_0
% 0.30/0.57 thf(fact_2678_power__0,axiom,
% 0.30/0.57 ! [A: nat] :
% 0.30/0.57 ( ( power_power_nat @ A @ zero_zero_nat )
% 0.30/0.57 = one_one_nat ) ).
% 0.30/0.57
% 0.30/0.57 % power_0
% 0.30/0.57 thf(fact_2679_power__0,axiom,
% 0.30/0.57 ! [A: real] :
% 0.30/0.57 ( ( power_power_real @ A @ zero_zero_nat )
% 0.30/0.57 = one_one_real ) ).
% 0.30/0.57
% 0.30/0.57 % power_0
% 0.30/0.57 thf(fact_2680_power__0,axiom,
% 0.30/0.57 ! [A: int] :
% 0.30/0.57 ( ( power_power_int @ A @ zero_zero_nat )
% 0.30/0.57 = one_one_int ) ).
% 0.30/0.57
% 0.30/0.57 % power_0
% 0.30/0.57 thf(fact_2681_power__0,axiom,
% 0.30/0.57 ! [A: complex] :
% 0.30/0.57 ( ( power_power_complex @ A @ zero_zero_nat )
% 0.30/0.57 = one_one_complex ) ).
% 0.30/0.57
% 0.30/0.57 % power_0
% 0.30/0.57 thf(fact_2682_power__add,axiom,
% 0.30/0.57 ! [A: complex,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_complex @ A @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.57 = ( times_times_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_add
% 0.30/0.57 thf(fact_2683_power__add,axiom,
% 0.30/0.57 ! [A: real,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_real @ A @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.57 = ( times_times_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_add
% 0.30/0.57 thf(fact_2684_power__add,axiom,
% 0.30/0.57 ! [A: rat,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_rat @ A @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.57 = ( times_times_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_add
% 0.30/0.57 thf(fact_2685_power__add,axiom,
% 0.30/0.57 ! [A: nat,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_nat @ A @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.57 = ( times_times_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_add
% 0.30/0.57 thf(fact_2686_power__add,axiom,
% 0.30/0.57 ! [A: int,M2: nat,N: nat] :
% 0.30/0.57 ( ( power_power_int @ A @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.57 = ( times_times_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_add
% 0.30/0.57 thf(fact_2687_nat__power__less__imp__less,axiom,
% 0.30/0.57 ! [I2: nat,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 0.30/0.57 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M2 ) @ ( power_power_nat @ I2 @ N ) )
% 0.30/0.57 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nat_power_less_imp_less
% 0.30/0.57 thf(fact_2688_le__enumerate,axiom,
% 0.30/0.57 ! [S3: set_nat,N: nat] :
% 0.30/0.57 ( ~ ( finite_finite_nat @ S3 )
% 0.30/0.57 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % le_enumerate
% 0.30/0.57 thf(fact_2689_card__eq__0__iff,axiom,
% 0.30/0.57 ! [A4: set_list_nat] :
% 0.30/0.57 ( ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( A4 = bot_bot_set_list_nat )
% 0.30/0.57 | ~ ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_0_iff
% 0.30/0.57 thf(fact_2690_card__eq__0__iff,axiom,
% 0.30/0.57 ! [A4: set_set_nat] :
% 0.30/0.57 ( ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( A4 = bot_bot_set_set_nat )
% 0.30/0.57 | ~ ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_0_iff
% 0.30/0.57 thf(fact_2691_card__eq__0__iff,axiom,
% 0.30/0.57 ! [A4: set_complex] :
% 0.30/0.57 ( ( ( finite_card_complex @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( A4 = bot_bot_set_complex )
% 0.30/0.57 | ~ ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_0_iff
% 0.30/0.57 thf(fact_2692_card__eq__0__iff,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ( ( finite_card_nat @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( A4 = bot_bot_set_nat )
% 0.30/0.57 | ~ ( finite_finite_nat @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_0_iff
% 0.30/0.57 thf(fact_2693_card__eq__0__iff,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ( ( finite_card_int @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( A4 = bot_bot_set_int )
% 0.30/0.57 | ~ ( finite_finite_int @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_0_iff
% 0.30/0.57 thf(fact_2694_card__eq__0__iff,axiom,
% 0.30/0.57 ! [A4: set_real] :
% 0.30/0.57 ( ( ( finite_card_real @ A4 )
% 0.30/0.57 = zero_zero_nat )
% 0.30/0.57 = ( ( A4 = bot_bot_set_real )
% 0.30/0.57 | ~ ( finite_finite_real @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_0_iff
% 0.30/0.57 thf(fact_2695_card__ge__0__finite,axiom,
% 0.30/0.57 ! [A4: set_list_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 0.30/0.57 => ( finite8100373058378681591st_nat @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_ge_0_finite
% 0.30/0.57 thf(fact_2696_card__ge__0__finite,axiom,
% 0.30/0.57 ! [A4: set_set_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 0.30/0.57 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_ge_0_finite
% 0.30/0.57 thf(fact_2697_card__ge__0__finite,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 0.30/0.57 => ( finite_finite_nat @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_ge_0_finite
% 0.30/0.57 thf(fact_2698_card__ge__0__finite,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 0.30/0.57 => ( finite_finite_int @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_ge_0_finite
% 0.30/0.57 thf(fact_2699_card__ge__0__finite,axiom,
% 0.30/0.57 ! [A4: set_complex] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.30/0.57 => ( finite3207457112153483333omplex @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_ge_0_finite
% 0.30/0.57 thf(fact_2700_card__insert__if,axiom,
% 0.30/0.57 ! [A4: set_real,X: real] :
% 0.30/0.57 ( ( finite_finite_real @ A4 )
% 0.30/0.57 => ( ( ( member_real @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 0.30/0.57 = ( finite_card_real @ A4 ) ) )
% 0.30/0.57 & ( ~ ( member_real @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_if
% 0.30/0.57 thf(fact_2701_card__insert__if,axiom,
% 0.30/0.57 ! [A4: set_list_nat,X: list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ( ( member_list_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.30/0.57 = ( finite_card_list_nat @ A4 ) ) )
% 0.30/0.57 & ( ~ ( member_list_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_if
% 0.30/0.57 thf(fact_2702_card__insert__if,axiom,
% 0.30/0.57 ! [A4: set_set_nat,X: set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ( ( member_set_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.30/0.57 = ( finite_card_set_nat @ A4 ) ) )
% 0.30/0.57 & ( ~ ( member_set_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_if
% 0.30/0.57 thf(fact_2703_card__insert__if,axiom,
% 0.30/0.57 ! [A4: set_nat,X: nat] :
% 0.30/0.57 ( ( finite_finite_nat @ A4 )
% 0.30/0.57 => ( ( ( member_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.30/0.57 = ( finite_card_nat @ A4 ) ) )
% 0.30/0.57 & ( ~ ( member_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_if
% 0.30/0.57 thf(fact_2704_card__insert__if,axiom,
% 0.30/0.57 ! [A4: set_int,X: int] :
% 0.30/0.57 ( ( finite_finite_int @ A4 )
% 0.30/0.57 => ( ( ( member_int @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.30/0.57 = ( finite_card_int @ A4 ) ) )
% 0.30/0.57 & ( ~ ( member_int @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_if
% 0.30/0.57 thf(fact_2705_card__insert__if,axiom,
% 0.30/0.57 ! [A4: set_complex,X: complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ( ( member_complex @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.30/0.57 = ( finite_card_complex @ A4 ) ) )
% 0.30/0.57 & ( ~ ( member_complex @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_insert_if
% 0.30/0.57 thf(fact_2706_card__Suc__eq__finite,axiom,
% 0.30/0.57 ! [A4: set_real,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_real @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: real,B7: set_real] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_real @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_real @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_real @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( finite_finite_real @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq_finite
% 0.30/0.57 thf(fact_2707_card__Suc__eq__finite,axiom,
% 0.30/0.57 ! [A4: set_list_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: list_nat,B7: set_list_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_list_nat @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_list_nat @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_list_nat @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( finite8100373058378681591st_nat @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq_finite
% 0.30/0.57 thf(fact_2708_card__Suc__eq__finite,axiom,
% 0.30/0.57 ! [A4: set_set_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: set_nat,B7: set_set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_set_nat @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_set_nat @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_set_nat @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( finite1152437895449049373et_nat @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq_finite
% 0.30/0.57 thf(fact_2709_card__Suc__eq__finite,axiom,
% 0.30/0.57 ! [A4: set_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: nat,B7: set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_nat @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_nat @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_nat @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq_finite
% 0.30/0.57 thf(fact_2710_card__Suc__eq__finite,axiom,
% 0.30/0.57 ! [A4: set_int,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_int @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: int,B7: set_int] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_int @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_int @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_int @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( finite_finite_int @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq_finite
% 0.30/0.57 thf(fact_2711_card__Suc__eq__finite,axiom,
% 0.30/0.57 ! [A4: set_complex,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_complex @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: complex,B7: set_complex] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_complex @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_complex @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_complex @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( finite3207457112153483333omplex @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq_finite
% 0.30/0.57 thf(fact_2712_power__less__imp__less__base,axiom,
% 0.30/0.57 ! [A: real,N: nat,B: real] :
% 0.30/0.57 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.57 => ( ord_less_real @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_imp_less_base
% 0.30/0.57 thf(fact_2713_power__less__imp__less__base,axiom,
% 0.30/0.57 ! [A: rat,N: nat,B: rat] :
% 0.30/0.57 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( ord_less_rat @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_imp_less_base
% 0.30/0.57 thf(fact_2714_power__less__imp__less__base,axiom,
% 0.30/0.57 ! [A: nat,N: nat,B: nat] :
% 0.30/0.57 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( ord_less_nat @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_imp_less_base
% 0.30/0.57 thf(fact_2715_power__less__imp__less__base,axiom,
% 0.30/0.57 ! [A: int,N: nat,B: int] :
% 0.30/0.57 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57 => ( ord_less_int @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_imp_less_base
% 0.30/0.57 thf(fact_2716_card__mono,axiom,
% 0.30/0.57 ! [B5: set_list_nat,A4: set_list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ B5 )
% 0.30/0.57 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_mono
% 0.30/0.57 thf(fact_2717_card__mono,axiom,
% 0.30/0.57 ! [B5: set_set_nat,A4: set_set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ B5 )
% 0.30/0.57 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_mono
% 0.30/0.57 thf(fact_2718_card__mono,axiom,
% 0.30/0.57 ! [B5: set_int,A4: set_int] :
% 0.30/0.57 ( ( finite_finite_int @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_mono
% 0.30/0.57 thf(fact_2719_card__mono,axiom,
% 0.30/0.57 ! [B5: set_complex,A4: set_complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ B5 )
% 0.30/0.57 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_mono
% 0.30/0.57 thf(fact_2720_card__mono,axiom,
% 0.30/0.57 ! [B5: set_nat,A4: set_nat] :
% 0.30/0.57 ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_mono
% 0.30/0.57 thf(fact_2721_card__seteq,axiom,
% 0.30/0.57 ! [B5: set_list_nat,A4: set_list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ B5 )
% 0.30/0.57 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B5 ) @ ( finite_card_list_nat @ A4 ) )
% 0.30/0.57 => ( A4 = B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_seteq
% 0.30/0.57 thf(fact_2722_card__seteq,axiom,
% 0.30/0.57 ! [B5: set_set_nat,A4: set_set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ B5 )
% 0.30/0.57 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B5 ) @ ( finite_card_set_nat @ A4 ) )
% 0.30/0.57 => ( A4 = B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_seteq
% 0.30/0.57 thf(fact_2723_card__seteq,axiom,
% 0.30/0.57 ! [B5: set_int,A4: set_int] :
% 0.30/0.57 ( ( finite_finite_int @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_int @ A4 ) )
% 0.30/0.57 => ( A4 = B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_seteq
% 0.30/0.57 thf(fact_2724_card__seteq,axiom,
% 0.30/0.57 ! [B5: set_complex,A4: set_complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ B5 )
% 0.30/0.57 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_complex @ B5 ) @ ( finite_card_complex @ A4 ) )
% 0.30/0.57 => ( A4 = B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_seteq
% 0.30/0.57 thf(fact_2725_card__seteq,axiom,
% 0.30/0.57 ! [B5: set_nat,A4: set_nat] :
% 0.30/0.57 ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_nat @ A4 ) )
% 0.30/0.57 => ( A4 = B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_seteq
% 0.30/0.57 thf(fact_2726_finite__if__finite__subsets__card__bdd,axiom,
% 0.30/0.57 ! [F3: set_list_nat,C4: nat] :
% 0.30/0.57 ( ! [G: set_list_nat] :
% 0.30/0.57 ( ( ord_le6045566169113846134st_nat @ G @ F3 )
% 0.30/0.57 => ( ( finite8100373058378681591st_nat @ G )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G ) @ C4 ) ) )
% 0.30/0.57 => ( ( finite8100373058378681591st_nat @ F3 )
% 0.30/0.57 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F3 ) @ C4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_if_finite_subsets_card_bdd
% 0.30/0.57 thf(fact_2727_finite__if__finite__subsets__card__bdd,axiom,
% 0.30/0.57 ! [F3: set_set_nat,C4: nat] :
% 0.30/0.57 ( ! [G: set_set_nat] :
% 0.30/0.57 ( ( ord_le6893508408891458716et_nat @ G @ F3 )
% 0.30/0.57 => ( ( finite1152437895449049373et_nat @ G )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G ) @ C4 ) ) )
% 0.30/0.57 => ( ( finite1152437895449049373et_nat @ F3 )
% 0.30/0.57 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F3 ) @ C4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_if_finite_subsets_card_bdd
% 0.30/0.57 thf(fact_2728_finite__if__finite__subsets__card__bdd,axiom,
% 0.30/0.57 ! [F3: set_int,C4: nat] :
% 0.30/0.57 ( ! [G: set_int] :
% 0.30/0.57 ( ( ord_less_eq_set_int @ G @ F3 )
% 0.30/0.57 => ( ( finite_finite_int @ G )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_int @ G ) @ C4 ) ) )
% 0.30/0.57 => ( ( finite_finite_int @ F3 )
% 0.30/0.57 & ( ord_less_eq_nat @ ( finite_card_int @ F3 ) @ C4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_if_finite_subsets_card_bdd
% 0.30/0.57 thf(fact_2729_finite__if__finite__subsets__card__bdd,axiom,
% 0.30/0.57 ! [F3: set_complex,C4: nat] :
% 0.30/0.57 ( ! [G: set_complex] :
% 0.30/0.57 ( ( ord_le211207098394363844omplex @ G @ F3 )
% 0.30/0.57 => ( ( finite3207457112153483333omplex @ G )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_complex @ G ) @ C4 ) ) )
% 0.30/0.57 => ( ( finite3207457112153483333omplex @ F3 )
% 0.30/0.57 & ( ord_less_eq_nat @ ( finite_card_complex @ F3 ) @ C4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_if_finite_subsets_card_bdd
% 0.30/0.57 thf(fact_2730_finite__if__finite__subsets__card__bdd,axiom,
% 0.30/0.57 ! [F3: set_nat,C4: nat] :
% 0.30/0.57 ( ! [G: set_nat] :
% 0.30/0.57 ( ( ord_less_eq_set_nat @ G @ F3 )
% 0.30/0.57 => ( ( finite_finite_nat @ G )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C4 ) ) )
% 0.30/0.57 => ( ( finite_finite_nat @ F3 )
% 0.30/0.57 & ( ord_less_eq_nat @ ( finite_card_nat @ F3 ) @ C4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % finite_if_finite_subsets_card_bdd
% 0.30/0.57 thf(fact_2731_obtain__subset__with__card__n,axiom,
% 0.30/0.57 ! [N: nat,S3: set_list_nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ S3 ) )
% 0.30/0.57 => ~ ! [T3: set_list_nat] :
% 0.30/0.57 ( ( ord_le6045566169113846134st_nat @ T3 @ S3 )
% 0.30/0.57 => ( ( ( finite_card_list_nat @ T3 )
% 0.30/0.57 = N )
% 0.30/0.57 => ~ ( finite8100373058378681591st_nat @ T3 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % obtain_subset_with_card_n
% 0.30/0.57 thf(fact_2732_obtain__subset__with__card__n,axiom,
% 0.30/0.57 ! [N: nat,S3: set_set_nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ S3 ) )
% 0.30/0.57 => ~ ! [T3: set_set_nat] :
% 0.30/0.57 ( ( ord_le6893508408891458716et_nat @ T3 @ S3 )
% 0.30/0.57 => ( ( ( finite_card_set_nat @ T3 )
% 0.30/0.57 = N )
% 0.30/0.57 => ~ ( finite1152437895449049373et_nat @ T3 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % obtain_subset_with_card_n
% 0.30/0.57 thf(fact_2733_obtain__subset__with__card__n,axiom,
% 0.30/0.57 ! [N: nat,S3: set_int] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ ( finite_card_int @ S3 ) )
% 0.30/0.57 => ~ ! [T3: set_int] :
% 0.30/0.57 ( ( ord_less_eq_set_int @ T3 @ S3 )
% 0.30/0.57 => ( ( ( finite_card_int @ T3 )
% 0.30/0.57 = N )
% 0.30/0.57 => ~ ( finite_finite_int @ T3 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % obtain_subset_with_card_n
% 0.30/0.57 thf(fact_2734_obtain__subset__with__card__n,axiom,
% 0.30/0.57 ! [N: nat,S3: set_complex] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ ( finite_card_complex @ S3 ) )
% 0.30/0.57 => ~ ! [T3: set_complex] :
% 0.30/0.57 ( ( ord_le211207098394363844omplex @ T3 @ S3 )
% 0.30/0.57 => ( ( ( finite_card_complex @ T3 )
% 0.30/0.57 = N )
% 0.30/0.57 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % obtain_subset_with_card_n
% 0.30/0.57 thf(fact_2735_obtain__subset__with__card__n,axiom,
% 0.30/0.57 ! [N: nat,S3: set_nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S3 ) )
% 0.30/0.57 => ~ ! [T3: set_nat] :
% 0.30/0.57 ( ( ord_less_eq_set_nat @ T3 @ S3 )
% 0.30/0.57 => ( ( ( finite_card_nat @ T3 )
% 0.30/0.57 = N )
% 0.30/0.57 => ~ ( finite_finite_nat @ T3 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % obtain_subset_with_card_n
% 0.30/0.57 thf(fact_2736_power__le__one,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.57 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_one
% 0.30/0.57 thf(fact_2737_power__le__one,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.30/0.57 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_one
% 0.30/0.57 thf(fact_2738_power__le__one,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.57 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_one
% 0.30/0.57 thf(fact_2739_power__le__one,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.57 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_one
% 0.30/0.57 thf(fact_2740_power__le__one,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.57 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_one
% 0.30/0.57 thf(fact_2741_power__inject__base,axiom,
% 0.30/0.57 ! [A: real,N: nat,B: real] :
% 0.30/0.57 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 0.30/0.57 = ( power_power_real @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.57 => ( A = B ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_inject_base
% 0.30/0.57 thf(fact_2742_power__inject__base,axiom,
% 0.30/0.57 ! [A: rat,N: nat,B: rat] :
% 0.30/0.57 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 0.30/0.57 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( A = B ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_inject_base
% 0.30/0.57 thf(fact_2743_power__inject__base,axiom,
% 0.30/0.57 ! [A: nat,N: nat,B: nat] :
% 0.30/0.57 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 0.30/0.57 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( A = B ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_inject_base
% 0.30/0.57 thf(fact_2744_power__inject__base,axiom,
% 0.30/0.57 ! [A: int,N: nat,B: int] :
% 0.30/0.57 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 0.30/0.57 = ( power_power_int @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57 => ( A = B ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_inject_base
% 0.30/0.57 thf(fact_2745_power__le__imp__le__base,axiom,
% 0.30/0.57 ! [A: real,N: nat,B: real] :
% 0.30/0.57 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.57 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_base
% 0.30/0.57 thf(fact_2746_power__le__imp__le__base,axiom,
% 0.30/0.57 ! [A: rat,N: nat,B: rat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_base
% 0.30/0.57 thf(fact_2747_power__le__imp__le__base,axiom,
% 0.30/0.57 ! [A: nat,N: nat,B: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_base
% 0.30/0.57 thf(fact_2748_power__le__imp__le__base,axiom,
% 0.30/0.57 ! [A: int,N: nat,B: int] :
% 0.30/0.57 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_base
% 0.30/0.57 thf(fact_2749_power__less__power__Suc,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_power_Suc
% 0.30/0.57 thf(fact_2750_power__less__power__Suc,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ one_one_real @ A )
% 0.30/0.57 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_power_Suc
% 0.30/0.57 thf(fact_2751_power__less__power__Suc,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_power_Suc
% 0.30/0.57 thf(fact_2752_power__less__power__Suc,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_power_Suc
% 0.30/0.57 thf(fact_2753_power__less__power__Suc,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.57 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_less_power_Suc
% 0.30/0.57 thf(fact_2754_power__gt1__lemma,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1_lemma
% 0.30/0.57 thf(fact_2755_power__gt1__lemma,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ one_one_real @ A )
% 0.30/0.57 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1_lemma
% 0.30/0.57 thf(fact_2756_power__gt1__lemma,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1_lemma
% 0.30/0.57 thf(fact_2757_power__gt1__lemma,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1_lemma
% 0.30/0.57 thf(fact_2758_power__gt1__lemma,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.57 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1_lemma
% 0.30/0.57 thf(fact_2759_card__le__sym__Diff,axiom,
% 0.30/0.57 ! [A4: set_list_nat,B5: set_list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ( finite8100373058378681591st_nat @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_sym_Diff
% 0.30/0.57 thf(fact_2760_card__le__sym__Diff,axiom,
% 0.30/0.57 ! [A4: set_set_nat,B5: set_set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ( finite1152437895449049373et_nat @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_sym_Diff
% 0.30/0.57 thf(fact_2761_card__le__sym__Diff,axiom,
% 0.30/0.57 ! [A4: set_int,B5: set_int] :
% 0.30/0.57 ( ( finite_finite_int @ A4 )
% 0.30/0.57 => ( ( finite_finite_int @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B5 @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_sym_Diff
% 0.30/0.57 thf(fact_2762_card__le__sym__Diff,axiom,
% 0.30/0.57 ! [A4: set_complex,B5: set_complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ( finite3207457112153483333omplex @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_sym_Diff
% 0.30/0.57 thf(fact_2763_card__le__sym__Diff,axiom,
% 0.30/0.57 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 0.30/0.57 ( ( finite6177210948735845034at_nat @ A4 )
% 0.30/0.57 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_sym_Diff
% 0.30/0.57 thf(fact_2764_card__le__sym__Diff,axiom,
% 0.30/0.57 ! [A4: set_nat,B5: set_nat] :
% 0.30/0.57 ( ( finite_finite_nat @ A4 )
% 0.30/0.57 => ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_sym_Diff
% 0.30/0.57 thf(fact_2765_card__length,axiom,
% 0.30/0.57 ! [Xs2: list_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( set_complex2 @ Xs2 ) ) @ ( size_s3451745648224563538omplex @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_length
% 0.30/0.57 thf(fact_2766_card__length,axiom,
% 0.30/0.57 ! [Xs2: list_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) ) @ ( size_s3023201423986296836st_nat @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_length
% 0.30/0.57 thf(fact_2767_card__length,axiom,
% 0.30/0.57 ! [Xs2: list_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) ) @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_length
% 0.30/0.57 thf(fact_2768_card__length,axiom,
% 0.30/0.57 ! [Xs2: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_length
% 0.30/0.57 thf(fact_2769_card__length,axiom,
% 0.30/0.57 ! [Xs2: list_o] : ( ord_less_eq_nat @ ( finite_card_o @ ( set_o2 @ Xs2 ) ) @ ( size_size_list_o @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_length
% 0.30/0.57 thf(fact_2770_card__length,axiom,
% 0.30/0.57 ! [Xs2: list_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( set_nat2 @ Xs2 ) ) @ ( size_size_list_nat @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_length
% 0.30/0.57 thf(fact_2771_card__length,axiom,
% 0.30/0.57 ! [Xs2: list_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( set_int2 @ Xs2 ) ) @ ( size_size_list_int @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_length
% 0.30/0.57 thf(fact_2772_power__gt1,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1
% 0.30/0.57 thf(fact_2773_power__gt1,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ one_one_real @ A )
% 0.30/0.57 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1
% 0.30/0.57 thf(fact_2774_power__gt1,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1
% 0.30/0.57 thf(fact_2775_power__gt1,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1
% 0.30/0.57 thf(fact_2776_power__gt1,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.57 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt1
% 0.30/0.57 thf(fact_2777_power__0__left,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 0.30/0.57 = one_one_Code_integer ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 0.30/0.57 = zero_z3403309356797280102nteger ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_left
% 0.30/0.57 thf(fact_2778_power__0__left,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.30/0.57 = one_one_rat ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.30/0.57 = zero_zero_rat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_left
% 0.30/0.57 thf(fact_2779_power__0__left,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.30/0.57 = one_one_nat ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.30/0.57 = zero_zero_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_left
% 0.30/0.57 thf(fact_2780_power__0__left,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( power_power_real @ zero_zero_real @ N )
% 0.30/0.57 = one_one_real ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( power_power_real @ zero_zero_real @ N )
% 0.30/0.57 = zero_zero_real ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_left
% 0.30/0.57 thf(fact_2781_power__0__left,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( power_power_int @ zero_zero_int @ N )
% 0.30/0.57 = one_one_int ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( power_power_int @ zero_zero_int @ N )
% 0.30/0.57 = zero_zero_int ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_left
% 0.30/0.57 thf(fact_2782_power__0__left,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ( N = zero_zero_nat )
% 0.30/0.57 => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.30/0.57 = one_one_complex ) )
% 0.30/0.57 & ( ( N != zero_zero_nat )
% 0.30/0.57 => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.30/0.57 = zero_zero_complex ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_0_left
% 0.30/0.57 thf(fact_2783_power__increasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: code_integer] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N6 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing
% 0.30/0.57 thf(fact_2784_power__increasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: real] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_real @ one_one_real @ A )
% 0.30/0.57 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N6 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing
% 0.30/0.57 thf(fact_2785_power__increasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: rat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N6 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing
% 0.30/0.57 thf(fact_2786_power__increasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing
% 0.30/0.57 thf(fact_2787_power__increasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: int] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_int @ one_one_int @ A )
% 0.30/0.57 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_increasing
% 0.30/0.57 thf(fact_2788_zero__power,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( power_power_rat @ zero_zero_rat @ N )
% 0.30/0.57 = zero_zero_rat ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_power
% 0.30/0.57 thf(fact_2789_zero__power,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( power_power_nat @ zero_zero_nat @ N )
% 0.30/0.57 = zero_zero_nat ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_power
% 0.30/0.57 thf(fact_2790_zero__power,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( power_power_real @ zero_zero_real @ N )
% 0.30/0.57 = zero_zero_real ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_power
% 0.30/0.57 thf(fact_2791_zero__power,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( power_power_int @ zero_zero_int @ N )
% 0.30/0.57 = zero_zero_int ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_power
% 0.30/0.57 thf(fact_2792_zero__power,axiom,
% 0.30/0.57 ! [N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( power_power_complex @ zero_zero_complex @ N )
% 0.30/0.57 = zero_zero_complex ) ) ).
% 0.30/0.57
% 0.30/0.57 % zero_power
% 0.30/0.57 thf(fact_2793_lenlex__length,axiom,
% 0.30/0.57 ! [Ms: list_VEBT_VEBT,Ns: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 0.30/0.57 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R3 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_length
% 0.30/0.57 thf(fact_2794_lenlex__length,axiom,
% 0.30/0.57 ! [Ms: list_o,Ns: list_o,R3: set_Product_prod_o_o] :
% 0.30/0.57 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R3 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_length
% 0.30/0.57 thf(fact_2795_lenlex__length,axiom,
% 0.30/0.57 ! [Ms: list_nat,Ns: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.30/0.57 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R3 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_length
% 0.30/0.57 thf(fact_2796_lenlex__length,axiom,
% 0.30/0.57 ! [Ms: list_int,Ns: list_int,R3: set_Pr958786334691620121nt_int] :
% 0.30/0.57 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R3 ) )
% 0.30/0.57 => ( ord_less_eq_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % lenlex_length
% 0.30/0.57 thf(fact_2797_power__gt__expt,axiom,
% 0.30/0.57 ! [N: nat,K2: nat] :
% 0.30/0.57 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.30/0.57 => ( ord_less_nat @ K2 @ ( power_power_nat @ N @ K2 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_gt_expt
% 0.30/0.57 thf(fact_2798_nat__one__le__power,axiom,
% 0.30/0.57 ! [I2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % nat_one_le_power
% 0.30/0.57 thf(fact_2799_enumerate__step,axiom,
% 0.30/0.57 ! [S3: set_nat,N: nat] :
% 0.30/0.57 ( ~ ( finite_finite_nat @ S3 )
% 0.30/0.57 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % enumerate_step
% 0.30/0.57 thf(fact_2800_card__gt__0__iff,axiom,
% 0.30/0.57 ! [A4: set_list_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 0.30/0.57 = ( ( A4 != bot_bot_set_list_nat )
% 0.30/0.57 & ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_gt_0_iff
% 0.30/0.57 thf(fact_2801_card__gt__0__iff,axiom,
% 0.30/0.57 ! [A4: set_set_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 0.30/0.57 = ( ( A4 != bot_bot_set_set_nat )
% 0.30/0.57 & ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_gt_0_iff
% 0.30/0.57 thf(fact_2802_card__gt__0__iff,axiom,
% 0.30/0.57 ! [A4: set_complex] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.30/0.57 = ( ( A4 != bot_bot_set_complex )
% 0.30/0.57 & ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_gt_0_iff
% 0.30/0.57 thf(fact_2803_card__gt__0__iff,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 0.30/0.57 = ( ( A4 != bot_bot_set_nat )
% 0.30/0.57 & ( finite_finite_nat @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_gt_0_iff
% 0.30/0.57 thf(fact_2804_card__gt__0__iff,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 0.30/0.57 = ( ( A4 != bot_bot_set_int )
% 0.30/0.57 & ( finite_finite_int @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_gt_0_iff
% 0.30/0.57 thf(fact_2805_card__gt__0__iff,axiom,
% 0.30/0.57 ! [A4: set_real] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 0.30/0.57 = ( ( A4 != bot_bot_set_real )
% 0.30/0.57 & ( finite_finite_real @ A4 ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_gt_0_iff
% 0.30/0.57 thf(fact_2806_card__1__singleton__iff,axiom,
% 0.30/0.57 ! [A4: set_complex] :
% 0.30/0.57 ( ( ( finite_card_complex @ A4 )
% 0.30/0.57 = ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ? [X4: complex] :
% 0.30/0.57 ( A4
% 0.30/0.57 = ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_1_singleton_iff
% 0.30/0.57 thf(fact_2807_card__1__singleton__iff,axiom,
% 0.30/0.57 ! [A4: set_list_nat] :
% 0.30/0.57 ( ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ? [X4: list_nat] :
% 0.30/0.57 ( A4
% 0.30/0.57 = ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_1_singleton_iff
% 0.30/0.57 thf(fact_2808_card__1__singleton__iff,axiom,
% 0.30/0.57 ! [A4: set_set_nat] :
% 0.30/0.57 ( ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ? [X4: set_nat] :
% 0.30/0.57 ( A4
% 0.30/0.57 = ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_1_singleton_iff
% 0.30/0.57 thf(fact_2809_card__1__singleton__iff,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ( ( finite_card_nat @ A4 )
% 0.30/0.57 = ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ? [X4: nat] :
% 0.30/0.57 ( A4
% 0.30/0.57 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_1_singleton_iff
% 0.30/0.57 thf(fact_2810_card__1__singleton__iff,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ( ( finite_card_int @ A4 )
% 0.30/0.57 = ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ? [X4: int] :
% 0.30/0.57 ( A4
% 0.30/0.57 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_1_singleton_iff
% 0.30/0.57 thf(fact_2811_card__1__singleton__iff,axiom,
% 0.30/0.57 ! [A4: set_real] :
% 0.30/0.57 ( ( ( finite_card_real @ A4 )
% 0.30/0.57 = ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ? [X4: real] :
% 0.30/0.57 ( A4
% 0.30/0.57 = ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_1_singleton_iff
% 0.30/0.57 thf(fact_2812_card__eq__SucD,axiom,
% 0.30/0.57 ! [A4: set_complex,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_complex @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 => ? [B3: complex,B8: set_complex] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_complex @ B3 @ B8 ) )
% 0.30/0.57 & ~ ( member_complex @ B3 @ B8 )
% 0.30/0.57 & ( ( finite_card_complex @ B8 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B8 = bot_bot_set_complex ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_SucD
% 0.30/0.57 thf(fact_2813_card__eq__SucD,axiom,
% 0.30/0.57 ! [A4: set_list_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 => ? [B3: list_nat,B8: set_list_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_list_nat @ B3 @ B8 ) )
% 0.30/0.57 & ~ ( member_list_nat @ B3 @ B8 )
% 0.30/0.57 & ( ( finite_card_list_nat @ B8 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B8 = bot_bot_set_list_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_SucD
% 0.30/0.57 thf(fact_2814_card__eq__SucD,axiom,
% 0.30/0.57 ! [A4: set_set_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 => ? [B3: set_nat,B8: set_set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_set_nat @ B3 @ B8 ) )
% 0.30/0.57 & ~ ( member_set_nat @ B3 @ B8 )
% 0.30/0.57 & ( ( finite_card_set_nat @ B8 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B8 = bot_bot_set_set_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_SucD
% 0.30/0.57 thf(fact_2815_card__eq__SucD,axiom,
% 0.30/0.57 ! [A4: set_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 => ? [B3: nat,B8: set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_nat @ B3 @ B8 ) )
% 0.30/0.57 & ~ ( member_nat @ B3 @ B8 )
% 0.30/0.57 & ( ( finite_card_nat @ B8 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B8 = bot_bot_set_nat ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_SucD
% 0.30/0.57 thf(fact_2816_card__eq__SucD,axiom,
% 0.30/0.57 ! [A4: set_int,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_int @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 => ? [B3: int,B8: set_int] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_int @ B3 @ B8 ) )
% 0.30/0.57 & ~ ( member_int @ B3 @ B8 )
% 0.30/0.57 & ( ( finite_card_int @ B8 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B8 = bot_bot_set_int ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_SucD
% 0.30/0.57 thf(fact_2817_card__eq__SucD,axiom,
% 0.30/0.57 ! [A4: set_real,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_real @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 => ? [B3: real,B8: set_real] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_real @ B3 @ B8 ) )
% 0.30/0.57 & ~ ( member_real @ B3 @ B8 )
% 0.30/0.57 & ( ( finite_card_real @ B8 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B8 = bot_bot_set_real ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_eq_SucD
% 0.30/0.57 thf(fact_2818_card__Suc__eq,axiom,
% 0.30/0.57 ! [A4: set_complex,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_complex @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: complex,B7: set_complex] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_complex @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_complex @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_complex @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B7 = bot_bot_set_complex ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq
% 0.30/0.57 thf(fact_2819_card__Suc__eq,axiom,
% 0.30/0.57 ! [A4: set_list_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: list_nat,B7: set_list_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_list_nat @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_list_nat @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_list_nat @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B7 = bot_bot_set_list_nat ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq
% 0.30/0.57 thf(fact_2820_card__Suc__eq,axiom,
% 0.30/0.57 ! [A4: set_set_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: set_nat,B7: set_set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_set_nat @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_set_nat @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_set_nat @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B7 = bot_bot_set_set_nat ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq
% 0.30/0.57 thf(fact_2821_card__Suc__eq,axiom,
% 0.30/0.57 ! [A4: set_nat,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_nat @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: nat,B7: set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_nat @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_nat @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_nat @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B7 = bot_bot_set_nat ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq
% 0.30/0.57 thf(fact_2822_card__Suc__eq,axiom,
% 0.30/0.57 ! [A4: set_int,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_int @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: int,B7: set_int] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_int @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_int @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_int @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B7 = bot_bot_set_int ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq
% 0.30/0.57 thf(fact_2823_card__Suc__eq,axiom,
% 0.30/0.57 ! [A4: set_real,K2: nat] :
% 0.30/0.57 ( ( ( finite_card_real @ A4 )
% 0.30/0.57 = ( suc @ K2 ) )
% 0.30/0.57 = ( ? [B4: real,B7: set_real] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_real @ B4 @ B7 ) )
% 0.30/0.57 & ~ ( member_real @ B4 @ B7 )
% 0.30/0.57 & ( ( finite_card_real @ B7 )
% 0.30/0.57 = K2 )
% 0.30/0.57 & ( ( K2 = zero_zero_nat )
% 0.30/0.57 => ( B7 = bot_bot_set_real ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Suc_eq
% 0.30/0.57 thf(fact_2824_card__le__Suc0__iff__eq,axiom,
% 0.30/0.57 ! [A4: set_list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ! [X4: list_nat] :
% 0.30/0.57 ( ( member_list_nat @ X4 @ A4 )
% 0.30/0.57 => ! [Y4: list_nat] :
% 0.30/0.57 ( ( member_list_nat @ Y4 @ A4 )
% 0.30/0.57 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc0_iff_eq
% 0.30/0.57 thf(fact_2825_card__le__Suc0__iff__eq,axiom,
% 0.30/0.57 ! [A4: set_set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ! [X4: set_nat] :
% 0.30/0.57 ( ( member_set_nat @ X4 @ A4 )
% 0.30/0.57 => ! [Y4: set_nat] :
% 0.30/0.57 ( ( member_set_nat @ Y4 @ A4 )
% 0.30/0.57 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc0_iff_eq
% 0.30/0.57 thf(fact_2826_card__le__Suc0__iff__eq,axiom,
% 0.30/0.57 ! [A4: set_nat] :
% 0.30/0.57 ( ( finite_finite_nat @ A4 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ! [X4: nat] :
% 0.30/0.57 ( ( member_nat @ X4 @ A4 )
% 0.30/0.57 => ! [Y4: nat] :
% 0.30/0.57 ( ( member_nat @ Y4 @ A4 )
% 0.30/0.57 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc0_iff_eq
% 0.30/0.57 thf(fact_2827_card__le__Suc0__iff__eq,axiom,
% 0.30/0.57 ! [A4: set_int] :
% 0.30/0.57 ( ( finite_finite_int @ A4 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ! [X4: int] :
% 0.30/0.57 ( ( member_int @ X4 @ A4 )
% 0.30/0.57 => ! [Y4: int] :
% 0.30/0.57 ( ( member_int @ Y4 @ A4 )
% 0.30/0.57 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc0_iff_eq
% 0.30/0.57 thf(fact_2828_card__le__Suc0__iff__eq,axiom,
% 0.30/0.57 ! [A4: set_complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( suc @ zero_zero_nat ) )
% 0.30/0.57 = ( ! [X4: complex] :
% 0.30/0.57 ( ( member_complex @ X4 @ A4 )
% 0.30/0.57 => ! [Y4: complex] :
% 0.30/0.57 ( ( member_complex @ Y4 @ A4 )
% 0.30/0.57 => ( X4 = Y4 ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc0_iff_eq
% 0.30/0.57 thf(fact_2829_card__le__Suc__iff,axiom,
% 0.30/0.57 ! [N: nat,A4: set_real] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_real @ A4 ) )
% 0.30/0.57 = ( ? [A5: real,B7: set_real] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_real @ A5 @ B7 ) )
% 0.30/0.57 & ~ ( member_real @ A5 @ B7 )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( finite_card_real @ B7 ) )
% 0.30/0.57 & ( finite_finite_real @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc_iff
% 0.30/0.57 thf(fact_2830_card__le__Suc__iff,axiom,
% 0.30/0.57 ! [N: nat,A4: set_list_nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_list_nat @ A4 ) )
% 0.30/0.57 = ( ? [A5: list_nat,B7: set_list_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_list_nat @ A5 @ B7 ) )
% 0.30/0.57 & ~ ( member_list_nat @ A5 @ B7 )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ B7 ) )
% 0.30/0.57 & ( finite8100373058378681591st_nat @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc_iff
% 0.30/0.57 thf(fact_2831_card__le__Suc__iff,axiom,
% 0.30/0.57 ! [N: nat,A4: set_set_nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_set_nat @ A4 ) )
% 0.30/0.57 = ( ? [A5: set_nat,B7: set_set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_set_nat @ A5 @ B7 ) )
% 0.30/0.57 & ~ ( member_set_nat @ A5 @ B7 )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ B7 ) )
% 0.30/0.57 & ( finite1152437895449049373et_nat @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc_iff
% 0.30/0.57 thf(fact_2832_card__le__Suc__iff,axiom,
% 0.30/0.57 ! [N: nat,A4: set_nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_nat @ A4 ) )
% 0.30/0.57 = ( ? [A5: nat,B7: set_nat] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_nat @ A5 @ B7 ) )
% 0.30/0.57 & ~ ( member_nat @ A5 @ B7 )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( finite_card_nat @ B7 ) )
% 0.30/0.57 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc_iff
% 0.30/0.57 thf(fact_2833_card__le__Suc__iff,axiom,
% 0.30/0.57 ! [N: nat,A4: set_int] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_int @ A4 ) )
% 0.30/0.57 = ( ? [A5: int,B7: set_int] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_int @ A5 @ B7 ) )
% 0.30/0.57 & ~ ( member_int @ A5 @ B7 )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( finite_card_int @ B7 ) )
% 0.30/0.57 & ( finite_finite_int @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc_iff
% 0.30/0.57 thf(fact_2834_card__le__Suc__iff,axiom,
% 0.30/0.57 ! [N: nat,A4: set_complex] :
% 0.30/0.57 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_complex @ A4 ) )
% 0.30/0.57 = ( ? [A5: complex,B7: set_complex] :
% 0.30/0.57 ( ( A4
% 0.30/0.57 = ( insert_complex @ A5 @ B7 ) )
% 0.30/0.57 & ~ ( member_complex @ A5 @ B7 )
% 0.30/0.57 & ( ord_less_eq_nat @ N @ ( finite_card_complex @ B7 ) )
% 0.30/0.57 & ( finite3207457112153483333omplex @ B7 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_le_Suc_iff
% 0.30/0.57 thf(fact_2835_power__Suc__less,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.30/0.57 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less
% 0.30/0.57 thf(fact_2836_power__Suc__less,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_real @ A @ one_one_real )
% 0.30/0.57 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less
% 0.30/0.57 thf(fact_2837_power__Suc__less,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.30/0.57 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less
% 0.30/0.57 thf(fact_2838_power__Suc__less,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.30/0.57 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less
% 0.30/0.57 thf(fact_2839_power__Suc__less,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_int @ A @ one_one_int )
% 0.30/0.57 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less
% 0.30/0.57 thf(fact_2840_power__Suc__le__self,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.57 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_le_self
% 0.30/0.57 thf(fact_2841_power__Suc__le__self,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.30/0.57 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_le_self
% 0.30/0.57 thf(fact_2842_power__Suc__le__self,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.57 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_le_self
% 0.30/0.57 thf(fact_2843_power__Suc__le__self,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.57 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_le_self
% 0.30/0.57 thf(fact_2844_power__Suc__le__self,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.57 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_le_self
% 0.30/0.57 thf(fact_2845_power__Suc__less__one,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.30/0.57 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less_one
% 0.30/0.57 thf(fact_2846_power__Suc__less__one,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_real @ A @ one_one_real )
% 0.30/0.57 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less_one
% 0.30/0.57 thf(fact_2847_power__Suc__less__one,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.30/0.57 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less_one
% 0.30/0.57 thf(fact_2848_power__Suc__less__one,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.30/0.57 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less_one
% 0.30/0.57 thf(fact_2849_power__Suc__less__one,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_int @ A @ one_one_int )
% 0.30/0.57 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_Suc_less_one
% 0.30/0.57 thf(fact_2850_card__Diff1__le,axiom,
% 0.30/0.57 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Diff1_le
% 0.30/0.57 thf(fact_2851_card__Diff1__le,axiom,
% 0.30/0.57 ! [A4: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Diff1_le
% 0.30/0.57 thf(fact_2852_card__Diff1__le,axiom,
% 0.30/0.57 ! [A4: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Diff1_le
% 0.30/0.57 thf(fact_2853_card__Diff1__le,axiom,
% 0.30/0.57 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Diff1_le
% 0.30/0.57 thf(fact_2854_card__Diff1__le,axiom,
% 0.30/0.57 ! [A4: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Diff1_le
% 0.30/0.57 thf(fact_2855_card__Diff1__le,axiom,
% 0.30/0.57 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Diff1_le
% 0.30/0.57 thf(fact_2856_card__Diff1__le,axiom,
% 0.30/0.57 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ).
% 0.30/0.57
% 0.30/0.57 % card_Diff1_le
% 0.30/0.57 thf(fact_2857_power__strict__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: code_integer] :
% 0.30/0.57 ( ( ord_less_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 0.30/0.57 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing
% 0.30/0.57 thf(fact_2858_power__strict__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: real] :
% 0.30/0.57 ( ( ord_less_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_real @ A @ one_one_real )
% 0.30/0.57 => ( ord_less_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing
% 0.30/0.57 thf(fact_2859_power__strict__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: rat] :
% 0.30/0.57 ( ( ord_less_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_rat @ A @ one_one_rat )
% 0.30/0.57 => ( ord_less_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing
% 0.30/0.57 thf(fact_2860_power__strict__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: nat] :
% 0.30/0.57 ( ( ord_less_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_nat @ A @ one_one_nat )
% 0.30/0.57 => ( ord_less_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing
% 0.30/0.57 thf(fact_2861_power__strict__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: int] :
% 0.30/0.57 ( ( ord_less_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_int @ A @ one_one_int )
% 0.30/0.57 => ( ord_less_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_strict_decreasing
% 0.30/0.57 thf(fact_2862_power__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: code_integer] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 0.30/0.57 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing
% 0.30/0.57 thf(fact_2863_power__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: real] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ A @ one_one_real )
% 0.30/0.57 => ( ord_less_eq_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing
% 0.30/0.57 thf(fact_2864_power__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: rat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 0.30/0.57 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing
% 0.30/0.57 thf(fact_2865_power__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 0.30/0.57 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing
% 0.30/0.57 thf(fact_2866_power__decreasing,axiom,
% 0.30/0.57 ! [N: nat,N6: nat,A: int] :
% 0.30/0.57 ( ( ord_less_eq_nat @ N @ N6 )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ A @ one_one_int )
% 0.30/0.57 => ( ord_less_eq_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_decreasing
% 0.30/0.57 thf(fact_2867_power__le__imp__le__exp,axiom,
% 0.30/0.57 ! [A: code_integer,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.30/0.57 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_exp
% 0.30/0.57 thf(fact_2868_power__le__imp__le__exp,axiom,
% 0.30/0.57 ! [A: real,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ one_one_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) )
% 0.30/0.57 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_exp
% 0.30/0.57 thf(fact_2869_power__le__imp__le__exp,axiom,
% 0.30/0.57 ! [A: rat,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 0.30/0.57 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_exp
% 0.30/0.57 thf(fact_2870_power__le__imp__le__exp,axiom,
% 0.30/0.57 ! [A: nat,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 0.30/0.57 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_exp
% 0.30/0.57 thf(fact_2871_power__le__imp__le__exp,axiom,
% 0.30/0.57 ! [A: int,M2: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 0.30/0.57 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_le_imp_le_exp
% 0.30/0.57 thf(fact_2872_power__eq__iff__eq__base,axiom,
% 0.30/0.57 ! [N: nat,A: real,B: real] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.57 => ( ( ( power_power_real @ A @ N )
% 0.30/0.57 = ( power_power_real @ B @ N ) )
% 0.30/0.57 = ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_iff_eq_base
% 0.30/0.57 thf(fact_2873_power__eq__iff__eq__base,axiom,
% 0.30/0.57 ! [N: nat,A: rat,B: rat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( ( ( power_power_rat @ A @ N )
% 0.30/0.57 = ( power_power_rat @ B @ N ) )
% 0.30/0.57 = ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_iff_eq_base
% 0.30/0.57 thf(fact_2874_power__eq__iff__eq__base,axiom,
% 0.30/0.57 ! [N: nat,A: nat,B: nat] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( ( ( power_power_nat @ A @ N )
% 0.30/0.57 = ( power_power_nat @ B @ N ) )
% 0.30/0.57 = ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_iff_eq_base
% 0.30/0.57 thf(fact_2875_power__eq__iff__eq__base,axiom,
% 0.30/0.57 ! [N: nat,A: int,B: int] :
% 0.30/0.57 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57 => ( ( ( power_power_int @ A @ N )
% 0.30/0.57 = ( power_power_int @ B @ N ) )
% 0.30/0.57 = ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_iff_eq_base
% 0.30/0.57 thf(fact_2876_power__eq__imp__eq__base,axiom,
% 0.30/0.57 ! [A: real,N: nat,B: real] :
% 0.30/0.57 ( ( ( power_power_real @ A @ N )
% 0.30/0.57 = ( power_power_real @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.57 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_imp_eq_base
% 0.30/0.57 thf(fact_2877_power__eq__imp__eq__base,axiom,
% 0.30/0.57 ! [A: rat,N: nat,B: rat] :
% 0.30/0.57 ( ( ( power_power_rat @ A @ N )
% 0.30/0.57 = ( power_power_rat @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.57 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_imp_eq_base
% 0.30/0.57 thf(fact_2878_power__eq__imp__eq__base,axiom,
% 0.30/0.57 ! [A: nat,N: nat,B: nat] :
% 0.30/0.57 ( ( ( power_power_nat @ A @ N )
% 0.30/0.57 = ( power_power_nat @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.57 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_imp_eq_base
% 0.30/0.57 thf(fact_2879_power__eq__imp__eq__base,axiom,
% 0.30/0.57 ! [A: int,N: nat,B: int] :
% 0.30/0.57 ( ( ( power_power_int @ A @ N )
% 0.30/0.57 = ( power_power_int @ B @ N ) )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.57 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( A = B ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % power_eq_imp_eq_base
% 0.30/0.57 thf(fact_2880_diff__card__le__card__Diff,axiom,
% 0.30/0.57 ! [B5: set_list_nat,A4: set_list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % diff_card_le_card_Diff
% 0.30/0.57 thf(fact_2881_diff__card__le__card__Diff,axiom,
% 0.30/0.57 ! [B5: set_set_nat,A4: set_set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % diff_card_le_card_Diff
% 0.30/0.57 thf(fact_2882_diff__card__le__card__Diff,axiom,
% 0.30/0.57 ! [B5: set_int,A4: set_int] :
% 0.30/0.57 ( ( finite_finite_int @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % diff_card_le_card_Diff
% 0.30/0.57 thf(fact_2883_diff__card__le__card__Diff,axiom,
% 0.30/0.57 ! [B5: set_complex,A4: set_complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % diff_card_le_card_Diff
% 0.30/0.57 thf(fact_2884_diff__card__le__card__Diff,axiom,
% 0.30/0.57 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 0.30/0.57 ( ( finite6177210948735845034at_nat @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % diff_card_le_card_Diff
% 0.30/0.57 thf(fact_2885_diff__card__le__card__Diff,axiom,
% 0.30/0.57 ! [B5: set_nat,A4: set_nat] :
% 0.30/0.57 ( ( finite_finite_nat @ B5 )
% 0.30/0.57 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % diff_card_le_card_Diff
% 0.30/0.57 thf(fact_2886_self__le__power,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % self_le_power
% 0.30/0.57 thf(fact_2887_self__le__power,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_real @ one_one_real @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % self_le_power
% 0.30/0.57 thf(fact_2888_self__le__power,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % self_le_power
% 0.30/0.57 thf(fact_2889_self__le__power,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % self_le_power
% 0.30/0.57 thf(fact_2890_self__le__power,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_eq_int @ one_one_int @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % self_le_power
% 0.30/0.57 thf(fact_2891_one__less__power,axiom,
% 0.30/0.57 ! [A: code_integer,N: nat] :
% 0.30/0.57 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_less_power
% 0.30/0.57 thf(fact_2892_one__less__power,axiom,
% 0.30/0.57 ! [A: real,N: nat] :
% 0.30/0.57 ( ( ord_less_real @ one_one_real @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_less_power
% 0.30/0.57 thf(fact_2893_one__less__power,axiom,
% 0.30/0.57 ! [A: rat,N: nat] :
% 0.30/0.57 ( ( ord_less_rat @ one_one_rat @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_less_power
% 0.30/0.57 thf(fact_2894_one__less__power,axiom,
% 0.30/0.57 ! [A: nat,N: nat] :
% 0.30/0.57 ( ( ord_less_nat @ one_one_nat @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_less_power
% 0.30/0.57 thf(fact_2895_one__less__power,axiom,
% 0.30/0.57 ! [A: int,N: nat] :
% 0.30/0.57 ( ( ord_less_int @ one_one_int @ A )
% 0.30/0.57 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.57 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % one_less_power
% 0.30/0.57 thf(fact_2896_count__le__length,axiom,
% 0.30/0.57 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs2 @ X ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_le_length
% 0.30/0.57 thf(fact_2897_count__le__length,axiom,
% 0.30/0.57 ! [Xs2: list_o,X: $o] : ( ord_less_eq_nat @ ( count_list_o @ Xs2 @ X ) @ ( size_size_list_o @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_le_length
% 0.30/0.57 thf(fact_2898_count__le__length,axiom,
% 0.30/0.57 ! [Xs2: list_nat,X: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs2 @ X ) @ ( size_size_list_nat @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_le_length
% 0.30/0.57 thf(fact_2899_count__le__length,axiom,
% 0.30/0.57 ! [Xs2: list_int,X: int] : ( ord_less_eq_nat @ ( count_list_int @ Xs2 @ X ) @ ( size_size_list_int @ Xs2 ) ) ).
% 0.30/0.57
% 0.30/0.57 % count_le_length
% 0.30/0.57 thf(fact_2900_dbl__inc__def,axiom,
% 0.30/0.57 ( neg_nu5831290666863070958nteger
% 0.30/0.57 = ( ^ [X4: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X4 @ X4 ) @ one_one_Code_integer ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_def
% 0.30/0.57 thf(fact_2901_dbl__inc__def,axiom,
% 0.30/0.57 ( neg_nu8557863876264182079omplex
% 0.30/0.57 = ( ^ [X4: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X4 @ X4 ) @ one_one_complex ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_def
% 0.30/0.57 thf(fact_2902_dbl__inc__def,axiom,
% 0.30/0.57 ( neg_nu8295874005876285629c_real
% 0.30/0.57 = ( ^ [X4: real] : ( plus_plus_real @ ( plus_plus_real @ X4 @ X4 ) @ one_one_real ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_def
% 0.30/0.57 thf(fact_2903_dbl__inc__def,axiom,
% 0.30/0.57 ( neg_nu5219082963157363817nc_rat
% 0.30/0.57 = ( ^ [X4: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X4 @ X4 ) @ one_one_rat ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_def
% 0.30/0.57 thf(fact_2904_dbl__inc__def,axiom,
% 0.30/0.57 ( neg_nu5851722552734809277nc_int
% 0.30/0.57 = ( ^ [X4: int] : ( plus_plus_int @ ( plus_plus_int @ X4 @ X4 ) @ one_one_int ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % dbl_inc_def
% 0.30/0.57 thf(fact_2905_card_Oremove,axiom,
% 0.30/0.57 ! [A4: set_list_nat,X: list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ( member_list_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_list_nat @ A4 )
% 0.30/0.57 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.remove
% 0.30/0.57 thf(fact_2906_card_Oremove,axiom,
% 0.30/0.57 ! [A4: set_set_nat,X: set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ( member_set_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_set_nat @ A4 )
% 0.30/0.57 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.remove
% 0.30/0.57 thf(fact_2907_card_Oremove,axiom,
% 0.30/0.57 ! [A4: set_complex,X: complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ( member_complex @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_complex @ A4 )
% 0.30/0.57 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.remove
% 0.30/0.57 thf(fact_2908_card_Oremove,axiom,
% 0.30/0.57 ! [A4: set_int,X: int] :
% 0.30/0.57 ( ( finite_finite_int @ A4 )
% 0.30/0.57 => ( ( member_int @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_int @ A4 )
% 0.30/0.57 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.remove
% 0.30/0.57 thf(fact_2909_card_Oremove,axiom,
% 0.30/0.57 ! [A4: set_real,X: real] :
% 0.30/0.57 ( ( finite_finite_real @ A4 )
% 0.30/0.57 => ( ( member_real @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_real @ A4 )
% 0.30/0.57 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.remove
% 0.30/0.57 thf(fact_2910_card_Oremove,axiom,
% 0.30/0.57 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.30/0.57 ( ( finite6177210948735845034at_nat @ A4 )
% 0.30/0.57 => ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite711546835091564841at_nat @ A4 )
% 0.30/0.57 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.remove
% 0.30/0.57 thf(fact_2911_card_Oremove,axiom,
% 0.30/0.57 ! [A4: set_nat,X: nat] :
% 0.30/0.57 ( ( finite_finite_nat @ A4 )
% 0.30/0.57 => ( ( member_nat @ X @ A4 )
% 0.30/0.57 => ( ( finite_card_nat @ A4 )
% 0.30/0.57 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.remove
% 0.30/0.57 thf(fact_2912_card_Oinsert__remove,axiom,
% 0.30/0.57 ! [A4: set_list_nat,X: list_nat] :
% 0.30/0.57 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.57 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.insert_remove
% 0.30/0.57 thf(fact_2913_card_Oinsert__remove,axiom,
% 0.30/0.57 ! [A4: set_set_nat,X: set_nat] :
% 0.30/0.57 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.57 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.insert_remove
% 0.30/0.57 thf(fact_2914_card_Oinsert__remove,axiom,
% 0.30/0.57 ! [A4: set_complex,X: complex] :
% 0.30/0.57 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.57 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 0.30/0.57 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.30/0.57
% 0.30/0.57 % card.insert_remove
% 0.30/0.57 thf(fact_2915_card_Oinsert__remove,axiom,
% 0.30/0.57 ! [A4: set_int,X: int] :
% 0.30/0.58 ( ( finite_finite_int @ A4 )
% 0.30/0.58 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 0.30/0.58 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card.insert_remove
% 0.30/0.58 thf(fact_2916_card_Oinsert__remove,axiom,
% 0.30/0.58 ! [A4: set_real,X: real] :
% 0.30/0.58 ( ( finite_finite_real @ A4 )
% 0.30/0.58 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 0.30/0.58 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card.insert_remove
% 0.30/0.58 thf(fact_2917_card_Oinsert__remove,axiom,
% 0.30/0.58 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.30/0.58 ( ( finite6177210948735845034at_nat @ A4 )
% 0.30/0.58 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) )
% 0.30/0.58 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card.insert_remove
% 0.30/0.58 thf(fact_2918_card_Oinsert__remove,axiom,
% 0.30/0.58 ! [A4: set_nat,X: nat] :
% 0.30/0.58 ( ( finite_finite_nat @ A4 )
% 0.30/0.58 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 0.30/0.58 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card.insert_remove
% 0.30/0.58 thf(fact_2919_card__Suc__Diff1,axiom,
% 0.30/0.58 ! [A4: set_list_nat,X: list_nat] :
% 0.30/0.58 ( ( finite8100373058378681591st_nat @ A4 )
% 0.30/0.58 => ( ( member_list_nat @ X @ A4 )
% 0.30/0.58 => ( ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) )
% 0.30/0.58 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card_Suc_Diff1
% 0.30/0.58 thf(fact_2920_card__Suc__Diff1,axiom,
% 0.30/0.58 ! [A4: set_set_nat,X: set_nat] :
% 0.30/0.58 ( ( finite1152437895449049373et_nat @ A4 )
% 0.30/0.58 => ( ( member_set_nat @ X @ A4 )
% 0.30/0.58 => ( ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 0.30/0.58 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card_Suc_Diff1
% 0.30/0.58 thf(fact_2921_card__Suc__Diff1,axiom,
% 0.30/0.58 ! [A4: set_complex,X: complex] :
% 0.30/0.58 ( ( finite3207457112153483333omplex @ A4 )
% 0.30/0.58 => ( ( member_complex @ X @ A4 )
% 0.30/0.58 => ( ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 0.30/0.58 = ( finite_card_complex @ A4 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card_Suc_Diff1
% 0.30/0.58 thf(fact_2922_card__Suc__Diff1,axiom,
% 0.30/0.58 ! [A4: set_int,X: int] :
% 0.30/0.58 ( ( finite_finite_int @ A4 )
% 0.30/0.58 => ( ( member_int @ X @ A4 )
% 0.30/0.58 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 0.30/0.58 = ( finite_card_int @ A4 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card_Suc_Diff1
% 0.30/0.58 thf(fact_2923_card__Suc__Diff1,axiom,
% 0.30/0.58 ! [A4: set_real,X: real] :
% 0.30/0.58 ( ( finite_finite_real @ A4 )
% 0.30/0.58 => ( ( member_real @ X @ A4 )
% 0.30/0.58 => ( ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 0.30/0.58 = ( finite_card_real @ A4 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card_Suc_Diff1
% 0.30/0.58 thf(fact_2924_card__Suc__Diff1,axiom,
% 0.30/0.58 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 0.30/0.58 ( ( finite6177210948735845034at_nat @ A4 )
% 0.30/0.58 => ( ( member8440522571783428010at_nat @ X @ A4 )
% 0.30/0.58 => ( ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) )
% 0.30/0.58 = ( finite711546835091564841at_nat @ A4 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card_Suc_Diff1
% 0.30/0.58 thf(fact_2925_card__Suc__Diff1,axiom,
% 0.30/0.58 ! [A4: set_nat,X: nat] :
% 0.30/0.58 ( ( finite_finite_nat @ A4 )
% 0.30/0.58 => ( ( member_nat @ X @ A4 )
% 0.30/0.58 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 0.30/0.58 = ( finite_card_nat @ A4 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % card_Suc_Diff1
% 0.30/0.58 thf(fact_2926_power__strict__mono,axiom,
% 0.30/0.58 ! [A: real,B: real,N: nat] :
% 0.30/0.58 ( ( ord_less_real @ A @ B )
% 0.30/0.58 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.30/0.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_strict_mono
% 0.30/0.58 thf(fact_2927_power__strict__mono,axiom,
% 0.30/0.58 ! [A: rat,B: rat,N: nat] :
% 0.30/0.58 ( ( ord_less_rat @ A @ B )
% 0.30/0.58 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.30/0.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_strict_mono
% 0.30/0.58 thf(fact_2928_power__strict__mono,axiom,
% 0.30/0.58 ! [A: nat,B: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_nat @ A @ B )
% 0.30/0.58 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.30/0.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_strict_mono
% 0.30/0.58 thf(fact_2929_power__strict__mono,axiom,
% 0.30/0.58 ! [A: int,B: int,N: nat] :
% 0.30/0.58 ( ( ord_less_int @ A @ B )
% 0.30/0.58 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.30/0.58 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_strict_mono
% 0.30/0.58 thf(fact_2930_power__eq__if,axiom,
% 0.30/0.58 ( power_8256067586552552935nteger
% 0.30/0.58 = ( ^ [P5: code_integer,M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P5 @ ( power_8256067586552552935nteger @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_eq_if
% 0.30/0.58 thf(fact_2931_power__eq__if,axiom,
% 0.30/0.58 ( power_power_complex
% 0.30/0.58 = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_eq_if
% 0.30/0.58 thf(fact_2932_power__eq__if,axiom,
% 0.30/0.58 ( power_power_real
% 0.30/0.58 = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_eq_if
% 0.30/0.58 thf(fact_2933_power__eq__if,axiom,
% 0.30/0.58 ( power_power_rat
% 0.30/0.58 = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_eq_if
% 0.30/0.58 thf(fact_2934_power__eq__if,axiom,
% 0.30/0.58 ( power_power_nat
% 0.30/0.58 = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_eq_if
% 0.30/0.58 thf(fact_2935_power__eq__if,axiom,
% 0.30/0.58 ( power_power_int
% 0.30/0.58 = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_eq_if
% 0.30/0.58 thf(fact_2936_power__minus__mult,axiom,
% 0.30/0.58 ! [N: nat,A: complex] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.58 = ( power_power_complex @ A @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_minus_mult
% 0.30/0.58 thf(fact_2937_power__minus__mult,axiom,
% 0.30/0.58 ! [N: nat,A: real] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.58 = ( power_power_real @ A @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_minus_mult
% 0.30/0.58 thf(fact_2938_power__minus__mult,axiom,
% 0.30/0.58 ! [N: nat,A: rat] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.58 = ( power_power_rat @ A @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_minus_mult
% 0.30/0.58 thf(fact_2939_power__minus__mult,axiom,
% 0.30/0.58 ! [N: nat,A: nat] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.58 = ( power_power_nat @ A @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_minus_mult
% 0.30/0.58 thf(fact_2940_power__minus__mult,axiom,
% 0.30/0.58 ! [N: nat,A: int] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 0.30/0.58 = ( power_power_int @ A @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_minus_mult
% 0.30/0.58 thf(fact_2941_Cons__in__lex,axiom,
% 0.30/0.58 ! [X: code_integer,Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 0.30/0.58 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) ) @ ( lex_Code_integer @ R3 ) )
% 0.30/0.58 = ( ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ R3 )
% 0.30/0.58 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 0.30/0.58 = ( size_s3445333598471063425nteger @ Ys ) ) )
% 0.30/0.58 | ( ( X = Y )
% 0.30/0.58 & ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( lex_Code_integer @ R3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Cons_in_lex
% 0.30/0.58 thf(fact_2942_Cons__in__lex,axiom,
% 0.30/0.58 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 0.30/0.58 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( lex_Pr8571645452597969515at_nat @ R3 ) )
% 0.30/0.58 = ( ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R3 )
% 0.30/0.58 & ( ( size_s5460976970255530739at_nat @ Xs2 )
% 0.30/0.58 = ( size_s5460976970255530739at_nat @ Ys ) ) )
% 0.30/0.58 | ( ( X = Y )
% 0.30/0.58 & ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Ys ) @ ( lex_Pr8571645452597969515at_nat @ R3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Cons_in_lex
% 0.30/0.58 thf(fact_2943_Cons__in__lex,axiom,
% 0.30/0.58 ! [X: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.30/0.58 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( lex_se2245640040323279819at_nat @ R3 ) )
% 0.30/0.58 = ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R3 )
% 0.30/0.58 & ( ( size_s8736152011456118867at_nat @ Xs2 )
% 0.30/0.58 = ( size_s8736152011456118867at_nat @ Ys ) ) )
% 0.30/0.58 | ( ( X = Y )
% 0.30/0.58 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Ys ) @ ( lex_se2245640040323279819at_nat @ R3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Cons_in_lex
% 0.30/0.58 thf(fact_2944_Cons__in__lex,axiom,
% 0.30/0.58 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y: vEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 0.30/0.58 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( cons_VEBT_VEBT @ Y @ Ys ) ) @ ( lex_VEBT_VEBT @ R3 ) )
% 0.30/0.58 = ( ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y ) @ R3 )
% 0.30/0.58 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.58 = ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.30/0.58 | ( ( X = Y )
% 0.30/0.58 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( lex_VEBT_VEBT @ R3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Cons_in_lex
% 0.30/0.58 thf(fact_2945_Cons__in__lex,axiom,
% 0.30/0.58 ! [X: $o,Xs2: list_o,Y: $o,Ys: list_o,R3: set_Product_prod_o_o] :
% 0.30/0.58 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs2 ) @ ( cons_o @ Y @ Ys ) ) @ ( lex_o @ R3 ) )
% 0.30/0.58 = ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R3 )
% 0.30/0.58 & ( ( size_size_list_o @ Xs2 )
% 0.30/0.58 = ( size_size_list_o @ Ys ) ) )
% 0.30/0.58 | ( ( X = Y )
% 0.30/0.58 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( lex_o @ R3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Cons_in_lex
% 0.30/0.58 thf(fact_2946_Cons__in__lex,axiom,
% 0.30/0.58 ! [X: nat,Xs2: list_nat,Y: nat,Ys: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.30/0.58 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) ) @ ( lex_nat @ R3 ) )
% 0.30/0.58 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 )
% 0.30/0.58 & ( ( size_size_list_nat @ Xs2 )
% 0.30/0.58 = ( size_size_list_nat @ Ys ) ) )
% 0.30/0.58 | ( ( X = Y )
% 0.30/0.58 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Ys ) @ ( lex_nat @ R3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Cons_in_lex
% 0.30/0.58 thf(fact_2947_Cons__in__lex,axiom,
% 0.30/0.58 ! [X: int,Xs2: list_int,Y: int,Ys: list_int,R3: set_Pr958786334691620121nt_int] :
% 0.30/0.58 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) ) @ ( lex_int @ R3 ) )
% 0.30/0.58 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 )
% 0.30/0.58 & ( ( size_size_list_int @ Xs2 )
% 0.30/0.58 = ( size_size_list_int @ Ys ) ) )
% 0.30/0.58 | ( ( X = Y )
% 0.30/0.58 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Ys ) @ ( lex_int @ R3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Cons_in_lex
% 0.30/0.58 thf(fact_2948_realpow__pos__nth__unique,axiom,
% 0.30/0.58 ! [N: nat,A: real] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.58 => ? [X3: real] :
% 0.30/0.58 ( ( ord_less_real @ zero_zero_real @ X3 )
% 0.30/0.58 & ( ( power_power_real @ X3 @ N )
% 0.30/0.58 = A )
% 0.30/0.58 & ! [Y6: real] :
% 0.30/0.58 ( ( ( ord_less_real @ zero_zero_real @ Y6 )
% 0.30/0.58 & ( ( power_power_real @ Y6 @ N )
% 0.30/0.58 = A ) )
% 0.30/0.58 => ( Y6 = X3 ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % realpow_pos_nth_unique
% 0.30/0.58 thf(fact_2949_realpow__pos__nth,axiom,
% 0.30/0.58 ! [N: nat,A: real] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.30/0.58 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.30/0.58 => ? [R4: real] :
% 0.30/0.58 ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.30/0.58 & ( ( power_power_real @ R4 @ N )
% 0.30/0.58 = A ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % realpow_pos_nth
% 0.30/0.58 thf(fact_2950_sprop1,axiom,
% 0.30/0.58 ( ( sa
% 0.30/0.58 = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 0.30/0.58 & ( deg
% 0.30/0.58 = ( plus_plus_nat @ na @ m ) )
% 0.30/0.58 & ( ( size_s6755466524823107622T_VEBT @ treeList )
% 0.30/0.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.30/0.58 & ( vEBT_invar_vebt @ summary @ m )
% 0.30/0.58 & ! [X5: vEBT_VEBT] :
% 0.30/0.58 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 0.30/0.58 => ( vEBT_invar_vebt @ X5 @ na ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % sprop1
% 0.30/0.58 thf(fact_2951_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_Code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 0.30/0.58 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) )
% 0.30/0.58 = ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 0.30/0.58 = ( size_s3445333598471063425nteger @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_s3445333598471063425nteger @ Xs2 ) )
% 0.30/0.58 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ N4 ) @ ( nth_Code_integer @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2952_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 0.30/0.58 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( listre1230615542750757617T_VEBT @ R3 ) )
% 0.30/0.58 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.58 => ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2953_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_o,R3: set_Pr3175402225741728619VEBT_o] :
% 0.30/0.58 ( ( member3126162362653435956list_o @ ( produc2717590391345394939list_o @ Xs2 @ Ys ) @ ( listrel_VEBT_VEBT_o @ R3 ) )
% 0.30/0.58 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.58 = ( size_size_list_o @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.58 => ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_o @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2954_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,R3: set_Pr7556676689462069481BT_nat] :
% 0.30/0.58 ( ( member6193324644334088288st_nat @ ( produc5570133714943300547st_nat @ Xs2 @ Ys ) @ ( listre5900670229112895443BT_nat @ R3 ) )
% 0.30/0.58 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.58 = ( size_size_list_nat @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.58 => ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_nat @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2955_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_int,R3: set_Pr5066593544530342725BT_int] :
% 0.30/0.58 ( ( member3703241499402361532st_int @ ( produc1392282695434103839st_int @ Xs2 @ Ys ) @ ( listre5898179758603845167BT_int @ R3 ) )
% 0.30/0.58 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.30/0.58 = ( size_size_list_int @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.30/0.58 => ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_int @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2956_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_o,Ys: list_VEBT_VEBT,R3: set_Pr7543698050874017315T_VEBT] :
% 0.30/0.58 ( ( member1087064965665443052T_VEBT @ ( produc6043759678074843571T_VEBT @ Xs2 @ Ys ) @ ( listrel_o_VEBT_VEBT @ R3 ) )
% 0.30/0.58 = ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.58 => ( member5477980866518848620T_VEBT @ ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2957_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_o,Ys: list_o,R3: set_Product_prod_o_o] :
% 0.30/0.58 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( listrel_o_o @ R3 ) )
% 0.30/0.58 = ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.58 = ( size_size_list_o @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.58 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs2 @ N4 ) @ ( nth_o @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2958_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_o,Ys: list_nat,R3: set_Pr2101469702781467981_o_nat] :
% 0.30/0.58 ( ( member1519744053835550788st_nat @ ( produc7128876500814652583st_nat @ Xs2 @ Ys ) @ ( listrel_o_nat @ R3 ) )
% 0.30/0.58 = ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.58 = ( size_size_list_nat @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.58 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ ( nth_o @ Xs2 @ N4 ) @ ( nth_nat @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2959_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_o,Ys: list_int,R3: set_Pr8834758594704517033_o_int] :
% 0.30/0.58 ( ( member8253032945758599840st_int @ ( produc2951025481305455875st_int @ Xs2 @ Ys ) @ ( listrel_o_int @ R3 ) )
% 0.30/0.58 = ( ( ( size_size_list_o @ Xs2 )
% 0.30/0.58 = ( size_size_list_int @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 0.30/0.58 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ ( nth_o @ Xs2 @ N4 ) @ ( nth_int @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2960_listrel__iff__nth,axiom,
% 0.30/0.58 ! [Xs2: list_nat,Ys: list_VEBT_VEBT,R3: set_Pr6167073792073659919T_VEBT] :
% 0.30/0.58 ( ( member5968030670617646438T_VEBT @ ( produc8335345208264861441T_VEBT @ Xs2 @ Ys ) @ ( listre5761932458788874033T_VEBT @ R3 ) )
% 0.30/0.58 = ( ( ( size_size_list_nat @ Xs2 )
% 0.30/0.58 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 0.30/0.58 & ! [N4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ N4 @ ( size_size_list_nat @ Xs2 ) )
% 0.30/0.58 => ( member8549952807677709168T_VEBT @ ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % listrel_iff_nth
% 0.30/0.58 thf(fact_2961_in__measures_I2_J,axiom,
% 0.30/0.58 ! [X: code_integer,Y: code_integer,F2: code_integer > nat,Fs: list_C4705013386053401436er_nat] :
% 0.30/0.58 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) )
% 0.30/0.58 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.30/0.58 | ( ( ( F2 @ X )
% 0.30/0.58 = ( F2 @ Y ) )
% 0.30/0.58 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ Fs ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_measures(2)
% 0.30/0.58 thf(fact_2962_in__measures_I2_J,axiom,
% 0.30/0.58 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,F2: product_prod_nat_nat > nat,Fs: list_P9162950289778280392at_nat] :
% 0.30/0.58 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) )
% 0.30/0.58 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.30/0.58 | ( ( ( F2 @ X )
% 0.30/0.58 = ( F2 @ Y ) )
% 0.30/0.58 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ Fs ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_measures(2)
% 0.30/0.58 thf(fact_2963_in__measures_I2_J,axiom,
% 0.30/0.58 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F2: set_Pr1261947904930325089at_nat > nat,Fs: list_s9130966667114977576at_nat] :
% 0.30/0.58 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) )
% 0.30/0.58 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.30/0.58 | ( ( ( F2 @ X )
% 0.30/0.58 = ( F2 @ Y ) )
% 0.30/0.58 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ Fs ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_measures(2)
% 0.30/0.58 thf(fact_2964_in__measures_I2_J,axiom,
% 0.30/0.58 ! [X: nat,Y: nat,F2: nat > nat,Fs: list_nat_nat] :
% 0.30/0.58 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) )
% 0.30/0.58 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.30/0.58 | ( ( ( F2 @ X )
% 0.30/0.58 = ( F2 @ Y ) )
% 0.30/0.58 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_measures(2)
% 0.30/0.58 thf(fact_2965_in__measures_I2_J,axiom,
% 0.30/0.58 ! [X: int,Y: int,F2: int > nat,Fs: list_int_nat] :
% 0.30/0.58 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) )
% 0.30/0.58 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.30/0.58 | ( ( ( F2 @ X )
% 0.30/0.58 = ( F2 @ Y ) )
% 0.30/0.58 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_measures(2)
% 0.30/0.58 thf(fact_2966_of__nat__zero__less__power__iff,axiom,
% 0.30/0.58 ! [X: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 0.30/0.58 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.30/0.58 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_zero_less_power_iff
% 0.30/0.58 thf(fact_2967_of__nat__zero__less__power__iff,axiom,
% 0.30/0.58 ! [X: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 0.30/0.58 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.30/0.58 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_zero_less_power_iff
% 0.30/0.58 thf(fact_2968_of__nat__zero__less__power__iff,axiom,
% 0.30/0.58 ! [X: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 0.30/0.58 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.30/0.58 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_zero_less_power_iff
% 0.30/0.58 thf(fact_2969_of__nat__zero__less__power__iff,axiom,
% 0.30/0.58 ! [X: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 0.30/0.58 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.30/0.58 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_zero_less_power_iff
% 0.30/0.58 thf(fact_2970__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.30/0.58 ~ ! [TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Info: option4927543243414619207at_nat] :
% 0.30/0.58 ~ ( ( sa
% 0.30/0.58 = ( vEBT_Node @ Info @ deg @ TreeList3 @ Summary3 ) )
% 0.30/0.58 & ( deg
% 0.30/0.58 = ( plus_plus_nat @ na @ m ) )
% 0.30/0.58 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 0.30/0.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.30/0.58 & ( vEBT_invar_vebt @ Summary3 @ m )
% 0.30/0.58 & ! [X5: vEBT_VEBT] :
% 0.30/0.58 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 0.30/0.58 => ( vEBT_invar_vebt @ X5 @ na ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % \<open>\<And>thesis. (\<And>treeList' summary' info. s = Node info deg treeList' summary' \<and> deg = n + m \<and> length treeList' = 2 ^ m \<and> invar_vebt summary' m \<and> (\<forall>t\<in>set treeList'. invar_vebt t n) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.30/0.58 thf(fact_2971_intind,axiom,
% 0.30/0.58 ! [I2: nat,N: nat,P2: nat > $o,X: nat] :
% 0.30/0.58 ( ( ord_less_nat @ I2 @ N )
% 0.30/0.58 => ( ( P2 @ X )
% 0.30/0.58 => ( P2 @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % intind
% 0.30/0.58 thf(fact_2972_intind,axiom,
% 0.30/0.58 ! [I2: nat,N: nat,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 0.30/0.58 ( ( ord_less_nat @ I2 @ N )
% 0.30/0.58 => ( ( P2 @ X )
% 0.30/0.58 => ( P2 @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % intind
% 0.30/0.58 thf(fact_2973_numeral__eq__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ( numera1916890842035813515d_enat @ M2 )
% 0.30/0.58 = ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_iff
% 0.30/0.58 thf(fact_2974_numeral__eq__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ( numera6690914467698888265omplex @ M2 )
% 0.30/0.58 = ( numera6690914467698888265omplex @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_iff
% 0.30/0.58 thf(fact_2975_numeral__eq__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ( numeral_numeral_real @ M2 )
% 0.30/0.58 = ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_iff
% 0.30/0.58 thf(fact_2976_numeral__eq__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ( numeral_numeral_nat @ M2 )
% 0.30/0.58 = ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_iff
% 0.30/0.58 thf(fact_2977_numeral__eq__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ( numeral_numeral_int @ M2 )
% 0.30/0.58 = ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_iff
% 0.30/0.58 thf(fact_2978_semiring__norm_I13_J,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( times_times_num @ ( bit0 @ M2 ) @ ( bit0 @ N ) )
% 0.30/0.58 = ( bit0 @ ( bit0 @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % semiring_norm(13)
% 0.30/0.58 thf(fact_2979_semiring__norm_I11_J,axiom,
% 0.30/0.58 ! [M2: num] :
% 0.30/0.58 ( ( times_times_num @ M2 @ one )
% 0.30/0.58 = M2 ) ).
% 0.30/0.58
% 0.30/0.58 % semiring_norm(11)
% 0.30/0.58 thf(fact_2980_semiring__norm_I12_J,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( times_times_num @ one @ N )
% 0.30/0.58 = N ) ).
% 0.30/0.58
% 0.30/0.58 % semiring_norm(12)
% 0.30/0.58 thf(fact_2981_case4_I10_J,axiom,
% 0.30/0.58 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 0.30/0.58
% 0.30/0.58 % case4(10)
% 0.30/0.58 thf(fact_2982_case4_I4_J,axiom,
% 0.30/0.58 ( ( size_s6755466524823107622T_VEBT @ treeList2 )
% 0.30/0.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 0.30/0.58
% 0.30/0.58 % case4(4)
% 0.30/0.58 thf(fact_2983_of__nat__eq__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ( semiri5074537144036343181t_real @ M2 )
% 0.30/0.58 = ( semiri5074537144036343181t_real @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_iff
% 0.30/0.58 thf(fact_2984_of__nat__eq__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ( semiri1314217659103216013at_int @ M2 )
% 0.30/0.58 = ( semiri1314217659103216013at_int @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_iff
% 0.30/0.58 thf(fact_2985_of__nat__eq__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 0.30/0.58 = ( semiri1316708129612266289at_nat @ N ) )
% 0.30/0.58 = ( M2 = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_iff
% 0.30/0.58 thf(fact_2986_a0,axiom,
% 0.30/0.58 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 0.30/0.58
% 0.30/0.58 % a0
% 0.30/0.58 thf(fact_2987_case4_I7_J,axiom,
% 0.30/0.58 ! [I4: nat] :
% 0.30/0.58 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.30/0.58 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ X7 ) )
% 0.30/0.58 = ( vEBT_V8194947554948674370ptions @ summary2 @ I4 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % case4(7)
% 0.30/0.58 thf(fact_2988_member__bound,axiom,
% 0.30/0.58 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 0.30/0.58 ( ( vEBT_vebt_member @ Tree @ X )
% 0.30/0.58 => ( ( vEBT_invar_vebt @ Tree @ N )
% 0.30/0.58 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % member_bound
% 0.30/0.58 thf(fact_2989_valid__pres__insert,axiom,
% 0.30/0.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.58 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ T @ X ) @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % valid_pres_insert
% 0.30/0.58 thf(fact_2990_numeral__le__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_iff
% 0.30/0.58 thf(fact_2991_numeral__le__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_iff
% 0.30/0.58 thf(fact_2992_numeral__le__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 0.30/0.58 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_iff
% 0.30/0.58 thf(fact_2993_numeral__le__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_iff
% 0.30/0.58 thf(fact_2994_numeral__le__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_iff
% 0.30/0.58 thf(fact_2995_numeral__less__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 0.30/0.58 = ( ord_less_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_less_iff
% 0.30/0.58 thf(fact_2996_numeral__less__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( ord_less_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_less_iff
% 0.30/0.58 thf(fact_2997_numeral__less__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( ord_less_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_less_iff
% 0.30/0.58 thf(fact_2998_numeral__less__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( ord_less_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_less_iff
% 0.30/0.58 thf(fact_2999_numeral__less__iff,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( ord_less_num @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_less_iff
% 0.30/0.58 thf(fact_3000_numeral__times__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 0.30/0.58 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_times_numeral
% 0.30/0.58 thf(fact_3001_numeral__times__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( numera1916890842035813515d_enat @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_times_numeral
% 0.30/0.58 thf(fact_3002_numeral__times__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 0.30/0.58 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_times_numeral
% 0.30/0.58 thf(fact_3003_numeral__times__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_times_numeral
% 0.30/0.58 thf(fact_3004_numeral__times__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( times_times_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_times_numeral
% 0.30/0.58 thf(fact_3005_numeral__times__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_times_numeral
% 0.30/0.58 thf(fact_3006_mult__numeral__left__semiring__numeral,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: rat] :
% 0.30/0.58 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % mult_numeral_left_semiring_numeral
% 0.30/0.58 thf(fact_3007_mult__numeral__left__semiring__numeral,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: extended_enat] :
% 0.30/0.58 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % mult_numeral_left_semiring_numeral
% 0.30/0.58 thf(fact_3008_mult__numeral__left__semiring__numeral,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: complex] :
% 0.30/0.58 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % mult_numeral_left_semiring_numeral
% 0.30/0.58 thf(fact_3009_mult__numeral__left__semiring__numeral,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: real] :
% 0.30/0.58 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % mult_numeral_left_semiring_numeral
% 0.30/0.58 thf(fact_3010_mult__numeral__left__semiring__numeral,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: nat] :
% 0.30/0.58 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % mult_numeral_left_semiring_numeral
% 0.30/0.58 thf(fact_3011_mult__numeral__left__semiring__numeral,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: int] :
% 0.30/0.58 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % mult_numeral_left_semiring_numeral
% 0.30/0.58 thf(fact_3012_add__numeral__left,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: rat] :
% 0.30/0.58 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V2 ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % add_numeral_left
% 0.30/0.58 thf(fact_3013_add__numeral__left,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: extended_enat] :
% 0.30/0.58 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % add_numeral_left
% 0.30/0.58 thf(fact_3014_add__numeral__left,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: complex] :
% 0.30/0.58 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % add_numeral_left
% 0.30/0.58 thf(fact_3015_add__numeral__left,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: real] :
% 0.30/0.58 ( ( plus_plus_real @ ( numeral_numeral_real @ V2 ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % add_numeral_left
% 0.30/0.58 thf(fact_3016_add__numeral__left,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: nat] :
% 0.30/0.58 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % add_numeral_left
% 0.30/0.58 thf(fact_3017_add__numeral__left,axiom,
% 0.30/0.58 ! [V2: num,W2: num,Z3: int] :
% 0.30/0.58 ( ( plus_plus_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 0.30/0.58 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 0.30/0.58
% 0.30/0.58 % add_numeral_left
% 0.30/0.58 thf(fact_3018_numeral__plus__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 0.30/0.58 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_numeral
% 0.30/0.58 thf(fact_3019_numeral__plus__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_numeral
% 0.30/0.58 thf(fact_3020_numeral__plus__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 0.30/0.58 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_numeral
% 0.30/0.58 thf(fact_3021_numeral__plus__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_numeral
% 0.30/0.58 thf(fact_3022_numeral__plus__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_numeral
% 0.30/0.58 thf(fact_3023_numeral__plus__numeral,axiom,
% 0.30/0.58 ! [M2: num,N: num] :
% 0.30/0.58 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_numeral
% 0.30/0.58 thf(fact_3024_num__double,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 0.30/0.58 = ( bit0 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % num_double
% 0.30/0.58 thf(fact_3025_power__mult__numeral,axiom,
% 0.30/0.58 ! [A: nat,M2: num,N: num] :
% 0.30/0.58 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_mult_numeral
% 0.30/0.58 thf(fact_3026_power__mult__numeral,axiom,
% 0.30/0.58 ! [A: real,M2: num,N: num] :
% 0.30/0.58 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_mult_numeral
% 0.30/0.58 thf(fact_3027_power__mult__numeral,axiom,
% 0.30/0.58 ! [A: int,M2: num,N: num] :
% 0.30/0.58 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_mult_numeral
% 0.30/0.58 thf(fact_3028_power__mult__numeral,axiom,
% 0.30/0.58 ! [A: complex,M2: num,N: num] :
% 0.30/0.58 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_mult_numeral
% 0.30/0.58 thf(fact_3029_insert__simp__mima,axiom,
% 0.30/0.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.30/0.58 ( ( ( X = Mi )
% 0.30/0.58 | ( X = Ma ) )
% 0.30/0.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.30/0.58 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.30/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % insert_simp_mima
% 0.30/0.58 thf(fact_3030_misiz,axiom,
% 0.30/0.58 ! [T: vEBT_VEBT,N: nat,M2: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.58 => ( ( ( some_nat @ M2 )
% 0.30/0.58 = ( vEBT_vebt_mint @ T ) )
% 0.30/0.58 => ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % misiz
% 0.30/0.58 thf(fact_3031_not__real__square__gt__zero,axiom,
% 0.30/0.58 ! [X: real] :
% 0.30/0.58 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 0.30/0.58 = ( X = zero_zero_real ) ) ).
% 0.30/0.58
% 0.30/0.58 % not_real_square_gt_zero
% 0.30/0.58 thf(fact_3032_valid__insert__both__member__options__add,axiom,
% 0.30/0.58 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.58 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % valid_insert_both_member_options_add
% 0.30/0.58 thf(fact_3033_valid__insert__both__member__options__pres,axiom,
% 0.30/0.58 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.58 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 0.30/0.58 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % valid_insert_both_member_options_pres
% 0.30/0.58 thf(fact_3034_helpypredd,axiom,
% 0.30/0.58 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.58 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.30/0.58 = ( some_nat @ Y ) )
% 0.30/0.58 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % helpypredd
% 0.30/0.58 thf(fact_3035_helpyd,axiom,
% 0.30/0.58 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.58 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.30/0.58 = ( some_nat @ Y ) )
% 0.30/0.58 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % helpyd
% 0.30/0.58 thf(fact_3036_post__member__pre__member,axiom,
% 0.30/0.58 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ T @ N )
% 0.30/0.58 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.30/0.58 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 0.30/0.58 => ( ( vEBT_vebt_member @ T @ Y )
% 0.30/0.58 | ( X = Y ) ) ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % post_member_pre_member
% 0.30/0.58 thf(fact_3037_replicate__eq__replicate,axiom,
% 0.30/0.58 ! [M2: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 0.30/0.58 ( ( ( replicate_VEBT_VEBT @ M2 @ X )
% 0.30/0.58 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 0.30/0.58 = ( ( M2 = N )
% 0.30/0.58 & ( ( M2 != zero_zero_nat )
% 0.30/0.58 => ( X = Y ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % replicate_eq_replicate
% 0.30/0.58 thf(fact_3038_length__replicate,axiom,
% 0.30/0.58 ! [N: nat,X: vEBT_VEBT] :
% 0.30/0.58 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.30/0.58 = N ) ).
% 0.30/0.58
% 0.30/0.58 % length_replicate
% 0.30/0.58 thf(fact_3039_length__replicate,axiom,
% 0.30/0.58 ! [N: nat,X: $o] :
% 0.30/0.58 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 0.30/0.58 = N ) ).
% 0.30/0.58
% 0.30/0.58 % length_replicate
% 0.30/0.58 thf(fact_3040_length__replicate,axiom,
% 0.30/0.58 ! [N: nat,X: nat] :
% 0.30/0.58 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 0.30/0.58 = N ) ).
% 0.30/0.58
% 0.30/0.58 % length_replicate
% 0.30/0.58 thf(fact_3041_length__replicate,axiom,
% 0.30/0.58 ! [N: nat,X: int] :
% 0.30/0.58 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 0.30/0.58 = N ) ).
% 0.30/0.58
% 0.30/0.58 % length_replicate
% 0.30/0.58 thf(fact_3042_delt__out__of__range,axiom,
% 0.30/0.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.30/0.58 ( ( ( ord_less_nat @ X @ Mi )
% 0.30/0.58 | ( ord_less_nat @ Ma @ X ) )
% 0.30/0.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.30/0.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.30/0.58 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % delt_out_of_range
% 0.30/0.58 thf(fact_3043_del__single__cont,axiom,
% 0.30/0.58 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.30/0.58 ( ( ( X = Mi )
% 0.30/0.58 & ( X = Ma ) )
% 0.30/0.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.30/0.58 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.30/0.58 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % del_single_cont
% 0.30/0.58 thf(fact_3044_set__n__deg__not__0,axiom,
% 0.30/0.58 ! [TreeList2: list_VEBT_VEBT,N: nat,M2: nat] :
% 0.30/0.58 ( ! [X3: vEBT_VEBT] :
% 0.30/0.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.30/0.58 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.30/0.58 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.30/0.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.30/0.58 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % set_n_deg_not_0
% 0.30/0.58 thf(fact_3045_mi__ma__2__deg,axiom,
% 0.30/0.58 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.30/0.58 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.30/0.58 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.30/0.58 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % mi_ma_2_deg
% 0.30/0.58 thf(fact_3046_pred__max,axiom,
% 0.30/0.58 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.30/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.30/0.58 => ( ( ord_less_nat @ Ma @ X )
% 0.30/0.58 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.30/0.58 = ( some_nat @ Ma ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % pred_max
% 0.30/0.58 thf(fact_3047_succ__min,axiom,
% 0.30/0.58 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.30/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.30/0.58 => ( ( ord_less_nat @ X @ Mi )
% 0.30/0.58 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.30/0.58 = ( some_nat @ Mi ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % succ_min
% 0.30/0.58 thf(fact_3048_bit__concat__def,axiom,
% 0.30/0.58 ( vEBT_VEBT_bit_concat
% 0.30/0.58 = ( ^ [H2: nat,L2: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % bit_concat_def
% 0.30/0.58 thf(fact_3049_distrib__left__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: rat,C2: rat] :
% 0.30/0.58 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 0.30/0.58 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_left_numeral
% 0.30/0.58 thf(fact_3050_distrib__left__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: extended_enat,C2: extended_enat] :
% 0.30/0.58 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( plus_p3455044024723400733d_enat @ B @ C2 ) )
% 0.30/0.58 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_left_numeral
% 0.30/0.58 thf(fact_3051_distrib__left__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: complex,C2: complex] :
% 0.30/0.58 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( plus_plus_complex @ B @ C2 ) )
% 0.30/0.58 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_left_numeral
% 0.30/0.58 thf(fact_3052_distrib__left__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: real,C2: real] :
% 0.30/0.58 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( plus_plus_real @ B @ C2 ) )
% 0.30/0.58 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_left_numeral
% 0.30/0.58 thf(fact_3053_distrib__left__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: nat,C2: nat] :
% 0.30/0.58 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 0.30/0.58 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_left_numeral
% 0.30/0.58 thf(fact_3054_distrib__left__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: int,C2: int] :
% 0.30/0.58 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ B @ C2 ) )
% 0.30/0.58 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_left_numeral
% 0.30/0.58 thf(fact_3055_distrib__right__numeral,axiom,
% 0.30/0.58 ! [A: rat,B: rat,V2: num] :
% 0.30/0.58 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 0.30/0.58 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_right_numeral
% 0.30/0.58 thf(fact_3056_distrib__right__numeral,axiom,
% 0.30/0.58 ! [A: extended_enat,B: extended_enat,V2: num] :
% 0.30/0.58 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 0.30/0.58 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V2 ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_right_numeral
% 0.30/0.58 thf(fact_3057_distrib__right__numeral,axiom,
% 0.30/0.58 ! [A: complex,B: complex,V2: num] :
% 0.30/0.58 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V2 ) )
% 0.30/0.58 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_right_numeral
% 0.30/0.58 thf(fact_3058_distrib__right__numeral,axiom,
% 0.30/0.58 ! [A: real,B: real,V2: num] :
% 0.30/0.58 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V2 ) )
% 0.30/0.58 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_right_numeral
% 0.30/0.58 thf(fact_3059_distrib__right__numeral,axiom,
% 0.30/0.58 ! [A: nat,B: nat,V2: num] :
% 0.30/0.58 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V2 ) )
% 0.30/0.58 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V2 ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_right_numeral
% 0.30/0.58 thf(fact_3060_distrib__right__numeral,axiom,
% 0.30/0.58 ! [A: int,B: int,V2: num] :
% 0.30/0.58 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 0.30/0.58 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % distrib_right_numeral
% 0.30/0.58 thf(fact_3061_numeral__eq__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ( numera6620942414471956472nteger @ N )
% 0.30/0.58 = one_one_Code_integer )
% 0.30/0.58 = ( N = one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_one_iff
% 0.30/0.58 thf(fact_3062_numeral__eq__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ( numera1916890842035813515d_enat @ N )
% 0.30/0.58 = one_on7984719198319812577d_enat )
% 0.30/0.58 = ( N = one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_one_iff
% 0.30/0.58 thf(fact_3063_numeral__eq__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ( numera6690914467698888265omplex @ N )
% 0.30/0.58 = one_one_complex )
% 0.30/0.58 = ( N = one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_one_iff
% 0.30/0.58 thf(fact_3064_numeral__eq__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ( numeral_numeral_real @ N )
% 0.30/0.58 = one_one_real )
% 0.30/0.58 = ( N = one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_one_iff
% 0.30/0.58 thf(fact_3065_numeral__eq__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ( numeral_numeral_nat @ N )
% 0.30/0.58 = one_one_nat )
% 0.30/0.58 = ( N = one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_one_iff
% 0.30/0.58 thf(fact_3066_numeral__eq__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ( numeral_numeral_int @ N )
% 0.30/0.58 = one_one_int )
% 0.30/0.58 = ( N = one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_eq_one_iff
% 0.30/0.58 thf(fact_3067_one__eq__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( one_one_Code_integer
% 0.30/0.58 = ( numera6620942414471956472nteger @ N ) )
% 0.30/0.58 = ( one = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_eq_numeral_iff
% 0.30/0.58 thf(fact_3068_one__eq__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( one_on7984719198319812577d_enat
% 0.30/0.58 = ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( one = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_eq_numeral_iff
% 0.30/0.58 thf(fact_3069_one__eq__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( one_one_complex
% 0.30/0.58 = ( numera6690914467698888265omplex @ N ) )
% 0.30/0.58 = ( one = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_eq_numeral_iff
% 0.30/0.58 thf(fact_3070_one__eq__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( one_one_real
% 0.30/0.58 = ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( one = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_eq_numeral_iff
% 0.30/0.58 thf(fact_3071_one__eq__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( one_one_nat
% 0.30/0.58 = ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( one = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_eq_numeral_iff
% 0.30/0.58 thf(fact_3072_one__eq__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( one_one_int
% 0.30/0.58 = ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( one = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_eq_numeral_iff
% 0.30/0.58 thf(fact_3073_left__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [A: rat,B: rat,V2: num] :
% 0.30/0.58 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 0.30/0.58 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % left_diff_distrib_numeral
% 0.30/0.58 thf(fact_3074_left__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [A: complex,B: complex,V2: num] :
% 0.30/0.58 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V2 ) )
% 0.30/0.58 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % left_diff_distrib_numeral
% 0.30/0.58 thf(fact_3075_left__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [A: real,B: real,V2: num] :
% 0.30/0.58 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V2 ) )
% 0.30/0.58 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % left_diff_distrib_numeral
% 0.30/0.58 thf(fact_3076_left__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [A: int,B: int,V2: num] :
% 0.30/0.58 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 0.30/0.58 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % left_diff_distrib_numeral
% 0.30/0.58 thf(fact_3077_right__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: rat,C2: rat] :
% 0.30/0.58 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( minus_minus_rat @ B @ C2 ) )
% 0.30/0.58 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % right_diff_distrib_numeral
% 0.30/0.58 thf(fact_3078_right__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: complex,C2: complex] :
% 0.30/0.58 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( minus_minus_complex @ B @ C2 ) )
% 0.30/0.58 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % right_diff_distrib_numeral
% 0.30/0.58 thf(fact_3079_right__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: real,C2: real] :
% 0.30/0.58 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( minus_minus_real @ B @ C2 ) )
% 0.30/0.58 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % right_diff_distrib_numeral
% 0.30/0.58 thf(fact_3080_right__diff__distrib__numeral,axiom,
% 0.30/0.58 ! [V2: num,B: int,C2: int] :
% 0.30/0.58 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( minus_minus_int @ B @ C2 ) )
% 0.30/0.58 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C2 ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % right_diff_distrib_numeral
% 0.30/0.58 thf(fact_3081_power__zero__numeral,axiom,
% 0.30/0.58 ! [K2: num] :
% 0.30/0.58 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K2 ) )
% 0.30/0.58 = zero_zero_rat ) ).
% 0.30/0.58
% 0.30/0.58 % power_zero_numeral
% 0.30/0.58 thf(fact_3082_power__zero__numeral,axiom,
% 0.30/0.58 ! [K2: num] :
% 0.30/0.58 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K2 ) )
% 0.30/0.58 = zero_zero_nat ) ).
% 0.30/0.58
% 0.30/0.58 % power_zero_numeral
% 0.30/0.58 thf(fact_3083_power__zero__numeral,axiom,
% 0.30/0.58 ! [K2: num] :
% 0.30/0.58 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K2 ) )
% 0.30/0.58 = zero_zero_real ) ).
% 0.30/0.58
% 0.30/0.58 % power_zero_numeral
% 0.30/0.58 thf(fact_3084_power__zero__numeral,axiom,
% 0.30/0.58 ! [K2: num] :
% 0.30/0.58 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K2 ) )
% 0.30/0.58 = zero_zero_int ) ).
% 0.30/0.58
% 0.30/0.58 % power_zero_numeral
% 0.30/0.58 thf(fact_3085_power__zero__numeral,axiom,
% 0.30/0.58 ! [K2: num] :
% 0.30/0.58 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K2 ) )
% 0.30/0.58 = zero_zero_complex ) ).
% 0.30/0.58
% 0.30/0.58 % power_zero_numeral
% 0.30/0.58 thf(fact_3086_Suc__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Suc_numeral
% 0.30/0.58 thf(fact_3087_power__add__numeral,axiom,
% 0.30/0.58 ! [A: complex,M2: num,N: num] :
% 0.30/0.58 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral
% 0.30/0.58 thf(fact_3088_power__add__numeral,axiom,
% 0.30/0.58 ! [A: real,M2: num,N: num] :
% 0.30/0.58 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral
% 0.30/0.58 thf(fact_3089_power__add__numeral,axiom,
% 0.30/0.58 ! [A: rat,M2: num,N: num] :
% 0.30/0.58 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral
% 0.30/0.58 thf(fact_3090_power__add__numeral,axiom,
% 0.30/0.58 ! [A: nat,M2: num,N: num] :
% 0.30/0.58 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral
% 0.30/0.58 thf(fact_3091_power__add__numeral,axiom,
% 0.30/0.58 ! [A: int,M2: num,N: num] :
% 0.30/0.58 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 0.30/0.58 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral
% 0.30/0.58 thf(fact_3092_power__add__numeral2,axiom,
% 0.30/0.58 ! [A: complex,M2: num,N: num,B: complex] :
% 0.30/0.58 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral2
% 0.30/0.58 thf(fact_3093_power__add__numeral2,axiom,
% 0.30/0.58 ! [A: real,M2: num,N: num,B: real] :
% 0.30/0.58 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral2
% 0.30/0.58 thf(fact_3094_power__add__numeral2,axiom,
% 0.30/0.58 ! [A: rat,M2: num,N: num,B: rat] :
% 0.30/0.58 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral2
% 0.30/0.58 thf(fact_3095_power__add__numeral2,axiom,
% 0.30/0.58 ! [A: nat,M2: num,N: num,B: nat] :
% 0.30/0.58 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral2
% 0.30/0.58 thf(fact_3096_power__add__numeral2,axiom,
% 0.30/0.58 ! [A: int,M2: num,N: num,B: int] :
% 0.30/0.58 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 0.30/0.58 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 0.30/0.58
% 0.30/0.58 % power_add_numeral2
% 0.30/0.58 thf(fact_3097_of__nat__eq__0__iff,axiom,
% 0.30/0.58 ! [M2: nat] :
% 0.30/0.58 ( ( ( semiri8010041392384452111omplex @ M2 )
% 0.30/0.58 = zero_zero_complex )
% 0.30/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_0_iff
% 0.30/0.58 thf(fact_3098_of__nat__eq__0__iff,axiom,
% 0.30/0.58 ! [M2: nat] :
% 0.30/0.58 ( ( ( semiri681578069525770553at_rat @ M2 )
% 0.30/0.58 = zero_zero_rat )
% 0.30/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_0_iff
% 0.30/0.58 thf(fact_3099_of__nat__eq__0__iff,axiom,
% 0.30/0.58 ! [M2: nat] :
% 0.30/0.58 ( ( ( semiri5074537144036343181t_real @ M2 )
% 0.30/0.58 = zero_zero_real )
% 0.30/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_0_iff
% 0.30/0.58 thf(fact_3100_of__nat__eq__0__iff,axiom,
% 0.30/0.58 ! [M2: nat] :
% 0.30/0.58 ( ( ( semiri1314217659103216013at_int @ M2 )
% 0.30/0.58 = zero_zero_int )
% 0.30/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_0_iff
% 0.30/0.58 thf(fact_3101_of__nat__eq__0__iff,axiom,
% 0.30/0.58 ! [M2: nat] :
% 0.30/0.58 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 0.30/0.58 = zero_zero_nat )
% 0.30/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_0_iff
% 0.30/0.58 thf(fact_3102_of__nat__0__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( zero_zero_complex
% 0.30/0.58 = ( semiri8010041392384452111omplex @ N ) )
% 0.30/0.58 = ( zero_zero_nat = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0_eq_iff
% 0.30/0.58 thf(fact_3103_of__nat__0__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( zero_zero_rat
% 0.30/0.58 = ( semiri681578069525770553at_rat @ N ) )
% 0.30/0.58 = ( zero_zero_nat = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0_eq_iff
% 0.30/0.58 thf(fact_3104_of__nat__0__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( zero_zero_real
% 0.30/0.58 = ( semiri5074537144036343181t_real @ N ) )
% 0.30/0.58 = ( zero_zero_nat = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0_eq_iff
% 0.30/0.58 thf(fact_3105_of__nat__0__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( zero_zero_int
% 0.30/0.58 = ( semiri1314217659103216013at_int @ N ) )
% 0.30/0.58 = ( zero_zero_nat = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0_eq_iff
% 0.30/0.58 thf(fact_3106_of__nat__0__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( zero_zero_nat
% 0.30/0.58 = ( semiri1316708129612266289at_nat @ N ) )
% 0.30/0.58 = ( zero_zero_nat = N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0_eq_iff
% 0.30/0.58 thf(fact_3107_of__nat__0,axiom,
% 0.30/0.58 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 0.30/0.58 = zero_zero_complex ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0
% 0.30/0.58 thf(fact_3108_of__nat__0,axiom,
% 0.30/0.58 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 0.30/0.58 = zero_zero_rat ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0
% 0.30/0.58 thf(fact_3109_of__nat__0,axiom,
% 0.30/0.58 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 0.30/0.58 = zero_zero_real ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0
% 0.30/0.58 thf(fact_3110_of__nat__0,axiom,
% 0.30/0.58 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.30/0.58 = zero_zero_int ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0
% 0.30/0.58 thf(fact_3111_of__nat__0,axiom,
% 0.30/0.58 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 0.30/0.58 = zero_zero_nat ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_0
% 0.30/0.58 thf(fact_3112_of__nat__less__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.30/0.58 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_less_iff
% 0.30/0.58 thf(fact_3113_of__nat__less__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.30/0.58 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_less_iff
% 0.30/0.58 thf(fact_3114_of__nat__less__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.30/0.58 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_less_iff
% 0.30/0.58 thf(fact_3115_of__nat__less__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.30/0.58 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_less_iff
% 0.30/0.58 thf(fact_3116_of__nat__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numera1916890842035813515d_enat @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_numeral
% 0.30/0.58 thf(fact_3117_of__nat__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numera6690914467698888265omplex @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_numeral
% 0.30/0.58 thf(fact_3118_of__nat__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numeral_numeral_real @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_numeral
% 0.30/0.58 thf(fact_3119_of__nat__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numeral_numeral_int @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_numeral
% 0.30/0.58 thf(fact_3120_of__nat__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numeral_numeral_nat @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_numeral
% 0.30/0.58 thf(fact_3121_of__nat__le__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.30/0.58 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_le_iff
% 0.30/0.58 thf(fact_3122_of__nat__le__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.30/0.58 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_le_iff
% 0.30/0.58 thf(fact_3123_of__nat__le__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.30/0.58 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_le_iff
% 0.30/0.58 thf(fact_3124_of__nat__le__iff,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.30/0.58 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_le_iff
% 0.30/0.58 thf(fact_3125_of__nat__add,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.58 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_add
% 0.30/0.58 thf(fact_3126_of__nat__add,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.58 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_add
% 0.30/0.58 thf(fact_3127_of__nat__add,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_add
% 0.30/0.58 thf(fact_3128_of__nat__add,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N ) )
% 0.30/0.58 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_add
% 0.30/0.58 thf(fact_3129_of__nat__mult,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.58 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_mult
% 0.30/0.58 thf(fact_3130_of__nat__mult,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.58 = ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_mult
% 0.30/0.58 thf(fact_3131_of__nat__mult,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.58 = ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_mult
% 0.30/0.58 thf(fact_3132_of__nat__mult,axiom,
% 0.30/0.58 ! [M2: nat,N: nat] :
% 0.30/0.58 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M2 @ N ) )
% 0.30/0.58 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_mult
% 0.30/0.58 thf(fact_3133_of__nat__eq__1__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( ( semiri4939895301339042750nteger @ N )
% 0.30/0.58 = one_one_Code_integer )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_1_iff
% 0.30/0.58 thf(fact_3134_of__nat__eq__1__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( ( semiri8010041392384452111omplex @ N )
% 0.30/0.58 = one_one_complex )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_1_iff
% 0.30/0.58 thf(fact_3135_of__nat__eq__1__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( ( semiri5074537144036343181t_real @ N )
% 0.30/0.58 = one_one_real )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_1_iff
% 0.30/0.58 thf(fact_3136_of__nat__eq__1__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( ( semiri1314217659103216013at_int @ N )
% 0.30/0.58 = one_one_int )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_1_iff
% 0.30/0.58 thf(fact_3137_of__nat__eq__1__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( ( semiri1316708129612266289at_nat @ N )
% 0.30/0.58 = one_one_nat )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_eq_1_iff
% 0.30/0.58 thf(fact_3138_of__nat__1__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( one_one_Code_integer
% 0.30/0.58 = ( semiri4939895301339042750nteger @ N ) )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1_eq_iff
% 0.30/0.58 thf(fact_3139_of__nat__1__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( one_one_complex
% 0.30/0.58 = ( semiri8010041392384452111omplex @ N ) )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1_eq_iff
% 0.30/0.58 thf(fact_3140_of__nat__1__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( one_one_real
% 0.30/0.58 = ( semiri5074537144036343181t_real @ N ) )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1_eq_iff
% 0.30/0.58 thf(fact_3141_of__nat__1__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( one_one_int
% 0.30/0.58 = ( semiri1314217659103216013at_int @ N ) )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1_eq_iff
% 0.30/0.58 thf(fact_3142_of__nat__1__eq__iff,axiom,
% 0.30/0.58 ! [N: nat] :
% 0.30/0.58 ( ( one_one_nat
% 0.30/0.58 = ( semiri1316708129612266289at_nat @ N ) )
% 0.30/0.58 = ( N = one_one_nat ) ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1_eq_iff
% 0.30/0.58 thf(fact_3143_of__nat__1,axiom,
% 0.30/0.58 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 0.30/0.58 = one_one_Code_integer ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1
% 0.30/0.58 thf(fact_3144_of__nat__1,axiom,
% 0.30/0.58 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 0.30/0.58 = one_one_complex ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1
% 0.30/0.58 thf(fact_3145_of__nat__1,axiom,
% 0.30/0.58 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 0.30/0.58 = one_one_real ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1
% 0.30/0.58 thf(fact_3146_of__nat__1,axiom,
% 0.30/0.58 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 0.30/0.58 = one_one_int ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1
% 0.30/0.58 thf(fact_3147_of__nat__1,axiom,
% 0.30/0.58 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 0.30/0.58 = one_one_nat ) ).
% 0.30/0.58
% 0.30/0.58 % of_nat_1
% 0.30/0.58 thf(fact_3148_in__set__replicate,axiom,
% 0.30/0.58 ! [X: complex,N: nat,Y: complex] :
% 0.30/0.58 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 0.30/0.58 = ( ( X = Y )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_set_replicate
% 0.30/0.58 thf(fact_3149_in__set__replicate,axiom,
% 0.30/0.58 ! [X: real,N: nat,Y: real] :
% 0.30/0.58 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 0.30/0.58 = ( ( X = Y )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_set_replicate
% 0.30/0.58 thf(fact_3150_in__set__replicate,axiom,
% 0.30/0.58 ! [X: set_nat,N: nat,Y: set_nat] :
% 0.30/0.58 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 0.30/0.58 = ( ( X = Y )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_set_replicate
% 0.30/0.58 thf(fact_3151_in__set__replicate,axiom,
% 0.30/0.58 ! [X: int,N: nat,Y: int] :
% 0.30/0.58 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 0.30/0.58 = ( ( X = Y )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_set_replicate
% 0.30/0.58 thf(fact_3152_in__set__replicate,axiom,
% 0.30/0.58 ! [X: nat,N: nat,Y: nat] :
% 0.30/0.58 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 0.30/0.58 = ( ( X = Y )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_set_replicate
% 0.30/0.58 thf(fact_3153_in__set__replicate,axiom,
% 0.30/0.58 ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 0.30/0.58 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 0.30/0.58 = ( ( X = Y )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % in_set_replicate
% 0.30/0.58 thf(fact_3154_Bex__set__replicate,axiom,
% 0.30/0.58 ! [N: nat,A: nat,P2: nat > $o] :
% 0.30/0.58 ( ( ? [X4: nat] :
% 0.30/0.58 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.30/0.58 & ( P2 @ X4 ) ) )
% 0.30/0.58 = ( ( P2 @ A )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Bex_set_replicate
% 0.30/0.58 thf(fact_3155_Bex__set__replicate,axiom,
% 0.30/0.58 ! [N: nat,A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.30/0.58 ( ( ? [X4: vEBT_VEBT] :
% 0.30/0.58 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.30/0.58 & ( P2 @ X4 ) ) )
% 0.30/0.58 = ( ( P2 @ A )
% 0.30/0.58 & ( N != zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Bex_set_replicate
% 0.30/0.58 thf(fact_3156_Ball__set__replicate,axiom,
% 0.30/0.58 ! [N: nat,A: nat,P2: nat > $o] :
% 0.30/0.58 ( ( ! [X4: nat] :
% 0.30/0.58 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 0.30/0.58 => ( P2 @ X4 ) ) )
% 0.30/0.58 = ( ( P2 @ A )
% 0.30/0.58 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Ball_set_replicate
% 0.30/0.58 thf(fact_3157_Ball__set__replicate,axiom,
% 0.30/0.58 ! [N: nat,A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 0.30/0.58 ( ( ! [X4: vEBT_VEBT] :
% 0.30/0.58 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 0.30/0.58 => ( P2 @ X4 ) ) )
% 0.30/0.58 = ( ( P2 @ A )
% 0.30/0.58 | ( N = zero_zero_nat ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % Ball_set_replicate
% 0.30/0.58 thf(fact_3158_numeral__le__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 0.30/0.58 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_one_iff
% 0.30/0.58 thf(fact_3159_numeral__le__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 0.30/0.58 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_one_iff
% 0.30/0.58 thf(fact_3160_numeral__le__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.30/0.58 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_one_iff
% 0.30/0.58 thf(fact_3161_numeral__le__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.30/0.58 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_one_iff
% 0.30/0.58 thf(fact_3162_numeral__le__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.30/0.58 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_one_iff
% 0.30/0.58 thf(fact_3163_numeral__le__one__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.30/0.58 = ( ord_less_eq_num @ N @ one ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_le_one_iff
% 0.30/0.58 thf(fact_3164_one__less__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.58 = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_less_numeral_iff
% 0.30/0.58 thf(fact_3165_one__less__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.30/0.58 = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_less_numeral_iff
% 0.30/0.58 thf(fact_3166_one__less__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_less_numeral_iff
% 0.30/0.58 thf(fact_3167_one__less__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_less_numeral_iff
% 0.30/0.58 thf(fact_3168_one__less__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_less_numeral_iff
% 0.30/0.58 thf(fact_3169_one__less__numeral__iff,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( ord_less_num @ one @ N ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_less_numeral_iff
% 0.30/0.58 thf(fact_3170_one__plus__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.30/0.58 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_plus_numeral
% 0.30/0.58 thf(fact_3171_one__plus__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 0.30/0.58 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_plus_numeral
% 0.30/0.58 thf(fact_3172_one__plus__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 0.30/0.58 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_plus_numeral
% 0.30/0.58 thf(fact_3173_one__plus__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 0.30/0.58 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_plus_numeral
% 0.30/0.58 thf(fact_3174_one__plus__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 0.30/0.58 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_plus_numeral
% 0.30/0.58 thf(fact_3175_one__plus__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 0.30/0.58 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_plus_numeral
% 0.30/0.58 thf(fact_3176_one__plus__numeral,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 0.30/0.58 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % one_plus_numeral
% 0.30/0.58 thf(fact_3177_numeral__plus__one,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 0.30/0.58 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_one
% 0.30/0.58 thf(fact_3178_numeral__plus__one,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 0.30/0.58 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_one
% 0.30/0.58 thf(fact_3179_numeral__plus__one,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 0.30/0.58 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_one
% 0.30/0.58 thf(fact_3180_numeral__plus__one,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 0.30/0.58 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.30/0.58
% 0.30/0.58 % numeral_plus_one
% 0.30/0.58 thf(fact_3181_numeral__plus__one,axiom,
% 0.30/0.58 ! [N: num] :
% 0.30/0.58 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 0.35/0.58 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_plus_one
% 0.35/0.58 thf(fact_3182_numeral__plus__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 0.35/0.58 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_plus_one
% 0.35/0.58 thf(fact_3183_numeral__plus__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 0.35/0.58 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_plus_one
% 0.35/0.58 thf(fact_3184_of__nat__le__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real )
% 0.35/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_0_iff
% 0.35/0.58 thf(fact_3185_of__nat__le__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat )
% 0.35/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_0_iff
% 0.35/0.58 thf(fact_3186_of__nat__le__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat )
% 0.35/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_0_iff
% 0.35/0.58 thf(fact_3187_of__nat__le__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int )
% 0.35/0.58 = ( M2 = zero_zero_nat ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_0_iff
% 0.35/0.58 thf(fact_3188_of__nat__Suc,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( semiri4939895301339042750nteger @ ( suc @ M2 ) )
% 0.35/0.58 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_Suc
% 0.35/0.58 thf(fact_3189_of__nat__Suc,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( semiri8010041392384452111omplex @ ( suc @ M2 ) )
% 0.35/0.58 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_Suc
% 0.35/0.58 thf(fact_3190_of__nat__Suc,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( semiri681578069525770553at_rat @ ( suc @ M2 ) )
% 0.35/0.58 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_Suc
% 0.35/0.58 thf(fact_3191_of__nat__Suc,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( semiri5074537144036343181t_real @ ( suc @ M2 ) )
% 0.35/0.58 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_Suc
% 0.35/0.58 thf(fact_3192_of__nat__Suc,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 0.35/0.58 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_Suc
% 0.35/0.58 thf(fact_3193_of__nat__Suc,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 0.35/0.58 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_Suc
% 0.35/0.58 thf(fact_3194_one__add__one,axiom,
% 0.35/0.58 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 0.35/0.58 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_add_one
% 0.35/0.58 thf(fact_3195_one__add__one,axiom,
% 0.35/0.58 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 0.35/0.58 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_add_one
% 0.35/0.58 thf(fact_3196_one__add__one,axiom,
% 0.35/0.58 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 0.35/0.58 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_add_one
% 0.35/0.58 thf(fact_3197_one__add__one,axiom,
% 0.35/0.58 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 0.35/0.58 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_add_one
% 0.35/0.58 thf(fact_3198_one__add__one,axiom,
% 0.35/0.58 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.35/0.58 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_add_one
% 0.35/0.58 thf(fact_3199_one__add__one,axiom,
% 0.35/0.58 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_add_one
% 0.35/0.58 thf(fact_3200_one__add__one,axiom,
% 0.35/0.58 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.35/0.58 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_add_one
% 0.35/0.58 thf(fact_3201_zero__eq__power2,axiom,
% 0.35/0.58 ! [A: rat] :
% 0.35/0.58 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_rat )
% 0.35/0.58 = ( A = zero_zero_rat ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_eq_power2
% 0.35/0.58 thf(fact_3202_zero__eq__power2,axiom,
% 0.35/0.58 ! [A: nat] :
% 0.35/0.58 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_nat )
% 0.35/0.58 = ( A = zero_zero_nat ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_eq_power2
% 0.35/0.58 thf(fact_3203_zero__eq__power2,axiom,
% 0.35/0.58 ! [A: real] :
% 0.35/0.58 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_real )
% 0.35/0.58 = ( A = zero_zero_real ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_eq_power2
% 0.35/0.58 thf(fact_3204_zero__eq__power2,axiom,
% 0.35/0.58 ! [A: int] :
% 0.35/0.58 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_int )
% 0.35/0.58 = ( A = zero_zero_int ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_eq_power2
% 0.35/0.58 thf(fact_3205_zero__eq__power2,axiom,
% 0.35/0.58 ! [A: complex] :
% 0.35/0.58 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_complex )
% 0.35/0.58 = ( A = zero_zero_complex ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_eq_power2
% 0.35/0.58 thf(fact_3206_of__nat__0__less__iff,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.58 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_less_iff
% 0.35/0.58 thf(fact_3207_of__nat__0__less__iff,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.58 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_less_iff
% 0.35/0.58 thf(fact_3208_of__nat__0__less__iff,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.58 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_less_iff
% 0.35/0.58 thf(fact_3209_of__nat__0__less__iff,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.58 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_less_iff
% 0.35/0.58 thf(fact_3210_add__2__eq__Suc,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.58 = ( suc @ ( suc @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % add_2_eq_Suc
% 0.35/0.58 thf(fact_3211_add__2__eq__Suc_H,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( suc @ ( suc @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % add_2_eq_Suc'
% 0.35/0.58 thf(fact_3212_Suc__1,axiom,
% 0.35/0.58 ( ( suc @ one_one_nat )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % Suc_1
% 0.35/0.58 thf(fact_3213_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.35/0.58 ! [B: nat,W2: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_of_nat_power_cancel_iff
% 0.35/0.58 thf(fact_3214_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.35/0.58 ! [B: nat,W2: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_of_nat_power_cancel_iff
% 0.35/0.58 thf(fact_3215_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.35/0.58 ! [B: nat,W2: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_of_nat_power_cancel_iff
% 0.35/0.58 thf(fact_3216_of__nat__le__of__nat__power__cancel__iff,axiom,
% 0.35/0.58 ! [B: nat,W2: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_of_nat_power_cancel_iff
% 0.35/0.58 thf(fact_3217_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,B: nat,W2: nat] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3218_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,B: nat,W2: nat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3219_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,B: nat,W2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3220_of__nat__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,B: nat,W2: nat] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3221_set__replicate,axiom,
% 0.35/0.58 ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.58 ( ( N != zero_zero_nat )
% 0.35/0.58 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.35/0.58 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % set_replicate
% 0.35/0.58 thf(fact_3222_set__replicate,axiom,
% 0.35/0.58 ! [N: nat,X: nat] :
% 0.35/0.58 ( ( N != zero_zero_nat )
% 0.35/0.58 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.35/0.58 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % set_replicate
% 0.35/0.58 thf(fact_3223_set__replicate,axiom,
% 0.35/0.58 ! [N: nat,X: int] :
% 0.35/0.58 ( ( N != zero_zero_nat )
% 0.35/0.58 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.35/0.58 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % set_replicate
% 0.35/0.58 thf(fact_3224_set__replicate,axiom,
% 0.35/0.58 ! [N: nat,X: real] :
% 0.35/0.58 ( ( N != zero_zero_nat )
% 0.35/0.58 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.35/0.58 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % set_replicate
% 0.35/0.58 thf(fact_3225_power2__eq__iff__nonneg,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.58 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_iff_nonneg
% 0.35/0.58 thf(fact_3226_power2__eq__iff__nonneg,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.58 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.58 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_iff_nonneg
% 0.35/0.58 thf(fact_3227_power2__eq__iff__nonneg,axiom,
% 0.35/0.58 ! [X: nat,Y: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.35/0.58 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.35/0.58 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_iff_nonneg
% 0.35/0.58 thf(fact_3228_power2__eq__iff__nonneg,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.35/0.58 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_iff_nonneg
% 0.35/0.58 thf(fact_3229_power2__less__eq__zero__iff,axiom,
% 0.35/0.58 ! [A: real] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 0.35/0.58 = ( A = zero_zero_real ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_eq_zero_iff
% 0.35/0.58 thf(fact_3230_power2__less__eq__zero__iff,axiom,
% 0.35/0.58 ! [A: rat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 0.35/0.58 = ( A = zero_zero_rat ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_eq_zero_iff
% 0.35/0.58 thf(fact_3231_power2__less__eq__zero__iff,axiom,
% 0.35/0.58 ! [A: int] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 0.35/0.58 = ( A = zero_zero_int ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_eq_zero_iff
% 0.35/0.58 thf(fact_3232_zero__less__power2,axiom,
% 0.35/0.58 ! [A: real] :
% 0.35/0.58 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( A != zero_zero_real ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_power2
% 0.35/0.58 thf(fact_3233_zero__less__power2,axiom,
% 0.35/0.58 ! [A: rat] :
% 0.35/0.58 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( A != zero_zero_rat ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_power2
% 0.35/0.58 thf(fact_3234_zero__less__power2,axiom,
% 0.35/0.58 ! [A: int] :
% 0.35/0.58 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( A != zero_zero_int ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_power2
% 0.35/0.58 thf(fact_3235_sum__power2__eq__zero__iff,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = zero_zero_rat )
% 0.35/0.58 = ( ( X = zero_zero_rat )
% 0.35/0.58 & ( Y = zero_zero_rat ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_eq_zero_iff
% 0.35/0.58 thf(fact_3236_sum__power2__eq__zero__iff,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = zero_zero_real )
% 0.35/0.58 = ( ( X = zero_zero_real )
% 0.35/0.58 & ( Y = zero_zero_real ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_eq_zero_iff
% 0.35/0.58 thf(fact_3237_sum__power2__eq__zero__iff,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = zero_zero_int )
% 0.35/0.58 = ( ( X = zero_zero_int )
% 0.35/0.58 & ( Y = zero_zero_int ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_eq_zero_iff
% 0.35/0.58 thf(fact_3238_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [I2: num,N: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3239_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [I2: num,N: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3240_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [I2: num,N: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3241_numeral__power__le__of__nat__cancel__iff,axiom,
% 0.35/0.58 ! [I2: num,N: nat,X: nat] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 0.35/0.58 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_power_le_of_nat_cancel_iff
% 0.35/0.58 thf(fact_3242_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,I2: num,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_numeral_power_cancel_iff
% 0.35/0.58 thf(fact_3243_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,I2: num,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_numeral_power_cancel_iff
% 0.35/0.58 thf(fact_3244_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,I2: num,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_numeral_power_cancel_iff
% 0.35/0.58 thf(fact_3245_of__nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.58 ! [X: nat,I2: num,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 0.35/0.58 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_le_numeral_power_cancel_iff
% 0.35/0.58 thf(fact_3246_power2__nat__le__imp__le,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 0.35/0.58 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_nat_le_imp_le
% 0.35/0.58 thf(fact_3247_power2__nat__le__eq__le,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_nat_le_eq_le
% 0.35/0.58 thf(fact_3248_self__le__ge2__pow,axiom,
% 0.35/0.58 ! [K2: nat,M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 0.35/0.58 => ( ord_less_eq_nat @ M2 @ ( power_power_nat @ K2 @ M2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % self_le_ge2_pow
% 0.35/0.58 thf(fact_3249_card__2__iff_H,axiom,
% 0.35/0.58 ! [S3: set_nat] :
% 0.35/0.58 ( ( ( finite_card_nat @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: nat] :
% 0.35/0.58 ( ( member_nat @ X4 @ S3 )
% 0.35/0.58 & ? [Y4: nat] :
% 0.35/0.58 ( ( member_nat @ Y4 @ S3 )
% 0.35/0.58 & ( X4 != Y4 )
% 0.35/0.58 & ! [Z4: nat] :
% 0.35/0.58 ( ( member_nat @ Z4 @ S3 )
% 0.35/0.58 => ( ( Z4 = X4 )
% 0.35/0.58 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff'
% 0.35/0.58 thf(fact_3250_card__2__iff_H,axiom,
% 0.35/0.58 ! [S3: set_complex] :
% 0.35/0.58 ( ( ( finite_card_complex @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: complex] :
% 0.35/0.58 ( ( member_complex @ X4 @ S3 )
% 0.35/0.58 & ? [Y4: complex] :
% 0.35/0.58 ( ( member_complex @ Y4 @ S3 )
% 0.35/0.58 & ( X4 != Y4 )
% 0.35/0.58 & ! [Z4: complex] :
% 0.35/0.58 ( ( member_complex @ Z4 @ S3 )
% 0.35/0.58 => ( ( Z4 = X4 )
% 0.35/0.58 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff'
% 0.35/0.58 thf(fact_3251_card__2__iff_H,axiom,
% 0.35/0.58 ! [S3: set_int] :
% 0.35/0.58 ( ( ( finite_card_int @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: int] :
% 0.35/0.58 ( ( member_int @ X4 @ S3 )
% 0.35/0.58 & ? [Y4: int] :
% 0.35/0.58 ( ( member_int @ Y4 @ S3 )
% 0.35/0.58 & ( X4 != Y4 )
% 0.35/0.58 & ! [Z4: int] :
% 0.35/0.58 ( ( member_int @ Z4 @ S3 )
% 0.35/0.58 => ( ( Z4 = X4 )
% 0.35/0.58 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff'
% 0.35/0.58 thf(fact_3252_card__2__iff_H,axiom,
% 0.35/0.58 ! [S3: set_list_nat] :
% 0.35/0.58 ( ( ( finite_card_list_nat @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: list_nat] :
% 0.35/0.58 ( ( member_list_nat @ X4 @ S3 )
% 0.35/0.58 & ? [Y4: list_nat] :
% 0.35/0.58 ( ( member_list_nat @ Y4 @ S3 )
% 0.35/0.58 & ( X4 != Y4 )
% 0.35/0.58 & ! [Z4: list_nat] :
% 0.35/0.58 ( ( member_list_nat @ Z4 @ S3 )
% 0.35/0.58 => ( ( Z4 = X4 )
% 0.35/0.58 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff'
% 0.35/0.58 thf(fact_3253_card__2__iff_H,axiom,
% 0.35/0.58 ! [S3: set_set_nat] :
% 0.35/0.58 ( ( ( finite_card_set_nat @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: set_nat] :
% 0.35/0.58 ( ( member_set_nat @ X4 @ S3 )
% 0.35/0.58 & ? [Y4: set_nat] :
% 0.35/0.58 ( ( member_set_nat @ Y4 @ S3 )
% 0.35/0.58 & ( X4 != Y4 )
% 0.35/0.58 & ! [Z4: set_nat] :
% 0.35/0.58 ( ( member_set_nat @ Z4 @ S3 )
% 0.35/0.58 => ( ( Z4 = X4 )
% 0.35/0.58 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff'
% 0.35/0.58 thf(fact_3254_reals__Archimedean3,axiom,
% 0.35/0.58 ! [X: real] :
% 0.35/0.58 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.58 => ! [Y6: real] :
% 0.35/0.58 ? [N3: nat] : ( ord_less_real @ Y6 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % reals_Archimedean3
% 0.35/0.58 thf(fact_3255_add__One__commute,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( plus_plus_num @ one @ N )
% 0.35/0.58 = ( plus_plus_num @ N @ one ) ) ).
% 0.35/0.58
% 0.35/0.58 % add_One_commute
% 0.35/0.58 thf(fact_3256_numeral__Bit0,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.35/0.58 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_Bit0
% 0.35/0.58 thf(fact_3257_numeral__Bit0,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 0.35/0.58 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_Bit0
% 0.35/0.58 thf(fact_3258_numeral__Bit0,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.35/0.58 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_Bit0
% 0.35/0.58 thf(fact_3259_numeral__Bit0,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.35/0.58 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_Bit0
% 0.35/0.58 thf(fact_3260_numeral__Bit0,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.35/0.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_Bit0
% 0.35/0.58 thf(fact_3261_numeral__Bit0,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.35/0.58 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_Bit0
% 0.35/0.58 thf(fact_3262_mult__numeral__1__right,axiom,
% 0.35/0.58 ! [A: rat] :
% 0.35/0.58 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1_right
% 0.35/0.58 thf(fact_3263_mult__numeral__1__right,axiom,
% 0.35/0.58 ! [A: extended_enat] :
% 0.35/0.58 ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1_right
% 0.35/0.58 thf(fact_3264_mult__numeral__1__right,axiom,
% 0.35/0.58 ! [A: complex] :
% 0.35/0.58 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1_right
% 0.35/0.58 thf(fact_3265_mult__numeral__1__right,axiom,
% 0.35/0.58 ! [A: real] :
% 0.35/0.58 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1_right
% 0.35/0.58 thf(fact_3266_mult__numeral__1__right,axiom,
% 0.35/0.58 ! [A: nat] :
% 0.35/0.58 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1_right
% 0.35/0.58 thf(fact_3267_mult__numeral__1__right,axiom,
% 0.35/0.58 ! [A: int] :
% 0.35/0.58 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1_right
% 0.35/0.58 thf(fact_3268_mult__numeral__1,axiom,
% 0.35/0.58 ! [A: rat] :
% 0.35/0.58 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1
% 0.35/0.58 thf(fact_3269_mult__numeral__1,axiom,
% 0.35/0.58 ! [A: extended_enat] :
% 0.35/0.58 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1
% 0.35/0.58 thf(fact_3270_mult__numeral__1,axiom,
% 0.35/0.58 ! [A: complex] :
% 0.35/0.58 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1
% 0.35/0.58 thf(fact_3271_mult__numeral__1,axiom,
% 0.35/0.58 ! [A: real] :
% 0.35/0.58 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1
% 0.35/0.58 thf(fact_3272_mult__numeral__1,axiom,
% 0.35/0.58 ! [A: nat] :
% 0.35/0.58 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1
% 0.35/0.58 thf(fact_3273_mult__numeral__1,axiom,
% 0.35/0.58 ! [A: int] :
% 0.35/0.58 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 0.35/0.58 = A ) ).
% 0.35/0.58
% 0.35/0.58 % mult_numeral_1
% 0.35/0.58 thf(fact_3274_numeral__One,axiom,
% 0.35/0.58 ( ( numera6620942414471956472nteger @ one )
% 0.35/0.58 = one_one_Code_integer ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_One
% 0.35/0.58 thf(fact_3275_numeral__One,axiom,
% 0.35/0.58 ( ( numera1916890842035813515d_enat @ one )
% 0.35/0.58 = one_on7984719198319812577d_enat ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_One
% 0.35/0.58 thf(fact_3276_numeral__One,axiom,
% 0.35/0.58 ( ( numera6690914467698888265omplex @ one )
% 0.35/0.58 = one_one_complex ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_One
% 0.35/0.58 thf(fact_3277_numeral__One,axiom,
% 0.35/0.58 ( ( numeral_numeral_real @ one )
% 0.35/0.58 = one_one_real ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_One
% 0.35/0.58 thf(fact_3278_numeral__One,axiom,
% 0.35/0.58 ( ( numeral_numeral_nat @ one )
% 0.35/0.58 = one_one_nat ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_One
% 0.35/0.58 thf(fact_3279_numeral__One,axiom,
% 0.35/0.58 ( ( numeral_numeral_int @ one )
% 0.35/0.58 = one_one_int ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_One
% 0.35/0.58 thf(fact_3280_pos2,axiom,
% 0.35/0.58 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 0.35/0.58
% 0.35/0.58 % pos2
% 0.35/0.58 thf(fact_3281_numerals_I1_J,axiom,
% 0.35/0.58 ( ( numeral_numeral_nat @ one )
% 0.35/0.58 = one_one_nat ) ).
% 0.35/0.58
% 0.35/0.58 % numerals(1)
% 0.35/0.58 thf(fact_3282_le__num__One__iff,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( ord_less_eq_num @ X @ one )
% 0.35/0.58 = ( X = one ) ) ).
% 0.35/0.58
% 0.35/0.58 % le_num_One_iff
% 0.35/0.58 thf(fact_3283_mult__2,axiom,
% 0.35/0.58 ! [Z3: rat] :
% 0.35/0.58 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 )
% 0.35/0.58 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2
% 0.35/0.58 thf(fact_3284_mult__2,axiom,
% 0.35/0.58 ! [Z3: extended_enat] :
% 0.35/0.58 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z3 )
% 0.35/0.58 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2
% 0.35/0.58 thf(fact_3285_mult__2,axiom,
% 0.35/0.58 ! [Z3: complex] :
% 0.35/0.58 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 )
% 0.35/0.58 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2
% 0.35/0.58 thf(fact_3286_mult__2,axiom,
% 0.35/0.58 ! [Z3: real] :
% 0.35/0.58 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 )
% 0.35/0.58 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2
% 0.35/0.58 thf(fact_3287_mult__2,axiom,
% 0.35/0.58 ! [Z3: nat] :
% 0.35/0.58 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z3 )
% 0.35/0.58 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2
% 0.35/0.58 thf(fact_3288_mult__2,axiom,
% 0.35/0.58 ! [Z3: int] :
% 0.35/0.58 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z3 )
% 0.35/0.58 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2
% 0.35/0.58 thf(fact_3289_mult__2__right,axiom,
% 0.35/0.58 ! [Z3: rat] :
% 0.35/0.58 ( ( times_times_rat @ Z3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2_right
% 0.35/0.58 thf(fact_3290_mult__2__right,axiom,
% 0.35/0.58 ! [Z3: extended_enat] :
% 0.35/0.58 ( ( times_7803423173614009249d_enat @ Z3 @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2_right
% 0.35/0.58 thf(fact_3291_mult__2__right,axiom,
% 0.35/0.58 ! [Z3: complex] :
% 0.35/0.58 ( ( times_times_complex @ Z3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2_right
% 0.35/0.58 thf(fact_3292_mult__2__right,axiom,
% 0.35/0.58 ! [Z3: real] :
% 0.35/0.58 ( ( times_times_real @ Z3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2_right
% 0.35/0.58 thf(fact_3293_mult__2__right,axiom,
% 0.35/0.58 ! [Z3: nat] :
% 0.35/0.58 ( ( times_times_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2_right
% 0.35/0.58 thf(fact_3294_mult__2__right,axiom,
% 0.35/0.58 ! [Z3: int] :
% 0.35/0.58 ( ( times_times_int @ Z3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_2_right
% 0.35/0.58 thf(fact_3295_left__add__twice,axiom,
% 0.35/0.58 ! [A: rat,B: rat] :
% 0.35/0.58 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.58 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.35/0.58
% 0.35/0.58 % left_add_twice
% 0.35/0.58 thf(fact_3296_left__add__twice,axiom,
% 0.35/0.58 ! [A: extended_enat,B: extended_enat] :
% 0.35/0.58 ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 0.35/0.58 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.35/0.58
% 0.35/0.58 % left_add_twice
% 0.35/0.58 thf(fact_3297_left__add__twice,axiom,
% 0.35/0.58 ! [A: complex,B: complex] :
% 0.35/0.58 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.58 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.35/0.58
% 0.35/0.58 % left_add_twice
% 0.35/0.58 thf(fact_3298_left__add__twice,axiom,
% 0.35/0.58 ! [A: real,B: real] :
% 0.35/0.58 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.35/0.58 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.35/0.58
% 0.35/0.58 % left_add_twice
% 0.35/0.58 thf(fact_3299_left__add__twice,axiom,
% 0.35/0.58 ! [A: nat,B: nat] :
% 0.35/0.58 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.35/0.58 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.35/0.58
% 0.35/0.58 % left_add_twice
% 0.35/0.58 thf(fact_3300_left__add__twice,axiom,
% 0.35/0.58 ! [A: int,B: int] :
% 0.35/0.58 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.35/0.58 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 0.35/0.58
% 0.35/0.58 % left_add_twice
% 0.35/0.58 thf(fact_3301_zero__power2,axiom,
% 0.35/0.58 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_rat ) ).
% 0.35/0.58
% 0.35/0.58 % zero_power2
% 0.35/0.58 thf(fact_3302_zero__power2,axiom,
% 0.35/0.58 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_nat ) ).
% 0.35/0.58
% 0.35/0.58 % zero_power2
% 0.35/0.58 thf(fact_3303_zero__power2,axiom,
% 0.35/0.58 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_real ) ).
% 0.35/0.58
% 0.35/0.58 % zero_power2
% 0.35/0.58 thf(fact_3304_zero__power2,axiom,
% 0.35/0.58 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % zero_power2
% 0.35/0.58 thf(fact_3305_zero__power2,axiom,
% 0.35/0.58 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = zero_zero_complex ) ).
% 0.35/0.58
% 0.35/0.58 % zero_power2
% 0.35/0.58 thf(fact_3306_power2__eq__square,axiom,
% 0.35/0.58 ! [A: complex] :
% 0.35/0.58 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( times_times_complex @ A @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_square
% 0.35/0.58 thf(fact_3307_power2__eq__square,axiom,
% 0.35/0.58 ! [A: real] :
% 0.35/0.58 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( times_times_real @ A @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_square
% 0.35/0.58 thf(fact_3308_power2__eq__square,axiom,
% 0.35/0.58 ! [A: rat] :
% 0.35/0.58 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( times_times_rat @ A @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_square
% 0.35/0.58 thf(fact_3309_power2__eq__square,axiom,
% 0.35/0.58 ! [A: nat] :
% 0.35/0.58 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( times_times_nat @ A @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_square
% 0.35/0.58 thf(fact_3310_power2__eq__square,axiom,
% 0.35/0.58 ! [A: int] :
% 0.35/0.58 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( times_times_int @ A @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_square
% 0.35/0.58 thf(fact_3311_power4__eq__xxxx,axiom,
% 0.35/0.58 ! [X: complex] :
% 0.35/0.58 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % power4_eq_xxxx
% 0.35/0.58 thf(fact_3312_power4__eq__xxxx,axiom,
% 0.35/0.58 ! [X: real] :
% 0.35/0.58 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % power4_eq_xxxx
% 0.35/0.58 thf(fact_3313_power4__eq__xxxx,axiom,
% 0.35/0.58 ! [X: rat] :
% 0.35/0.58 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % power4_eq_xxxx
% 0.35/0.58 thf(fact_3314_power4__eq__xxxx,axiom,
% 0.35/0.58 ! [X: nat] :
% 0.35/0.58 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % power4_eq_xxxx
% 0.35/0.58 thf(fact_3315_power4__eq__xxxx,axiom,
% 0.35/0.58 ! [X: int] :
% 0.35/0.58 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.58 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 0.35/0.58
% 0.35/0.58 % power4_eq_xxxx
% 0.35/0.58 thf(fact_3316_numeral__2__eq__2,axiom,
% 0.35/0.58 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.35/0.58 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_2_eq_2
% 0.35/0.58 thf(fact_3317_power__even__eq,axiom,
% 0.35/0.58 ! [A: nat,N: nat] :
% 0.35/0.58 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.58 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_even_eq
% 0.35/0.58 thf(fact_3318_power__even__eq,axiom,
% 0.35/0.58 ! [A: real,N: nat] :
% 0.35/0.58 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.58 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_even_eq
% 0.35/0.58 thf(fact_3319_power__even__eq,axiom,
% 0.35/0.58 ! [A: int,N: nat] :
% 0.35/0.58 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.58 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_even_eq
% 0.35/0.58 thf(fact_3320_power__even__eq,axiom,
% 0.35/0.58 ! [A: complex,N: nat] :
% 0.35/0.58 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.58 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_even_eq
% 0.35/0.58 thf(fact_3321_diff__le__diff__pow,axiom,
% 0.35/0.58 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 0.35/0.58 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K2 @ M2 ) @ ( power_power_nat @ K2 @ N ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % diff_le_diff_pow
% 0.35/0.58 thf(fact_3322_nat__1__add__1,axiom,
% 0.35/0.58 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % nat_1_add_1
% 0.35/0.58 thf(fact_3323_power2__sum,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_sum
% 0.35/0.58 thf(fact_3324_power2__sum,axiom,
% 0.35/0.58 ! [X: extended_enat,Y: extended_enat] :
% 0.35/0.58 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_sum
% 0.35/0.58 thf(fact_3325_power2__sum,axiom,
% 0.35/0.58 ! [X: complex,Y: complex] :
% 0.35/0.58 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_sum
% 0.35/0.58 thf(fact_3326_power2__sum,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_sum
% 0.35/0.58 thf(fact_3327_power2__sum,axiom,
% 0.35/0.58 ! [X: nat,Y: nat] :
% 0.35/0.58 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_sum
% 0.35/0.58 thf(fact_3328_power2__sum,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_sum
% 0.35/0.58 thf(fact_3329_sum__squares__bound,axiom,
% 0.35/0.58 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_squares_bound
% 0.35/0.58 thf(fact_3330_sum__squares__bound,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_squares_bound
% 0.35/0.58 thf(fact_3331_power2__diff,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_diff
% 0.35/0.58 thf(fact_3332_power2__diff,axiom,
% 0.35/0.58 ! [X: complex,Y: complex] :
% 0.35/0.58 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_diff
% 0.35/0.58 thf(fact_3333_power2__diff,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_diff
% 0.35/0.58 thf(fact_3334_power2__diff,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_diff
% 0.35/0.58 thf(fact_3335_power2__le__imp__le,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.58 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_le_imp_le
% 0.35/0.58 thf(fact_3336_power2__le__imp__le,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.58 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_le_imp_le
% 0.35/0.58 thf(fact_3337_power2__le__imp__le,axiom,
% 0.35/0.58 ! [X: nat,Y: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.35/0.58 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_le_imp_le
% 0.35/0.58 thf(fact_3338_power2__le__imp__le,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.35/0.58 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_le_imp_le
% 0.35/0.58 thf(fact_3339_power2__eq__imp__eq,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.58 => ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_imp_eq
% 0.35/0.58 thf(fact_3340_power2__eq__imp__eq,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.58 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.58 => ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_imp_eq
% 0.35/0.58 thf(fact_3341_power2__eq__imp__eq,axiom,
% 0.35/0.58 ! [X: nat,Y: nat] :
% 0.35/0.58 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.35/0.58 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.35/0.58 => ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_imp_eq
% 0.35/0.58 thf(fact_3342_power2__eq__imp__eq,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.35/0.58 => ( X = Y ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_eq_imp_eq
% 0.35/0.58 thf(fact_3343_zero__le__power2,axiom,
% 0.35/0.58 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_power2
% 0.35/0.58 thf(fact_3344_zero__le__power2,axiom,
% 0.35/0.58 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_power2
% 0.35/0.58 thf(fact_3345_zero__le__power2,axiom,
% 0.35/0.58 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_power2
% 0.35/0.58 thf(fact_3346_power2__less__0,axiom,
% 0.35/0.58 ! [A: real] :
% 0.35/0.58 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_0
% 0.35/0.58 thf(fact_3347_power2__less__0,axiom,
% 0.35/0.58 ! [A: rat] :
% 0.35/0.58 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_0
% 0.35/0.58 thf(fact_3348_power2__less__0,axiom,
% 0.35/0.58 ! [A: int] :
% 0.35/0.58 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_0
% 0.35/0.58 thf(fact_3349_less__2__cases,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 => ( ( N = zero_zero_nat )
% 0.35/0.58 | ( N
% 0.35/0.58 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % less_2_cases
% 0.35/0.58 thf(fact_3350_less__2__cases__iff,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ( N = zero_zero_nat )
% 0.35/0.58 | ( N
% 0.35/0.58 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % less_2_cases_iff
% 0.35/0.58 thf(fact_3351_card__2__iff,axiom,
% 0.35/0.58 ! [S3: set_complex] :
% 0.35/0.58 ( ( ( finite_card_complex @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: complex,Y4: complex] :
% 0.35/0.58 ( ( S3
% 0.35/0.58 = ( insert_complex @ X4 @ ( insert_complex @ Y4 @ bot_bot_set_complex ) ) )
% 0.35/0.58 & ( X4 != Y4 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff
% 0.35/0.58 thf(fact_3352_card__2__iff,axiom,
% 0.35/0.58 ! [S3: set_list_nat] :
% 0.35/0.58 ( ( ( finite_card_list_nat @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: list_nat,Y4: list_nat] :
% 0.35/0.58 ( ( S3
% 0.35/0.58 = ( insert_list_nat @ X4 @ ( insert_list_nat @ Y4 @ bot_bot_set_list_nat ) ) )
% 0.35/0.58 & ( X4 != Y4 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff
% 0.35/0.58 thf(fact_3353_card__2__iff,axiom,
% 0.35/0.58 ! [S3: set_set_nat] :
% 0.35/0.58 ( ( ( finite_card_set_nat @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: set_nat,Y4: set_nat] :
% 0.35/0.58 ( ( S3
% 0.35/0.58 = ( insert_set_nat @ X4 @ ( insert_set_nat @ Y4 @ bot_bot_set_set_nat ) ) )
% 0.35/0.58 & ( X4 != Y4 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff
% 0.35/0.58 thf(fact_3354_card__2__iff,axiom,
% 0.35/0.58 ! [S3: set_nat] :
% 0.35/0.58 ( ( ( finite_card_nat @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: nat,Y4: nat] :
% 0.35/0.58 ( ( S3
% 0.35/0.58 = ( insert_nat @ X4 @ ( insert_nat @ Y4 @ bot_bot_set_nat ) ) )
% 0.35/0.58 & ( X4 != Y4 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff
% 0.35/0.58 thf(fact_3355_card__2__iff,axiom,
% 0.35/0.58 ! [S3: set_int] :
% 0.35/0.58 ( ( ( finite_card_int @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: int,Y4: int] :
% 0.35/0.58 ( ( S3
% 0.35/0.58 = ( insert_int @ X4 @ ( insert_int @ Y4 @ bot_bot_set_int ) ) )
% 0.35/0.58 & ( X4 != Y4 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff
% 0.35/0.58 thf(fact_3356_card__2__iff,axiom,
% 0.35/0.58 ! [S3: set_real] :
% 0.35/0.58 ( ( ( finite_card_real @ S3 )
% 0.35/0.58 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.58 = ( ? [X4: real,Y4: real] :
% 0.35/0.58 ( ( S3
% 0.35/0.58 = ( insert_real @ X4 @ ( insert_real @ Y4 @ bot_bot_set_real ) ) )
% 0.35/0.58 & ( X4 != Y4 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % card_2_iff
% 0.35/0.58 thf(fact_3357_numeral__1__eq__Suc__0,axiom,
% 0.35/0.58 ( ( numeral_numeral_nat @ one )
% 0.35/0.58 = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.58
% 0.35/0.58 % numeral_1_eq_Suc_0
% 0.35/0.58 thf(fact_3358_Suc__nat__number__of__add,axiom,
% 0.35/0.58 ! [V2: num,N: nat] :
% 0.35/0.58 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ N ) )
% 0.35/0.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ one ) ) @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % Suc_nat_number_of_add
% 0.35/0.58 thf(fact_3359_real__arch__simple,axiom,
% 0.35/0.58 ! [X: real] :
% 0.35/0.58 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % real_arch_simple
% 0.35/0.58 thf(fact_3360_real__arch__simple,axiom,
% 0.35/0.58 ! [X: rat] :
% 0.35/0.58 ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % real_arch_simple
% 0.35/0.58 thf(fact_3361_reals__Archimedean2,axiom,
% 0.35/0.58 ! [X: rat] :
% 0.35/0.58 ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % reals_Archimedean2
% 0.35/0.58 thf(fact_3362_reals__Archimedean2,axiom,
% 0.35/0.58 ! [X: real] :
% 0.35/0.58 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 0.35/0.58
% 0.35/0.58 % reals_Archimedean2
% 0.35/0.58 thf(fact_3363_mult__of__nat__commute,axiom,
% 0.35/0.58 ! [X: nat,Y: rat] :
% 0.35/0.58 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 0.35/0.58 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_of_nat_commute
% 0.35/0.58 thf(fact_3364_mult__of__nat__commute,axiom,
% 0.35/0.58 ! [X: nat,Y: real] :
% 0.35/0.58 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 0.35/0.58 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_of_nat_commute
% 0.35/0.58 thf(fact_3365_mult__of__nat__commute,axiom,
% 0.35/0.58 ! [X: nat,Y: int] :
% 0.35/0.58 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 0.35/0.58 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_of_nat_commute
% 0.35/0.58 thf(fact_3366_mult__of__nat__commute,axiom,
% 0.35/0.58 ! [X: nat,Y: nat] :
% 0.35/0.58 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 0.35/0.58 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % mult_of_nat_commute
% 0.35/0.58 thf(fact_3367_zless__iff__Suc__zadd,axiom,
% 0.35/0.58 ( ord_less_int
% 0.35/0.58 = ( ^ [W3: int,Z4: int] :
% 0.35/0.58 ? [N4: nat] :
% 0.35/0.58 ( Z4
% 0.35/0.58 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zless_iff_Suc_zadd
% 0.35/0.58 thf(fact_3368_int__Suc,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.35/0.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 0.35/0.58
% 0.35/0.58 % int_Suc
% 0.35/0.58 thf(fact_3369_int__ops_I4_J,axiom,
% 0.35/0.58 ! [A: nat] :
% 0.35/0.58 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 0.35/0.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 0.35/0.58
% 0.35/0.58 % int_ops(4)
% 0.35/0.58 thf(fact_3370_zero__neq__numeral,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( zero_zero_rat
% 0.35/0.58 != ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_neq_numeral
% 0.35/0.58 thf(fact_3371_zero__neq__numeral,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( zero_z5237406670263579293d_enat
% 0.35/0.58 != ( numera1916890842035813515d_enat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_neq_numeral
% 0.35/0.58 thf(fact_3372_zero__neq__numeral,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( zero_zero_complex
% 0.35/0.58 != ( numera6690914467698888265omplex @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_neq_numeral
% 0.35/0.58 thf(fact_3373_zero__neq__numeral,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( zero_zero_real
% 0.35/0.58 != ( numeral_numeral_real @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_neq_numeral
% 0.35/0.58 thf(fact_3374_zero__neq__numeral,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( zero_zero_nat
% 0.35/0.58 != ( numeral_numeral_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_neq_numeral
% 0.35/0.58 thf(fact_3375_zero__neq__numeral,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ( zero_zero_int
% 0.35/0.58 != ( numeral_numeral_int @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_neq_numeral
% 0.35/0.58 thf(fact_3376_int__ops_I1_J,axiom,
% 0.35/0.58 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 0.35/0.58 = zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % int_ops(1)
% 0.35/0.58 thf(fact_3377_nat__le__real__less,axiom,
% 0.35/0.58 ( ord_less_eq_nat
% 0.35/0.58 = ( ^ [N4: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % nat_le_real_less
% 0.35/0.58 thf(fact_3378_zle__int,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.58 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zle_int
% 0.35/0.58 thf(fact_3379_nat__int__comparison_I3_J,axiom,
% 0.35/0.58 ( ord_less_eq_nat
% 0.35/0.58 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % nat_int_comparison(3)
% 0.35/0.58 thf(fact_3380_int__ops_I7_J,axiom,
% 0.35/0.58 ! [A: nat,B: nat] :
% 0.35/0.58 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 0.35/0.58 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % int_ops(7)
% 0.35/0.58 thf(fact_3381_power2__less__imp__less,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.58 => ( ord_less_real @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_imp_less
% 0.35/0.58 thf(fact_3382_power2__less__imp__less,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.58 => ( ord_less_rat @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_imp_less
% 0.35/0.58 thf(fact_3383_power2__less__imp__less,axiom,
% 0.35/0.58 ! [X: nat,Y: nat] :
% 0.35/0.58 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 0.35/0.58 => ( ord_less_nat @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_imp_less
% 0.35/0.58 thf(fact_3384_power2__less__imp__less,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.35/0.58 => ( ord_less_int @ X @ Y ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power2_less_imp_less
% 0.35/0.58 thf(fact_3385_sum__power2__le__zero__iff,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 0.35/0.58 = ( ( X = zero_zero_real )
% 0.35/0.58 & ( Y = zero_zero_real ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_le_zero_iff
% 0.35/0.58 thf(fact_3386_sum__power2__le__zero__iff,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 0.35/0.58 = ( ( X = zero_zero_rat )
% 0.35/0.58 & ( Y = zero_zero_rat ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_le_zero_iff
% 0.35/0.58 thf(fact_3387_sum__power2__le__zero__iff,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 0.35/0.58 = ( ( X = zero_zero_int )
% 0.35/0.58 & ( Y = zero_zero_int ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_le_zero_iff
% 0.35/0.58 thf(fact_3388_sum__power2__ge__zero,axiom,
% 0.35/0.58 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_ge_zero
% 0.35/0.58 thf(fact_3389_sum__power2__ge__zero,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_ge_zero
% 0.35/0.58 thf(fact_3390_sum__power2__ge__zero,axiom,
% 0.35/0.58 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_ge_zero
% 0.35/0.58 thf(fact_3391_sum__power2__gt__zero__iff,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.58 = ( ( X != zero_zero_real )
% 0.35/0.58 | ( Y != zero_zero_real ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_gt_zero_iff
% 0.35/0.58 thf(fact_3392_sum__power2__gt__zero__iff,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.58 = ( ( X != zero_zero_rat )
% 0.35/0.58 | ( Y != zero_zero_rat ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_gt_zero_iff
% 0.35/0.58 thf(fact_3393_sum__power2__gt__zero__iff,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.58 = ( ( X != zero_zero_int )
% 0.35/0.58 | ( Y != zero_zero_int ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % sum_power2_gt_zero_iff
% 0.35/0.58 thf(fact_3394_not__sum__power2__lt__zero,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 0.35/0.58
% 0.35/0.58 % not_sum_power2_lt_zero
% 0.35/0.58 thf(fact_3395_not__sum__power2__lt__zero,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 0.35/0.58
% 0.35/0.58 % not_sum_power2_lt_zero
% 0.35/0.58 thf(fact_3396_not__sum__power2__lt__zero,axiom,
% 0.35/0.58 ! [X: int,Y: int] :
% 0.35/0.58 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % not_sum_power2_lt_zero
% 0.35/0.58 thf(fact_3397_num_Osize_I4_J,axiom,
% 0.35/0.58 ( ( size_size_num @ one )
% 0.35/0.58 = zero_zero_nat ) ).
% 0.35/0.58
% 0.35/0.58 % num.size(4)
% 0.35/0.58 thf(fact_3398_zero__le__even__power_H,axiom,
% 0.35/0.58 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_even_power'
% 0.35/0.58 thf(fact_3399_zero__le__even__power_H,axiom,
% 0.35/0.58 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_even_power'
% 0.35/0.58 thf(fact_3400_zero__le__even__power_H,axiom,
% 0.35/0.58 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_even_power'
% 0.35/0.58 thf(fact_3401_power__odd__eq,axiom,
% 0.35/0.58 ! [A: complex,N: nat] :
% 0.35/0.58 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.58 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_odd_eq
% 0.35/0.58 thf(fact_3402_power__odd__eq,axiom,
% 0.35/0.58 ! [A: real,N: nat] :
% 0.35/0.58 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.58 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_odd_eq
% 0.35/0.58 thf(fact_3403_power__odd__eq,axiom,
% 0.35/0.58 ! [A: rat,N: nat] :
% 0.35/0.58 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.58 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_odd_eq
% 0.35/0.58 thf(fact_3404_power__odd__eq,axiom,
% 0.35/0.58 ! [A: nat,N: nat] :
% 0.35/0.58 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.58 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_odd_eq
% 0.35/0.58 thf(fact_3405_power__odd__eq,axiom,
% 0.35/0.58 ! [A: int,N: nat] :
% 0.35/0.58 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.58 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % power_odd_eq
% 0.35/0.58 thf(fact_3406_ex__power__ivl1,axiom,
% 0.35/0.58 ! [B: nat,K2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.58 => ( ( ord_less_eq_nat @ one_one_nat @ K2 )
% 0.35/0.58 => ? [N3: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K2 )
% 0.35/0.58 & ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % ex_power_ivl1
% 0.35/0.58 thf(fact_3407_ex__power__ivl2,axiom,
% 0.35/0.58 ! [B: nat,K2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 0.35/0.58 => ? [N3: nat] :
% 0.35/0.58 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K2 )
% 0.35/0.58 & ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % ex_power_ivl2
% 0.35/0.58 thf(fact_3408_VEBT__internal_Oinsert_H_Osimps_I2_J,axiom,
% 0.35/0.58 ! [Deg: nat,X: nat,Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.58 ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 0.35/0.58 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.58 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) )
% 0.35/0.58 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 0.35/0.58 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.58 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % VEBT_internal.insert'.simps(2)
% 0.35/0.58 thf(fact_3409_odd__0__le__power__imp__0__le,axiom,
% 0.35/0.58 ! [A: real,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.58 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % odd_0_le_power_imp_0_le
% 0.35/0.58 thf(fact_3410_odd__0__le__power__imp__0__le,axiom,
% 0.35/0.58 ! [A: rat,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.58 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % odd_0_le_power_imp_0_le
% 0.35/0.58 thf(fact_3411_odd__0__le__power__imp__0__le,axiom,
% 0.35/0.58 ! [A: int,N: nat] :
% 0.35/0.58 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.58 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.58
% 0.35/0.58 % odd_0_le_power_imp_0_le
% 0.35/0.58 thf(fact_3412_odd__power__less__zero,axiom,
% 0.35/0.58 ! [A: real,N: nat] :
% 0.35/0.58 ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.58 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.58
% 0.35/0.58 % odd_power_less_zero
% 0.35/0.58 thf(fact_3413_odd__power__less__zero,axiom,
% 0.35/0.58 ! [A: rat,N: nat] :
% 0.35/0.58 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.58 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 0.35/0.58
% 0.35/0.58 % odd_power_less_zero
% 0.35/0.58 thf(fact_3414_odd__power__less__zero,axiom,
% 0.35/0.58 ! [A: int,N: nat] :
% 0.35/0.58 ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.58 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 0.35/0.58
% 0.35/0.58 % odd_power_less_zero
% 0.35/0.58 thf(fact_3415_VEBT__internal_Oinsert_H_Oelims,axiom,
% 0.35/0.58 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.35/0.58 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 0.35/0.58 = Y )
% 0.35/0.58 => ( ! [A3: $o,B3: $o] :
% 0.35/0.58 ( ( X
% 0.35/0.58 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.58 => ( Y
% 0.35/0.58 != ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) )
% 0.35/0.58 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.58 ( ( X
% 0.35/0.58 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.58 => ~ ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.35/0.58 => ( Y
% 0.35/0.58 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 0.35/0.58 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.35/0.58 => ( Y
% 0.35/0.58 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % VEBT_internal.insert'.elims
% 0.35/0.58 thf(fact_3416_of__nat__0__le__iff,axiom,
% 0.35/0.58 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_le_iff
% 0.35/0.58 thf(fact_3417_of__nat__0__le__iff,axiom,
% 0.35/0.58 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_le_iff
% 0.35/0.58 thf(fact_3418_of__nat__0__le__iff,axiom,
% 0.35/0.58 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_le_iff
% 0.35/0.58 thf(fact_3419_of__nat__0__le__iff,axiom,
% 0.35/0.58 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_0_le_iff
% 0.35/0.58 thf(fact_3420_of__nat__less__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_0_iff
% 0.35/0.58 thf(fact_3421_of__nat__less__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_0_iff
% 0.35/0.58 thf(fact_3422_of__nat__less__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_0_iff
% 0.35/0.58 thf(fact_3423_of__nat__less__0__iff,axiom,
% 0.35/0.58 ! [M2: nat] :
% 0.35/0.58 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_0_iff
% 0.35/0.58 thf(fact_3424_of__nat__neq__0,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 0.35/0.58 != zero_zero_complex ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_neq_0
% 0.35/0.58 thf(fact_3425_of__nat__neq__0,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 0.35/0.58 != zero_zero_rat ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_neq_0
% 0.35/0.58 thf(fact_3426_of__nat__neq__0,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 0.35/0.58 != zero_zero_real ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_neq_0
% 0.35/0.58 thf(fact_3427_of__nat__neq__0,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 0.35/0.58 != zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_neq_0
% 0.35/0.58 thf(fact_3428_of__nat__neq__0,axiom,
% 0.35/0.58 ! [N: nat] :
% 0.35/0.58 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 0.35/0.58 != zero_zero_nat ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_neq_0
% 0.35/0.58 thf(fact_3429_of__nat__less__imp__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.58 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_imp_less
% 0.35/0.58 thf(fact_3430_of__nat__less__imp__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.58 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_imp_less
% 0.35/0.58 thf(fact_3431_of__nat__less__imp__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.58 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_imp_less
% 0.35/0.58 thf(fact_3432_of__nat__less__imp__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 0.35/0.58 => ( ord_less_nat @ M2 @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_less_imp_less
% 0.35/0.58 thf(fact_3433_less__imp__of__nat__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ M2 @ N )
% 0.35/0.58 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % less_imp_of_nat_less
% 0.35/0.58 thf(fact_3434_less__imp__of__nat__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ M2 @ N )
% 0.35/0.58 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % less_imp_of_nat_less
% 0.35/0.58 thf(fact_3435_less__imp__of__nat__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ M2 @ N )
% 0.35/0.58 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % less_imp_of_nat_less
% 0.35/0.58 thf(fact_3436_less__imp__of__nat__less,axiom,
% 0.35/0.58 ! [M2: nat,N: nat] :
% 0.35/0.58 ( ( ord_less_nat @ M2 @ N )
% 0.35/0.58 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % less_imp_of_nat_less
% 0.35/0.58 thf(fact_3437_of__nat__mono,axiom,
% 0.35/0.58 ! [I2: nat,J2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.58 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_mono
% 0.35/0.58 thf(fact_3438_of__nat__mono,axiom,
% 0.35/0.58 ! [I2: nat,J2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.58 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_mono
% 0.35/0.58 thf(fact_3439_of__nat__mono,axiom,
% 0.35/0.58 ! [I2: nat,J2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.58 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_mono
% 0.35/0.58 thf(fact_3440_of__nat__mono,axiom,
% 0.35/0.58 ! [I2: nat,J2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.58 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_mono
% 0.35/0.58 thf(fact_3441_zero__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_numeral
% 0.35/0.58 thf(fact_3442_zero__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_numeral
% 0.35/0.58 thf(fact_3443_zero__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_numeral
% 0.35/0.58 thf(fact_3444_zero__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_numeral
% 0.35/0.58 thf(fact_3445_zero__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_le_numeral
% 0.35/0.58 thf(fact_3446_not__numeral__le__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_le_zero
% 0.35/0.58 thf(fact_3447_not__numeral__le__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_le_zero
% 0.35/0.58 thf(fact_3448_not__numeral__le__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_le_zero
% 0.35/0.58 thf(fact_3449_not__numeral__le__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_le_zero
% 0.35/0.58 thf(fact_3450_not__numeral__le__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_le_zero
% 0.35/0.58 thf(fact_3451_not__numeral__less__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_zero
% 0.35/0.58 thf(fact_3452_not__numeral__less__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_zero
% 0.35/0.58 thf(fact_3453_not__numeral__less__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_zero
% 0.35/0.58 thf(fact_3454_not__numeral__less__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_zero
% 0.35/0.58 thf(fact_3455_not__numeral__less__zero,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_zero
% 0.35/0.58 thf(fact_3456_zero__less__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_numeral
% 0.35/0.58 thf(fact_3457_zero__less__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_numeral
% 0.35/0.58 thf(fact_3458_zero__less__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_numeral
% 0.35/0.58 thf(fact_3459_zero__less__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_numeral
% 0.35/0.58 thf(fact_3460_zero__less__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_numeral
% 0.35/0.58 thf(fact_3461_replicate__Suc,axiom,
% 0.35/0.58 ! [N: nat,X: nat] :
% 0.35/0.58 ( ( replicate_nat @ ( suc @ N ) @ X )
% 0.35/0.58 = ( cons_nat @ X @ ( replicate_nat @ N @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_Suc
% 0.35/0.58 thf(fact_3462_replicate__Suc,axiom,
% 0.35/0.58 ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.58 ( ( replicate_VEBT_VEBT @ ( suc @ N ) @ X )
% 0.35/0.58 = ( cons_VEBT_VEBT @ X @ ( replicate_VEBT_VEBT @ N @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_Suc
% 0.35/0.58 thf(fact_3463_real__archimedian__rdiv__eq__0,axiom,
% 0.35/0.58 ! [X: real,C2: real] :
% 0.35/0.58 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.58 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.35/0.58 => ( ! [M: nat] :
% 0.35/0.58 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.35/0.58 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ X ) @ C2 ) )
% 0.35/0.58 => ( X = zero_zero_real ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % real_archimedian_rdiv_eq_0
% 0.35/0.58 thf(fact_3464_one__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_le_numeral
% 0.35/0.58 thf(fact_3465_one__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_le_numeral
% 0.35/0.58 thf(fact_3466_one__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_le_numeral
% 0.35/0.58 thf(fact_3467_one__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_le_numeral
% 0.35/0.58 thf(fact_3468_one__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_le_numeral
% 0.35/0.58 thf(fact_3469_one__le__numeral,axiom,
% 0.35/0.58 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_le_numeral
% 0.35/0.58 thf(fact_3470_pos__int__cases,axiom,
% 0.35/0.58 ! [K2: int] :
% 0.35/0.58 ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.58 => ~ ! [N3: nat] :
% 0.35/0.58 ( ( K2
% 0.35/0.58 = ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.58 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % pos_int_cases
% 0.35/0.58 thf(fact_3471_zero__less__imp__eq__int,axiom,
% 0.35/0.58 ! [K2: int] :
% 0.35/0.58 ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.58 => ? [N3: nat] :
% 0.35/0.58 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.58 & ( K2
% 0.35/0.58 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zero_less_imp_eq_int
% 0.35/0.58 thf(fact_3472_zmult__zless__mono2__lemma,axiom,
% 0.35/0.58 ! [I2: int,J2: int,K2: nat] :
% 0.35/0.58 ( ( ord_less_int @ I2 @ J2 )
% 0.35/0.58 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.58 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ J2 ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zmult_zless_mono2_lemma
% 0.35/0.58 thf(fact_3473_not__numeral__less__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_one
% 0.35/0.58 thf(fact_3474_not__numeral__less__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_one
% 0.35/0.58 thf(fact_3475_not__numeral__less__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_one
% 0.35/0.58 thf(fact_3476_not__numeral__less__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_one
% 0.35/0.58 thf(fact_3477_not__numeral__less__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_one
% 0.35/0.58 thf(fact_3478_not__numeral__less__one,axiom,
% 0.35/0.58 ! [N: num] :
% 0.35/0.58 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 0.35/0.58
% 0.35/0.58 % not_numeral_less_one
% 0.35/0.58 thf(fact_3479_one__plus__numeral__commute,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 0.35/0.58 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_plus_numeral_commute
% 0.35/0.58 thf(fact_3480_one__plus__numeral__commute,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 0.35/0.58 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_plus_numeral_commute
% 0.35/0.58 thf(fact_3481_one__plus__numeral__commute,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 0.35/0.58 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_plus_numeral_commute
% 0.35/0.58 thf(fact_3482_one__plus__numeral__commute,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 0.35/0.58 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_plus_numeral_commute
% 0.35/0.58 thf(fact_3483_one__plus__numeral__commute,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 0.35/0.58 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_plus_numeral_commute
% 0.35/0.58 thf(fact_3484_one__plus__numeral__commute,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.35/0.58 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_plus_numeral_commute
% 0.35/0.58 thf(fact_3485_one__plus__numeral__commute,axiom,
% 0.35/0.58 ! [X: num] :
% 0.35/0.58 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.35/0.58 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 0.35/0.58
% 0.35/0.58 % one_plus_numeral_commute
% 0.35/0.58 thf(fact_3486_replicate__length__same,axiom,
% 0.35/0.58 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.35/0.58 ( ! [X3: vEBT_VEBT] :
% 0.35/0.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.58 => ( X3 = X ) )
% 0.35/0.58 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 0.35/0.58 = Xs2 ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_length_same
% 0.35/0.58 thf(fact_3487_replicate__length__same,axiom,
% 0.35/0.58 ! [Xs2: list_o,X: $o] :
% 0.35/0.58 ( ! [X3: $o] :
% 0.35/0.58 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 0.35/0.58 => ( X3 = X ) )
% 0.35/0.58 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 0.35/0.58 = Xs2 ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_length_same
% 0.35/0.58 thf(fact_3488_replicate__length__same,axiom,
% 0.35/0.58 ! [Xs2: list_nat,X: nat] :
% 0.35/0.58 ( ! [X3: nat] :
% 0.35/0.58 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 0.35/0.58 => ( X3 = X ) )
% 0.35/0.58 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 0.35/0.58 = Xs2 ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_length_same
% 0.35/0.58 thf(fact_3489_replicate__length__same,axiom,
% 0.35/0.58 ! [Xs2: list_int,X: int] :
% 0.35/0.58 ( ! [X3: int] :
% 0.35/0.58 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 0.35/0.58 => ( X3 = X ) )
% 0.35/0.58 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 0.35/0.58 = Xs2 ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_length_same
% 0.35/0.58 thf(fact_3490_replicate__eqI,axiom,
% 0.35/0.58 ! [Xs2: list_complex,N: nat,X: complex] :
% 0.35/0.58 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 0.35/0.58 = N )
% 0.35/0.58 => ( ! [Y3: complex] :
% 0.35/0.58 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 0.35/0.58 => ( Y3 = X ) )
% 0.35/0.58 => ( Xs2
% 0.35/0.58 = ( replicate_complex @ N @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_eqI
% 0.35/0.58 thf(fact_3491_replicate__eqI,axiom,
% 0.35/0.58 ! [Xs2: list_real,N: nat,X: real] :
% 0.35/0.58 ( ( ( size_size_list_real @ Xs2 )
% 0.35/0.58 = N )
% 0.35/0.58 => ( ! [Y3: real] :
% 0.35/0.58 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 0.35/0.58 => ( Y3 = X ) )
% 0.35/0.58 => ( Xs2
% 0.35/0.58 = ( replicate_real @ N @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_eqI
% 0.35/0.58 thf(fact_3492_replicate__eqI,axiom,
% 0.35/0.58 ! [Xs2: list_set_nat,N: nat,X: set_nat] :
% 0.35/0.58 ( ( ( size_s3254054031482475050et_nat @ Xs2 )
% 0.35/0.58 = N )
% 0.35/0.58 => ( ! [Y3: set_nat] :
% 0.35/0.58 ( ( member_set_nat @ Y3 @ ( set_set_nat2 @ Xs2 ) )
% 0.35/0.58 => ( Y3 = X ) )
% 0.35/0.58 => ( Xs2
% 0.35/0.58 = ( replicate_set_nat @ N @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_eqI
% 0.35/0.58 thf(fact_3493_replicate__eqI,axiom,
% 0.35/0.58 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 0.35/0.58 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.35/0.58 = N )
% 0.35/0.58 => ( ! [Y3: vEBT_VEBT] :
% 0.35/0.58 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.58 => ( Y3 = X ) )
% 0.35/0.58 => ( Xs2
% 0.35/0.58 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_eqI
% 0.35/0.58 thf(fact_3494_replicate__eqI,axiom,
% 0.35/0.58 ! [Xs2: list_o,N: nat,X: $o] :
% 0.35/0.58 ( ( ( size_size_list_o @ Xs2 )
% 0.35/0.58 = N )
% 0.35/0.58 => ( ! [Y3: $o] :
% 0.35/0.58 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 0.35/0.58 => ( Y3 = X ) )
% 0.35/0.58 => ( Xs2
% 0.35/0.58 = ( replicate_o @ N @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_eqI
% 0.35/0.58 thf(fact_3495_replicate__eqI,axiom,
% 0.35/0.58 ! [Xs2: list_nat,N: nat,X: nat] :
% 0.35/0.58 ( ( ( size_size_list_nat @ Xs2 )
% 0.35/0.58 = N )
% 0.35/0.58 => ( ! [Y3: nat] :
% 0.35/0.58 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 0.35/0.58 => ( Y3 = X ) )
% 0.35/0.58 => ( Xs2
% 0.35/0.58 = ( replicate_nat @ N @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_eqI
% 0.35/0.58 thf(fact_3496_replicate__eqI,axiom,
% 0.35/0.58 ! [Xs2: list_int,N: nat,X: int] :
% 0.35/0.58 ( ( ( size_size_list_int @ Xs2 )
% 0.35/0.58 = N )
% 0.35/0.58 => ( ! [Y3: int] :
% 0.35/0.58 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 0.35/0.58 => ( Y3 = X ) )
% 0.35/0.58 => ( Xs2
% 0.35/0.58 = ( replicate_int @ N @ X ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % replicate_eqI
% 0.35/0.58 thf(fact_3497_invar__vebt_Ointros_I2_J,axiom,
% 0.35/0.58 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 0.35/0.58 ( ! [X3: vEBT_VEBT] :
% 0.35/0.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.58 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.35/0.58 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 0.35/0.58 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.58 => ( ( M2 = N )
% 0.35/0.58 => ( ( Deg
% 0.35/0.58 = ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.58 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 0.35/0.58 => ( ! [X3: vEBT_VEBT] :
% 0.35/0.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.58 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 0.35/0.58 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % invar_vebt.intros(2)
% 0.35/0.58 thf(fact_3498_invar__vebt_Ointros_I3_J,axiom,
% 0.35/0.58 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 0.35/0.58 ( ! [X3: vEBT_VEBT] :
% 0.35/0.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.58 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.35/0.58 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 0.35/0.58 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.58 => ( ( M2
% 0.35/0.58 = ( suc @ N ) )
% 0.35/0.58 => ( ( Deg
% 0.35/0.58 = ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.58 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 0.35/0.58 => ( ! [X3: vEBT_VEBT] :
% 0.35/0.58 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.58 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 0.35/0.58 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % invar_vebt.intros(3)
% 0.35/0.58 thf(fact_3499_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 0.35/0.58 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( listre1230615542750757617T_VEBT @ R3 ) )
% 0.35/0.58 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.35/0.58 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3500_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_o,R3: set_Pr3175402225741728619VEBT_o] :
% 0.35/0.58 ( ( member3126162362653435956list_o @ ( produc2717590391345394939list_o @ Xs2 @ Ys ) @ ( listrel_VEBT_VEBT_o @ R3 ) )
% 0.35/0.58 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.35/0.58 = ( size_size_list_o @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3501_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,R3: set_Pr7556676689462069481BT_nat] :
% 0.35/0.58 ( ( member6193324644334088288st_nat @ ( produc5570133714943300547st_nat @ Xs2 @ Ys ) @ ( listre5900670229112895443BT_nat @ R3 ) )
% 0.35/0.58 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.35/0.58 = ( size_size_list_nat @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3502_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_VEBT_VEBT,Ys: list_int,R3: set_Pr5066593544530342725BT_int] :
% 0.35/0.58 ( ( member3703241499402361532st_int @ ( produc1392282695434103839st_int @ Xs2 @ Ys ) @ ( listre5898179758603845167BT_int @ R3 ) )
% 0.35/0.58 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 0.35/0.58 = ( size_size_list_int @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3503_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_o,Ys: list_VEBT_VEBT,R3: set_Pr7543698050874017315T_VEBT] :
% 0.35/0.58 ( ( member1087064965665443052T_VEBT @ ( produc6043759678074843571T_VEBT @ Xs2 @ Ys ) @ ( listrel_o_VEBT_VEBT @ R3 ) )
% 0.35/0.58 => ( ( size_size_list_o @ Xs2 )
% 0.35/0.58 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3504_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_o,Ys: list_o,R3: set_Product_prod_o_o] :
% 0.35/0.58 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( listrel_o_o @ R3 ) )
% 0.35/0.58 => ( ( size_size_list_o @ Xs2 )
% 0.35/0.58 = ( size_size_list_o @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3505_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_o,Ys: list_nat,R3: set_Pr2101469702781467981_o_nat] :
% 0.35/0.58 ( ( member1519744053835550788st_nat @ ( produc7128876500814652583st_nat @ Xs2 @ Ys ) @ ( listrel_o_nat @ R3 ) )
% 0.35/0.58 => ( ( size_size_list_o @ Xs2 )
% 0.35/0.58 = ( size_size_list_nat @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3506_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_o,Ys: list_int,R3: set_Pr8834758594704517033_o_int] :
% 0.35/0.58 ( ( member8253032945758599840st_int @ ( produc2951025481305455875st_int @ Xs2 @ Ys ) @ ( listrel_o_int @ R3 ) )
% 0.35/0.58 => ( ( size_size_list_o @ Xs2 )
% 0.35/0.58 = ( size_size_list_int @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3507_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_nat,Ys: list_VEBT_VEBT,R3: set_Pr6167073792073659919T_VEBT] :
% 0.35/0.58 ( ( member5968030670617646438T_VEBT @ ( produc8335345208264861441T_VEBT @ Xs2 @ Ys ) @ ( listre5761932458788874033T_VEBT @ R3 ) )
% 0.35/0.58 => ( ( size_size_list_nat @ Xs2 )
% 0.35/0.58 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3508_listrel__eq__len,axiom,
% 0.35/0.58 ! [Xs2: list_nat,Ys: list_o,R3: set_Pr3149072824959771635_nat_o] :
% 0.35/0.58 ( ( member6688923169008879818list_o @ ( produc699922362453767013list_o @ Xs2 @ Ys ) @ ( listrel_nat_o @ R3 ) )
% 0.35/0.58 => ( ( size_size_list_nat @ Xs2 )
% 0.35/0.58 = ( size_size_list_o @ Ys ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_eq_len
% 0.35/0.58 thf(fact_3509_ex__less__of__nat__mult,axiom,
% 0.35/0.58 ! [X: rat,Y: rat] :
% 0.35/0.58 ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.58 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % ex_less_of_nat_mult
% 0.35/0.58 thf(fact_3510_ex__less__of__nat__mult,axiom,
% 0.35/0.58 ! [X: real,Y: real] :
% 0.35/0.58 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.58 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % ex_less_of_nat_mult
% 0.35/0.58 thf(fact_3511_of__nat__diff,axiom,
% 0.35/0.58 ! [N: nat,M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.58 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.58 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_diff
% 0.35/0.58 thf(fact_3512_of__nat__diff,axiom,
% 0.35/0.58 ! [N: nat,M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.58 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.58 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_diff
% 0.35/0.58 thf(fact_3513_of__nat__diff,axiom,
% 0.35/0.58 ! [N: nat,M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.58 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.58 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_diff
% 0.35/0.58 thf(fact_3514_of__nat__diff,axiom,
% 0.35/0.58 ! [N: nat,M2: nat] :
% 0.35/0.58 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.58 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.58 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % of_nat_diff
% 0.35/0.58 thf(fact_3515_zdiff__int__split,axiom,
% 0.35/0.58 ! [P2: int > $o,X: nat,Y: nat] :
% 0.35/0.58 ( ( P2 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 0.35/0.58 = ( ( ( ord_less_eq_nat @ Y @ X )
% 0.35/0.58 => ( P2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 0.35/0.58 & ( ( ord_less_nat @ X @ Y )
% 0.35/0.58 => ( P2 @ zero_zero_int ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % zdiff_int_split
% 0.35/0.58 thf(fact_3516_num_Osize_I5_J,axiom,
% 0.35/0.58 ! [X2: num] :
% 0.35/0.58 ( ( size_size_num @ ( bit0 @ X2 ) )
% 0.35/0.58 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % num.size(5)
% 0.35/0.58 thf(fact_3517_realpow__pos__nth2,axiom,
% 0.35/0.58 ! [A: real,N: nat] :
% 0.35/0.58 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.58 => ? [R4: real] :
% 0.35/0.58 ( ( ord_less_real @ zero_zero_real @ R4 )
% 0.35/0.58 & ( ( power_power_real @ R4 @ ( suc @ N ) )
% 0.35/0.58 = A ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % realpow_pos_nth2
% 0.35/0.58 thf(fact_3518_listrel__Cons2,axiom,
% 0.35/0.58 ! [Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 0.35/0.58 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ ( cons_Code_integer @ Y @ Ys ) ) @ ( listre5734910445319291053nteger @ R3 ) )
% 0.35/0.58 => ~ ! [X3: code_integer,Xs3: list_Code_integer] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_Code_integer @ X3 @ Xs3 ) )
% 0.35/0.58 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y ) @ R3 )
% 0.35/0.58 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs3 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons2
% 0.35/0.58 thf(fact_3519_listrel__Cons2,axiom,
% 0.35/0.58 ! [Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 0.35/0.58 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( listre818007680106770737at_nat @ R3 ) )
% 0.35/0.58 => ~ ! [X3: product_prod_nat_nat,Xs3: list_P6011104703257516679at_nat] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_P6512896166579812791at_nat @ X3 @ Xs3 ) )
% 0.35/0.58 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y ) @ R3 )
% 0.35/0.58 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs3 @ Ys ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons2
% 0.35/0.58 thf(fact_3520_listrel__Cons2,axiom,
% 0.35/0.58 ! [Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.35/0.58 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 0.35/0.58 => ~ ! [X3: set_Pr1261947904930325089at_nat,Xs3: list_s1210847774152347623at_nat] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_s6881495754146722583at_nat @ X3 @ Xs3 ) )
% 0.35/0.58 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y ) @ R3 )
% 0.35/0.58 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs3 @ Ys ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons2
% 0.35/0.58 thf(fact_3521_listrel__Cons2,axiom,
% 0.35/0.58 ! [Xs2: list_nat,Y: nat,Ys: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.35/0.58 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R3 ) )
% 0.35/0.58 => ~ ! [X3: nat,Xs3: list_nat] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_nat @ X3 @ Xs3 ) )
% 0.35/0.58 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R3 )
% 0.35/0.58 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs3 @ Ys ) @ ( listrel_nat_nat @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons2
% 0.35/0.58 thf(fact_3522_listrel__Cons2,axiom,
% 0.35/0.58 ! [Xs2: list_int,Y: int,Ys: list_int,R3: set_Pr958786334691620121nt_int] :
% 0.35/0.58 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R3 ) )
% 0.35/0.58 => ~ ! [X3: int,Xs3: list_int] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_int @ X3 @ Xs3 ) )
% 0.35/0.58 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ R3 )
% 0.35/0.58 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs3 @ Ys ) @ ( listrel_int_int @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons2
% 0.35/0.58 thf(fact_3523_listrel__Cons1,axiom,
% 0.35/0.58 ! [Y: code_integer,Ys: list_Code_integer,Xs2: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 0.35/0.58 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ Y @ Ys ) @ Xs2 ) @ ( listre5734910445319291053nteger @ R3 ) )
% 0.35/0.58 => ~ ! [Y3: code_integer,Ys5: list_Code_integer] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_Code_integer @ Y3 @ Ys5 ) )
% 0.35/0.58 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ Y @ Y3 ) @ R3 )
% 0.35/0.58 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Ys @ Ys5 ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons1
% 0.35/0.58 thf(fact_3524_listrel__Cons1,axiom,
% 0.35/0.58 ! [Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,Xs2: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 0.35/0.58 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) @ Xs2 ) @ ( listre818007680106770737at_nat @ R3 ) )
% 0.35/0.58 => ~ ! [Y3: product_prod_nat_nat,Ys5: list_P6011104703257516679at_nat] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_P6512896166579812791at_nat @ Y3 @ Ys5 ) )
% 0.35/0.58 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y @ Y3 ) @ R3 )
% 0.35/0.58 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Ys @ Ys5 ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons1
% 0.35/0.58 thf(fact_3525_listrel__Cons1,axiom,
% 0.35/0.58 ! [Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,Xs2: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 0.35/0.58 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) @ Xs2 ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 0.35/0.58 => ~ ! [Y3: set_Pr1261947904930325089at_nat,Ys5: list_s1210847774152347623at_nat] :
% 0.35/0.58 ( ( Xs2
% 0.35/0.58 = ( cons_s6881495754146722583at_nat @ Y3 @ Ys5 ) )
% 0.35/0.58 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Y3 ) @ R3 )
% 0.35/0.58 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ys @ Ys5 ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ) ).
% 0.35/0.58
% 0.35/0.58 % listrel_Cons1
% 0.35/0.58 thf(fact_3526_listrel__Cons1,axiom,
% 0.35/0.59 ! [Y: nat,Ys: list_nat,Xs2: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ Y @ Ys ) @ Xs2 ) @ ( listrel_nat_nat @ R3 ) )
% 0.35/0.59 => ~ ! [Y3: nat,Ys5: list_nat] :
% 0.35/0.59 ( ( Xs2
% 0.35/0.59 = ( cons_nat @ Y3 @ Ys5 ) )
% 0.35/0.59 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Y3 ) @ R3 )
% 0.35/0.59 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ys @ Ys5 ) @ ( listrel_nat_nat @ R3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % listrel_Cons1
% 0.35/0.59 thf(fact_3527_listrel__Cons1,axiom,
% 0.35/0.59 ! [Y: int,Ys: list_int,Xs2: list_int,R3: set_Pr958786334691620121nt_int] :
% 0.35/0.59 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ Y @ Ys ) @ Xs2 ) @ ( listrel_int_int @ R3 ) )
% 0.35/0.59 => ~ ! [Y3: int,Ys5: list_int] :
% 0.35/0.59 ( ( Xs2
% 0.35/0.59 = ( cons_int @ Y3 @ Ys5 ) )
% 0.35/0.59 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Y3 ) @ R3 )
% 0.35/0.59 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ys @ Ys5 ) @ ( listrel_int_int @ R3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % listrel_Cons1
% 0.35/0.59 thf(fact_3528_listrel_OCons,axiom,
% 0.35/0.59 ! [X: code_integer,Y: code_integer,R3: set_Pr4811707699266497531nteger,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 0.35/0.59 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ R3 )
% 0.35/0.59 => ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) )
% 0.35/0.59 => ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % listrel.Cons
% 0.35/0.59 thf(fact_3529_listrel_OCons,axiom,
% 0.35/0.59 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 0.35/0.59 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R3 )
% 0.35/0.59 => ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Ys ) @ ( listre818007680106770737at_nat @ R3 ) )
% 0.35/0.59 => ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % listrel.Cons
% 0.35/0.59 thf(fact_3530_listrel_OCons,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 0.35/0.59 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R3 )
% 0.35/0.59 => ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Ys ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 0.35/0.59 => ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % listrel.Cons
% 0.35/0.59 thf(fact_3531_listrel_OCons,axiom,
% 0.35/0.59 ! [X: nat,Y: nat,R3: set_Pr1261947904930325089at_nat,Xs2: list_nat,Ys: list_nat] :
% 0.35/0.59 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 )
% 0.35/0.59 => ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Ys ) @ ( listrel_nat_nat @ R3 ) )
% 0.35/0.59 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % listrel.Cons
% 0.35/0.59 thf(fact_3532_listrel_OCons,axiom,
% 0.35/0.59 ! [X: int,Y: int,R3: set_Pr958786334691620121nt_int,Xs2: list_int,Ys: list_int] :
% 0.35/0.59 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 )
% 0.35/0.59 => ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Ys ) @ ( listrel_int_int @ R3 ) )
% 0.35/0.59 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % listrel.Cons
% 0.35/0.59 thf(fact_3533_measures__less,axiom,
% 0.35/0.59 ! [F2: code_integer > nat,X: code_integer,Y: code_integer,Fs: list_C4705013386053401436er_nat] :
% 0.35/0.59 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_less
% 0.35/0.59 thf(fact_3534_measures__less,axiom,
% 0.35/0.59 ! [F2: product_prod_nat_nat > nat,X: product_prod_nat_nat,Y: product_prod_nat_nat,Fs: list_P9162950289778280392at_nat] :
% 0.35/0.59 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_less
% 0.35/0.59 thf(fact_3535_measures__less,axiom,
% 0.35/0.59 ! [F2: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Fs: list_s9130966667114977576at_nat] :
% 0.35/0.59 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_less
% 0.35/0.59 thf(fact_3536_measures__less,axiom,
% 0.35/0.59 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 0.35/0.59 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_less
% 0.35/0.59 thf(fact_3537_measures__less,axiom,
% 0.35/0.59 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 0.35/0.59 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_less
% 0.35/0.59 thf(fact_3538_measures__lesseq,axiom,
% 0.35/0.59 ! [F2: code_integer > nat,X: code_integer,Y: code_integer,Fs: list_C4705013386053401436er_nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ Fs ) )
% 0.35/0.59 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_lesseq
% 0.35/0.59 thf(fact_3539_measures__lesseq,axiom,
% 0.35/0.59 ! [F2: product_prod_nat_nat > nat,X: product_prod_nat_nat,Y: product_prod_nat_nat,Fs: list_P9162950289778280392at_nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ Fs ) )
% 0.35/0.59 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_lesseq
% 0.35/0.59 thf(fact_3540_measures__lesseq,axiom,
% 0.35/0.59 ! [F2: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Fs: list_s9130966667114977576at_nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ Fs ) )
% 0.35/0.59 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_lesseq
% 0.35/0.59 thf(fact_3541_measures__lesseq,axiom,
% 0.35/0.59 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) )
% 0.35/0.59 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_lesseq
% 0.35/0.59 thf(fact_3542_measures__lesseq,axiom,
% 0.35/0.59 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 0.35/0.59 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) )
% 0.35/0.59 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % measures_lesseq
% 0.35/0.59 thf(fact_3543_set__replicate__Suc,axiom,
% 0.35/0.59 ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.59 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 0.35/0.59 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_Suc
% 0.35/0.59 thf(fact_3544_set__replicate__Suc,axiom,
% 0.35/0.59 ! [N: nat,X: nat] :
% 0.35/0.59 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 0.35/0.59 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_Suc
% 0.35/0.59 thf(fact_3545_set__replicate__Suc,axiom,
% 0.35/0.59 ! [N: nat,X: int] :
% 0.35/0.59 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 0.35/0.59 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_Suc
% 0.35/0.59 thf(fact_3546_set__replicate__Suc,axiom,
% 0.35/0.59 ! [N: nat,X: real] :
% 0.35/0.59 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 0.35/0.59 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_Suc
% 0.35/0.59 thf(fact_3547_set__replicate__conv__if,axiom,
% 0.35/0.59 ! [N: nat,X: vEBT_VEBT] :
% 0.35/0.59 ( ( ( N = zero_zero_nat )
% 0.35/0.59 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.35/0.59 = bot_bo8194388402131092736T_VEBT ) )
% 0.35/0.59 & ( ( N != zero_zero_nat )
% 0.35/0.59 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 0.35/0.59 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_conv_if
% 0.35/0.59 thf(fact_3548_set__replicate__conv__if,axiom,
% 0.35/0.59 ! [N: nat,X: nat] :
% 0.35/0.59 ( ( ( N = zero_zero_nat )
% 0.35/0.59 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.35/0.59 = bot_bot_set_nat ) )
% 0.35/0.59 & ( ( N != zero_zero_nat )
% 0.35/0.59 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 0.35/0.59 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_conv_if
% 0.35/0.59 thf(fact_3549_set__replicate__conv__if,axiom,
% 0.35/0.59 ! [N: nat,X: int] :
% 0.35/0.59 ( ( ( N = zero_zero_nat )
% 0.35/0.59 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.35/0.59 = bot_bot_set_int ) )
% 0.35/0.59 & ( ( N != zero_zero_nat )
% 0.35/0.59 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 0.35/0.59 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_conv_if
% 0.35/0.59 thf(fact_3550_set__replicate__conv__if,axiom,
% 0.35/0.59 ! [N: nat,X: real] :
% 0.35/0.59 ( ( ( N = zero_zero_nat )
% 0.35/0.59 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.35/0.59 = bot_bot_set_real ) )
% 0.35/0.59 & ( ( N != zero_zero_nat )
% 0.35/0.59 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 0.35/0.59 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_replicate_conv_if
% 0.35/0.59 thf(fact_3551_Cons__replicate__eq,axiom,
% 0.35/0.59 ! [X: nat,Xs2: list_nat,N: nat,Y: nat] :
% 0.35/0.59 ( ( ( cons_nat @ X @ Xs2 )
% 0.35/0.59 = ( replicate_nat @ N @ Y ) )
% 0.35/0.59 = ( ( X = Y )
% 0.35/0.59 & ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 & ( Xs2
% 0.35/0.59 = ( replicate_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ X ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Cons_replicate_eq
% 0.35/0.59 thf(fact_3552_Cons__replicate__eq,axiom,
% 0.35/0.59 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 0.35/0.59 ( ( ( cons_VEBT_VEBT @ X @ Xs2 )
% 0.35/0.59 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 0.35/0.59 = ( ( X = Y )
% 0.35/0.59 & ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 & ( Xs2
% 0.35/0.59 = ( replicate_VEBT_VEBT @ ( minus_minus_nat @ N @ one_one_nat ) @ X ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Cons_replicate_eq
% 0.35/0.59 thf(fact_3553_divmod__step__eq,axiom,
% 0.35/0.59 ! [L: num,R3: nat,Q2: nat] :
% 0.35/0.59 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 0.35/0.59 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 0.35/0.59 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 0.35/0.59 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 0.35/0.59 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 0.35/0.59 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divmod_step_eq
% 0.35/0.59 thf(fact_3554_divmod__step__eq,axiom,
% 0.35/0.59 ! [L: num,R3: int,Q2: int] :
% 0.35/0.59 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 0.35/0.59 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.59 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 0.35/0.59 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 0.35/0.59 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.59 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divmod_step_eq
% 0.35/0.59 thf(fact_3555_divmod__step__eq,axiom,
% 0.35/0.59 ! [L: num,R3: code_integer,Q2: code_integer] :
% 0.35/0.59 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 0.35/0.59 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 0.35/0.59 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 0.35/0.59 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 0.35/0.59 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 0.35/0.59 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divmod_step_eq
% 0.35/0.59 thf(fact_3556_mintlistlength,axiom,
% 0.35/0.59 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.35/0.59 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.35/0.59 => ( ( Mi != Ma )
% 0.35/0.59 => ( ( ord_less_nat @ Mi @ Ma )
% 0.35/0.59 & ? [M: nat] :
% 0.35/0.59 ( ( ( some_nat @ M )
% 0.35/0.59 = ( vEBT_vebt_mint @ Summary ) )
% 0.35/0.59 & ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mintlistlength
% 0.35/0.59 thf(fact_3557_insert__correct,axiom,
% 0.35/0.59 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.59 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.59 => ( ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.35/0.59 = ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % insert_correct
% 0.35/0.59 thf(fact_3558_insert__corr,axiom,
% 0.35/0.59 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.59 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.59 => ( ( sup_sup_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.35/0.59 = ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % insert_corr
% 0.35/0.59 thf(fact_3559_inrange,axiom,
% 0.35/0.59 ! [T: vEBT_VEBT,N: nat] :
% 0.35/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.59 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inrange
% 0.35/0.59 thf(fact_3560_nat__bit__induct,axiom,
% 0.35/0.59 ! [P2: nat > $o,N: nat] :
% 0.35/0.59 ( ( P2 @ zero_zero_nat )
% 0.35/0.59 => ( ! [N3: nat] :
% 0.35/0.59 ( ( P2 @ N3 )
% 0.35/0.59 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.59 => ( P2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.35/0.59 => ( ! [N3: nat] :
% 0.35/0.59 ( ( P2 @ N3 )
% 0.35/0.59 => ( P2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 0.35/0.59 => ( P2 @ N ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nat_bit_induct
% 0.35/0.59 thf(fact_3561_nat__induct2,axiom,
% 0.35/0.59 ! [P2: nat > $o,N: nat] :
% 0.35/0.59 ( ( P2 @ zero_zero_nat )
% 0.35/0.59 => ( ( P2 @ one_one_nat )
% 0.35/0.59 => ( ! [N3: nat] :
% 0.35/0.59 ( ( P2 @ N3 )
% 0.35/0.59 => ( P2 @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.59 => ( P2 @ N ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nat_induct2
% 0.35/0.59 thf(fact_3562_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.59 != zero_zero_nat )
% 0.35/0.59 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 0.35/0.59 != zero_zero_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % exp_not_zero_imp_exp_diff_not_zero
% 0.35/0.59 thf(fact_3563_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.59 != zero_zero_int )
% 0.35/0.59 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 0.35/0.59 != zero_zero_int ) ) ).
% 0.35/0.59
% 0.35/0.59 % exp_not_zero_imp_exp_diff_not_zero
% 0.35/0.59 thf(fact_3564_exp__add__not__zero__imp__left,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 0.35/0.59 != zero_zero_nat )
% 0.35/0.59 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 0.35/0.59 != zero_zero_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % exp_add_not_zero_imp_left
% 0.35/0.59 thf(fact_3565_exp__add__not__zero__imp__left,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 0.35/0.59 != zero_zero_int )
% 0.35/0.59 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 0.35/0.59 != zero_zero_int ) ) ).
% 0.35/0.59
% 0.35/0.59 % exp_add_not_zero_imp_left
% 0.35/0.59 thf(fact_3566_pow__sum,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.59 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % pow_sum
% 0.35/0.59 thf(fact_3567_power__minus__is__div,axiom,
% 0.35/0.59 ! [B: nat,A: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.59 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 0.35/0.59 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_minus_is_div
% 0.35/0.59 thf(fact_3568_bits__div__by__0,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.35/0.59 = zero_zero_nat ) ).
% 0.35/0.59
% 0.35/0.59 % bits_div_by_0
% 0.35/0.59 thf(fact_3569_bits__div__by__0,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( divide_divide_int @ A @ zero_zero_int )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % bits_div_by_0
% 0.35/0.59 thf(fact_3570_bits__div__0,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.35/0.59 = zero_zero_nat ) ).
% 0.35/0.59
% 0.35/0.59 % bits_div_0
% 0.35/0.59 thf(fact_3571_bits__div__0,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( divide_divide_int @ zero_zero_int @ A )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % bits_div_0
% 0.35/0.59 thf(fact_3572_div__by__0,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.35/0.59 = zero_zero_complex ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_0
% 0.35/0.59 thf(fact_3573_div__by__0,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( divide_divide_real @ A @ zero_zero_real )
% 0.35/0.59 = zero_zero_real ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_0
% 0.35/0.59 thf(fact_3574_div__by__0,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.35/0.59 = zero_zero_rat ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_0
% 0.35/0.59 thf(fact_3575_div__by__0,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 0.35/0.59 = zero_zero_nat ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_0
% 0.35/0.59 thf(fact_3576_div__by__0,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( divide_divide_int @ A @ zero_zero_int )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_0
% 0.35/0.59 thf(fact_3577_div__0,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 0.35/0.59 = zero_zero_complex ) ).
% 0.35/0.59
% 0.35/0.59 % div_0
% 0.35/0.59 thf(fact_3578_div__0,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( divide_divide_real @ zero_zero_real @ A )
% 0.35/0.59 = zero_zero_real ) ).
% 0.35/0.59
% 0.35/0.59 % div_0
% 0.35/0.59 thf(fact_3579_div__0,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 0.35/0.59 = zero_zero_rat ) ).
% 0.35/0.59
% 0.35/0.59 % div_0
% 0.35/0.59 thf(fact_3580_div__0,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 0.35/0.59 = zero_zero_nat ) ).
% 0.35/0.59
% 0.35/0.59 % div_0
% 0.35/0.59 thf(fact_3581_div__0,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( divide_divide_int @ zero_zero_int @ A )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % div_0
% 0.35/0.59 thf(fact_3582_division__ring__divide__zero,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 0.35/0.59 = zero_zero_complex ) ).
% 0.35/0.59
% 0.35/0.59 % division_ring_divide_zero
% 0.35/0.59 thf(fact_3583_division__ring__divide__zero,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( divide_divide_real @ A @ zero_zero_real )
% 0.35/0.59 = zero_zero_real ) ).
% 0.35/0.59
% 0.35/0.59 % division_ring_divide_zero
% 0.35/0.59 thf(fact_3584_division__ring__divide__zero,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 0.35/0.59 = zero_zero_rat ) ).
% 0.35/0.59
% 0.35/0.59 % division_ring_divide_zero
% 0.35/0.59 thf(fact_3585_divide__cancel__right,axiom,
% 0.35/0.59 ! [A: complex,C2: complex,B: complex] :
% 0.35/0.59 ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 0.35/0.59 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.59 = ( ( C2 = zero_zero_complex )
% 0.35/0.59 | ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_cancel_right
% 0.35/0.59 thf(fact_3586_divide__cancel__right,axiom,
% 0.35/0.59 ! [A: real,C2: real,B: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ A @ C2 )
% 0.35/0.59 = ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( C2 = zero_zero_real )
% 0.35/0.59 | ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_cancel_right
% 0.35/0.59 thf(fact_3587_divide__cancel__right,axiom,
% 0.35/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ A @ C2 )
% 0.35/0.59 = ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( C2 = zero_zero_rat )
% 0.35/0.59 | ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_cancel_right
% 0.35/0.59 thf(fact_3588_divide__cancel__left,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( ( divide1717551699836669952omplex @ C2 @ A )
% 0.35/0.59 = ( divide1717551699836669952omplex @ C2 @ B ) )
% 0.35/0.59 = ( ( C2 = zero_zero_complex )
% 0.35/0.59 | ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_cancel_left
% 0.35/0.59 thf(fact_3589_divide__cancel__left,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ C2 @ A )
% 0.35/0.59 = ( divide_divide_real @ C2 @ B ) )
% 0.35/0.59 = ( ( C2 = zero_zero_real )
% 0.35/0.59 | ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_cancel_left
% 0.35/0.59 thf(fact_3590_divide__cancel__left,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ C2 @ A )
% 0.35/0.59 = ( divide_divide_rat @ C2 @ B ) )
% 0.35/0.59 = ( ( C2 = zero_zero_rat )
% 0.35/0.59 | ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_cancel_left
% 0.35/0.59 thf(fact_3591_divide__eq__0__iff,axiom,
% 0.35/0.59 ! [A: complex,B: complex] :
% 0.35/0.59 ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.35/0.59 = zero_zero_complex )
% 0.35/0.59 = ( ( A = zero_zero_complex )
% 0.35/0.59 | ( B = zero_zero_complex ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_0_iff
% 0.35/0.59 thf(fact_3592_divide__eq__0__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ A @ B )
% 0.35/0.59 = zero_zero_real )
% 0.35/0.59 = ( ( A = zero_zero_real )
% 0.35/0.59 | ( B = zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_0_iff
% 0.35/0.59 thf(fact_3593_divide__eq__0__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ A @ B )
% 0.35/0.59 = zero_zero_rat )
% 0.35/0.59 = ( ( A = zero_zero_rat )
% 0.35/0.59 | ( B = zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_0_iff
% 0.35/0.59 thf(fact_3594_times__divide__eq__right,axiom,
% 0.35/0.59 ! [A: complex,B: complex,C2: complex] :
% 0.35/0.59 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_eq_right
% 0.35/0.59 thf(fact_3595_times__divide__eq__right,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_eq_right
% 0.35/0.59 thf(fact_3596_times__divide__eq__right,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_eq_right
% 0.35/0.59 thf(fact_3597_divide__divide__eq__right,axiom,
% 0.35/0.59 ! [A: complex,B: complex,C2: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_right
% 0.35/0.59 thf(fact_3598_divide__divide__eq__right,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_right
% 0.35/0.59 thf(fact_3599_divide__divide__eq__right,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_right
% 0.35/0.59 thf(fact_3600_divide__divide__eq__left,axiom,
% 0.35/0.59 ! [A: complex,B: complex,C2: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C2 )
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_left
% 0.35/0.59 thf(fact_3601_divide__divide__eq__left,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C2 )
% 0.35/0.59 = ( divide_divide_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_left
% 0.35/0.59 thf(fact_3602_divide__divide__eq__left,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C2 )
% 0.35/0.59 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_left
% 0.35/0.59 thf(fact_3603_times__divide__eq__left,axiom,
% 0.35/0.59 ! [B: complex,C2: complex,A: complex] :
% 0.35/0.59 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C2 ) @ A )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_eq_left
% 0.35/0.59 thf(fact_3604_times__divide__eq__left,axiom,
% 0.35/0.59 ! [B: real,C2: real,A: real] :
% 0.35/0.59 ( ( times_times_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 0.35/0.59 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_eq_left
% 0.35/0.59 thf(fact_3605_times__divide__eq__left,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.59 ( ( times_times_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_eq_left
% 0.35/0.59 thf(fact_3606_div__by__1,axiom,
% 0.35/0.59 ! [A: code_integer] :
% 0.35/0.59 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_1
% 0.35/0.59 thf(fact_3607_div__by__1,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_1
% 0.35/0.59 thf(fact_3608_div__by__1,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( divide_divide_real @ A @ one_one_real )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_1
% 0.35/0.59 thf(fact_3609_div__by__1,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ A @ one_one_rat )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_1
% 0.35/0.59 thf(fact_3610_div__by__1,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ A @ one_one_nat )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_1
% 0.35/0.59 thf(fact_3611_div__by__1,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( divide_divide_int @ A @ one_one_int )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_1
% 0.35/0.59 thf(fact_3612_atLeastAtMost__iff,axiom,
% 0.35/0.59 ! [I2: set_nat,L: set_nat,U: set_nat] :
% 0.35/0.59 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 0.35/0.59 = ( ( ord_less_eq_set_nat @ L @ I2 )
% 0.35/0.59 & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_iff
% 0.35/0.59 thf(fact_3613_atLeastAtMost__iff,axiom,
% 0.35/0.59 ! [I2: rat,L: rat,U: rat] :
% 0.35/0.59 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.35/0.59 = ( ( ord_less_eq_rat @ L @ I2 )
% 0.35/0.59 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_iff
% 0.35/0.59 thf(fact_3614_atLeastAtMost__iff,axiom,
% 0.35/0.59 ! [I2: num,L: num,U: num] :
% 0.35/0.59 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 0.35/0.59 = ( ( ord_less_eq_num @ L @ I2 )
% 0.35/0.59 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_iff
% 0.35/0.59 thf(fact_3615_atLeastAtMost__iff,axiom,
% 0.35/0.59 ! [I2: nat,L: nat,U: nat] :
% 0.35/0.59 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.35/0.59 = ( ( ord_less_eq_nat @ L @ I2 )
% 0.35/0.59 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_iff
% 0.35/0.59 thf(fact_3616_atLeastAtMost__iff,axiom,
% 0.35/0.59 ! [I2: int,L: int,U: int] :
% 0.35/0.59 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.35/0.59 = ( ( ord_less_eq_int @ L @ I2 )
% 0.35/0.59 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_iff
% 0.35/0.59 thf(fact_3617_atLeastAtMost__iff,axiom,
% 0.35/0.59 ! [I2: real,L: real,U: real] :
% 0.35/0.59 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L @ U ) )
% 0.35/0.59 = ( ( ord_less_eq_real @ L @ I2 )
% 0.35/0.59 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_iff
% 0.35/0.59 thf(fact_3618_Icc__eq__Icc,axiom,
% 0.35/0.59 ! [L: set_nat,H: set_nat,L3: set_nat,H3: set_nat] :
% 0.35/0.59 ( ( ( set_or4548717258645045905et_nat @ L @ H )
% 0.35/0.59 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 0.35/0.59 = ( ( ( L = L3 )
% 0.35/0.59 & ( H = H3 ) )
% 0.35/0.59 | ( ~ ( ord_less_eq_set_nat @ L @ H )
% 0.35/0.59 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Icc_eq_Icc
% 0.35/0.59 thf(fact_3619_Icc__eq__Icc,axiom,
% 0.35/0.59 ! [L: rat,H: rat,L3: rat,H3: rat] :
% 0.35/0.59 ( ( ( set_or633870826150836451st_rat @ L @ H )
% 0.35/0.59 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 0.35/0.59 = ( ( ( L = L3 )
% 0.35/0.59 & ( H = H3 ) )
% 0.35/0.59 | ( ~ ( ord_less_eq_rat @ L @ H )
% 0.35/0.59 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Icc_eq_Icc
% 0.35/0.59 thf(fact_3620_Icc__eq__Icc,axiom,
% 0.35/0.59 ! [L: num,H: num,L3: num,H3: num] :
% 0.35/0.59 ( ( ( set_or7049704709247886629st_num @ L @ H )
% 0.35/0.59 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 0.35/0.59 = ( ( ( L = L3 )
% 0.35/0.59 & ( H = H3 ) )
% 0.35/0.59 | ( ~ ( ord_less_eq_num @ L @ H )
% 0.35/0.59 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Icc_eq_Icc
% 0.35/0.59 thf(fact_3621_Icc__eq__Icc,axiom,
% 0.35/0.59 ! [L: nat,H: nat,L3: nat,H3: nat] :
% 0.35/0.59 ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 0.35/0.59 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 0.35/0.59 = ( ( ( L = L3 )
% 0.35/0.59 & ( H = H3 ) )
% 0.35/0.59 | ( ~ ( ord_less_eq_nat @ L @ H )
% 0.35/0.59 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Icc_eq_Icc
% 0.35/0.59 thf(fact_3622_Icc__eq__Icc,axiom,
% 0.35/0.59 ! [L: int,H: int,L3: int,H3: int] :
% 0.35/0.59 ( ( ( set_or1266510415728281911st_int @ L @ H )
% 0.35/0.59 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 0.35/0.59 = ( ( ( L = L3 )
% 0.35/0.59 & ( H = H3 ) )
% 0.35/0.59 | ( ~ ( ord_less_eq_int @ L @ H )
% 0.35/0.59 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Icc_eq_Icc
% 0.35/0.59 thf(fact_3623_Icc__eq__Icc,axiom,
% 0.35/0.59 ! [L: real,H: real,L3: real,H3: real] :
% 0.35/0.59 ( ( ( set_or1222579329274155063t_real @ L @ H )
% 0.35/0.59 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 0.35/0.59 = ( ( ( L = L3 )
% 0.35/0.59 & ( H = H3 ) )
% 0.35/0.59 | ( ~ ( ord_less_eq_real @ L @ H )
% 0.35/0.59 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Icc_eq_Icc
% 0.35/0.59 thf(fact_3624_finite__atLeastAtMost,axiom,
% 0.35/0.59 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.35/0.59
% 0.35/0.59 % finite_atLeastAtMost
% 0.35/0.59 thf(fact_3625_nonzero__mult__div__cancel__left,axiom,
% 0.35/0.59 ! [A: complex,B: complex] :
% 0.35/0.59 ( ( A != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 0.35/0.59 = B ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_left
% 0.35/0.59 thf(fact_3626_nonzero__mult__div__cancel__left,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( A != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 0.35/0.59 = B ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_left
% 0.35/0.59 thf(fact_3627_nonzero__mult__div__cancel__left,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( A != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 0.35/0.59 = B ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_left
% 0.35/0.59 thf(fact_3628_nonzero__mult__div__cancel__left,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( A != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 0.35/0.59 = B ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_left
% 0.35/0.59 thf(fact_3629_nonzero__mult__div__cancel__left,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( A != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 0.35/0.59 = B ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_left
% 0.35/0.59 thf(fact_3630_nonzero__mult__div__cancel__right,axiom,
% 0.35/0.59 ! [B: complex,A: complex] :
% 0.35/0.59 ( ( B != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_right
% 0.35/0.59 thf(fact_3631_nonzero__mult__div__cancel__right,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( B != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_right
% 0.35/0.59 thf(fact_3632_nonzero__mult__div__cancel__right,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( B != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_right
% 0.35/0.59 thf(fact_3633_nonzero__mult__div__cancel__right,axiom,
% 0.35/0.59 ! [B: nat,A: nat] :
% 0.35/0.59 ( ( B != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_right
% 0.35/0.59 thf(fact_3634_nonzero__mult__div__cancel__right,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( B != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_div_cancel_right
% 0.35/0.59 thf(fact_3635_mult__divide__mult__cancel__left__if,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( ( C2 = zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 0.35/0.59 = zero_zero_complex ) )
% 0.35/0.59 & ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_divide_mult_cancel_left_if
% 0.35/0.59 thf(fact_3636_mult__divide__mult__cancel__left__if,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( ( C2 = zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.35/0.59 = zero_zero_real ) )
% 0.35/0.59 & ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_divide_mult_cancel_left_if
% 0.35/0.59 thf(fact_3637_mult__divide__mult__cancel__left__if,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ( C2 = zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.35/0.59 = zero_zero_rat ) )
% 0.35/0.59 & ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_divide_mult_cancel_left_if
% 0.35/0.59 thf(fact_3638_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_left
% 0.35/0.59 thf(fact_3639_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_left
% 0.35/0.59 thf(fact_3640_nonzero__mult__divide__mult__cancel__left,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_left
% 0.35/0.59 thf(fact_3641_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ B @ C2 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_left2
% 0.35/0.59 thf(fact_3642_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_left2
% 0.35/0.59 thf(fact_3643_nonzero__mult__divide__mult__cancel__left2,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_left2
% 0.35/0.59 thf(fact_3644_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ B @ C2 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_right
% 0.35/0.59 thf(fact_3645_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_right
% 0.35/0.59 thf(fact_3646_nonzero__mult__divide__mult__cancel__right,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_right
% 0.35/0.59 thf(fact_3647_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ C2 @ B ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_right2
% 0.35/0.59 thf(fact_3648_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_right2
% 0.35/0.59 thf(fact_3649_nonzero__mult__divide__mult__cancel__right2,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_mult_divide_mult_cancel_right2
% 0.35/0.59 thf(fact_3650_div__self,axiom,
% 0.35/0.59 ! [A: code_integer] :
% 0.35/0.59 ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.59 => ( ( divide6298287555418463151nteger @ A @ A )
% 0.35/0.59 = one_one_Code_integer ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_self
% 0.35/0.59 thf(fact_3651_div__self,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( A != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ A @ A )
% 0.35/0.59 = one_one_complex ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_self
% 0.35/0.59 thf(fact_3652_div__self,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( A != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ A @ A )
% 0.35/0.59 = one_one_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_self
% 0.35/0.59 thf(fact_3653_div__self,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( A != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ A @ A )
% 0.35/0.59 = one_one_rat ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_self
% 0.35/0.59 thf(fact_3654_div__self,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( A != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ A @ A )
% 0.35/0.59 = one_one_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_self
% 0.35/0.59 thf(fact_3655_div__self,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( A != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ A @ A )
% 0.35/0.59 = one_one_int ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_self
% 0.35/0.59 thf(fact_3656_zero__eq__1__divide__iff,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( zero_zero_real
% 0.35/0.59 = ( divide_divide_real @ one_one_real @ A ) )
% 0.35/0.59 = ( A = zero_zero_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_eq_1_divide_iff
% 0.35/0.59 thf(fact_3657_zero__eq__1__divide__iff,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( zero_zero_rat
% 0.35/0.59 = ( divide_divide_rat @ one_one_rat @ A ) )
% 0.35/0.59 = ( A = zero_zero_rat ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_eq_1_divide_iff
% 0.35/0.59 thf(fact_3658_one__divide__eq__0__iff,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ one_one_real @ A )
% 0.35/0.59 = zero_zero_real )
% 0.35/0.59 = ( A = zero_zero_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % one_divide_eq_0_iff
% 0.35/0.59 thf(fact_3659_one__divide__eq__0__iff,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 0.35/0.59 = zero_zero_rat )
% 0.35/0.59 = ( A = zero_zero_rat ) ) ).
% 0.35/0.59
% 0.35/0.59 % one_divide_eq_0_iff
% 0.35/0.59 thf(fact_3660_eq__divide__eq__1,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( one_one_real
% 0.35/0.59 = ( divide_divide_real @ B @ A ) )
% 0.35/0.59 = ( ( A != zero_zero_real )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_1
% 0.35/0.59 thf(fact_3661_eq__divide__eq__1,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( one_one_rat
% 0.35/0.59 = ( divide_divide_rat @ B @ A ) )
% 0.35/0.59 = ( ( A != zero_zero_rat )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_1
% 0.35/0.59 thf(fact_3662_divide__eq__eq__1,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ B @ A )
% 0.35/0.59 = one_one_real )
% 0.35/0.59 = ( ( A != zero_zero_real )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_1
% 0.35/0.59 thf(fact_3663_divide__eq__eq__1,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ B @ A )
% 0.35/0.59 = one_one_rat )
% 0.35/0.59 = ( ( A != zero_zero_rat )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_1
% 0.35/0.59 thf(fact_3664_divide__self__if,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( ( A = zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ A @ A )
% 0.35/0.59 = zero_zero_complex ) )
% 0.35/0.59 & ( ( A != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ A @ A )
% 0.35/0.59 = one_one_complex ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_self_if
% 0.35/0.59 thf(fact_3665_divide__self__if,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ( A = zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ A @ A )
% 0.35/0.59 = zero_zero_real ) )
% 0.35/0.59 & ( ( A != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ A @ A )
% 0.35/0.59 = one_one_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_self_if
% 0.35/0.59 thf(fact_3666_divide__self__if,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ( A = zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ A @ A )
% 0.35/0.59 = zero_zero_rat ) )
% 0.35/0.59 & ( ( A != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ A @ A )
% 0.35/0.59 = one_one_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_self_if
% 0.35/0.59 thf(fact_3667_divide__self,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( A != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ A @ A )
% 0.35/0.59 = one_one_complex ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_self
% 0.35/0.59 thf(fact_3668_divide__self,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( A != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ A @ A )
% 0.35/0.59 = one_one_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_self
% 0.35/0.59 thf(fact_3669_divide__self,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( A != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ A @ A )
% 0.35/0.59 = one_one_rat ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_self
% 0.35/0.59 thf(fact_3670_one__eq__divide__iff,axiom,
% 0.35/0.59 ! [A: complex,B: complex] :
% 0.35/0.59 ( ( one_one_complex
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.59 = ( ( B != zero_zero_complex )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % one_eq_divide_iff
% 0.35/0.59 thf(fact_3671_one__eq__divide__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( one_one_real
% 0.35/0.59 = ( divide_divide_real @ A @ B ) )
% 0.35/0.59 = ( ( B != zero_zero_real )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % one_eq_divide_iff
% 0.35/0.59 thf(fact_3672_one__eq__divide__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( one_one_rat
% 0.35/0.59 = ( divide_divide_rat @ A @ B ) )
% 0.35/0.59 = ( ( B != zero_zero_rat )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % one_eq_divide_iff
% 0.35/0.59 thf(fact_3673_divide__eq__1__iff,axiom,
% 0.35/0.59 ! [A: complex,B: complex] :
% 0.35/0.59 ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.35/0.59 = one_one_complex )
% 0.35/0.59 = ( ( B != zero_zero_complex )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_1_iff
% 0.35/0.59 thf(fact_3674_divide__eq__1__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ A @ B )
% 0.35/0.59 = one_one_real )
% 0.35/0.59 = ( ( B != zero_zero_real )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_1_iff
% 0.35/0.59 thf(fact_3675_divide__eq__1__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ A @ B )
% 0.35/0.59 = one_one_rat )
% 0.35/0.59 = ( ( B != zero_zero_rat )
% 0.35/0.59 & ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_1_iff
% 0.35/0.59 thf(fact_3676_atLeastatMost__empty__iff,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat] :
% 0.35/0.59 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 0.35/0.59 = bot_bot_set_set_nat )
% 0.35/0.59 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff
% 0.35/0.59 thf(fact_3677_atLeastatMost__empty__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 0.35/0.59 = bot_bot_set_rat )
% 0.35/0.59 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff
% 0.35/0.59 thf(fact_3678_atLeastatMost__empty__iff,axiom,
% 0.35/0.59 ! [A: num,B: num] :
% 0.35/0.59 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 0.35/0.59 = bot_bot_set_num )
% 0.35/0.59 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff
% 0.35/0.59 thf(fact_3679_atLeastatMost__empty__iff,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.35/0.59 = bot_bot_set_nat )
% 0.35/0.59 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff
% 0.35/0.59 thf(fact_3680_atLeastatMost__empty__iff,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.35/0.59 = bot_bot_set_int )
% 0.35/0.59 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff
% 0.35/0.59 thf(fact_3681_atLeastatMost__empty__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.35/0.59 = bot_bot_set_real )
% 0.35/0.59 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff
% 0.35/0.59 thf(fact_3682_atLeastatMost__empty__iff2,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat] :
% 0.35/0.59 ( ( bot_bot_set_set_nat
% 0.35/0.59 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff2
% 0.35/0.59 thf(fact_3683_atLeastatMost__empty__iff2,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( bot_bot_set_rat
% 0.35/0.59 = ( set_or633870826150836451st_rat @ A @ B ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff2
% 0.35/0.59 thf(fact_3684_atLeastatMost__empty__iff2,axiom,
% 0.35/0.59 ! [A: num,B: num] :
% 0.35/0.59 ( ( bot_bot_set_num
% 0.35/0.59 = ( set_or7049704709247886629st_num @ A @ B ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff2
% 0.35/0.59 thf(fact_3685_atLeastatMost__empty__iff2,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( bot_bot_set_nat
% 0.35/0.59 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff2
% 0.35/0.59 thf(fact_3686_atLeastatMost__empty__iff2,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( bot_bot_set_int
% 0.35/0.59 = ( set_or1266510415728281911st_int @ A @ B ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff2
% 0.35/0.59 thf(fact_3687_atLeastatMost__empty__iff2,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( bot_bot_set_real
% 0.35/0.59 = ( set_or1222579329274155063t_real @ A @ B ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty_iff2
% 0.35/0.59 thf(fact_3688_atLeastatMost__subset__iff,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat,C2: set_nat,D: set_nat] :
% 0.35/0.59 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C2 @ D ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_set_nat @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_subset_iff
% 0.35/0.59 thf(fact_3689_atLeastatMost__subset__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.35/0.59 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_subset_iff
% 0.35/0.59 thf(fact_3690_atLeastatMost__subset__iff,axiom,
% 0.35/0.59 ! [A: num,B: num,C2: num,D: num] :
% 0.35/0.59 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_num @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_num @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_subset_iff
% 0.35/0.59 thf(fact_3691_atLeastatMost__subset__iff,axiom,
% 0.35/0.59 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_nat @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_subset_iff
% 0.35/0.59 thf(fact_3692_atLeastatMost__subset__iff,axiom,
% 0.35/0.59 ! [A: int,B: int,C2: int,D: int] :
% 0.35/0.59 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_int @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_subset_iff
% 0.35/0.59 thf(fact_3693_atLeastatMost__subset__iff,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real,D: real] :
% 0.35/0.59 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C2 @ D ) )
% 0.35/0.59 = ( ~ ( ord_less_eq_real @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_real @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_subset_iff
% 0.35/0.59 thf(fact_3694_atLeastatMost__empty,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ B @ A )
% 0.35/0.59 => ( ( set_or633870826150836451st_rat @ A @ B )
% 0.35/0.59 = bot_bot_set_rat ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty
% 0.35/0.59 thf(fact_3695_atLeastatMost__empty,axiom,
% 0.35/0.59 ! [B: num,A: num] :
% 0.35/0.59 ( ( ord_less_num @ B @ A )
% 0.35/0.59 => ( ( set_or7049704709247886629st_num @ A @ B )
% 0.35/0.59 = bot_bot_set_num ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty
% 0.35/0.59 thf(fact_3696_atLeastatMost__empty,axiom,
% 0.35/0.59 ! [B: nat,A: nat] :
% 0.35/0.59 ( ( ord_less_nat @ B @ A )
% 0.35/0.59 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.35/0.59 = bot_bot_set_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty
% 0.35/0.59 thf(fact_3697_atLeastatMost__empty,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( ord_less_int @ B @ A )
% 0.35/0.59 => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.35/0.59 = bot_bot_set_int ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty
% 0.35/0.59 thf(fact_3698_atLeastatMost__empty,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ B @ A )
% 0.35/0.59 => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.35/0.59 = bot_bot_set_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_empty
% 0.35/0.59 thf(fact_3699_infinite__Icc__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 0.35/0.59 = ( ord_less_rat @ A @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % infinite_Icc_iff
% 0.35/0.59 thf(fact_3700_infinite__Icc__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 0.35/0.59 = ( ord_less_real @ A @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % infinite_Icc_iff
% 0.35/0.59 thf(fact_3701_atLeastAtMost__singleton,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( set_or1269000886237332187st_nat @ A @ A )
% 0.35/0.59 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton
% 0.35/0.59 thf(fact_3702_atLeastAtMost__singleton,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( set_or1266510415728281911st_int @ A @ A )
% 0.35/0.59 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton
% 0.35/0.59 thf(fact_3703_atLeastAtMost__singleton,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( set_or1222579329274155063t_real @ A @ A )
% 0.35/0.59 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton
% 0.35/0.59 thf(fact_3704_atLeastAtMost__singleton__iff,axiom,
% 0.35/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.59 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.35/0.59 = ( insert_nat @ C2 @ bot_bot_set_nat ) )
% 0.35/0.59 = ( ( A = B )
% 0.35/0.59 & ( B = C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton_iff
% 0.35/0.59 thf(fact_3705_atLeastAtMost__singleton__iff,axiom,
% 0.35/0.59 ! [A: int,B: int,C2: int] :
% 0.35/0.59 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 0.35/0.59 = ( insert_int @ C2 @ bot_bot_set_int ) )
% 0.35/0.59 = ( ( A = B )
% 0.35/0.59 & ( B = C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton_iff
% 0.35/0.59 thf(fact_3706_atLeastAtMost__singleton__iff,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 0.35/0.59 = ( insert_real @ C2 @ bot_bot_set_real ) )
% 0.35/0.59 = ( ( A = B )
% 0.35/0.59 & ( B = C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton_iff
% 0.35/0.59 thf(fact_3707_nat__mult__div__cancel__disj,axiom,
% 0.35/0.59 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.59 ( ( ( K2 = zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.35/0.59 = zero_zero_nat ) )
% 0.35/0.59 & ( ( K2 != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.35/0.59 = ( divide_divide_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nat_mult_div_cancel_disj
% 0.35/0.59 thf(fact_3708_zero__le__divide__1__iff,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.35/0.59 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_le_divide_1_iff
% 0.35/0.59 thf(fact_3709_zero__le__divide__1__iff,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.35/0.59 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_le_divide_1_iff
% 0.35/0.59 thf(fact_3710_divide__le__0__1__iff,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.35/0.59 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_0_1_iff
% 0.35/0.59 thf(fact_3711_divide__le__0__1__iff,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.35/0.59 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_0_1_iff
% 0.35/0.59 thf(fact_3712_zero__less__divide__1__iff,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 0.35/0.59 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_less_divide_1_iff
% 0.35/0.59 thf(fact_3713_zero__less__divide__1__iff,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 0.35/0.59 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_less_divide_1_iff
% 0.35/0.59 thf(fact_3714_less__divide__eq__1__pos,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.35/0.59 = ( ord_less_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_1_pos
% 0.35/0.59 thf(fact_3715_less__divide__eq__1__pos,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.35/0.59 = ( ord_less_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_1_pos
% 0.35/0.59 thf(fact_3716_less__divide__eq__1__neg,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.35/0.59 = ( ord_less_real @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_1_neg
% 0.35/0.59 thf(fact_3717_less__divide__eq__1__neg,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.35/0.59 = ( ord_less_rat @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_1_neg
% 0.35/0.59 thf(fact_3718_divide__less__eq__1__pos,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.35/0.59 = ( ord_less_real @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_1_pos
% 0.35/0.59 thf(fact_3719_divide__less__eq__1__pos,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.35/0.59 = ( ord_less_rat @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_1_pos
% 0.35/0.59 thf(fact_3720_divide__less__eq__1__neg,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.35/0.59 = ( ord_less_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_1_neg
% 0.35/0.59 thf(fact_3721_divide__less__eq__1__neg,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.35/0.59 = ( ord_less_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_1_neg
% 0.35/0.59 thf(fact_3722_divide__less__0__1__iff,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 0.35/0.59 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_0_1_iff
% 0.35/0.59 thf(fact_3723_divide__less__0__1__iff,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 0.35/0.59 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_0_1_iff
% 0.35/0.59 thf(fact_3724_divide__le__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [B: real,W2: num,A: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 0.35/0.59 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_numeral1(1)
% 0.35/0.59 thf(fact_3725_divide__le__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [B: rat,W2: num,A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 0.35/0.59 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_numeral1(1)
% 0.35/0.59 thf(fact_3726_le__divide__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [A: real,B: real,W2: num] :
% 0.35/0.59 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.59 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_numeral1(1)
% 0.35/0.59 thf(fact_3727_le__divide__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [A: rat,B: rat,W2: num] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.59 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_numeral1(1)
% 0.35/0.59 thf(fact_3728_divide__eq__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [B: complex,W2: num,A: complex] :
% 0.35/0.59 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.59 = A )
% 0.35/0.59 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 0.35/0.59 != zero_zero_complex )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 0.35/0.59 & ( ( ( numera6690914467698888265omplex @ W2 )
% 0.35/0.59 = zero_zero_complex )
% 0.35/0.59 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_numeral1(1)
% 0.35/0.59 thf(fact_3729_divide__eq__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [B: real,W2: num,A: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.59 = A )
% 0.35/0.59 = ( ( ( ( numeral_numeral_real @ W2 )
% 0.35/0.59 != zero_zero_real )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.35/0.59 & ( ( ( numeral_numeral_real @ W2 )
% 0.35/0.59 = zero_zero_real )
% 0.35/0.59 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_numeral1(1)
% 0.35/0.59 thf(fact_3730_divide__eq__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [B: rat,W2: num,A: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.59 = A )
% 0.35/0.59 = ( ( ( ( numeral_numeral_rat @ W2 )
% 0.35/0.59 != zero_zero_rat )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.35/0.59 & ( ( ( numeral_numeral_rat @ W2 )
% 0.35/0.59 = zero_zero_rat )
% 0.35/0.59 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_numeral1(1)
% 0.35/0.59 thf(fact_3731_eq__divide__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [A: complex,B: complex,W2: num] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.35/0.59 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 0.35/0.59 != zero_zero_complex )
% 0.35/0.59 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( ( numera6690914467698888265omplex @ W2 )
% 0.35/0.59 = zero_zero_complex )
% 0.35/0.59 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_numeral1(1)
% 0.35/0.59 thf(fact_3732_eq__divide__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [A: real,B: real,W2: num] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.59 = ( ( ( ( numeral_numeral_real @ W2 )
% 0.35/0.59 != zero_zero_real )
% 0.35/0.59 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( ( numeral_numeral_real @ W2 )
% 0.35/0.59 = zero_zero_real )
% 0.35/0.59 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_numeral1(1)
% 0.35/0.59 thf(fact_3733_eq__divide__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [A: rat,B: rat,W2: num] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.59 = ( ( ( ( numeral_numeral_rat @ W2 )
% 0.35/0.59 != zero_zero_rat )
% 0.35/0.59 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( ( numeral_numeral_rat @ W2 )
% 0.35/0.59 = zero_zero_rat )
% 0.35/0.59 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_numeral1(1)
% 0.35/0.59 thf(fact_3734_less__divide__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [A: real,B: real,W2: num] :
% 0.35/0.59 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.59 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_numeral1(1)
% 0.35/0.59 thf(fact_3735_less__divide__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [A: rat,B: rat,W2: num] :
% 0.35/0.59 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.59 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_numeral1(1)
% 0.35/0.59 thf(fact_3736_divide__less__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [B: real,W2: num,A: real] :
% 0.35/0.59 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 0.35/0.59 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_numeral1(1)
% 0.35/0.59 thf(fact_3737_divide__less__eq__numeral1_I1_J,axiom,
% 0.35/0.59 ! [B: rat,W2: num,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 0.35/0.59 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_numeral1(1)
% 0.35/0.59 thf(fact_3738_nonzero__divide__mult__cancel__left,axiom,
% 0.35/0.59 ! [A: complex,B: complex] :
% 0.35/0.59 ( ( A != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_mult_cancel_left
% 0.35/0.59 thf(fact_3739_nonzero__divide__mult__cancel__left,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( A != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 0.35/0.59 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_mult_cancel_left
% 0.35/0.59 thf(fact_3740_nonzero__divide__mult__cancel__left,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( A != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 0.35/0.59 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_mult_cancel_left
% 0.35/0.59 thf(fact_3741_nonzero__divide__mult__cancel__right,axiom,
% 0.35/0.59 ! [B: complex,A: complex] :
% 0.35/0.59 ( ( B != zero_zero_complex )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_mult_cancel_right
% 0.35/0.59 thf(fact_3742_nonzero__divide__mult__cancel__right,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( B != zero_zero_real )
% 0.35/0.59 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 0.35/0.59 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_mult_cancel_right
% 0.35/0.59 thf(fact_3743_nonzero__divide__mult__cancel__right,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( B != zero_zero_rat )
% 0.35/0.59 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 0.35/0.59 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_mult_cancel_right
% 0.35/0.59 thf(fact_3744_numeral__le__real__of__nat__iff,axiom,
% 0.35/0.59 ! [N: num,M2: nat] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M2 ) )
% 0.35/0.59 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % numeral_le_real_of_nat_iff
% 0.35/0.59 thf(fact_3745_card__atLeastAtMost,axiom,
% 0.35/0.59 ! [L: nat,U: nat] :
% 0.35/0.59 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.35/0.59 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 0.35/0.59
% 0.35/0.59 % card_atLeastAtMost
% 0.35/0.59 thf(fact_3746_le__divide__eq__1__pos,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.35/0.59 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_1_pos
% 0.35/0.59 thf(fact_3747_le__divide__eq__1__pos,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.35/0.59 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_1_pos
% 0.35/0.59 thf(fact_3748_le__divide__eq__1__neg,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.35/0.59 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_1_neg
% 0.35/0.59 thf(fact_3749_le__divide__eq__1__neg,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.35/0.59 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_1_neg
% 0.35/0.59 thf(fact_3750_divide__le__eq__1__pos,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.35/0.59 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_1_pos
% 0.35/0.59 thf(fact_3751_divide__le__eq__1__pos,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.35/0.59 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_1_pos
% 0.35/0.59 thf(fact_3752_divide__le__eq__1__neg,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.35/0.59 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_1_neg
% 0.35/0.59 thf(fact_3753_divide__le__eq__1__neg,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.35/0.59 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_1_neg
% 0.35/0.59 thf(fact_3754_bits__1__div__2,axiom,
% 0.35/0.59 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.59 = zero_z3403309356797280102nteger ) ).
% 0.35/0.59
% 0.35/0.59 % bits_1_div_2
% 0.35/0.59 thf(fact_3755_bits__1__div__2,axiom,
% 0.35/0.59 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59 = zero_zero_nat ) ).
% 0.35/0.59
% 0.35/0.59 % bits_1_div_2
% 0.35/0.59 thf(fact_3756_bits__1__div__2,axiom,
% 0.35/0.59 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % bits_1_div_2
% 0.35/0.59 thf(fact_3757_decr__mult__lemma,axiom,
% 0.35/0.59 ! [D: int,P2: int > $o,K2: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ D )
% 0.35/0.59 => ( ! [X3: int] :
% 0.35/0.59 ( ( P2 @ X3 )
% 0.35/0.59 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 0.35/0.59 => ! [X5: int] :
% 0.35/0.59 ( ( P2 @ X5 )
% 0.35/0.59 => ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % decr_mult_lemma
% 0.35/0.59 thf(fact_3758_minusinfinity,axiom,
% 0.35/0.59 ! [D: int,P1: int > $o,P2: int > $o] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ D )
% 0.35/0.59 => ( ! [X3: int,K: int] :
% 0.35/0.59 ( ( P1 @ X3 )
% 0.35/0.59 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 0.35/0.59 => ( ? [Z5: int] :
% 0.35/0.59 ! [X3: int] :
% 0.35/0.59 ( ( ord_less_int @ X3 @ Z5 )
% 0.35/0.59 => ( ( P2 @ X3 )
% 0.35/0.59 = ( P1 @ X3 ) ) )
% 0.35/0.59 => ( ? [X_1: int] : ( P1 @ X_1 )
% 0.35/0.59 => ? [X_12: int] : ( P2 @ X_12 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % minusinfinity
% 0.35/0.59 thf(fact_3759_plusinfinity,axiom,
% 0.35/0.59 ! [D: int,P6: int > $o,P2: int > $o] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ D )
% 0.35/0.59 => ( ! [X3: int,K: int] :
% 0.35/0.59 ( ( P6 @ X3 )
% 0.35/0.59 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 0.35/0.59 => ( ? [Z5: int] :
% 0.35/0.59 ! [X3: int] :
% 0.35/0.59 ( ( ord_less_int @ Z5 @ X3 )
% 0.35/0.59 => ( ( P2 @ X3 )
% 0.35/0.59 = ( P6 @ X3 ) ) )
% 0.35/0.59 => ( ? [X_1: int] : ( P6 @ X_1 )
% 0.35/0.59 => ? [X_12: int] : ( P2 @ X_12 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % plusinfinity
% 0.35/0.59 thf(fact_3760_times__int__code_I2_J,axiom,
% 0.35/0.59 ! [L: int] :
% 0.35/0.59 ( ( times_times_int @ zero_zero_int @ L )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % times_int_code(2)
% 0.35/0.59 thf(fact_3761_times__int__code_I1_J,axiom,
% 0.35/0.59 ! [K2: int] :
% 0.35/0.59 ( ( times_times_int @ K2 @ zero_zero_int )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % times_int_code(1)
% 0.35/0.59 thf(fact_3762_pos__zmult__eq__1__iff,axiom,
% 0.35/0.59 ! [M2: int,N: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ M2 )
% 0.35/0.59 => ( ( ( times_times_int @ M2 @ N )
% 0.35/0.59 = one_one_int )
% 0.35/0.59 = ( ( M2 = one_one_int )
% 0.35/0.59 & ( N = one_one_int ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_zmult_eq_1_iff
% 0.35/0.59 thf(fact_3763_zmult__zless__mono2,axiom,
% 0.35/0.59 ! [I2: int,J2: int,K2: int] :
% 0.35/0.59 ( ( ord_less_int @ I2 @ J2 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.59 => ( ord_less_int @ ( times_times_int @ K2 @ I2 ) @ ( times_times_int @ K2 @ J2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zmult_zless_mono2
% 0.35/0.59 thf(fact_3764_unique__quotient__lemma__neg,axiom,
% 0.35/0.59 ! [B: int,Q4: int,R5: int,Q2: int,R3: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 0.35/0.59 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_int @ B @ R3 )
% 0.35/0.59 => ( ( ord_less_int @ B @ R5 )
% 0.35/0.59 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % unique_quotient_lemma_neg
% 0.35/0.59 thf(fact_3765_unique__quotient__lemma,axiom,
% 0.35/0.59 ! [B: int,Q4: int,R5: int,Q2: int,R3: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 0.35/0.59 => ( ( ord_less_int @ R5 @ B )
% 0.35/0.59 => ( ( ord_less_int @ R3 @ B )
% 0.35/0.59 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % unique_quotient_lemma
% 0.35/0.59 thf(fact_3766_zdiv__mono2__neg__lemma,axiom,
% 0.35/0.59 ! [B: int,Q2: int,R3: int,B2: int,Q4: int,R5: int] :
% 0.35/0.59 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 )
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 0.35/0.59 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_int @ R3 @ B )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.35/0.59 => ( ( ord_less_eq_int @ B2 @ B )
% 0.35/0.59 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_mono2_neg_lemma
% 0.35/0.59 thf(fact_3767_zdiv__mono2__lemma,axiom,
% 0.35/0.59 ! [B: int,Q2: int,R3: int,B2: int,Q4: int,R5: int] :
% 0.35/0.59 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 )
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 0.35/0.59 => ( ( ord_less_int @ R5 @ B2 )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.35/0.59 => ( ( ord_less_eq_int @ B2 @ B )
% 0.35/0.59 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_mono2_lemma
% 0.35/0.59 thf(fact_3768_q__pos__lemma,axiom,
% 0.35/0.59 ! [B2: int,Q4: int,R5: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 0.35/0.59 => ( ( ord_less_int @ R5 @ B2 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.35/0.59 => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % q_pos_lemma
% 0.35/0.59 thf(fact_3769_incr__mult__lemma,axiom,
% 0.35/0.59 ! [D: int,P2: int > $o,K2: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ D )
% 0.35/0.59 => ( ! [X3: int] :
% 0.35/0.59 ( ( P2 @ X3 )
% 0.35/0.59 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 0.35/0.59 => ! [X5: int] :
% 0.35/0.59 ( ( P2 @ X5 )
% 0.35/0.59 => ( P2 @ ( plus_plus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % incr_mult_lemma
% 0.35/0.59 thf(fact_3770_ivl__disj__un__two__touch_I4_J,axiom,
% 0.35/0.59 ! [L: rat,M2: rat,U: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ L @ M2 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ M2 @ U )
% 0.35/0.59 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or633870826150836451st_rat @ M2 @ U ) )
% 0.35/0.59 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % ivl_disj_un_two_touch(4)
% 0.35/0.59 thf(fact_3771_ivl__disj__un__two__touch_I4_J,axiom,
% 0.35/0.59 ! [L: num,M2: num,U: num] :
% 0.35/0.59 ( ( ord_less_eq_num @ L @ M2 )
% 0.35/0.59 => ( ( ord_less_eq_num @ M2 @ U )
% 0.35/0.59 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or7049704709247886629st_num @ M2 @ U ) )
% 0.35/0.59 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % ivl_disj_un_two_touch(4)
% 0.35/0.59 thf(fact_3772_ivl__disj__un__two__touch_I4_J,axiom,
% 0.35/0.59 ! [L: nat,M2: nat,U: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ L @ M2 )
% 0.35/0.59 => ( ( ord_less_eq_nat @ M2 @ U )
% 0.35/0.59 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or1269000886237332187st_nat @ M2 @ U ) )
% 0.35/0.59 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % ivl_disj_un_two_touch(4)
% 0.35/0.59 thf(fact_3773_ivl__disj__un__two__touch_I4_J,axiom,
% 0.35/0.59 ! [L: int,M2: int,U: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ L @ M2 )
% 0.35/0.59 => ( ( ord_less_eq_int @ M2 @ U )
% 0.35/0.59 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or1266510415728281911st_int @ M2 @ U ) )
% 0.35/0.59 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % ivl_disj_un_two_touch(4)
% 0.35/0.59 thf(fact_3774_ivl__disj__un__two__touch_I4_J,axiom,
% 0.35/0.59 ! [L: real,M2: real,U: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ L @ M2 )
% 0.35/0.59 => ( ( ord_less_eq_real @ M2 @ U )
% 0.35/0.59 => ( ( sup_sup_set_real @ ( set_or1222579329274155063t_real @ L @ M2 ) @ ( set_or1222579329274155063t_real @ M2 @ U ) )
% 0.35/0.59 = ( set_or1222579329274155063t_real @ L @ U ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % ivl_disj_un_two_touch(4)
% 0.35/0.59 thf(fact_3775_int__distrib_I2_J,axiom,
% 0.35/0.59 ! [W2: int,Z1: int,Z22: int] :
% 0.35/0.59 ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_distrib(2)
% 0.35/0.59 thf(fact_3776_int__distrib_I1_J,axiom,
% 0.35/0.59 ! [Z1: int,Z22: int,W2: int] :
% 0.35/0.59 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_distrib(1)
% 0.35/0.59 thf(fact_3777_int__distrib_I3_J,axiom,
% 0.35/0.59 ! [Z1: int,Z22: int,W2: int] :
% 0.35/0.59 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 0.35/0.59 = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_distrib(3)
% 0.35/0.59 thf(fact_3778_int__distrib_I4_J,axiom,
% 0.35/0.59 ! [W2: int,Z1: int,Z22: int] :
% 0.35/0.59 ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 0.35/0.59 = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_distrib(4)
% 0.35/0.59 thf(fact_3779_divide__divide__eq__left_H,axiom,
% 0.35/0.59 ! [A: complex,B: complex,C2: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C2 )
% 0.35/0.59 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C2 @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_left'
% 0.35/0.59 thf(fact_3780_divide__divide__eq__left_H,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C2 )
% 0.35/0.59 = ( divide_divide_real @ A @ ( times_times_real @ C2 @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_left'
% 0.35/0.59 thf(fact_3781_divide__divide__eq__left_H,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C2 )
% 0.35/0.59 = ( divide_divide_rat @ A @ ( times_times_rat @ C2 @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_eq_left'
% 0.35/0.59 thf(fact_3782_divide__divide__times__eq,axiom,
% 0.35/0.59 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W2 ) @ ( times_times_complex @ Y @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_times_eq
% 0.35/0.59 thf(fact_3783_divide__divide__times__eq,axiom,
% 0.35/0.59 ! [X: real,Y: real,Z3: real,W2: real] :
% 0.35/0.59 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 0.35/0.59 = ( divide_divide_real @ ( times_times_real @ X @ W2 ) @ ( times_times_real @ Y @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_times_eq
% 0.35/0.59 thf(fact_3784_divide__divide__times__eq,axiom,
% 0.35/0.59 ! [X: rat,Y: rat,Z3: rat,W2: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z3 @ W2 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( times_times_rat @ X @ W2 ) @ ( times_times_rat @ Y @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_divide_times_eq
% 0.35/0.59 thf(fact_3785_times__divide__times__eq,axiom,
% 0.35/0.59 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 0.35/0.59 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ Y @ W2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_times_eq
% 0.35/0.59 thf(fact_3786_times__divide__times__eq,axiom,
% 0.35/0.59 ! [X: real,Y: real,Z3: real,W2: real] :
% 0.35/0.59 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 0.35/0.59 = ( divide_divide_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ W2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_times_eq
% 0.35/0.59 thf(fact_3787_times__divide__times__eq,axiom,
% 0.35/0.59 ! [X: rat,Y: rat,Z3: rat,W2: rat] :
% 0.35/0.59 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z3 @ W2 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ W2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % times_divide_times_eq
% 0.35/0.59 thf(fact_3788_atLeastatMost__psubset__iff,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat,C2: set_nat,D: set_nat] :
% 0.35/0.59 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C2 @ D ) )
% 0.35/0.59 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_set_nat @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_set_nat @ B @ D )
% 0.35/0.59 & ( ( ord_less_set_nat @ C2 @ A )
% 0.35/0.59 | ( ord_less_set_nat @ B @ D ) ) ) )
% 0.35/0.59 & ( ord_less_eq_set_nat @ C2 @ D ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_psubset_iff
% 0.35/0.59 thf(fact_3789_atLeastatMost__psubset__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.35/0.59 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D ) )
% 0.35/0.59 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_rat @ B @ D )
% 0.35/0.59 & ( ( ord_less_rat @ C2 @ A )
% 0.35/0.59 | ( ord_less_rat @ B @ D ) ) ) )
% 0.35/0.59 & ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_psubset_iff
% 0.35/0.59 thf(fact_3790_atLeastatMost__psubset__iff,axiom,
% 0.35/0.59 ! [A: num,B: num,C2: num,D: num] :
% 0.35/0.59 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D ) )
% 0.35/0.59 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_num @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_num @ B @ D )
% 0.35/0.59 & ( ( ord_less_num @ C2 @ A )
% 0.35/0.59 | ( ord_less_num @ B @ D ) ) ) )
% 0.35/0.59 & ( ord_less_eq_num @ C2 @ D ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_psubset_iff
% 0.35/0.59 thf(fact_3791_atLeastatMost__psubset__iff,axiom,
% 0.35/0.59 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.35/0.59 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D ) )
% 0.35/0.59 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_nat @ B @ D )
% 0.35/0.59 & ( ( ord_less_nat @ C2 @ A )
% 0.35/0.59 | ( ord_less_nat @ B @ D ) ) ) )
% 0.35/0.59 & ( ord_less_eq_nat @ C2 @ D ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_psubset_iff
% 0.35/0.59 thf(fact_3792_atLeastatMost__psubset__iff,axiom,
% 0.35/0.59 ! [A: int,B: int,C2: int,D: int] :
% 0.35/0.59 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D ) )
% 0.35/0.59 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_int @ B @ D )
% 0.35/0.59 & ( ( ord_less_int @ C2 @ A )
% 0.35/0.59 | ( ord_less_int @ B @ D ) ) ) )
% 0.35/0.59 & ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_psubset_iff
% 0.35/0.59 thf(fact_3793_atLeastatMost__psubset__iff,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real,D: real] :
% 0.35/0.59 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C2 @ D ) )
% 0.35/0.59 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 0.35/0.59 | ( ( ord_less_eq_real @ C2 @ A )
% 0.35/0.59 & ( ord_less_eq_real @ B @ D )
% 0.35/0.59 & ( ( ord_less_real @ C2 @ A )
% 0.35/0.59 | ( ord_less_real @ B @ D ) ) ) )
% 0.35/0.59 & ( ord_less_eq_real @ C2 @ D ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastatMost_psubset_iff
% 0.35/0.59 thf(fact_3794_infinite__Icc,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ B )
% 0.35/0.59 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % infinite_Icc
% 0.35/0.59 thf(fact_3795_infinite__Icc,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ B )
% 0.35/0.59 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % infinite_Icc
% 0.35/0.59 thf(fact_3796_atLeastAtMost__singleton_H,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( A = B )
% 0.35/0.59 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 0.35/0.59 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton'
% 0.35/0.59 thf(fact_3797_atLeastAtMost__singleton_H,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( A = B )
% 0.35/0.59 => ( ( set_or1266510415728281911st_int @ A @ B )
% 0.35/0.59 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton'
% 0.35/0.59 thf(fact_3798_atLeastAtMost__singleton_H,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( A = B )
% 0.35/0.59 => ( ( set_or1222579329274155063t_real @ A @ B )
% 0.35/0.59 = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_singleton'
% 0.35/0.59 thf(fact_3799_divide__right__mono__neg,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ A @ B )
% 0.35/0.59 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( divide_divide_real @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_right_mono_neg
% 0.35/0.59 thf(fact_3800_divide__right__mono__neg,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( divide_divide_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_right_mono_neg
% 0.35/0.59 thf(fact_3801_divide__nonpos__nonpos,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_nonpos
% 0.35/0.59 thf(fact_3802_divide__nonpos__nonpos,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_nonpos
% 0.35/0.59 thf(fact_3803_divide__nonpos__nonneg,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_nonneg
% 0.35/0.59 thf(fact_3804_divide__nonpos__nonneg,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_nonneg
% 0.35/0.59 thf(fact_3805_divide__nonneg__nonpos,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_nonpos
% 0.35/0.59 thf(fact_3806_divide__nonneg__nonpos,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_nonpos
% 0.35/0.59 thf(fact_3807_divide__nonneg__nonneg,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_nonneg
% 0.35/0.59 thf(fact_3808_divide__nonneg__nonneg,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_nonneg
% 0.35/0.59 thf(fact_3809_zero__le__divide__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.59 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 0.35/0.59 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_le_divide_iff
% 0.35/0.59 thf(fact_3810_zero__le__divide__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.59 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 0.35/0.59 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_le_divide_iff
% 0.35/0.59 thf(fact_3811_divide__right__mono,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ A @ B )
% 0.35/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_right_mono
% 0.35/0.59 thf(fact_3812_divide__right__mono,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_right_mono
% 0.35/0.59 thf(fact_3813_divide__le__0__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.35/0.59 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 0.35/0.59 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_0_iff
% 0.35/0.59 thf(fact_3814_divide__le__0__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.35/0.59 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 0.35/0.59 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_0_iff
% 0.35/0.59 thf(fact_3815_divide__strict__right__mono__neg,axiom,
% 0.35/0.59 ! [B: real,A: real,C2: real] :
% 0.35/0.59 ( ( ord_less_real @ B @ A )
% 0.35/0.59 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_right_mono_neg
% 0.35/0.59 thf(fact_3816_divide__strict__right__mono__neg,axiom,
% 0.35/0.59 ! [B: rat,A: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_rat @ B @ A )
% 0.35/0.59 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_right_mono_neg
% 0.35/0.59 thf(fact_3817_divide__strict__right__mono,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ B )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_right_mono
% 0.35/0.59 thf(fact_3818_divide__strict__right__mono,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ B )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_right_mono
% 0.35/0.59 thf(fact_3819_zero__less__divide__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_real @ zero_zero_real @ B ) )
% 0.35/0.59 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_less_divide_iff
% 0.35/0.59 thf(fact_3820_zero__less__divide__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 0.35/0.59 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zero_less_divide_iff
% 0.35/0.59 thf(fact_3821_divide__less__cancel,axiom,
% 0.35/0.59 ! [A: real,C2: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_real @ A @ B ) )
% 0.35/0.59 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ B @ A ) )
% 0.35/0.59 & ( C2 != zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_cancel
% 0.35/0.59 thf(fact_3822_divide__less__cancel,axiom,
% 0.35/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_rat @ A @ B ) )
% 0.35/0.59 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ B @ A ) )
% 0.35/0.59 & ( C2 != zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_cancel
% 0.35/0.59 thf(fact_3823_divide__less__0__iff,axiom,
% 0.35/0.59 ! [A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_real @ B @ zero_zero_real ) )
% 0.35/0.59 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_0_iff
% 0.35/0.59 thf(fact_3824_divide__less__0__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 0.35/0.59 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_0_iff
% 0.35/0.59 thf(fact_3825_divide__pos__pos,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_pos_pos
% 0.35/0.59 thf(fact_3826_divide__pos__pos,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_pos_pos
% 0.35/0.59 thf(fact_3827_divide__pos__neg,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_pos_neg
% 0.35/0.59 thf(fact_3828_divide__pos__neg,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_pos_neg
% 0.35/0.59 thf(fact_3829_divide__neg__pos,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_neg_pos
% 0.35/0.59 thf(fact_3830_divide__neg__pos,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_neg_pos
% 0.35/0.59 thf(fact_3831_divide__neg__neg,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_neg_neg
% 0.35/0.59 thf(fact_3832_divide__neg__neg,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_rat @ X @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_neg_neg
% 0.35/0.59 thf(fact_3833_all__nat__less,axiom,
% 0.35/0.59 ! [N: nat,P2: nat > $o] :
% 0.35/0.59 ( ( ! [M6: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ M6 @ N )
% 0.35/0.59 => ( P2 @ M6 ) ) )
% 0.35/0.59 = ( ! [X4: nat] :
% 0.35/0.59 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.59 => ( P2 @ X4 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % all_nat_less
% 0.35/0.59 thf(fact_3834_ex__nat__less,axiom,
% 0.35/0.59 ! [N: nat,P2: nat > $o] :
% 0.35/0.59 ( ( ? [M6: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ M6 @ N )
% 0.35/0.59 & ( P2 @ M6 ) ) )
% 0.35/0.59 = ( ? [X4: nat] :
% 0.35/0.59 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.59 & ( P2 @ X4 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % ex_nat_less
% 0.35/0.59 thf(fact_3835_frac__eq__eq,axiom,
% 0.35/0.59 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 0.35/0.59 ( ( Y != zero_zero_complex )
% 0.35/0.59 => ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 0.35/0.59 = ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 0.35/0.59 = ( ( times_times_complex @ X @ Z3 )
% 0.35/0.59 = ( times_times_complex @ W2 @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_eq_eq
% 0.35/0.59 thf(fact_3836_frac__eq__eq,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real,W2: real] :
% 0.35/0.59 ( ( Y != zero_zero_real )
% 0.35/0.59 => ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( ( divide_divide_real @ X @ Y )
% 0.35/0.59 = ( divide_divide_real @ W2 @ Z3 ) )
% 0.35/0.59 = ( ( times_times_real @ X @ Z3 )
% 0.35/0.59 = ( times_times_real @ W2 @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_eq_eq
% 0.35/0.59 thf(fact_3837_frac__eq__eq,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 0.35/0.59 ( ( Y != zero_zero_rat )
% 0.35/0.59 => ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( ( divide_divide_rat @ X @ Y )
% 0.35/0.59 = ( divide_divide_rat @ W2 @ Z3 ) )
% 0.35/0.59 = ( ( times_times_rat @ X @ Z3 )
% 0.35/0.59 = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_eq_eq
% 0.35/0.59 thf(fact_3838_divide__eq__eq,axiom,
% 0.35/0.59 ! [B: complex,C2: complex,A: complex] :
% 0.35/0.59 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 0.35/0.59 = A )
% 0.35/0.59 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_complex @ A @ C2 ) ) )
% 0.35/0.59 & ( ( C2 = zero_zero_complex )
% 0.35/0.59 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq
% 0.35/0.59 thf(fact_3839_divide__eq__eq,axiom,
% 0.35/0.59 ! [B: real,C2: real,A: real] :
% 0.35/0.59 ( ( ( divide_divide_real @ B @ C2 )
% 0.35/0.59 = A )
% 0.35/0.59 = ( ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_real @ A @ C2 ) ) )
% 0.35/0.59 & ( ( C2 = zero_zero_real )
% 0.35/0.59 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq
% 0.35/0.59 thf(fact_3840_divide__eq__eq,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.59 ( ( ( divide_divide_rat @ B @ C2 )
% 0.35/0.59 = A )
% 0.35/0.59 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.59 & ( ( C2 = zero_zero_rat )
% 0.35/0.59 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq
% 0.35/0.59 thf(fact_3841_eq__divide__eq,axiom,
% 0.35/0.59 ! [A: complex,B: complex,C2: complex] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( times_times_complex @ A @ C2 )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( C2 = zero_zero_complex )
% 0.35/0.59 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq
% 0.35/0.59 thf(fact_3842_eq__divide__eq,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( times_times_real @ A @ C2 )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( C2 = zero_zero_real )
% 0.35/0.59 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq
% 0.35/0.59 thf(fact_3843_eq__divide__eq,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( times_times_rat @ A @ C2 )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( C2 = zero_zero_rat )
% 0.35/0.59 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq
% 0.35/0.59 thf(fact_3844_divide__eq__imp,axiom,
% 0.35/0.59 ! [C2: complex,B: complex,A: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( B
% 0.35/0.59 = ( times_times_complex @ A @ C2 ) )
% 0.35/0.59 => ( ( divide1717551699836669952omplex @ B @ C2 )
% 0.35/0.59 = A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_imp
% 0.35/0.59 thf(fact_3845_divide__eq__imp,axiom,
% 0.35/0.59 ! [C2: real,B: real,A: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( B
% 0.35/0.59 = ( times_times_real @ A @ C2 ) )
% 0.35/0.59 => ( ( divide_divide_real @ B @ C2 )
% 0.35/0.59 = A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_imp
% 0.35/0.59 thf(fact_3846_divide__eq__imp,axiom,
% 0.35/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( B
% 0.35/0.59 = ( times_times_rat @ A @ C2 ) )
% 0.35/0.59 => ( ( divide_divide_rat @ B @ C2 )
% 0.35/0.59 = A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_imp
% 0.35/0.59 thf(fact_3847_eq__divide__imp,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( ( times_times_complex @ A @ C2 )
% 0.35/0.59 = B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( divide1717551699836669952omplex @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_imp
% 0.35/0.59 thf(fact_3848_eq__divide__imp,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( ( times_times_real @ A @ C2 )
% 0.35/0.59 = B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_imp
% 0.35/0.59 thf(fact_3849_eq__divide__imp,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( ( times_times_rat @ A @ C2 )
% 0.35/0.59 = B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_imp
% 0.35/0.59 thf(fact_3850_nonzero__divide__eq__eq,axiom,
% 0.35/0.59 ! [C2: complex,B: complex,A: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 0.35/0.59 = A )
% 0.35/0.59 = ( B
% 0.35/0.59 = ( times_times_complex @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_eq_eq
% 0.35/0.59 thf(fact_3851_nonzero__divide__eq__eq,axiom,
% 0.35/0.59 ! [C2: real,B: real,A: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( ( divide_divide_real @ B @ C2 )
% 0.35/0.59 = A )
% 0.35/0.59 = ( B
% 0.35/0.59 = ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_eq_eq
% 0.35/0.59 thf(fact_3852_nonzero__divide__eq__eq,axiom,
% 0.35/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( ( divide_divide_rat @ B @ C2 )
% 0.35/0.59 = A )
% 0.35/0.59 = ( B
% 0.35/0.59 = ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_divide_eq_eq
% 0.35/0.59 thf(fact_3853_nonzero__eq__divide__eq,axiom,
% 0.35/0.59 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( A
% 0.35/0.59 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.59 = ( ( times_times_complex @ A @ C2 )
% 0.35/0.59 = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_eq_divide_eq
% 0.35/0.59 thf(fact_3854_nonzero__eq__divide__eq,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( A
% 0.35/0.59 = ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( times_times_real @ A @ C2 )
% 0.35/0.59 = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_eq_divide_eq
% 0.35/0.59 thf(fact_3855_nonzero__eq__divide__eq,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( A
% 0.35/0.59 = ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( times_times_rat @ A @ C2 )
% 0.35/0.59 = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonzero_eq_divide_eq
% 0.35/0.59 thf(fact_3856_right__inverse__eq,axiom,
% 0.35/0.59 ! [B: complex,A: complex] :
% 0.35/0.59 ( ( B != zero_zero_complex )
% 0.35/0.59 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.35/0.59 = one_one_complex )
% 0.35/0.59 = ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % right_inverse_eq
% 0.35/0.59 thf(fact_3857_right__inverse__eq,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( B != zero_zero_real )
% 0.35/0.59 => ( ( ( divide_divide_real @ A @ B )
% 0.35/0.59 = one_one_real )
% 0.35/0.59 = ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % right_inverse_eq
% 0.35/0.59 thf(fact_3858_right__inverse__eq,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( B != zero_zero_rat )
% 0.35/0.59 => ( ( ( divide_divide_rat @ A @ B )
% 0.35/0.59 = one_one_rat )
% 0.35/0.59 = ( A = B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % right_inverse_eq
% 0.35/0.59 thf(fact_3859_divide__numeral__1,axiom,
% 0.35/0.59 ! [A: complex] :
% 0.35/0.59 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % divide_numeral_1
% 0.35/0.59 thf(fact_3860_divide__numeral__1,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % divide_numeral_1
% 0.35/0.59 thf(fact_3861_divide__numeral__1,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 0.35/0.59 = A ) ).
% 0.35/0.59
% 0.35/0.59 % divide_numeral_1
% 0.35/0.59 thf(fact_3862_div__positive,axiom,
% 0.35/0.59 ! [B: nat,A: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.59 => ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.59 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_positive
% 0.35/0.59 thf(fact_3863_div__positive,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59 => ( ( ord_less_eq_int @ B @ A )
% 0.35/0.59 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_positive
% 0.35/0.59 thf(fact_3864_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.59 => ( ( ord_less_nat @ A @ B )
% 0.35/0.59 => ( ( divide_divide_nat @ A @ B )
% 0.35/0.59 = zero_zero_nat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % unique_euclidean_semiring_numeral_class.div_less
% 0.35/0.59 thf(fact_3865_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59 => ( ( ord_less_int @ A @ B )
% 0.35/0.59 => ( ( divide_divide_int @ A @ B )
% 0.35/0.59 = zero_zero_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % unique_euclidean_semiring_numeral_class.div_less
% 0.35/0.59 thf(fact_3866_divide__nonpos__pos,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_pos
% 0.35/0.59 thf(fact_3867_divide__nonpos__pos,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_pos
% 0.35/0.59 thf(fact_3868_divide__nonpos__neg,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_neg
% 0.35/0.59 thf(fact_3869_divide__nonpos__neg,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonpos_neg
% 0.35/0.59 thf(fact_3870_divide__nonneg__pos,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_pos
% 0.35/0.59 thf(fact_3871_divide__nonneg__pos,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_pos
% 0.35/0.59 thf(fact_3872_divide__nonneg__neg,axiom,
% 0.35/0.59 ! [X: real,Y: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_real @ Y @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_neg
% 0.35/0.59 thf(fact_3873_divide__nonneg__neg,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_nonneg_neg
% 0.35/0.59 thf(fact_3874_divide__le__cancel,axiom,
% 0.35/0.59 ! [A: real,C2: real,B: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_eq_real @ A @ B ) )
% 0.35/0.59 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_cancel
% 0.35/0.59 thf(fact_3875_divide__le__cancel,axiom,
% 0.35/0.59 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_eq_rat @ A @ B ) )
% 0.35/0.59 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_cancel
% 0.35/0.59 thf(fact_3876_frac__less2,axiom,
% 0.35/0.59 ! [X: real,Y: real,W2: real,Z3: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_eq_real @ X @ Y )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 0.35/0.59 => ( ( ord_less_real @ W2 @ Z3 )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_less2
% 0.35/0.59 thf(fact_3877_frac__less2,axiom,
% 0.35/0.59 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_eq_rat @ X @ Y )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.35/0.59 => ( ( ord_less_rat @ W2 @ Z3 )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_less2
% 0.35/0.59 thf(fact_3878_frac__less,axiom,
% 0.35/0.59 ! [X: real,Y: real,W2: real,Z3: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_real @ X @ Y )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 0.35/0.59 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_less
% 0.35/0.59 thf(fact_3879_frac__less,axiom,
% 0.35/0.59 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_rat @ X @ Y )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_less
% 0.35/0.59 thf(fact_3880_frac__le,axiom,
% 0.35/0.59 ! [Y: real,X: real,W2: real,Z3: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ( ord_less_eq_real @ X @ Y )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 0.35/0.59 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_le
% 0.35/0.59 thf(fact_3881_frac__le,axiom,
% 0.35/0.59 ! [Y: rat,X: rat,W2: rat,Z3: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ( ord_less_eq_rat @ X @ Y )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_le
% 0.35/0.59 thf(fact_3882_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.35/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.35/0.59 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.35/0.59 thf(fact_3883_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 0.35/0.59 ! [C2: int,A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.35/0.59 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 0.35/0.59 thf(fact_3884_divide__less__eq,axiom,
% 0.35/0.59 ! [B: real,C2: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq
% 0.35/0.59 thf(fact_3885_divide__less__eq,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq
% 0.35/0.59 thf(fact_3886_less__divide__eq,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq
% 0.35/0.59 thf(fact_3887_less__divide__eq,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq
% 0.35/0.59 thf(fact_3888_neg__divide__less__eq,axiom,
% 0.35/0.59 ! [C2: real,B: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_divide_less_eq
% 0.35/0.59 thf(fact_3889_neg__divide__less__eq,axiom,
% 0.35/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_divide_less_eq
% 0.35/0.59 thf(fact_3890_neg__less__divide__eq,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_less_divide_eq
% 0.35/0.59 thf(fact_3891_neg__less__divide__eq,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_less_divide_eq
% 0.35/0.59 thf(fact_3892_pos__divide__less__eq,axiom,
% 0.35/0.59 ! [C2: real,B: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_divide_less_eq
% 0.35/0.59 thf(fact_3893_pos__divide__less__eq,axiom,
% 0.35/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_divide_less_eq
% 0.35/0.59 thf(fact_3894_pos__less__divide__eq,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_less_divide_eq
% 0.35/0.59 thf(fact_3895_pos__less__divide__eq,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_less_divide_eq
% 0.35/0.59 thf(fact_3896_mult__imp__div__pos__less,axiom,
% 0.35/0.59 ! [Y: real,X: real,Z3: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ( ord_less_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_div_pos_less
% 0.35/0.59 thf(fact_3897_mult__imp__div__pos__less,axiom,
% 0.35/0.59 ! [Y: rat,X: rat,Z3: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_div_pos_less
% 0.35/0.59 thf(fact_3898_mult__imp__less__div__pos,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ( ord_less_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 0.35/0.59 => ( ord_less_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_less_div_pos
% 0.35/0.59 thf(fact_3899_mult__imp__less__div__pos,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ( ord_less_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 0.35/0.59 => ( ord_less_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_less_div_pos
% 0.35/0.59 thf(fact_3900_divide__strict__left__mono,axiom,
% 0.35/0.59 ! [B: real,A: real,C2: real] :
% 0.35/0.59 ( ( ord_less_real @ B @ A )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_left_mono
% 0.35/0.59 thf(fact_3901_divide__strict__left__mono,axiom,
% 0.35/0.59 ! [B: rat,A: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_rat @ B @ A )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_left_mono
% 0.35/0.59 thf(fact_3902_divide__strict__left__mono__neg,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_real @ A @ B )
% 0.35/0.59 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.35/0.59 => ( ord_less_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_left_mono_neg
% 0.35/0.59 thf(fact_3903_divide__strict__left__mono__neg,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_rat @ A @ B )
% 0.35/0.59 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.59 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_strict_left_mono_neg
% 0.35/0.59 thf(fact_3904_less__divide__eq__1,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_real @ A @ B ) )
% 0.35/0.59 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_real @ B @ A ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_1
% 0.35/0.59 thf(fact_3905_less__divide__eq__1,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_rat @ A @ B ) )
% 0.35/0.59 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_1
% 0.35/0.59 thf(fact_3906_divide__less__eq__1,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_real @ B @ A ) )
% 0.35/0.59 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_real @ A @ B ) )
% 0.35/0.59 | ( A = zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_1
% 0.35/0.59 thf(fact_3907_divide__less__eq__1,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_rat @ B @ A ) )
% 0.35/0.59 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_rat @ A @ B ) )
% 0.35/0.59 | ( A = zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_1
% 0.35/0.59 thf(fact_3908_divide__eq__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [B: complex,C2: complex,W2: num] :
% 0.35/0.59 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 0.35/0.59 = ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ( C2 = zero_zero_complex )
% 0.35/0.59 => ( ( numera6690914467698888265omplex @ W2 )
% 0.35/0.59 = zero_zero_complex ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_numeral(1)
% 0.35/0.59 thf(fact_3909_divide__eq__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [B: real,C2: real,W2: num] :
% 0.35/0.59 ( ( ( divide_divide_real @ B @ C2 )
% 0.35/0.59 = ( numeral_numeral_real @ W2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ( C2 = zero_zero_real )
% 0.35/0.59 => ( ( numeral_numeral_real @ W2 )
% 0.35/0.59 = zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_numeral(1)
% 0.35/0.59 thf(fact_3910_divide__eq__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,W2: num] :
% 0.35/0.59 ( ( ( divide_divide_rat @ B @ C2 )
% 0.35/0.59 = ( numeral_numeral_rat @ W2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( B
% 0.35/0.59 = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ( C2 = zero_zero_rat )
% 0.35/0.59 => ( ( numeral_numeral_rat @ W2 )
% 0.35/0.59 = zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_eq_eq_numeral(1)
% 0.35/0.59 thf(fact_3911_eq__divide__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [W2: num,B: complex,C2: complex] :
% 0.35/0.59 ( ( ( numera6690914467698888265omplex @ W2 )
% 0.35/0.59 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.59 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C2 )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( C2 = zero_zero_complex )
% 0.35/0.59 => ( ( numera6690914467698888265omplex @ W2 )
% 0.35/0.59 = zero_zero_complex ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_numeral(1)
% 0.35/0.59 thf(fact_3912_eq__divide__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [W2: num,B: real,C2: real] :
% 0.35/0.59 ( ( ( numeral_numeral_real @ W2 )
% 0.35/0.59 = ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_real )
% 0.35/0.59 => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( C2 = zero_zero_real )
% 0.35/0.59 => ( ( numeral_numeral_real @ W2 )
% 0.35/0.59 = zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_numeral(1)
% 0.35/0.59 thf(fact_3913_eq__divide__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [W2: num,B: rat,C2: rat] :
% 0.35/0.59 ( ( ( numeral_numeral_rat @ W2 )
% 0.35/0.59 = ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.59 => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( C2 = zero_zero_rat )
% 0.35/0.59 => ( ( numeral_numeral_rat @ W2 )
% 0.35/0.59 = zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % eq_divide_eq_numeral(1)
% 0.35/0.59 thf(fact_3914_add__divide__eq__if__simps_I2_J,axiom,
% 0.35/0.59 ! [Z3: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(2)
% 0.35/0.59 thf(fact_3915_add__divide__eq__if__simps_I2_J,axiom,
% 0.35/0.59 ! [Z3: real,A: real,B: real] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 0.35/0.59 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(2)
% 0.35/0.59 thf(fact_3916_add__divide__eq__if__simps_I2_J,axiom,
% 0.35/0.59 ! [Z3: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 0.35/0.59 = B ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 0.35/0.59 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(2)
% 0.35/0.59 thf(fact_3917_add__divide__eq__if__simps_I1_J,axiom,
% 0.35/0.59 ! [Z3: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 0.35/0.59 = A ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(1)
% 0.35/0.59 thf(fact_3918_add__divide__eq__if__simps_I1_J,axiom,
% 0.35/0.59 ! [Z3: real,A: real,B: real] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 0.35/0.59 = A ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 0.35/0.59 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(1)
% 0.35/0.59 thf(fact_3919_add__divide__eq__if__simps_I1_J,axiom,
% 0.35/0.59 ! [Z3: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 0.35/0.59 = A ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(1)
% 0.35/0.59 thf(fact_3920_add__frac__eq,axiom,
% 0.35/0.59 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 0.35/0.59 ( ( Y != zero_zero_complex )
% 0.35/0.59 => ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_frac_eq
% 0.35/0.59 thf(fact_3921_add__frac__eq,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real,W2: real] :
% 0.35/0.59 ( ( Y != zero_zero_real )
% 0.35/0.59 => ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 0.35/0.59 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_frac_eq
% 0.35/0.59 thf(fact_3922_add__frac__eq,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 0.35/0.59 ( ( Y != zero_zero_rat )
% 0.35/0.59 => ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_frac_eq
% 0.35/0.59 thf(fact_3923_add__frac__num,axiom,
% 0.35/0.59 ! [Y: complex,X: complex,Z3: complex] :
% 0.35/0.59 ( ( Y != zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z3 )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_frac_num
% 0.35/0.59 thf(fact_3924_add__frac__num,axiom,
% 0.35/0.59 ! [Y: real,X: real,Z3: real] :
% 0.35/0.59 ( ( Y != zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z3 )
% 0.35/0.59 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_frac_num
% 0.35/0.59 thf(fact_3925_add__frac__num,axiom,
% 0.35/0.59 ! [Y: rat,X: rat,Z3: rat] :
% 0.35/0.59 ( ( Y != zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 )
% 0.35/0.59 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_frac_num
% 0.35/0.59 thf(fact_3926_add__num__frac,axiom,
% 0.35/0.59 ! [Y: complex,Z3: complex,X: complex] :
% 0.35/0.59 ( ( Y != zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ X @ Y ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_num_frac
% 0.35/0.59 thf(fact_3927_add__num__frac,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real] :
% 0.35/0.59 ( ( Y != zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ Z3 @ ( divide_divide_real @ X @ Y ) )
% 0.35/0.59 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_num_frac
% 0.35/0.59 thf(fact_3928_add__num__frac,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat] :
% 0.35/0.59 ( ( Y != zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) )
% 0.35/0.59 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_num_frac
% 0.35/0.59 thf(fact_3929_add__divide__eq__iff,axiom,
% 0.35/0.59 ! [Z3: complex,X: complex,Y: complex] :
% 0.35/0.59 ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_iff
% 0.35/0.59 thf(fact_3930_add__divide__eq__iff,axiom,
% 0.35/0.59 ! [Z3: real,X: real,Y: real] :
% 0.35/0.59 ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 0.35/0.59 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_iff
% 0.35/0.59 thf(fact_3931_add__divide__eq__iff,axiom,
% 0.35/0.59 ! [Z3: rat,X: rat,Y: rat] :
% 0.35/0.59 ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z3 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_iff
% 0.35/0.59 thf(fact_3932_divide__add__eq__iff,axiom,
% 0.35/0.59 ! [Z3: complex,X: complex,Y: complex] :
% 0.35/0.59 ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_add_eq_iff
% 0.35/0.59 thf(fact_3933_divide__add__eq__iff,axiom,
% 0.35/0.59 ! [Z3: real,X: real,Y: real] :
% 0.35/0.59 ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 0.35/0.59 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_add_eq_iff
% 0.35/0.59 thf(fact_3934_divide__add__eq__iff,axiom,
% 0.35/0.59 ! [Z3: rat,X: rat,Y: rat] :
% 0.35/0.59 ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z3 ) @ Y )
% 0.35/0.59 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_add_eq_iff
% 0.35/0.59 thf(fact_3935_add__divide__eq__if__simps_I4_J,axiom,
% 0.35/0.59 ! [Z3: complex,A: complex,B: complex] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_complex )
% 0.35/0.59 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 0.35/0.59 = A ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(4)
% 0.35/0.59 thf(fact_3936_add__divide__eq__if__simps_I4_J,axiom,
% 0.35/0.59 ! [Z3: real,A: real,B: real] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_real )
% 0.35/0.59 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 0.35/0.59 = A ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 0.35/0.59 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(4)
% 0.35/0.59 thf(fact_3937_add__divide__eq__if__simps_I4_J,axiom,
% 0.35/0.59 ! [Z3: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ( Z3 = zero_zero_rat )
% 0.35/0.59 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 0.35/0.59 = A ) )
% 0.35/0.59 & ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % add_divide_eq_if_simps(4)
% 0.35/0.59 thf(fact_3938_diff__frac__eq,axiom,
% 0.35/0.59 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 0.35/0.59 ( ( Y != zero_zero_complex )
% 0.35/0.59 => ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % diff_frac_eq
% 0.35/0.59 thf(fact_3939_diff__frac__eq,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real,W2: real] :
% 0.35/0.59 ( ( Y != zero_zero_real )
% 0.35/0.59 => ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 0.35/0.59 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % diff_frac_eq
% 0.35/0.59 thf(fact_3940_diff__frac__eq,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 0.35/0.59 ( ( Y != zero_zero_rat )
% 0.35/0.59 => ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % diff_frac_eq
% 0.35/0.59 thf(fact_3941_diff__divide__eq__iff,axiom,
% 0.35/0.59 ! [Z3: complex,X: complex,Y: complex] :
% 0.35/0.59 ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % diff_divide_eq_iff
% 0.35/0.59 thf(fact_3942_diff__divide__eq__iff,axiom,
% 0.35/0.59 ! [Z3: real,X: real,Y: real] :
% 0.35/0.59 ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 0.35/0.59 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % diff_divide_eq_iff
% 0.35/0.59 thf(fact_3943_diff__divide__eq__iff,axiom,
% 0.35/0.59 ! [Z3: rat,X: rat,Y: rat] :
% 0.35/0.59 ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z3 ) )
% 0.35/0.59 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % diff_divide_eq_iff
% 0.35/0.59 thf(fact_3944_divide__diff__eq__iff,axiom,
% 0.35/0.59 ! [Z3: complex,X: complex,Y: complex] :
% 0.35/0.59 ( ( Z3 != zero_zero_complex )
% 0.35/0.59 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_diff_eq_iff
% 0.35/0.59 thf(fact_3945_divide__diff__eq__iff,axiom,
% 0.35/0.59 ! [Z3: real,X: real,Y: real] :
% 0.35/0.59 ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 0.35/0.59 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_diff_eq_iff
% 0.35/0.59 thf(fact_3946_divide__diff__eq__iff,axiom,
% 0.35/0.59 ! [Z3: rat,X: rat,Y: rat] :
% 0.35/0.59 ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z3 ) @ Y )
% 0.35/0.59 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_diff_eq_iff
% 0.35/0.59 thf(fact_3947_card__Un__le,axiom,
% 0.35/0.59 ! [A4: set_complex,B5: set_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % card_Un_le
% 0.35/0.59 thf(fact_3948_card__Un__le,axiom,
% 0.35/0.59 ! [A4: set_int,B5: set_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % card_Un_le
% 0.35/0.59 thf(fact_3949_card__Un__le,axiom,
% 0.35/0.59 ! [A4: set_list_nat,B5: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % card_Un_le
% 0.35/0.59 thf(fact_3950_card__Un__le,axiom,
% 0.35/0.59 ! [A4: set_set_nat,B5: set_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % card_Un_le
% 0.35/0.59 thf(fact_3951_card__Un__le,axiom,
% 0.35/0.59 ! [A4: set_nat,B5: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % card_Un_le
% 0.35/0.59 thf(fact_3952_atLeast0__atMost__Suc,axiom,
% 0.35/0.59 ! [N: nat] :
% 0.35/0.59 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.59 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeast0_atMost_Suc
% 0.35/0.59 thf(fact_3953_nat__mult__div__cancel1,axiom,
% 0.35/0.59 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.35/0.59 = ( divide_divide_nat @ M2 @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nat_mult_div_cancel1
% 0.35/0.59 thf(fact_3954_Icc__eq__insert__lb__nat,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.59 => ( ( set_or1269000886237332187st_nat @ M2 @ N )
% 0.35/0.59 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Icc_eq_insert_lb_nat
% 0.35/0.59 thf(fact_3955_atLeastAtMostSuc__conv,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.59 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) )
% 0.35/0.59 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMostSuc_conv
% 0.35/0.59 thf(fact_3956_atLeastAtMost__insertL,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.59 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 0.35/0.59 = ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMost_insertL
% 0.35/0.59 thf(fact_3957_subset__eq__atLeast0__atMost__finite,axiom,
% 0.35/0.59 ! [N6: set_nat,N: nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ N6 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.59 => ( finite_finite_nat @ N6 ) ) ).
% 0.35/0.59
% 0.35/0.59 % subset_eq_atLeast0_atMost_finite
% 0.35/0.59 thf(fact_3958_divide__le__eq,axiom,
% 0.35/0.59 ! [B: real,C2: real,A: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq
% 0.35/0.59 thf(fact_3959_divide__le__eq,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq
% 0.35/0.59 thf(fact_3960_le__divide__eq,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq
% 0.35/0.59 thf(fact_3961_le__divide__eq,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq
% 0.35/0.59 thf(fact_3962_divide__left__mono,axiom,
% 0.35/0.59 ! [B: real,A: real,C2: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ B @ A )
% 0.35/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_left_mono
% 0.35/0.59 thf(fact_3963_divide__left__mono,axiom,
% 0.35/0.59 ! [B: rat,A: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_left_mono
% 0.35/0.59 thf(fact_3964_neg__divide__le__eq,axiom,
% 0.35/0.59 ! [C2: real,B: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_divide_le_eq
% 0.35/0.59 thf(fact_3965_neg__divide__le__eq,axiom,
% 0.35/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_divide_le_eq
% 0.35/0.59 thf(fact_3966_neg__le__divide__eq,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_le_divide_eq
% 0.35/0.59 thf(fact_3967_neg__le__divide__eq,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_le_divide_eq
% 0.35/0.59 thf(fact_3968_pos__divide__le__eq,axiom,
% 0.35/0.59 ! [C2: real,B: real,A: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_divide_le_eq
% 0.35/0.59 thf(fact_3969_pos__divide__le__eq,axiom,
% 0.35/0.59 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_divide_le_eq
% 0.35/0.59 thf(fact_3970_pos__le__divide__eq,axiom,
% 0.35/0.59 ! [C2: real,A: real,B: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_le_divide_eq
% 0.35/0.59 thf(fact_3971_pos__le__divide__eq,axiom,
% 0.35/0.59 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_le_divide_eq
% 0.35/0.59 thf(fact_3972_mult__imp__div__pos__le,axiom,
% 0.35/0.59 ! [Y: real,X: real,Z3: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_div_pos_le
% 0.35/0.59 thf(fact_3973_mult__imp__div__pos__le,axiom,
% 0.35/0.59 ! [Y: rat,X: rat,Z3: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_div_pos_le
% 0.35/0.59 thf(fact_3974_mult__imp__le__div__pos,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 0.35/0.59 => ( ord_less_eq_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_le_div_pos
% 0.35/0.59 thf(fact_3975_mult__imp__le__div__pos,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 0.35/0.59 => ( ord_less_eq_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % mult_imp_le_div_pos
% 0.35/0.59 thf(fact_3976_divide__left__mono__neg,axiom,
% 0.35/0.59 ! [A: real,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ A @ B )
% 0.35/0.59 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_left_mono_neg
% 0.35/0.59 thf(fact_3977_divide__left__mono__neg,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_left_mono_neg
% 0.35/0.59 thf(fact_3978_divide__le__eq__1,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_eq_real @ B @ A ) )
% 0.35/0.59 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_eq_real @ A @ B ) )
% 0.35/0.59 | ( A = zero_zero_real ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_1
% 0.35/0.59 thf(fact_3979_divide__le__eq__1,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_eq_rat @ B @ A ) )
% 0.35/0.59 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_eq_rat @ A @ B ) )
% 0.35/0.59 | ( A = zero_zero_rat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_1
% 0.35/0.59 thf(fact_3980_le__divide__eq__1,axiom,
% 0.35/0.59 ! [B: real,A: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 & ( ord_less_eq_real @ A @ B ) )
% 0.35/0.59 | ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.59 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_1
% 0.35/0.59 thf(fact_3981_le__divide__eq__1,axiom,
% 0.35/0.59 ! [B: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 & ( ord_less_eq_rat @ A @ B ) )
% 0.35/0.59 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.59 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_1
% 0.35/0.59 thf(fact_3982_divide__less__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [B: real,C2: real,W2: num] :
% 0.35/0.59 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_numeral(1)
% 0.35/0.59 thf(fact_3983_divide__less__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,W2: num] :
% 0.35/0.59 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_less_eq_numeral(1)
% 0.35/0.59 thf(fact_3984_less__divide__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [W2: num,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_numeral(1)
% 0.35/0.59 thf(fact_3985_less__divide__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [W2: num,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_divide_eq_numeral(1)
% 0.35/0.59 thf(fact_3986_frac__le__eq,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real,W2: real] :
% 0.35/0.59 ( ( Y != zero_zero_real )
% 0.35/0.59 => ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 0.35/0.59 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_le_eq
% 0.35/0.59 thf(fact_3987_frac__le__eq,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 0.35/0.59 ( ( Y != zero_zero_rat )
% 0.35/0.59 => ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 0.35/0.59 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_le_eq
% 0.35/0.59 thf(fact_3988_frac__less__eq,axiom,
% 0.35/0.59 ! [Y: real,Z3: real,X: real,W2: real] :
% 0.35/0.59 ( ( Y != zero_zero_real )
% 0.35/0.59 => ( ( Z3 != zero_zero_real )
% 0.35/0.59 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 0.35/0.59 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_less_eq
% 0.35/0.59 thf(fact_3989_frac__less__eq,axiom,
% 0.35/0.59 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 0.35/0.59 ( ( Y != zero_zero_rat )
% 0.35/0.59 => ( ( Z3 != zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 0.35/0.59 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % frac_less_eq
% 0.35/0.59 thf(fact_3990_power__diff,axiom,
% 0.35/0.59 ! [A: complex,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_zero_complex )
% 0.35/0.59 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.59 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff
% 0.35/0.59 thf(fact_3991_power__diff,axiom,
% 0.35/0.59 ! [A: real,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_zero_real )
% 0.35/0.59 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( power_power_real @ A @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.59 = ( divide_divide_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff
% 0.35/0.59 thf(fact_3992_power__diff,axiom,
% 0.35/0.59 ! [A: rat,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_zero_rat )
% 0.35/0.59 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.59 = ( divide_divide_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff
% 0.35/0.59 thf(fact_3993_power__diff,axiom,
% 0.35/0.59 ! [A: nat,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_zero_nat )
% 0.35/0.59 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.59 = ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff
% 0.35/0.59 thf(fact_3994_power__diff,axiom,
% 0.35/0.59 ! [A: int,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_zero_int )
% 0.35/0.59 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.59 = ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff
% 0.35/0.59 thf(fact_3995_div__geq,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ~ ( ord_less_nat @ M2 @ N )
% 0.35/0.59 => ( ( divide_divide_nat @ M2 @ N )
% 0.35/0.59 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_geq
% 0.35/0.59 thf(fact_3996_four__x__squared,axiom,
% 0.35/0.59 ! [X: real] :
% 0.35/0.59 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.59 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % four_x_squared
% 0.35/0.59 thf(fact_3997_L2__set__mult__ineq__lemma,axiom,
% 0.35/0.59 ! [A: real,C2: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C2 ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % L2_set_mult_ineq_lemma
% 0.35/0.59 thf(fact_3998_divide__le__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [B: real,C2: real,W2: num] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_numeral(1)
% 0.35/0.59 thf(fact_3999_divide__le__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,W2: num] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % divide_le_eq_numeral(1)
% 0.35/0.59 thf(fact_4000_le__divide__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [W2: num,B: real,C2: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.59 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.59 => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_numeral(1)
% 0.35/0.59 thf(fact_4001_le__divide__eq__numeral_I1_J,axiom,
% 0.35/0.59 ! [W2: num,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.59 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 0.35/0.59 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.59 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_divide_eq_numeral(1)
% 0.35/0.59 thf(fact_4002_half__gt__zero,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.59 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % half_gt_zero
% 0.35/0.59 thf(fact_4003_half__gt__zero,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.59 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % half_gt_zero
% 0.35/0.59 thf(fact_4004_half__gt__zero__iff,axiom,
% 0.35/0.59 ! [A: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.59 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.59
% 0.35/0.59 % half_gt_zero_iff
% 0.35/0.59 thf(fact_4005_half__gt__zero__iff,axiom,
% 0.35/0.59 ! [A: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.35/0.59 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.59
% 0.35/0.59 % half_gt_zero_iff
% 0.35/0.59 thf(fact_4006_scaling__mono,axiom,
% 0.35/0.59 ! [U: real,V2: real,R3: real,S2: real] :
% 0.35/0.59 ( ( ord_less_eq_real @ U @ V2 )
% 0.35/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 0.35/0.59 => ( ( ord_less_eq_real @ R3 @ S2 )
% 0.35/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R3 @ ( minus_minus_real @ V2 @ U ) ) @ S2 ) ) @ V2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % scaling_mono
% 0.35/0.59 thf(fact_4007_scaling__mono,axiom,
% 0.35/0.59 ! [U: rat,V2: rat,R3: rat,S2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ U @ V2 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ R3 @ S2 )
% 0.35/0.59 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V2 @ U ) ) @ S2 ) ) @ V2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % scaling_mono
% 0.35/0.59 thf(fact_4008_nat__approx__posE,axiom,
% 0.35/0.59 ! [E: rat] :
% 0.35/0.59 ( ( ord_less_rat @ zero_zero_rat @ E )
% 0.35/0.59 => ~ ! [N3: nat] :
% 0.35/0.59 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 0.35/0.59
% 0.35/0.59 % nat_approx_posE
% 0.35/0.59 thf(fact_4009_nat__approx__posE,axiom,
% 0.35/0.59 ! [E: real] :
% 0.35/0.59 ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.59 => ~ ! [N3: nat] :
% 0.35/0.59 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 0.35/0.59
% 0.35/0.59 % nat_approx_posE
% 0.35/0.59 thf(fact_4010_inverse__of__nat__le,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( N != zero_zero_nat )
% 0.35/0.59 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inverse_of_nat_le
% 0.35/0.59 thf(fact_4011_inverse__of__nat__le,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( N != zero_zero_nat )
% 0.35/0.59 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inverse_of_nat_le
% 0.35/0.59 thf(fact_4012_triangle__def,axiom,
% 0.35/0.59 ( nat_triangle
% 0.35/0.59 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % triangle_def
% 0.35/0.59 thf(fact_4013_arith__geo__mean,axiom,
% 0.35/0.59 ! [U: real,X: real,Y: real] :
% 0.35/0.59 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59 = ( times_times_real @ X @ Y ) )
% 0.35/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.59 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % arith_geo_mean
% 0.35/0.59 thf(fact_4014_arith__geo__mean,axiom,
% 0.35/0.59 ! [U: rat,X: rat,Y: rat] :
% 0.35/0.59 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59 = ( times_times_rat @ X @ Y ) )
% 0.35/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.59 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.59 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % arith_geo_mean
% 0.35/0.59 thf(fact_4015_double__not__eq__Suc__double,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 0.35/0.59 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % double_not_eq_Suc_double
% 0.35/0.59 thf(fact_4016_Suc__double__not__eq__double,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.59 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.59
% 0.35/0.59 % Suc_double_not_eq_double
% 0.35/0.59 thf(fact_4017_exp__add__not__zero__imp__right,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 0.35/0.59 != zero_zero_nat )
% 0.35/0.59 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.59 != zero_zero_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % exp_add_not_zero_imp_right
% 0.35/0.59 thf(fact_4018_exp__add__not__zero__imp__right,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 0.35/0.59 != zero_zero_int )
% 0.35/0.59 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.59 != zero_zero_int ) ) ).
% 0.35/0.59
% 0.35/0.59 % exp_add_not_zero_imp_right
% 0.35/0.59 thf(fact_4019_one__div__two__eq__zero,axiom,
% 0.35/0.59 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.59 = zero_z3403309356797280102nteger ) ).
% 0.35/0.59
% 0.35/0.59 % one_div_two_eq_zero
% 0.35/0.59 thf(fact_4020_one__div__two__eq__zero,axiom,
% 0.35/0.59 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59 = zero_zero_nat ) ).
% 0.35/0.59
% 0.35/0.59 % one_div_two_eq_zero
% 0.35/0.59 thf(fact_4021_one__div__two__eq__zero,axiom,
% 0.35/0.59 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.59 = zero_zero_int ) ).
% 0.35/0.59
% 0.35/0.59 % one_div_two_eq_zero
% 0.35/0.59 thf(fact_4022_div2__Suc__Suc,axiom,
% 0.35/0.59 ! [M2: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.59 = ( suc @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div2_Suc_Suc
% 0.35/0.59 thf(fact_4023_insert_H__correct,axiom,
% 0.35/0.59 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.59 ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.59 => ( ( vEBT_set_vebt @ ( vEBT_VEBT_insert @ T @ X ) )
% 0.35/0.59 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % insert'_correct
% 0.35/0.59 thf(fact_4024_div__mult__self__is__m,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ M2 @ N ) @ N )
% 0.35/0.59 = M2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self_is_m
% 0.35/0.59 thf(fact_4025_div__mult__self1__is__m,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M2 ) @ N )
% 0.35/0.59 = M2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self1_is_m
% 0.35/0.59 thf(fact_4026_div__mult__self1,axiom,
% 0.35/0.59 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.59 ( ( B != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 0.35/0.59 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self1
% 0.35/0.59 thf(fact_4027_div__mult__self1,axiom,
% 0.35/0.59 ! [B: int,A: int,C2: int] :
% 0.35/0.59 ( ( B != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 0.35/0.59 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self1
% 0.35/0.59 thf(fact_4028_div__mult__self2,axiom,
% 0.35/0.59 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.59 ( ( B != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 0.35/0.59 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self2
% 0.35/0.59 thf(fact_4029_div__mult__self2,axiom,
% 0.35/0.59 ! [B: int,A: int,C2: int] :
% 0.35/0.59 ( ( B != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 0.35/0.59 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self2
% 0.35/0.59 thf(fact_4030_div__mult__self3,axiom,
% 0.35/0.59 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.59 ( ( B != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 0.35/0.59 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self3
% 0.35/0.59 thf(fact_4031_div__mult__self3,axiom,
% 0.35/0.59 ! [B: int,C2: int,A: int] :
% 0.35/0.59 ( ( B != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 0.35/0.59 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self3
% 0.35/0.59 thf(fact_4032_zdiv__numeral__Bit0,axiom,
% 0.35/0.59 ! [V2: num,W2: num] :
% 0.35/0.59 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.35/0.59 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_numeral_Bit0
% 0.35/0.59 thf(fact_4033_real__divide__square__eq,axiom,
% 0.35/0.59 ! [R3: real,A: real] :
% 0.35/0.59 ( ( divide_divide_real @ ( times_times_real @ R3 @ A ) @ ( times_times_real @ R3 @ R3 ) )
% 0.35/0.59 = ( divide_divide_real @ A @ R3 ) ) ).
% 0.35/0.59
% 0.35/0.59 % real_divide_square_eq
% 0.35/0.59 thf(fact_4034_div__mult__mult1__if,axiom,
% 0.35/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.59 ( ( ( C2 = zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 0.35/0.59 = zero_zero_nat ) )
% 0.35/0.59 & ( ( C2 != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_mult1_if
% 0.35/0.59 thf(fact_4035_div__mult__mult1__if,axiom,
% 0.35/0.59 ! [C2: int,A: int,B: int] :
% 0.35/0.59 ( ( ( C2 = zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.35/0.59 = zero_zero_int ) )
% 0.35/0.59 & ( ( C2 != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_mult1_if
% 0.35/0.59 thf(fact_4036_div__mult__mult2,axiom,
% 0.35/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.59 ( ( C2 != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_mult2
% 0.35/0.59 thf(fact_4037_div__mult__mult2,axiom,
% 0.35/0.59 ! [C2: int,A: int,B: int] :
% 0.35/0.59 ( ( C2 != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_int @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_mult2
% 0.35/0.59 thf(fact_4038_div__mult__mult1,axiom,
% 0.35/0.59 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.59 ( ( C2 != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_mult1
% 0.35/0.59 thf(fact_4039_div__mult__mult1,axiom,
% 0.35/0.59 ! [C2: int,A: int,B: int] :
% 0.35/0.59 ( ( C2 != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.35/0.59 = ( divide_divide_int @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_mult1
% 0.35/0.59 thf(fact_4040_div__by__Suc__0,axiom,
% 0.35/0.59 ! [M2: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 0.35/0.59 = M2 ) ).
% 0.35/0.59
% 0.35/0.59 % div_by_Suc_0
% 0.35/0.59 thf(fact_4041_div__less,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ M2 @ N )
% 0.35/0.59 => ( ( divide_divide_nat @ M2 @ N )
% 0.35/0.59 = zero_zero_nat ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_less
% 0.35/0.59 thf(fact_4042_div__mult__self4,axiom,
% 0.35/0.59 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.59 ( ( B != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 0.35/0.59 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self4
% 0.35/0.59 thf(fact_4043_div__mult__self4,axiom,
% 0.35/0.59 ! [B: int,C2: int,A: int] :
% 0.35/0.59 ( ( B != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 0.35/0.59 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult_self4
% 0.35/0.59 thf(fact_4044_zdiv__zmult2__eq,axiom,
% 0.35/0.59 ! [C2: int,A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.35/0.59 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.59 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_zmult2_eq
% 0.35/0.59 thf(fact_4045_div__neg__pos__less0,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_neg_pos_less0
% 0.35/0.59 thf(fact_4046_neg__imp__zdiv__neg__iff,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.35/0.59 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_imp_zdiv_neg_iff
% 0.35/0.59 thf(fact_4047_pos__imp__zdiv__neg__iff,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 0.35/0.59 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_imp_zdiv_neg_iff
% 0.35/0.59 thf(fact_4048_zdiv__int,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 0.35/0.59 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_int
% 0.35/0.59 thf(fact_4049_atLeastAtMostPlus1__int__conv,axiom,
% 0.35/0.59 ! [M2: int,N: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 0.35/0.59 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 0.35/0.59 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M2 @ N ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % atLeastAtMostPlus1_int_conv
% 0.35/0.59 thf(fact_4050_nonneg1__imp__zdiv__pos__iff,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.35/0.59 = ( ( ord_less_eq_int @ B @ A )
% 0.35/0.59 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % nonneg1_imp_zdiv_pos_iff
% 0.35/0.59 thf(fact_4051_pos__imp__zdiv__nonneg__iff,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.35/0.59 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_imp_zdiv_nonneg_iff
% 0.35/0.59 thf(fact_4052_neg__imp__zdiv__nonneg__iff,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 0.35/0.59 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_imp_zdiv_nonneg_iff
% 0.35/0.59 thf(fact_4053_pos__imp__zdiv__pos__iff,axiom,
% 0.35/0.59 ! [K2: int,I2: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K2 ) )
% 0.35/0.59 = ( ord_less_eq_int @ K2 @ I2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_imp_zdiv_pos_iff
% 0.35/0.59 thf(fact_4054_div__nonpos__pos__le0,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_nonpos_pos_le0
% 0.35/0.59 thf(fact_4055_div__nonneg__neg__le0,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_nonneg_neg_le0
% 0.35/0.59 thf(fact_4056_div__positive__int,axiom,
% 0.35/0.59 ! [L: int,K2: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ L @ K2 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ L )
% 0.35/0.59 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_positive_int
% 0.35/0.59 thf(fact_4057_div__int__pos__iff,axiom,
% 0.35/0.59 ! [K2: int,L: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) )
% 0.35/0.59 = ( ( K2 = zero_zero_int )
% 0.35/0.59 | ( L = zero_zero_int )
% 0.35/0.59 | ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 0.35/0.59 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 0.35/0.59 | ( ( ord_less_int @ K2 @ zero_zero_int )
% 0.35/0.59 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_int_pos_iff
% 0.35/0.59 thf(fact_4058_zdiv__mono2__neg,axiom,
% 0.35/0.59 ! [A: int,B2: int,B: int] :
% 0.35/0.59 ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.35/0.59 => ( ( ord_less_eq_int @ B2 @ B )
% 0.35/0.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_mono2_neg
% 0.35/0.59 thf(fact_4059_zdiv__mono1__neg,axiom,
% 0.35/0.59 ! [A: int,A2: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ A2 )
% 0.35/0.59 => ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.59 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_mono1_neg
% 0.35/0.59 thf(fact_4060_zdiv__eq__0__iff,axiom,
% 0.35/0.59 ! [I2: int,K2: int] :
% 0.35/0.59 ( ( ( divide_divide_int @ I2 @ K2 )
% 0.35/0.59 = zero_zero_int )
% 0.35/0.59 = ( ( K2 = zero_zero_int )
% 0.35/0.59 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.35/0.59 & ( ord_less_int @ I2 @ K2 ) )
% 0.35/0.59 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 0.35/0.59 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_eq_0_iff
% 0.35/0.59 thf(fact_4061_zdiv__mono2,axiom,
% 0.35/0.59 ! [A: int,B2: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 0.35/0.59 => ( ( ord_less_eq_int @ B2 @ B )
% 0.35/0.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_mono2
% 0.35/0.59 thf(fact_4062_zdiv__mono1,axiom,
% 0.35/0.59 ! [A: int,A2: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ A2 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.59 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % zdiv_mono1
% 0.35/0.59 thf(fact_4063_int__div__less__self,axiom,
% 0.35/0.59 ! [X: int,K2: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ X )
% 0.35/0.59 => ( ( ord_less_int @ one_one_int @ K2 )
% 0.35/0.59 => ( ord_less_int @ ( divide_divide_int @ X @ K2 ) @ X ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_div_less_self
% 0.35/0.59 thf(fact_4064_periodic__finite__ex,axiom,
% 0.35/0.59 ! [D: int,P2: int > $o] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ D )
% 0.35/0.59 => ( ! [X3: int,K: int] :
% 0.35/0.59 ( ( P2 @ X3 )
% 0.35/0.59 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 0.35/0.59 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 0.35/0.59 = ( ? [X4: int] :
% 0.35/0.59 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 0.35/0.59 & ( P2 @ X4 ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % periodic_finite_ex
% 0.35/0.59 thf(fact_4065_split__zdiv,axiom,
% 0.35/0.59 ! [P2: int > $o,N: int,K2: int] :
% 0.35/0.59 ( ( P2 @ ( divide_divide_int @ N @ K2 ) )
% 0.35/0.59 = ( ( ( K2 = zero_zero_int )
% 0.35/0.59 => ( P2 @ zero_zero_int ) )
% 0.35/0.59 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.59 => ! [I: int,J: int] :
% 0.35/0.59 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 0.35/0.59 & ( ord_less_int @ J @ K2 )
% 0.35/0.59 & ( N
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 0.35/0.59 => ( P2 @ I ) ) )
% 0.35/0.59 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 0.35/0.59 => ! [I: int,J: int] :
% 0.35/0.59 ( ( ( ord_less_int @ K2 @ J )
% 0.35/0.59 & ( ord_less_eq_int @ J @ zero_zero_int )
% 0.35/0.59 & ( N
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 0.35/0.59 => ( P2 @ I ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % split_zdiv
% 0.35/0.59 thf(fact_4066_int__div__neg__eq,axiom,
% 0.35/0.59 ! [A: int,B: int,Q2: int,R3: int] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 0.35/0.59 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 0.35/0.59 => ( ( ord_less_int @ B @ R3 )
% 0.35/0.59 => ( ( divide_divide_int @ A @ B )
% 0.35/0.59 = Q2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_div_neg_eq
% 0.35/0.59 thf(fact_4067_int__div__pos__eq,axiom,
% 0.35/0.59 ! [A: int,B: int,Q2: int,R3: int] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 0.35/0.59 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.35/0.59 => ( ( ord_less_int @ R3 @ B )
% 0.35/0.59 => ( ( divide_divide_int @ A @ B )
% 0.35/0.59 = Q2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_div_pos_eq
% 0.35/0.59 thf(fact_4068_cpmi,axiom,
% 0.35/0.59 ! [D3: int,P2: int > $o,P6: int > $o,B5: set_int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.35/0.59 => ( ? [Z5: int] :
% 0.35/0.59 ! [X3: int] :
% 0.35/0.59 ( ( ord_less_int @ X3 @ Z5 )
% 0.35/0.59 => ( ( P2 @ X3 )
% 0.35/0.59 = ( P6 @ X3 ) ) )
% 0.35/0.59 => ( ! [X3: int] :
% 0.35/0.59 ( ! [Xa: int] :
% 0.35/0.59 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.35/0.59 => ! [Xb2: int] :
% 0.35/0.59 ( ( member_int @ Xb2 @ B5 )
% 0.35/0.59 => ( X3
% 0.35/0.59 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.59 => ( ( P2 @ X3 )
% 0.35/0.59 => ( P2 @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 0.35/0.59 => ( ! [X3: int,K: int] :
% 0.35/0.59 ( ( P6 @ X3 )
% 0.35/0.59 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 0.35/0.59 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 0.35/0.59 = ( ? [X4: int] :
% 0.35/0.59 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.35/0.59 & ( P6 @ X4 ) )
% 0.35/0.59 | ? [X4: int] :
% 0.35/0.59 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.35/0.59 & ? [Y4: int] :
% 0.35/0.59 ( ( member_int @ Y4 @ B5 )
% 0.35/0.59 & ( P2 @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % cpmi
% 0.35/0.59 thf(fact_4069_cppi,axiom,
% 0.35/0.59 ! [D3: int,P2: int > $o,P6: int > $o,A4: set_int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ D3 )
% 0.35/0.59 => ( ? [Z5: int] :
% 0.35/0.59 ! [X3: int] :
% 0.35/0.59 ( ( ord_less_int @ Z5 @ X3 )
% 0.35/0.59 => ( ( P2 @ X3 )
% 0.35/0.59 = ( P6 @ X3 ) ) )
% 0.35/0.59 => ( ! [X3: int] :
% 0.35/0.59 ( ! [Xa: int] :
% 0.35/0.59 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.35/0.59 => ! [Xb2: int] :
% 0.35/0.59 ( ( member_int @ Xb2 @ A4 )
% 0.35/0.59 => ( X3
% 0.35/0.59 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 0.35/0.59 => ( ( P2 @ X3 )
% 0.35/0.59 => ( P2 @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 0.35/0.59 => ( ! [X3: int,K: int] :
% 0.35/0.59 ( ( P6 @ X3 )
% 0.35/0.59 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 0.35/0.59 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 0.35/0.59 = ( ? [X4: int] :
% 0.35/0.59 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.35/0.59 & ( P6 @ X4 ) )
% 0.35/0.59 | ? [X4: int] :
% 0.35/0.59 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 0.35/0.59 & ? [Y4: int] :
% 0.35/0.59 ( ( member_int @ Y4 @ A4 )
% 0.35/0.59 & ( P2 @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % cppi
% 0.35/0.59 thf(fact_4070_int__power__div__base,axiom,
% 0.35/0.59 ! [M2: nat,K2: int] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.59 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.59 => ( ( divide_divide_int @ ( power_power_int @ K2 @ M2 ) @ K2 )
% 0.35/0.59 = ( power_power_int @ K2 @ ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % int_power_div_base
% 0.35/0.59 thf(fact_4071_div__pos__geq,axiom,
% 0.35/0.59 ! [L: int,K2: int] :
% 0.35/0.59 ( ( ord_less_int @ zero_zero_int @ L )
% 0.35/0.59 => ( ( ord_less_eq_int @ L @ K2 )
% 0.35/0.59 => ( ( divide_divide_int @ K2 @ L )
% 0.35/0.59 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K2 @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_pos_geq
% 0.35/0.59 thf(fact_4072_div__le__dividend,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ).
% 0.35/0.59
% 0.35/0.59 % div_le_dividend
% 0.35/0.59 thf(fact_4073_div__le__mono,axiom,
% 0.35/0.59 ! [M2: nat,N: nat,K2: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.59 => ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ K2 ) @ ( divide_divide_nat @ N @ K2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_le_mono
% 0.35/0.59 thf(fact_4074_div__mult2__eq,axiom,
% 0.35/0.59 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ M2 @ ( times_times_nat @ N @ Q2 ) )
% 0.35/0.59 = ( divide_divide_nat @ ( divide_divide_nat @ M2 @ N ) @ Q2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult2_eq
% 0.35/0.59 thf(fact_4075_pos__zdiv__mult__2,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.59 = ( divide_divide_int @ B @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pos_zdiv_mult_2
% 0.35/0.59 thf(fact_4076_neg__zdiv__mult__2,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.59 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % neg_zdiv_mult_2
% 0.35/0.59 thf(fact_4077_div__mult2__eq_H,axiom,
% 0.35/0.59 ! [A: int,M2: nat,N: nat] :
% 0.35/0.59 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.59 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult2_eq'
% 0.35/0.59 thf(fact_4078_div__mult2__eq_H,axiom,
% 0.35/0.59 ! [A: nat,M2: nat,N: nat] :
% 0.35/0.59 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.35/0.59 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult2_eq'
% 0.35/0.59 thf(fact_4079_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ( divide_divide_nat @ M2 @ N )
% 0.35/0.59 = zero_zero_nat )
% 0.35/0.59 = ( ( ord_less_nat @ M2 @ N )
% 0.35/0.59 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Euclidean_Division.div_eq_0_iff
% 0.35/0.59 thf(fact_4080_Suc__div__le__mono,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ ( divide_divide_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.35/0.59
% 0.35/0.59 % Suc_div_le_mono
% 0.35/0.59 thf(fact_4081_less__mult__imp__div__less,axiom,
% 0.35/0.59 ! [M2: nat,I2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ M2 @ ( times_times_nat @ I2 @ N ) )
% 0.35/0.59 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ I2 ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_mult_imp_div_less
% 0.35/0.59 thf(fact_4082_times__div__less__eq__dividend,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) @ M2 ) ).
% 0.35/0.59
% 0.35/0.59 % times_div_less_eq_dividend
% 0.35/0.59 thf(fact_4083_div__times__less__eq__dividend,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) @ M2 ) ).
% 0.35/0.59
% 0.35/0.59 % div_times_less_eq_dividend
% 0.35/0.59 thf(fact_4084_div__mult2__numeral__eq,axiom,
% 0.35/0.59 ! [A: nat,K2: num,L: num] :
% 0.35/0.59 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K2 ) ) @ ( numeral_numeral_nat @ L ) )
% 0.35/0.59 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K2 @ L ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult2_numeral_eq
% 0.35/0.59 thf(fact_4085_div__mult2__numeral__eq,axiom,
% 0.35/0.59 ! [A: int,K2: num,L: num] :
% 0.35/0.59 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ L ) )
% 0.35/0.59 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K2 @ L ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_mult2_numeral_eq
% 0.35/0.59 thf(fact_4086_div__add__self1,axiom,
% 0.35/0.59 ! [B: code_integer,A: code_integer] :
% 0.35/0.59 ( ( B != zero_z3403309356797280102nteger )
% 0.35/0.59 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 0.35/0.59 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_add_self1
% 0.35/0.59 thf(fact_4087_div__add__self1,axiom,
% 0.35/0.59 ! [B: nat,A: nat] :
% 0.35/0.59 ( ( B != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 0.35/0.59 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_add_self1
% 0.35/0.59 thf(fact_4088_div__add__self1,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( B != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 0.35/0.59 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_add_self1
% 0.35/0.59 thf(fact_4089_div__add__self2,axiom,
% 0.35/0.59 ! [B: code_integer,A: code_integer] :
% 0.35/0.59 ( ( B != zero_z3403309356797280102nteger )
% 0.35/0.59 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 0.35/0.59 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_add_self2
% 0.35/0.59 thf(fact_4090_div__add__self2,axiom,
% 0.35/0.59 ! [B: nat,A: nat] :
% 0.35/0.59 ( ( B != zero_zero_nat )
% 0.35/0.59 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 0.35/0.59 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_add_self2
% 0.35/0.59 thf(fact_4091_div__add__self2,axiom,
% 0.35/0.59 ! [B: int,A: int] :
% 0.35/0.59 ( ( B != zero_zero_int )
% 0.35/0.59 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 0.35/0.59 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_add_self2
% 0.35/0.59 thf(fact_4092_div__le__mono2,axiom,
% 0.35/0.59 ! [M2: nat,N: nat,K2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.59 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.59 => ( ord_less_eq_nat @ ( divide_divide_nat @ K2 @ N ) @ ( divide_divide_nat @ K2 @ M2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_le_mono2
% 0.35/0.59 thf(fact_4093_div__greater__zero__iff,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M2 @ N ) )
% 0.35/0.59 = ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_greater_zero_iff
% 0.35/0.59 thf(fact_4094_div__less__iff__less__mult,axiom,
% 0.35/0.59 ! [Q2: nat,M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.35/0.59 => ( ( ord_less_nat @ ( divide_divide_nat @ M2 @ Q2 ) @ N )
% 0.35/0.59 = ( ord_less_nat @ M2 @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_less_iff_less_mult
% 0.35/0.59 thf(fact_4095_div__less__dividend,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ one_one_nat @ N )
% 0.35/0.59 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.59 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_less_dividend
% 0.35/0.59 thf(fact_4096_div__eq__dividend__iff,axiom,
% 0.35/0.59 ! [M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.59 => ( ( ( divide_divide_nat @ M2 @ N )
% 0.35/0.59 = M2 )
% 0.35/0.59 = ( N = one_one_nat ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_eq_dividend_iff
% 0.35/0.59 thf(fact_4097_div__if,axiom,
% 0.35/0.59 ( divide_divide_nat
% 0.35/0.59 = ( ^ [M6: nat,N4: nat] :
% 0.35/0.59 ( if_nat
% 0.35/0.59 @ ( ( ord_less_nat @ M6 @ N4 )
% 0.35/0.59 | ( N4 = zero_zero_nat ) )
% 0.35/0.59 @ zero_zero_nat
% 0.35/0.59 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_if
% 0.35/0.59 thf(fact_4098_div__nat__eqI,axiom,
% 0.35/0.59 ! [N: nat,Q2: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M2 )
% 0.35/0.59 => ( ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 0.35/0.59 => ( ( divide_divide_nat @ M2 @ N )
% 0.35/0.59 = Q2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_nat_eqI
% 0.35/0.59 thf(fact_4099_less__eq__div__iff__mult__less__eq,axiom,
% 0.35/0.59 ! [Q2: nat,M2: nat,N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 0.35/0.59 => ( ( ord_less_eq_nat @ M2 @ ( divide_divide_nat @ N @ Q2 ) )
% 0.35/0.59 = ( ord_less_eq_nat @ ( times_times_nat @ M2 @ Q2 ) @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % less_eq_div_iff_mult_less_eq
% 0.35/0.59 thf(fact_4100_dividend__less__times__div,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % dividend_less_times_div
% 0.35/0.59 thf(fact_4101_dividend__less__div__times,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % dividend_less_div_times
% 0.35/0.59 thf(fact_4102_split__div,axiom,
% 0.35/0.59 ! [P2: nat > $o,M2: nat,N: nat] :
% 0.35/0.59 ( ( P2 @ ( divide_divide_nat @ M2 @ N ) )
% 0.35/0.59 = ( ( ( N = zero_zero_nat )
% 0.35/0.59 => ( P2 @ zero_zero_nat ) )
% 0.35/0.59 & ( ( N != zero_zero_nat )
% 0.35/0.59 => ! [I: nat,J: nat] :
% 0.35/0.59 ( ( ord_less_nat @ J @ N )
% 0.35/0.59 => ( ( M2
% 0.35/0.59 = ( plus_plus_nat @ ( times_times_nat @ N @ I ) @ J ) )
% 0.35/0.59 => ( P2 @ I ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % split_div
% 0.35/0.59 thf(fact_4103_power__diff__power__eq,axiom,
% 0.35/0.59 ! [A: code_integer,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.59 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.35/0.59 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 0.35/0.59 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 0.35/0.59 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff_power_eq
% 0.35/0.59 thf(fact_4104_power__diff__power__eq,axiom,
% 0.35/0.59 ! [A: nat,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_zero_nat )
% 0.35/0.59 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 0.35/0.59 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 0.35/0.59 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 0.35/0.59 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff_power_eq
% 0.35/0.59 thf(fact_4105_power__diff__power__eq,axiom,
% 0.35/0.59 ! [A: int,N: nat,M2: nat] :
% 0.35/0.59 ( ( A != zero_zero_int )
% 0.35/0.59 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 0.35/0.59 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 0.35/0.59 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 0.35/0.59 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % power_diff_power_eq
% 0.35/0.59 thf(fact_4106_le__div__geq,axiom,
% 0.35/0.59 ! [N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.59 => ( ( divide_divide_nat @ M2 @ N )
% 0.35/0.59 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_div_geq
% 0.35/0.59 thf(fact_4107_split__div_H,axiom,
% 0.35/0.59 ! [P2: nat > $o,M2: nat,N: nat] :
% 0.35/0.59 ( ( P2 @ ( divide_divide_nat @ M2 @ N ) )
% 0.35/0.59 = ( ( ( N = zero_zero_nat )
% 0.35/0.59 & ( P2 @ zero_zero_nat ) )
% 0.35/0.59 | ? [Q5: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M2 )
% 0.35/0.59 & ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 0.35/0.59 & ( P2 @ Q5 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % split_div'
% 0.35/0.59 thf(fact_4108_div__2__gt__zero,axiom,
% 0.35/0.59 ! [N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.59 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % div_2_gt_zero
% 0.35/0.59 thf(fact_4109_Suc__n__div__2__gt__zero,axiom,
% 0.35/0.59 ! [N: nat] :
% 0.35/0.59 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % Suc_n_div_2_gt_zero
% 0.35/0.59 thf(fact_4110_linear__plus__1__le__power,axiom,
% 0.35/0.59 ! [X: real,N: nat] :
% 0.35/0.59 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.59 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % linear_plus_1_le_power
% 0.35/0.59 thf(fact_4111_succ__list__to__short,axiom,
% 0.35/0.59 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.59 => ( ( ord_less_eq_nat @ Mi @ X )
% 0.35/0.59 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.59 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.59 = none_nat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % succ_list_to_short
% 0.35/0.59 thf(fact_4112_pred__list__to__short,axiom,
% 0.35/0.59 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.59 => ( ( ord_less_eq_nat @ X @ Ma )
% 0.35/0.59 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.59 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.59 = none_nat ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % pred_list_to_short
% 0.35/0.59 thf(fact_4113_set__bit__0,axiom,
% 0.35/0.59 ! [A: code_integer] :
% 0.35/0.59 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 0.35/0.59 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_bit_0
% 0.35/0.59 thf(fact_4114_set__bit__0,axiom,
% 0.35/0.59 ! [A: nat] :
% 0.35/0.59 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 0.35/0.59 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_bit_0
% 0.35/0.59 thf(fact_4115_set__bit__0,axiom,
% 0.35/0.59 ! [A: int] :
% 0.35/0.59 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 0.35/0.59 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % set_bit_0
% 0.35/0.59 thf(fact_4116_case4_I11_J,axiom,
% 0.35/0.59 ( ( mi != ma )
% 0.35/0.59 => ! [I4: nat] :
% 0.35/0.59 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 0.35/0.59 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 0.35/0.59 = I4 )
% 0.35/0.59 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 0.35/0.59 & ! [X5: nat] :
% 0.35/0.59 ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 0.35/0.59 = I4 )
% 0.35/0.59 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 0.35/0.59 => ( ( ord_less_nat @ mi @ X5 )
% 0.35/0.59 & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % case4(11)
% 0.35/0.59 thf(fact_4117_enat__ord__number_I1_J,axiom,
% 0.35/0.59 ! [M2: num,N: num] :
% 0.35/0.59 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 0.35/0.59 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % enat_ord_number(1)
% 0.35/0.59 thf(fact_4118_le__sup__iff,axiom,
% 0.35/0.59 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z3 )
% 0.35/0.59 = ( ( ord_less_eq_set_nat @ X @ Z3 )
% 0.35/0.59 & ( ord_less_eq_set_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_sup_iff
% 0.35/0.59 thf(fact_4119_le__sup__iff,axiom,
% 0.35/0.59 ! [X: rat,Y: rat,Z3: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z3 )
% 0.35/0.59 = ( ( ord_less_eq_rat @ X @ Z3 )
% 0.35/0.59 & ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_sup_iff
% 0.35/0.59 thf(fact_4120_le__sup__iff,axiom,
% 0.35/0.59 ! [X: nat,Y: nat,Z3: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z3 )
% 0.35/0.59 = ( ( ord_less_eq_nat @ X @ Z3 )
% 0.35/0.59 & ( ord_less_eq_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_sup_iff
% 0.35/0.59 thf(fact_4121_le__sup__iff,axiom,
% 0.35/0.59 ! [X: int,Y: int,Z3: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z3 )
% 0.35/0.59 = ( ( ord_less_eq_int @ X @ Z3 )
% 0.35/0.59 & ( ord_less_eq_int @ Y @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_sup_iff
% 0.35/0.59 thf(fact_4122_sup_Obounded__iff,axiom,
% 0.35/0.59 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ord_less_eq_set_nat @ B @ A )
% 0.35/0.59 & ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % sup.bounded_iff
% 0.35/0.59 thf(fact_4123_sup_Obounded__iff,axiom,
% 0.35/0.59 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.59 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % sup.bounded_iff
% 0.35/0.59 thf(fact_4124_sup_Obounded__iff,axiom,
% 0.35/0.59 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.59 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % sup.bounded_iff
% 0.35/0.59 thf(fact_4125_sup_Obounded__iff,axiom,
% 0.35/0.59 ! [B: int,C2: int,A: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 0.35/0.59 = ( ( ord_less_eq_int @ B @ A )
% 0.35/0.59 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % sup.bounded_iff
% 0.35/0.59 thf(fact_4126_bit__split__inv,axiom,
% 0.35/0.59 ! [X: nat,D: nat] :
% 0.35/0.59 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 0.35/0.59 = X ) ).
% 0.35/0.59
% 0.35/0.59 % bit_split_inv
% 0.35/0.59 thf(fact_4127_finite__atLeastAtMost__int,axiom,
% 0.35/0.59 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.35/0.59
% 0.35/0.59 % finite_atLeastAtMost_int
% 0.35/0.59 thf(fact_4128_high__def,axiom,
% 0.35/0.59 ( vEBT_VEBT_high
% 0.35/0.59 = ( ^ [X4: nat,N4: nat] : ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % high_def
% 0.35/0.59 thf(fact_4129_high__bound__aux,axiom,
% 0.35/0.59 ! [Ma: nat,N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 0.35/0.59 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % high_bound_aux
% 0.35/0.59 thf(fact_4130_high__inv,axiom,
% 0.35/0.59 ! [X: nat,N: nat,Y: nat] :
% 0.35/0.59 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.59 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.35/0.59 = Y ) ) ).
% 0.35/0.59
% 0.35/0.59 % high_inv
% 0.35/0.59 thf(fact_4131_low__inv,axiom,
% 0.35/0.59 ! [X: nat,N: nat,Y: nat] :
% 0.35/0.59 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.59 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 0.35/0.59 = X ) ) ).
% 0.35/0.59
% 0.35/0.59 % low_inv
% 0.35/0.59 thf(fact_4132_le__inf__iff,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) )
% 0.35/0.59 = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 0.35/0.59 & ( ord_le3146513528884898305at_nat @ X @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_inf_iff
% 0.35/0.59 thf(fact_4133_le__inf__iff,axiom,
% 0.35/0.59 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) )
% 0.35/0.59 = ( ( ord_less_eq_set_nat @ X @ Y )
% 0.35/0.59 & ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_inf_iff
% 0.35/0.59 thf(fact_4134_le__inf__iff,axiom,
% 0.35/0.59 ! [X: rat,Y: rat,Z3: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) )
% 0.35/0.59 = ( ( ord_less_eq_rat @ X @ Y )
% 0.35/0.59 & ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_inf_iff
% 0.35/0.59 thf(fact_4135_le__inf__iff,axiom,
% 0.35/0.59 ! [X: nat,Y: nat,Z3: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) )
% 0.35/0.59 = ( ( ord_less_eq_nat @ X @ Y )
% 0.35/0.59 & ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_inf_iff
% 0.35/0.59 thf(fact_4136_le__inf__iff,axiom,
% 0.35/0.59 ! [X: int,Y: int,Z3: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) )
% 0.35/0.59 = ( ( ord_less_eq_int @ X @ Y )
% 0.35/0.59 & ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_inf_iff
% 0.35/0.59 thf(fact_4137_inf_Obounded__iff,axiom,
% 0.35/0.59 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 0.35/0.59 = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.35/0.59 & ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.bounded_iff
% 0.35/0.59 thf(fact_4138_inf_Obounded__iff,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 0.35/0.59 = ( ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.59 & ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.bounded_iff
% 0.35/0.59 thf(fact_4139_inf_Obounded__iff,axiom,
% 0.35/0.59 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 0.35/0.59 = ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 & ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.bounded_iff
% 0.35/0.59 thf(fact_4140_inf_Obounded__iff,axiom,
% 0.35/0.59 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 0.35/0.59 = ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.59 & ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.bounded_iff
% 0.35/0.59 thf(fact_4141_inf_Obounded__iff,axiom,
% 0.35/0.59 ! [A: int,B: int,C2: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 0.35/0.59 = ( ( ord_less_eq_int @ A @ B )
% 0.35/0.59 & ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.bounded_iff
% 0.35/0.59 thf(fact_4142_both__member__options__ding,axiom,
% 0.35/0.59 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.59 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 0.35/0.59 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.59 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.59 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % both_member_options_ding
% 0.35/0.59 thf(fact_4143_both__member__options__from__complete__tree__to__child,axiom,
% 0.35/0.59 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.35/0.59 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.59 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.59 | ( X = Mi )
% 0.35/0.59 | ( X = Ma ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % both_member_options_from_complete_tree_to_child
% 0.35/0.59 thf(fact_4144_member__inv,axiom,
% 0.35/0.59 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.59 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.59 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.59 & ( ( X = Mi )
% 0.35/0.59 | ( X = Ma )
% 0.35/0.59 | ( ( ord_less_nat @ X @ Ma )
% 0.35/0.59 & ( ord_less_nat @ Mi @ X )
% 0.35/0.59 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.59 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % member_inv
% 0.35/0.59 thf(fact_4145_both__member__options__from__chilf__to__complete__tree,axiom,
% 0.35/0.59 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.35/0.59 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.59 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 0.35/0.59 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.59 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % both_member_options_from_chilf_to_complete_tree
% 0.35/0.59 thf(fact_4146_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 0.35/0.59 ! [X: nat,N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 0.35/0.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.59 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % VEBT_internal.exp_split_high_low(2)
% 0.35/0.59 thf(fact_4147_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 0.35/0.59 ! [X: nat,N: nat,M2: nat] :
% 0.35/0.59 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 0.35/0.59 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.59 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.59 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % VEBT_internal.exp_split_high_low(1)
% 0.35/0.59 thf(fact_4148_inf__sup__ord_I2_J,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(2)
% 0.35/0.59 thf(fact_4149_inf__sup__ord_I2_J,axiom,
% 0.35/0.59 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(2)
% 0.35/0.59 thf(fact_4150_inf__sup__ord_I2_J,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(2)
% 0.35/0.59 thf(fact_4151_inf__sup__ord_I2_J,axiom,
% 0.35/0.59 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(2)
% 0.35/0.59 thf(fact_4152_inf__sup__ord_I2_J,axiom,
% 0.35/0.59 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(2)
% 0.35/0.59 thf(fact_4153_inf__sup__ord_I1_J,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(1)
% 0.35/0.59 thf(fact_4154_inf__sup__ord_I1_J,axiom,
% 0.35/0.59 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(1)
% 0.35/0.59 thf(fact_4155_inf__sup__ord_I1_J,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(1)
% 0.35/0.59 thf(fact_4156_inf__sup__ord_I1_J,axiom,
% 0.35/0.59 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(1)
% 0.35/0.59 thf(fact_4157_inf__sup__ord_I1_J,axiom,
% 0.35/0.59 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_sup_ord(1)
% 0.35/0.59 thf(fact_4158_inf__le1,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le1
% 0.35/0.59 thf(fact_4159_inf__le1,axiom,
% 0.35/0.59 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le1
% 0.35/0.59 thf(fact_4160_inf__le1,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le1
% 0.35/0.59 thf(fact_4161_inf__le1,axiom,
% 0.35/0.59 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le1
% 0.35/0.59 thf(fact_4162_inf__le1,axiom,
% 0.35/0.59 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le1
% 0.35/0.59 thf(fact_4163_inf__le2,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le2
% 0.35/0.59 thf(fact_4164_inf__le2,axiom,
% 0.35/0.59 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le2
% 0.35/0.59 thf(fact_4165_inf__le2,axiom,
% 0.35/0.59 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le2
% 0.35/0.59 thf(fact_4166_inf__le2,axiom,
% 0.35/0.59 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le2
% 0.35/0.59 thf(fact_4167_inf__le2,axiom,
% 0.35/0.59 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 0.35/0.59
% 0.35/0.59 % inf_le2
% 0.35/0.59 thf(fact_4168_le__infE,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 0.35/0.59 => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 0.35/0.59 => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infE
% 0.35/0.59 thf(fact_4169_le__infE,axiom,
% 0.35/0.59 ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 0.35/0.59 => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 0.35/0.59 => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infE
% 0.35/0.59 thf(fact_4170_le__infE,axiom,
% 0.35/0.59 ! [X: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 0.35/0.59 => ~ ( ( ord_less_eq_rat @ X @ A )
% 0.35/0.59 => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infE
% 0.35/0.59 thf(fact_4171_le__infE,axiom,
% 0.35/0.59 ! [X: nat,A: nat,B: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 0.35/0.59 => ~ ( ( ord_less_eq_nat @ X @ A )
% 0.35/0.59 => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infE
% 0.35/0.59 thf(fact_4172_le__infE,axiom,
% 0.35/0.59 ! [X: int,A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 0.35/0.59 => ~ ( ( ord_less_eq_int @ X @ A )
% 0.35/0.59 => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infE
% 0.35/0.59 thf(fact_4173_le__infI,axiom,
% 0.35/0.59 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ X @ A )
% 0.35/0.59 => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 0.35/0.59 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI
% 0.35/0.59 thf(fact_4174_le__infI,axiom,
% 0.35/0.59 ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ X @ A )
% 0.35/0.59 => ( ( ord_less_eq_set_nat @ X @ B )
% 0.35/0.59 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI
% 0.35/0.59 thf(fact_4175_le__infI,axiom,
% 0.35/0.59 ! [X: rat,A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X @ A )
% 0.35/0.59 => ( ( ord_less_eq_rat @ X @ B )
% 0.35/0.59 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI
% 0.35/0.59 thf(fact_4176_le__infI,axiom,
% 0.35/0.59 ! [X: nat,A: nat,B: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ X @ A )
% 0.35/0.59 => ( ( ord_less_eq_nat @ X @ B )
% 0.35/0.59 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI
% 0.35/0.59 thf(fact_4177_le__infI,axiom,
% 0.35/0.59 ! [X: int,A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ X @ A )
% 0.35/0.59 => ( ( ord_less_eq_int @ X @ B )
% 0.35/0.59 => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI
% 0.35/0.59 thf(fact_4178_inf__mono,axiom,
% 0.35/0.59 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 0.35/0.59 => ( ( ord_le3146513528884898305at_nat @ B @ D )
% 0.35/0.59 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C2 @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_mono
% 0.35/0.59 thf(fact_4179_inf__mono,axiom,
% 0.35/0.59 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ A @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_set_nat @ B @ D )
% 0.35/0.59 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C2 @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_mono
% 0.35/0.59 thf(fact_4180_inf__mono,axiom,
% 0.35/0.59 ! [A: rat,C2: rat,B: rat,D: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ B @ D )
% 0.35/0.59 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C2 @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_mono
% 0.35/0.59 thf(fact_4181_inf__mono,axiom,
% 0.35/0.59 ! [A: nat,C2: nat,B: nat,D: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ A @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_nat @ B @ D )
% 0.35/0.59 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C2 @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_mono
% 0.35/0.59 thf(fact_4182_inf__mono,axiom,
% 0.35/0.59 ! [A: int,C2: int,B: int,D: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ C2 )
% 0.35/0.59 => ( ( ord_less_eq_int @ B @ D )
% 0.35/0.59 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C2 @ D ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_mono
% 0.35/0.59 thf(fact_4183_le__infI1,axiom,
% 0.35/0.59 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ A @ X )
% 0.35/0.59 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI1
% 0.35/0.59 thf(fact_4184_le__infI1,axiom,
% 0.35/0.59 ! [A: set_nat,X: set_nat,B: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ A @ X )
% 0.35/0.59 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI1
% 0.35/0.59 thf(fact_4185_le__infI1,axiom,
% 0.35/0.59 ! [A: rat,X: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ X )
% 0.35/0.59 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI1
% 0.35/0.59 thf(fact_4186_le__infI1,axiom,
% 0.35/0.59 ! [A: nat,X: nat,B: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ A @ X )
% 0.35/0.59 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI1
% 0.35/0.59 thf(fact_4187_le__infI1,axiom,
% 0.35/0.59 ! [A: int,X: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ X )
% 0.35/0.59 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI1
% 0.35/0.59 thf(fact_4188_le__infI2,axiom,
% 0.35/0.59 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ B @ X )
% 0.35/0.59 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI2
% 0.35/0.59 thf(fact_4189_le__infI2,axiom,
% 0.35/0.59 ! [B: set_nat,X: set_nat,A: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ B @ X )
% 0.35/0.59 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI2
% 0.35/0.59 thf(fact_4190_le__infI2,axiom,
% 0.35/0.59 ! [B: rat,X: rat,A: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ B @ X )
% 0.35/0.59 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI2
% 0.35/0.59 thf(fact_4191_le__infI2,axiom,
% 0.35/0.59 ! [B: nat,X: nat,A: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ B @ X )
% 0.35/0.59 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI2
% 0.35/0.59 thf(fact_4192_le__infI2,axiom,
% 0.35/0.59 ! [B: int,X: int,A: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ B @ X )
% 0.35/0.59 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_infI2
% 0.35/0.59 thf(fact_4193_inf_OorderE,axiom,
% 0.35/0.59 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderE
% 0.35/0.59 thf(fact_4194_inf_OorderE,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderE
% 0.35/0.59 thf(fact_4195_inf_OorderE,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( inf_inf_rat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderE
% 0.35/0.59 thf(fact_4196_inf_OorderE,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( inf_inf_nat @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderE
% 0.35/0.59 thf(fact_4197_inf_OorderE,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ B )
% 0.35/0.59 => ( A
% 0.35/0.59 = ( inf_inf_int @ A @ B ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderE
% 0.35/0.59 thf(fact_4198_inf_OorderI,axiom,
% 0.35/0.59 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 0.35/0.59 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderI
% 0.35/0.59 thf(fact_4199_inf_OorderI,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( inf_inf_set_nat @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderI
% 0.35/0.59 thf(fact_4200_inf_OorderI,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( inf_inf_rat @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderI
% 0.35/0.59 thf(fact_4201_inf_OorderI,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( inf_inf_nat @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_nat @ A @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderI
% 0.35/0.59 thf(fact_4202_inf_OorderI,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( A
% 0.35/0.59 = ( inf_inf_int @ A @ B ) )
% 0.35/0.59 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.orderI
% 0.35/0.59 thf(fact_4203_inf__unique,axiom,
% 0.35/0.59 ! [F2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 0.35/0.59 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 0.35/0.59 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ X3 @ Y3 )
% 0.35/0.59 => ( ( ord_le3146513528884898305at_nat @ X3 @ Z )
% 0.35/0.59 => ( ord_le3146513528884898305at_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 0.35/0.59 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.35/0.59 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_unique
% 0.35/0.59 thf(fact_4204_inf__unique,axiom,
% 0.35/0.59 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 0.35/0.59 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 0.35/0.59 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 0.35/0.59 => ( ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 0.35/0.59 => ( ( ord_less_eq_set_nat @ X3 @ Z )
% 0.35/0.59 => ( ord_less_eq_set_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 0.35/0.59 => ( ( inf_inf_set_nat @ X @ Y )
% 0.35/0.59 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_unique
% 0.35/0.59 thf(fact_4205_inf__unique,axiom,
% 0.35/0.59 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 0.35/0.59 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 0.35/0.59 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 0.35/0.59 => ( ! [X3: rat,Y3: rat,Z: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 0.35/0.59 => ( ( ord_less_eq_rat @ X3 @ Z )
% 0.35/0.59 => ( ord_less_eq_rat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 0.35/0.59 => ( ( inf_inf_rat @ X @ Y )
% 0.35/0.59 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_unique
% 0.35/0.59 thf(fact_4206_inf__unique,axiom,
% 0.35/0.59 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 0.35/0.59 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 0.35/0.59 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 0.35/0.59 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 0.35/0.59 => ( ( ord_less_eq_nat @ X3 @ Z )
% 0.35/0.59 => ( ord_less_eq_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 0.35/0.59 => ( ( inf_inf_nat @ X @ Y )
% 0.35/0.59 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_unique
% 0.35/0.59 thf(fact_4207_inf__unique,axiom,
% 0.35/0.59 ! [F2: int > int > int,X: int,Y: int] :
% 0.35/0.59 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ X3 )
% 0.35/0.59 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 0.35/0.59 => ( ! [X3: int,Y3: int,Z: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ X3 @ Y3 )
% 0.35/0.59 => ( ( ord_less_eq_int @ X3 @ Z )
% 0.35/0.59 => ( ord_less_eq_int @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 0.35/0.59 => ( ( inf_inf_int @ X @ Y )
% 0.35/0.59 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf_unique
% 0.35/0.59 thf(fact_4208_le__iff__inf,axiom,
% 0.35/0.59 ( ord_le3146513528884898305at_nat
% 0.35/0.59 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( inf_in2572325071724192079at_nat @ X4 @ Y4 )
% 0.35/0.59 = X4 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_iff_inf
% 0.35/0.59 thf(fact_4209_le__iff__inf,axiom,
% 0.35/0.59 ( ord_less_eq_set_nat
% 0.35/0.59 = ( ^ [X4: set_nat,Y4: set_nat] :
% 0.35/0.59 ( ( inf_inf_set_nat @ X4 @ Y4 )
% 0.35/0.59 = X4 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_iff_inf
% 0.35/0.59 thf(fact_4210_le__iff__inf,axiom,
% 0.35/0.59 ( ord_less_eq_rat
% 0.35/0.59 = ( ^ [X4: rat,Y4: rat] :
% 0.35/0.59 ( ( inf_inf_rat @ X4 @ Y4 )
% 0.35/0.59 = X4 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_iff_inf
% 0.35/0.59 thf(fact_4211_le__iff__inf,axiom,
% 0.35/0.59 ( ord_less_eq_nat
% 0.35/0.59 = ( ^ [X4: nat,Y4: nat] :
% 0.35/0.59 ( ( inf_inf_nat @ X4 @ Y4 )
% 0.35/0.59 = X4 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_iff_inf
% 0.35/0.59 thf(fact_4212_le__iff__inf,axiom,
% 0.35/0.59 ( ord_less_eq_int
% 0.35/0.59 = ( ^ [X4: int,Y4: int] :
% 0.35/0.59 ( ( inf_inf_int @ X4 @ Y4 )
% 0.35/0.59 = X4 ) ) ) ).
% 0.35/0.59
% 0.35/0.59 % le_iff_inf
% 0.35/0.59 thf(fact_4213_inf_Oabsorb1,axiom,
% 0.35/0.59 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.35/0.59 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.absorb1
% 0.35/0.59 thf(fact_4214_inf_Oabsorb1,axiom,
% 0.35/0.59 ! [A: set_nat,B: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.59 => ( ( inf_inf_set_nat @ A @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.absorb1
% 0.35/0.59 thf(fact_4215_inf_Oabsorb1,axiom,
% 0.35/0.59 ! [A: rat,B: rat] :
% 0.35/0.59 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.59 => ( ( inf_inf_rat @ A @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.absorb1
% 0.35/0.59 thf(fact_4216_inf_Oabsorb1,axiom,
% 0.35/0.59 ! [A: nat,B: nat] :
% 0.35/0.59 ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.59 => ( ( inf_inf_nat @ A @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.absorb1
% 0.35/0.59 thf(fact_4217_inf_Oabsorb1,axiom,
% 0.35/0.59 ! [A: int,B: int] :
% 0.35/0.59 ( ( ord_less_eq_int @ A @ B )
% 0.35/0.59 => ( ( inf_inf_int @ A @ B )
% 0.35/0.59 = A ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.absorb1
% 0.35/0.59 thf(fact_4218_inf_Oabsorb2,axiom,
% 0.35/0.59 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.35/0.59 ( ( ord_le3146513528884898305at_nat @ B @ A )
% 0.35/0.59 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 0.35/0.59 = B ) ) ).
% 0.35/0.59
% 0.35/0.59 % inf.absorb2
% 0.35/0.59 thf(fact_4219_inf_Oabsorb2,axiom,
% 0.35/0.59 ! [B: set_nat,A: set_nat] :
% 0.35/0.59 ( ( ord_less_eq_set_nat @ B @ A )
% 0.35/0.60 => ( ( inf_inf_set_nat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb2
% 0.35/0.60 thf(fact_4220_inf_Oabsorb2,axiom,
% 0.35/0.60 ! [B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ( ( inf_inf_rat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb2
% 0.35/0.60 thf(fact_4221_inf_Oabsorb2,axiom,
% 0.35/0.60 ! [B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ( ( inf_inf_nat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb2
% 0.35/0.60 thf(fact_4222_inf_Oabsorb2,axiom,
% 0.35/0.60 ! [B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ( ( inf_inf_int @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb2
% 0.35/0.60 thf(fact_4223_inf__absorb1,axiom,
% 0.35/0.60 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 0.35/0.60 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb1
% 0.35/0.60 thf(fact_4224_inf__absorb1,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.35/0.60 => ( ( inf_inf_set_nat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb1
% 0.35/0.60 thf(fact_4225_inf__absorb1,axiom,
% 0.35/0.60 ! [X: rat,Y: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ X @ Y )
% 0.35/0.60 => ( ( inf_inf_rat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb1
% 0.35/0.60 thf(fact_4226_inf__absorb1,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ X @ Y )
% 0.35/0.60 => ( ( inf_inf_nat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb1
% 0.35/0.60 thf(fact_4227_inf__absorb1,axiom,
% 0.35/0.60 ! [X: int,Y: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ X @ Y )
% 0.35/0.60 => ( ( inf_inf_int @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb1
% 0.35/0.60 thf(fact_4228_inf__absorb2,axiom,
% 0.35/0.60 ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 0.35/0.60 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb2
% 0.35/0.60 thf(fact_4229_inf__absorb2,axiom,
% 0.35/0.60 ! [Y: set_nat,X: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ Y @ X )
% 0.35/0.60 => ( ( inf_inf_set_nat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb2
% 0.35/0.60 thf(fact_4230_inf__absorb2,axiom,
% 0.35/0.60 ! [Y: rat,X: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ Y @ X )
% 0.35/0.60 => ( ( inf_inf_rat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb2
% 0.35/0.60 thf(fact_4231_inf__absorb2,axiom,
% 0.35/0.60 ! [Y: nat,X: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ Y @ X )
% 0.35/0.60 => ( ( inf_inf_nat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb2
% 0.35/0.60 thf(fact_4232_inf__absorb2,axiom,
% 0.35/0.60 ! [Y: int,X: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ Y @ X )
% 0.35/0.60 => ( ( inf_inf_int @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_absorb2
% 0.35/0.60 thf(fact_4233_inf_OboundedE,axiom,
% 0.35/0.60 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 0.35/0.60 => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.35/0.60 => ~ ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedE
% 0.35/0.60 thf(fact_4234_inf_OboundedE,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 0.35/0.60 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.60 => ~ ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedE
% 0.35/0.60 thf(fact_4235_inf_OboundedE,axiom,
% 0.35/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 0.35/0.60 => ~ ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.60 => ~ ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedE
% 0.35/0.60 thf(fact_4236_inf_OboundedE,axiom,
% 0.35/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 0.35/0.60 => ~ ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.60 => ~ ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedE
% 0.35/0.60 thf(fact_4237_inf_OboundedE,axiom,
% 0.35/0.60 ! [A: int,B: int,C2: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 0.35/0.60 => ~ ( ( ord_less_eq_int @ A @ B )
% 0.35/0.60 => ~ ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedE
% 0.35/0.60 thf(fact_4238_inf_OboundedI,axiom,
% 0.35/0.60 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 0.35/0.60 => ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 0.35/0.60 => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedI
% 0.35/0.60 thf(fact_4239_inf_OboundedI,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedI
% 0.35/0.60 thf(fact_4240_inf_OboundedI,axiom,
% 0.35/0.60 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.60 => ( ( ord_less_eq_rat @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedI
% 0.35/0.60 thf(fact_4241_inf_OboundedI,axiom,
% 0.35/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.60 => ( ( ord_less_eq_nat @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedI
% 0.35/0.60 thf(fact_4242_inf_OboundedI,axiom,
% 0.35/0.60 ! [A: int,B: int,C2: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.35/0.60 => ( ( ord_less_eq_int @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.boundedI
% 0.35/0.60 thf(fact_4243_inf__greatest,axiom,
% 0.35/0.60 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 0.35/0.60 => ( ( ord_le3146513528884898305at_nat @ X @ Z3 )
% 0.35/0.60 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_greatest
% 0.35/0.60 thf(fact_4244_inf__greatest,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ X @ Z3 )
% 0.35/0.60 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_greatest
% 0.35/0.60 thf(fact_4245_inf__greatest,axiom,
% 0.35/0.60 ! [X: rat,Y: rat,Z3: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ X @ Y )
% 0.35/0.60 => ( ( ord_less_eq_rat @ X @ Z3 )
% 0.35/0.60 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_greatest
% 0.35/0.60 thf(fact_4246_inf__greatest,axiom,
% 0.35/0.60 ! [X: nat,Y: nat,Z3: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ X @ Y )
% 0.35/0.60 => ( ( ord_less_eq_nat @ X @ Z3 )
% 0.35/0.60 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_greatest
% 0.35/0.60 thf(fact_4247_inf__greatest,axiom,
% 0.35/0.60 ! [X: int,Y: int,Z3: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ X @ Y )
% 0.35/0.60 => ( ( ord_less_eq_int @ X @ Z3 )
% 0.35/0.60 => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_greatest
% 0.35/0.60 thf(fact_4248_inf_Oorder__iff,axiom,
% 0.35/0.60 ( ord_le3146513528884898305at_nat
% 0.35/0.60 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( inf_in2572325071724192079at_nat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.order_iff
% 0.35/0.60 thf(fact_4249_inf_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_set_nat
% 0.35/0.60 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( inf_inf_set_nat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.order_iff
% 0.35/0.60 thf(fact_4250_inf_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [A5: rat,B4: rat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( inf_inf_rat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.order_iff
% 0.35/0.60 thf(fact_4251_inf_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [A5: nat,B4: nat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( inf_inf_nat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.order_iff
% 0.35/0.60 thf(fact_4252_inf_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [A5: int,B4: int] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( inf_inf_int @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.order_iff
% 0.35/0.60 thf(fact_4253_inf_Ocobounded1,axiom,
% 0.35/0.60 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded1
% 0.35/0.60 thf(fact_4254_inf_Ocobounded1,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded1
% 0.35/0.60 thf(fact_4255_inf_Ocobounded1,axiom,
% 0.35/0.60 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded1
% 0.35/0.60 thf(fact_4256_inf_Ocobounded1,axiom,
% 0.35/0.60 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded1
% 0.35/0.60 thf(fact_4257_inf_Ocobounded1,axiom,
% 0.35/0.60 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded1
% 0.35/0.60 thf(fact_4258_inf_Ocobounded2,axiom,
% 0.35/0.60 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded2
% 0.35/0.60 thf(fact_4259_inf_Ocobounded2,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded2
% 0.35/0.60 thf(fact_4260_inf_Ocobounded2,axiom,
% 0.35/0.60 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded2
% 0.35/0.60 thf(fact_4261_inf_Ocobounded2,axiom,
% 0.35/0.60 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded2
% 0.35/0.60 thf(fact_4262_inf_Ocobounded2,axiom,
% 0.35/0.60 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 0.35/0.60
% 0.35/0.60 % inf.cobounded2
% 0.35/0.60 thf(fact_4263_inf_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_le3146513528884898305at_nat
% 0.35/0.60 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff1
% 0.35/0.60 thf(fact_4264_inf_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_set_nat
% 0.35/0.60 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.35/0.60 ( ( inf_inf_set_nat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff1
% 0.35/0.60 thf(fact_4265_inf_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [A5: rat,B4: rat] :
% 0.35/0.60 ( ( inf_inf_rat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff1
% 0.35/0.60 thf(fact_4266_inf_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [A5: nat,B4: nat] :
% 0.35/0.60 ( ( inf_inf_nat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff1
% 0.35/0.60 thf(fact_4267_inf_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [A5: int,B4: int] :
% 0.35/0.60 ( ( inf_inf_int @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff1
% 0.35/0.60 thf(fact_4268_inf_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_le3146513528884898305at_nat
% 0.35/0.60 = ( ^ [B4: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff2
% 0.35/0.60 thf(fact_4269_inf_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_set_nat
% 0.35/0.60 = ( ^ [B4: set_nat,A5: set_nat] :
% 0.35/0.60 ( ( inf_inf_set_nat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff2
% 0.35/0.60 thf(fact_4270_inf_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [B4: rat,A5: rat] :
% 0.35/0.60 ( ( inf_inf_rat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff2
% 0.35/0.60 thf(fact_4271_inf_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [B4: nat,A5: nat] :
% 0.35/0.60 ( ( inf_inf_nat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff2
% 0.35/0.60 thf(fact_4272_inf_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [B4: int,A5: int] :
% 0.35/0.60 ( ( inf_inf_int @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.absorb_iff2
% 0.35/0.60 thf(fact_4273_inf_OcoboundedI1,axiom,
% 0.35/0.60 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 0.35/0.60 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI1
% 0.35/0.60 thf(fact_4274_inf_OcoboundedI1,axiom,
% 0.35/0.60 ! [A: set_nat,C2: set_nat,B: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI1
% 0.35/0.60 thf(fact_4275_inf_OcoboundedI1,axiom,
% 0.35/0.60 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI1
% 0.35/0.60 thf(fact_4276_inf_OcoboundedI1,axiom,
% 0.35/0.60 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI1
% 0.35/0.60 thf(fact_4277_inf_OcoboundedI1,axiom,
% 0.35/0.60 ! [A: int,C2: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ A @ C2 )
% 0.35/0.60 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI1
% 0.35/0.60 thf(fact_4278_inf_OcoboundedI2,axiom,
% 0.35/0.60 ! [B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( ord_le3146513528884898305at_nat @ B @ C2 )
% 0.35/0.60 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI2
% 0.35/0.60 thf(fact_4279_inf_OcoboundedI2,axiom,
% 0.35/0.60 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ B @ C2 )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI2
% 0.35/0.60 thf(fact_4280_inf_OcoboundedI2,axiom,
% 0.35/0.60 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ C2 )
% 0.35/0.60 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI2
% 0.35/0.60 thf(fact_4281_inf_OcoboundedI2,axiom,
% 0.35/0.60 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ C2 )
% 0.35/0.60 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI2
% 0.35/0.60 thf(fact_4282_inf_OcoboundedI2,axiom,
% 0.35/0.60 ! [B: int,C2: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ C2 )
% 0.35/0.60 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf.coboundedI2
% 0.35/0.60 thf(fact_4283_sup_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: set_nat,B: set_nat,A: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI2
% 0.35/0.60 thf(fact_4284_sup_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI2
% 0.35/0.60 thf(fact_4285_sup_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI2
% 0.35/0.60 thf(fact_4286_sup_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: int,B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI2
% 0.35/0.60 thf(fact_4287_sup_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI1
% 0.35/0.60 thf(fact_4288_sup_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI1
% 0.35/0.60 thf(fact_4289_sup_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI1
% 0.35/0.60 thf(fact_4290_sup_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: int,A: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.coboundedI1
% 0.35/0.60 thf(fact_4291_sup_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_set_nat
% 0.35/0.60 = ( ^ [A5: set_nat,B4: set_nat] :
% 0.35/0.60 ( ( sup_sup_set_nat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff2
% 0.35/0.60 thf(fact_4292_sup_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [A5: rat,B4: rat] :
% 0.35/0.60 ( ( sup_sup_rat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff2
% 0.35/0.60 thf(fact_4293_sup_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [A5: nat,B4: nat] :
% 0.35/0.60 ( ( sup_sup_nat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff2
% 0.35/0.60 thf(fact_4294_sup_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [A5: int,B4: int] :
% 0.35/0.60 ( ( sup_sup_int @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff2
% 0.35/0.60 thf(fact_4295_sup_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_set_nat
% 0.35/0.60 = ( ^ [B4: set_nat,A5: set_nat] :
% 0.35/0.60 ( ( sup_sup_set_nat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff1
% 0.35/0.60 thf(fact_4296_sup_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [B4: rat,A5: rat] :
% 0.35/0.60 ( ( sup_sup_rat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff1
% 0.35/0.60 thf(fact_4297_sup_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [B4: nat,A5: nat] :
% 0.35/0.60 ( ( sup_sup_nat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff1
% 0.35/0.60 thf(fact_4298_sup_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [B4: int,A5: int] :
% 0.35/0.60 ( ( sup_sup_int @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb_iff1
% 0.35/0.60 thf(fact_4299_sup_Ocobounded2,axiom,
% 0.35/0.60 ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded2
% 0.35/0.60 thf(fact_4300_sup_Ocobounded2,axiom,
% 0.35/0.60 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded2
% 0.35/0.60 thf(fact_4301_sup_Ocobounded2,axiom,
% 0.35/0.60 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded2
% 0.35/0.60 thf(fact_4302_sup_Ocobounded2,axiom,
% 0.35/0.60 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded2
% 0.35/0.60 thf(fact_4303_sup_Ocobounded1,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded1
% 0.35/0.60 thf(fact_4304_sup_Ocobounded1,axiom,
% 0.35/0.60 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded1
% 0.35/0.60 thf(fact_4305_sup_Ocobounded1,axiom,
% 0.35/0.60 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded1
% 0.35/0.60 thf(fact_4306_sup_Ocobounded1,axiom,
% 0.35/0.60 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.cobounded1
% 0.35/0.60 thf(fact_4307_sup_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_set_nat
% 0.35/0.60 = ( ^ [B4: set_nat,A5: set_nat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( sup_sup_set_nat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.order_iff
% 0.35/0.60 thf(fact_4308_sup_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [B4: rat,A5: rat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( sup_sup_rat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.order_iff
% 0.35/0.60 thf(fact_4309_sup_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [B4: nat,A5: nat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( sup_sup_nat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.order_iff
% 0.35/0.60 thf(fact_4310_sup_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [B4: int,A5: int] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( sup_sup_int @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.order_iff
% 0.35/0.60 thf(fact_4311_sup_OboundedI,axiom,
% 0.35/0.60 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedI
% 0.35/0.60 thf(fact_4312_sup_OboundedI,axiom,
% 0.35/0.60 ! [B: rat,A: rat,C2: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedI
% 0.35/0.60 thf(fact_4313_sup_OboundedI,axiom,
% 0.35/0.60 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedI
% 0.35/0.60 thf(fact_4314_sup_OboundedI,axiom,
% 0.35/0.60 ! [B: int,A: int,C2: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedI
% 0.35/0.60 thf(fact_4315_sup_OboundedE,axiom,
% 0.35/0.60 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedE
% 0.35/0.60 thf(fact_4316_sup_OboundedE,axiom,
% 0.35/0.60 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedE
% 0.35/0.60 thf(fact_4317_sup_OboundedE,axiom,
% 0.35/0.60 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedE
% 0.35/0.60 thf(fact_4318_sup_OboundedE,axiom,
% 0.35/0.60 ! [B: int,C2: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.boundedE
% 0.35/0.60 thf(fact_4319_sup__absorb2,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.35/0.60 => ( ( sup_sup_set_nat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb2
% 0.35/0.60 thf(fact_4320_sup__absorb2,axiom,
% 0.35/0.60 ! [X: rat,Y: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ X @ Y )
% 0.35/0.60 => ( ( sup_sup_rat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb2
% 0.35/0.60 thf(fact_4321_sup__absorb2,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ X @ Y )
% 0.35/0.60 => ( ( sup_sup_nat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb2
% 0.35/0.60 thf(fact_4322_sup__absorb2,axiom,
% 0.35/0.60 ! [X: int,Y: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ X @ Y )
% 0.35/0.60 => ( ( sup_sup_int @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb2
% 0.35/0.60 thf(fact_4323_sup__absorb1,axiom,
% 0.35/0.60 ! [Y: set_nat,X: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ Y @ X )
% 0.35/0.60 => ( ( sup_sup_set_nat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb1
% 0.35/0.60 thf(fact_4324_sup__absorb1,axiom,
% 0.35/0.60 ! [Y: rat,X: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ Y @ X )
% 0.35/0.60 => ( ( sup_sup_rat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb1
% 0.35/0.60 thf(fact_4325_sup__absorb1,axiom,
% 0.35/0.60 ! [Y: nat,X: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ Y @ X )
% 0.35/0.60 => ( ( sup_sup_nat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb1
% 0.35/0.60 thf(fact_4326_sup__absorb1,axiom,
% 0.35/0.60 ! [Y: int,X: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ Y @ X )
% 0.35/0.60 => ( ( sup_sup_int @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_absorb1
% 0.35/0.60 thf(fact_4327_sup_Oabsorb2,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ A @ B )
% 0.35/0.60 => ( ( sup_sup_set_nat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb2
% 0.35/0.60 thf(fact_4328_sup_Oabsorb2,axiom,
% 0.35/0.60 ! [A: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.60 => ( ( sup_sup_rat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb2
% 0.35/0.60 thf(fact_4329_sup_Oabsorb2,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.60 => ( ( sup_sup_nat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb2
% 0.35/0.60 thf(fact_4330_sup_Oabsorb2,axiom,
% 0.35/0.60 ! [A: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.35/0.60 => ( ( sup_sup_int @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb2
% 0.35/0.60 thf(fact_4331_sup_Oabsorb1,axiom,
% 0.35/0.60 ! [B: set_nat,A: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ B @ A )
% 0.35/0.60 => ( ( sup_sup_set_nat @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb1
% 0.35/0.60 thf(fact_4332_sup_Oabsorb1,axiom,
% 0.35/0.60 ! [B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ( ( sup_sup_rat @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb1
% 0.35/0.60 thf(fact_4333_sup_Oabsorb1,axiom,
% 0.35/0.60 ! [B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ( ( sup_sup_nat @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb1
% 0.35/0.60 thf(fact_4334_sup_Oabsorb1,axiom,
% 0.35/0.60 ! [B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ( ( sup_sup_int @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.absorb1
% 0.35/0.60 thf(fact_4335_sup__unique,axiom,
% 0.35/0.60 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 0.35/0.60 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ Z @ X3 )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 0.35/0.60 => ( ( sup_sup_set_nat @ X @ Y )
% 0.35/0.60 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_unique
% 0.35/0.60 thf(fact_4336_sup__unique,axiom,
% 0.35/0.60 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 0.35/0.60 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: rat,Y3: rat,Z: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ Y3 @ X3 )
% 0.35/0.60 => ( ( ord_less_eq_rat @ Z @ X3 )
% 0.35/0.60 => ( ord_less_eq_rat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 0.35/0.60 => ( ( sup_sup_rat @ X @ Y )
% 0.35/0.60 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_unique
% 0.35/0.60 thf(fact_4337_sup__unique,axiom,
% 0.35/0.60 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 0.35/0.60 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Z @ X3 )
% 0.35/0.60 => ( ord_less_eq_nat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 0.35/0.60 => ( ( sup_sup_nat @ X @ Y )
% 0.35/0.60 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_unique
% 0.35/0.60 thf(fact_4338_sup__unique,axiom,
% 0.35/0.60 ! [F2: int > int > int,X: int,Y: int] :
% 0.35/0.60 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ X3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 0.35/0.60 => ( ! [X3: int,Y3: int,Z: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ Y3 @ X3 )
% 0.35/0.60 => ( ( ord_less_eq_int @ Z @ X3 )
% 0.35/0.60 => ( ord_less_eq_int @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 0.35/0.60 => ( ( sup_sup_int @ X @ Y )
% 0.35/0.60 = ( F2 @ X @ Y ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_unique
% 0.35/0.60 thf(fact_4339_sup_OorderI,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( sup_sup_set_nat @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderI
% 0.35/0.60 thf(fact_4340_sup_OorderI,axiom,
% 0.35/0.60 ! [A: rat,B: rat] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( sup_sup_rat @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderI
% 0.35/0.60 thf(fact_4341_sup_OorderI,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( sup_sup_nat @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderI
% 0.35/0.60 thf(fact_4342_sup_OorderI,axiom,
% 0.35/0.60 ! [A: int,B: int] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( sup_sup_int @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_int @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderI
% 0.35/0.60 thf(fact_4343_sup_OorderE,axiom,
% 0.35/0.60 ! [B: set_nat,A: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderE
% 0.35/0.60 thf(fact_4344_sup_OorderE,axiom,
% 0.35/0.60 ! [B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( sup_sup_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderE
% 0.35/0.60 thf(fact_4345_sup_OorderE,axiom,
% 0.35/0.60 ! [B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( sup_sup_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderE
% 0.35/0.60 thf(fact_4346_sup_OorderE,axiom,
% 0.35/0.60 ! [B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( sup_sup_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.orderE
% 0.35/0.60 thf(fact_4347_le__iff__sup,axiom,
% 0.35/0.60 ( ord_less_eq_set_nat
% 0.35/0.60 = ( ^ [X4: set_nat,Y4: set_nat] :
% 0.35/0.60 ( ( sup_sup_set_nat @ X4 @ Y4 )
% 0.35/0.60 = Y4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_iff_sup
% 0.35/0.60 thf(fact_4348_le__iff__sup,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [X4: rat,Y4: rat] :
% 0.35/0.60 ( ( sup_sup_rat @ X4 @ Y4 )
% 0.35/0.60 = Y4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_iff_sup
% 0.35/0.60 thf(fact_4349_le__iff__sup,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [X4: nat,Y4: nat] :
% 0.35/0.60 ( ( sup_sup_nat @ X4 @ Y4 )
% 0.35/0.60 = Y4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_iff_sup
% 0.35/0.60 thf(fact_4350_le__iff__sup,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [X4: int,Y4: int] :
% 0.35/0.60 ( ( sup_sup_int @ X4 @ Y4 )
% 0.35/0.60 = Y4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_iff_sup
% 0.35/0.60 thf(fact_4351_sup__least,axiom,
% 0.35/0.60 ! [Y: set_nat,X: set_nat,Z3: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ Y @ X )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ Z3 @ X )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z3 ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_least
% 0.35/0.60 thf(fact_4352_sup__least,axiom,
% 0.35/0.60 ! [Y: rat,X: rat,Z3: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ Y @ X )
% 0.35/0.60 => ( ( ord_less_eq_rat @ Z3 @ X )
% 0.35/0.60 => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z3 ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_least
% 0.35/0.60 thf(fact_4353_sup__least,axiom,
% 0.35/0.60 ! [Y: nat,X: nat,Z3: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ Y @ X )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Z3 @ X )
% 0.35/0.60 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z3 ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_least
% 0.35/0.60 thf(fact_4354_sup__least,axiom,
% 0.35/0.60 ! [Y: int,X: int,Z3: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ Y @ X )
% 0.35/0.60 => ( ( ord_less_eq_int @ Z3 @ X )
% 0.35/0.60 => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z3 ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_least
% 0.35/0.60 thf(fact_4355_sup__mono,axiom,
% 0.35/0.60 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ A @ C2 )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ B @ D )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C2 @ D ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_mono
% 0.35/0.60 thf(fact_4356_sup__mono,axiom,
% 0.35/0.60 ! [A: rat,C2: rat,B: rat,D: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ A @ C2 )
% 0.35/0.60 => ( ( ord_less_eq_rat @ B @ D )
% 0.35/0.60 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C2 @ D ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_mono
% 0.35/0.60 thf(fact_4357_sup__mono,axiom,
% 0.35/0.60 ! [A: nat,C2: nat,B: nat,D: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ A @ C2 )
% 0.35/0.60 => ( ( ord_less_eq_nat @ B @ D )
% 0.35/0.60 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C2 @ D ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_mono
% 0.35/0.60 thf(fact_4358_sup__mono,axiom,
% 0.35/0.60 ! [A: int,C2: int,B: int,D: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ A @ C2 )
% 0.35/0.60 => ( ( ord_less_eq_int @ B @ D )
% 0.35/0.60 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C2 @ D ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_mono
% 0.35/0.60 thf(fact_4359_sup_Omono,axiom,
% 0.35/0.60 ! [C2: set_nat,A: set_nat,D: set_nat,B: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ D @ B )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C2 @ D ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.mono
% 0.35/0.60 thf(fact_4360_sup_Omono,axiom,
% 0.35/0.60 ! [C2: rat,A: rat,D: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_rat @ D @ B )
% 0.35/0.60 => ( ord_less_eq_rat @ ( sup_sup_rat @ C2 @ D ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.mono
% 0.35/0.60 thf(fact_4361_sup_Omono,axiom,
% 0.35/0.60 ! [C2: nat,A: nat,D: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_nat @ D @ B )
% 0.35/0.60 => ( ord_less_eq_nat @ ( sup_sup_nat @ C2 @ D ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.mono
% 0.35/0.60 thf(fact_4362_sup_Omono,axiom,
% 0.35/0.60 ! [C2: int,A: int,D: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_int @ D @ B )
% 0.35/0.60 => ( ord_less_eq_int @ ( sup_sup_int @ C2 @ D ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup.mono
% 0.35/0.60 thf(fact_4363_le__supI2,axiom,
% 0.35/0.60 ! [X: set_nat,B: set_nat,A: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ X @ B )
% 0.35/0.60 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI2
% 0.35/0.60 thf(fact_4364_le__supI2,axiom,
% 0.35/0.60 ! [X: rat,B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ X @ B )
% 0.35/0.60 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI2
% 0.35/0.60 thf(fact_4365_le__supI2,axiom,
% 0.35/0.60 ! [X: nat,B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ X @ B )
% 0.35/0.60 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI2
% 0.35/0.60 thf(fact_4366_le__supI2,axiom,
% 0.35/0.60 ! [X: int,B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ X @ B )
% 0.35/0.60 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI2
% 0.35/0.60 thf(fact_4367_le__supI1,axiom,
% 0.35/0.60 ! [X: set_nat,A: set_nat,B: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ X @ A )
% 0.35/0.60 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI1
% 0.35/0.60 thf(fact_4368_le__supI1,axiom,
% 0.35/0.60 ! [X: rat,A: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ X @ A )
% 0.35/0.60 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI1
% 0.35/0.60 thf(fact_4369_le__supI1,axiom,
% 0.35/0.60 ! [X: nat,A: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ X @ A )
% 0.35/0.60 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI1
% 0.35/0.60 thf(fact_4370_le__supI1,axiom,
% 0.35/0.60 ! [X: int,A: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ X @ A )
% 0.35/0.60 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI1
% 0.35/0.60 thf(fact_4371_sup__ge2,axiom,
% 0.35/0.60 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge2
% 0.35/0.60 thf(fact_4372_sup__ge2,axiom,
% 0.35/0.60 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge2
% 0.35/0.60 thf(fact_4373_sup__ge2,axiom,
% 0.35/0.60 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge2
% 0.35/0.60 thf(fact_4374_sup__ge2,axiom,
% 0.35/0.60 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge2
% 0.35/0.60 thf(fact_4375_sup__ge1,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge1
% 0.35/0.60 thf(fact_4376_sup__ge1,axiom,
% 0.35/0.60 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge1
% 0.35/0.60 thf(fact_4377_sup__ge1,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge1
% 0.35/0.60 thf(fact_4378_sup__ge1,axiom,
% 0.35/0.60 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % sup_ge1
% 0.35/0.60 thf(fact_4379_le__supI,axiom,
% 0.35/0.60 ! [A: set_nat,X: set_nat,B: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ A @ X )
% 0.35/0.60 => ( ( ord_less_eq_set_nat @ B @ X )
% 0.35/0.60 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI
% 0.35/0.60 thf(fact_4380_le__supI,axiom,
% 0.35/0.60 ! [A: rat,X: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ A @ X )
% 0.35/0.60 => ( ( ord_less_eq_rat @ B @ X )
% 0.35/0.60 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI
% 0.35/0.60 thf(fact_4381_le__supI,axiom,
% 0.35/0.60 ! [A: nat,X: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ A @ X )
% 0.35/0.60 => ( ( ord_less_eq_nat @ B @ X )
% 0.35/0.60 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI
% 0.35/0.60 thf(fact_4382_le__supI,axiom,
% 0.35/0.60 ! [A: int,X: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ A @ X )
% 0.35/0.60 => ( ( ord_less_eq_int @ B @ X )
% 0.35/0.60 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supI
% 0.35/0.60 thf(fact_4383_le__supE,axiom,
% 0.35/0.60 ! [A: set_nat,B: set_nat,X: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 0.35/0.60 => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 0.35/0.60 => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supE
% 0.35/0.60 thf(fact_4384_le__supE,axiom,
% 0.35/0.60 ! [A: rat,B: rat,X: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 0.35/0.60 => ~ ( ( ord_less_eq_rat @ A @ X )
% 0.35/0.60 => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supE
% 0.35/0.60 thf(fact_4385_le__supE,axiom,
% 0.35/0.60 ! [A: nat,B: nat,X: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 0.35/0.60 => ~ ( ( ord_less_eq_nat @ A @ X )
% 0.35/0.60 => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supE
% 0.35/0.60 thf(fact_4386_le__supE,axiom,
% 0.35/0.60 ! [A: int,B: int,X: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 0.35/0.60 => ~ ( ( ord_less_eq_int @ A @ X )
% 0.35/0.60 => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_supE
% 0.35/0.60 thf(fact_4387_inf__sup__ord_I3_J,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(3)
% 0.35/0.60 thf(fact_4388_inf__sup__ord_I3_J,axiom,
% 0.35/0.60 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(3)
% 0.35/0.60 thf(fact_4389_inf__sup__ord_I3_J,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(3)
% 0.35/0.60 thf(fact_4390_inf__sup__ord_I3_J,axiom,
% 0.35/0.60 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(3)
% 0.35/0.60 thf(fact_4391_inf__sup__ord_I4_J,axiom,
% 0.35/0.60 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(4)
% 0.35/0.60 thf(fact_4392_inf__sup__ord_I4_J,axiom,
% 0.35/0.60 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(4)
% 0.35/0.60 thf(fact_4393_inf__sup__ord_I4_J,axiom,
% 0.35/0.60 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(4)
% 0.35/0.60 thf(fact_4394_inf__sup__ord_I4_J,axiom,
% 0.35/0.60 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % inf_sup_ord(4)
% 0.35/0.60 thf(fact_4395_invar__vebt_Ointros_I4_J,axiom,
% 0.35/0.60 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.35/0.60 ( ! [X3: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.35/0.60 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 0.35/0.60 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.60 => ( ( M2 = N )
% 0.35/0.60 => ( ( Deg
% 0.35/0.60 = ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.60 => ( ! [I3: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.60 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 0.35/0.60 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.35/0.60 => ( ( ( Mi = Ma )
% 0.35/0.60 => ! [X3: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.60 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.35/0.60 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.60 => ( ( ( Mi != Ma )
% 0.35/0.60 => ! [I3: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.60 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.35/0.60 = I3 )
% 0.35/0.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.35/0.60 & ! [X3: nat] :
% 0.35/0.60 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 0.35/0.60 = I3 )
% 0.35/0.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 0.35/0.60 => ( ( ord_less_nat @ Mi @ X3 )
% 0.35/0.60 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % invar_vebt.intros(4)
% 0.35/0.60 thf(fact_4396_invar__vebt_Ointros_I5_J,axiom,
% 0.35/0.60 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 0.35/0.60 ( ! [X3: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X3 @ N ) )
% 0.35/0.60 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 0.35/0.60 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.60 => ( ( M2
% 0.35/0.60 = ( suc @ N ) )
% 0.35/0.60 => ( ( Deg
% 0.35/0.60 = ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.60 => ( ! [I3: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.60 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 0.35/0.60 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 0.35/0.60 => ( ( ( Mi = Ma )
% 0.35/0.60 => ! [X3: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.60 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 0.35/0.60 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.60 => ( ( ( Mi != Ma )
% 0.35/0.60 => ! [I3: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.60 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 0.35/0.60 = I3 )
% 0.35/0.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 0.35/0.60 & ! [X3: nat] :
% 0.35/0.60 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 0.35/0.60 = I3 )
% 0.35/0.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 0.35/0.60 => ( ( ord_less_nat @ Mi @ X3 )
% 0.35/0.60 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % invar_vebt.intros(5)
% 0.35/0.60 thf(fact_4397_invar__vebt_Ocases,axiom,
% 0.35/0.60 ! [A12: vEBT_VEBT,A23: nat] :
% 0.35/0.60 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 0.35/0.60 => ( ( ? [A3: $o,B3: $o] :
% 0.35/0.60 ( A12
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( A23
% 0.35/0.60 != ( suc @ zero_zero_nat ) ) )
% 0.35/0.60 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat] :
% 0.35/0.60 ( ( A12
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( A23 = Deg2 )
% 0.35/0.60 => ( ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.60 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 0.35/0.60 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( M = N3 )
% 0.35/0.60 => ( ( Deg2
% 0.35/0.60 = ( plus_plus_nat @ N3 @ M ) )
% 0.35/0.60 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 0.35/0.60 => ~ ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat] :
% 0.35/0.60 ( ( A12
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( A23 = Deg2 )
% 0.35/0.60 => ( ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.60 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 0.35/0.60 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( M
% 0.35/0.60 = ( suc @ N3 ) )
% 0.35/0.60 => ( ( Deg2
% 0.35/0.60 = ( plus_plus_nat @ N3 @ M ) )
% 0.35/0.60 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 0.35/0.60 => ~ ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.35/0.60 ( ( A12
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( A23 = Deg2 )
% 0.35/0.60 => ( ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.60 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 0.35/0.60 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( M = N3 )
% 0.35/0.60 => ( ( Deg2
% 0.35/0.60 = ( plus_plus_nat @ N3 @ M ) )
% 0.35/0.60 => ( ! [I4: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X7 ) )
% 0.35/0.60 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.35/0.60 => ( ( ( Mi2 = Ma2 )
% 0.35/0.60 => ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.35/0.60 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.60 => ~ ( ( Mi2 != Ma2 )
% 0.35/0.60 => ! [I4: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.35/0.60 = I4 )
% 0.35/0.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.35/0.60 & ! [X5: nat] :
% 0.35/0.60 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 0.35/0.60 = I4 )
% 0.35/0.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 0.35/0.60 => ( ( ord_less_nat @ Mi2 @ X5 )
% 0.35/0.60 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 => ~ ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 0.35/0.60 ( ( A12
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( A23 = Deg2 )
% 0.35/0.60 => ( ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 0.35/0.60 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 0.35/0.60 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( M
% 0.35/0.60 = ( suc @ N3 ) )
% 0.35/0.60 => ( ( Deg2
% 0.35/0.60 = ( plus_plus_nat @ N3 @ M ) )
% 0.35/0.60 => ( ! [I4: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X7 ) )
% 0.35/0.60 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 0.35/0.60 => ( ( ( Mi2 = Ma2 )
% 0.35/0.60 => ! [X5: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.60 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 0.35/0.60 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.60 => ~ ( ( Mi2 != Ma2 )
% 0.35/0.60 => ! [I4: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 0.35/0.60 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 0.35/0.60 = I4 )
% 0.35/0.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 0.35/0.60 & ! [X5: nat] :
% 0.35/0.60 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 0.35/0.60 = I4 )
% 0.35/0.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 0.35/0.60 => ( ( ord_less_nat @ Mi2 @ X5 )
% 0.35/0.60 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % invar_vebt.cases
% 0.35/0.60 thf(fact_4398_invar__vebt_Osimps,axiom,
% 0.35/0.60 ( vEBT_invar_vebt
% 0.35/0.60 = ( ^ [A13: vEBT_VEBT,A24: nat] :
% 0.35/0.60 ( ( ? [A5: $o,B4: $o] :
% 0.35/0.60 ( A13
% 0.35/0.60 = ( vEBT_Leaf @ A5 @ B4 ) )
% 0.35/0.60 & ( A24
% 0.35/0.60 = ( suc @ zero_zero_nat ) ) )
% 0.35/0.60 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT] :
% 0.35/0.60 ( ( A13
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary4 ) )
% 0.35/0.60 & ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 0.35/0.60 & ( vEBT_invar_vebt @ Summary4 @ N4 )
% 0.35/0.60 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 0.35/0.60 & ( A24
% 0.35/0.60 = ( plus_plus_nat @ N4 @ N4 ) )
% 0.35/0.60 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X7 )
% 0.35/0.60 & ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.60 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT] :
% 0.35/0.60 ( ( A13
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary4 ) )
% 0.35/0.60 & ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 0.35/0.60 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N4 ) )
% 0.35/0.60 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 0.35/0.60 & ( A24
% 0.35/0.60 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 0.35/0.60 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X7 )
% 0.35/0.60 & ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.60 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.35/0.60 ( ( A13
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary4 ) )
% 0.35/0.60 & ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 0.35/0.60 & ( vEBT_invar_vebt @ Summary4 @ N4 )
% 0.35/0.60 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 0.35/0.60 & ( A24
% 0.35/0.60 = ( plus_plus_nat @ N4 @ N4 ) )
% 0.35/0.60 & ! [I: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 0.35/0.60 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ X7 ) )
% 0.35/0.60 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I ) ) )
% 0.35/0.60 & ( ( Mi3 = Ma3 )
% 0.35/0.60 => ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.60 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.60 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 0.35/0.60 & ( ( Mi3 != Ma3 )
% 0.35/0.60 => ! [I: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 0.35/0.60 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 0.35/0.60 = I )
% 0.35/0.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 0.35/0.60 & ! [X4: nat] :
% 0.35/0.60 ( ( ( ( vEBT_VEBT_high @ X4 @ N4 )
% 0.35/0.60 = I )
% 0.35/0.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) )
% 0.35/0.60 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.60 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) )
% 0.35/0.60 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 0.35/0.60 ( ( A13
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary4 ) )
% 0.35/0.60 & ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 0.35/0.60 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N4 ) )
% 0.35/0.60 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 0.35/0.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 0.35/0.60 & ( A24
% 0.35/0.60 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 0.35/0.60 & ! [I: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 0.35/0.60 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ X7 ) )
% 0.35/0.60 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I ) ) )
% 0.35/0.60 & ( ( Mi3 = Ma3 )
% 0.35/0.60 => ! [X4: vEBT_VEBT] :
% 0.35/0.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 0.35/0.60 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.60 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.60 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 0.35/0.60 & ( ( Mi3 != Ma3 )
% 0.35/0.60 => ! [I: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 0.35/0.60 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 0.35/0.60 = I )
% 0.35/0.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 0.35/0.60 & ! [X4: nat] :
% 0.35/0.60 ( ( ( ( vEBT_VEBT_high @ X4 @ N4 )
% 0.35/0.60 = I )
% 0.35/0.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) )
% 0.35/0.60 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.60 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % invar_vebt.simps
% 0.35/0.60 thf(fact_4399_distrib__inf__le,axiom,
% 0.35/0.60 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_inf_le
% 0.35/0.60 thf(fact_4400_distrib__inf__le,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z3 ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_inf_le
% 0.35/0.60 thf(fact_4401_distrib__inf__le,axiom,
% 0.35/0.60 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z3 ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_inf_le
% 0.35/0.60 thf(fact_4402_distrib__inf__le,axiom,
% 0.35/0.60 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z3 ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_inf_le
% 0.35/0.60 thf(fact_4403_distrib__inf__le,axiom,
% 0.35/0.60 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z3 ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_inf_le
% 0.35/0.60 thf(fact_4404_distrib__sup__le,axiom,
% 0.35/0.60 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_sup_le
% 0.35/0.60 thf(fact_4405_distrib__sup__le,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_sup_le
% 0.35/0.60 thf(fact_4406_distrib__sup__le,axiom,
% 0.35/0.60 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_sup_le
% 0.35/0.60 thf(fact_4407_distrib__sup__le,axiom,
% 0.35/0.60 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_sup_le
% 0.35/0.60 thf(fact_4408_distrib__sup__le,axiom,
% 0.35/0.60 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % distrib_sup_le
% 0.35/0.60 thf(fact_4409_in__children__def,axiom,
% 0.35/0.60 ( vEBT_V5917875025757280293ildren
% 0.35/0.60 = ( ^ [N4: nat,TreeList4: list_VEBT_VEBT,X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ ( vEBT_VEBT_high @ X4 @ N4 ) ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % in_children_def
% 0.35/0.60 thf(fact_4410_nested__mint,axiom,
% 0.35/0.60 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va3: nat] :
% 0.35/0.60 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 0.35/0.60 => ( ( N
% 0.35/0.60 = ( suc @ ( suc @ Va3 ) ) )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 0.35/0.60 => ( ( Ma != Mi )
% 0.35/0.60 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nested_mint
% 0.35/0.60 thf(fact_4411_summaxma,axiom,
% 0.35/0.60 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 0.35/0.60 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % summaxma
% 0.35/0.60 thf(fact_4412_set__encode__insert,axiom,
% 0.35/0.60 ! [A4: set_nat,N: nat] :
% 0.35/0.60 ( ( finite_finite_nat @ A4 )
% 0.35/0.60 => ( ~ ( member_nat @ N @ A4 )
% 0.35/0.60 => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 0.35/0.60 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_encode_insert
% 0.35/0.60 thf(fact_4413_unset__bit__0,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 0.35/0.60 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % unset_bit_0
% 0.35/0.60 thf(fact_4414_unset__bit__0,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 0.35/0.60 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % unset_bit_0
% 0.35/0.60 thf(fact_4415_del__x__mi__lets__in__not__minNull,axiom,
% 0.35/0.60 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.35/0.60 ( ( ( X = Mi )
% 0.35/0.60 & ( ord_less_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( Xn
% 0.35/0.60 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( Newnode
% 0.35/0.60 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 => ( ( Newlist
% 0.35/0.60 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 0.35/0.60 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_mi_lets_in_not_minNull
% 0.35/0.60 thf(fact_4416_del__x__not__mi__newnode__not__nil,axiom,
% 0.35/0.60 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( ord_less_nat @ Mi @ X )
% 0.35/0.60 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( Newnode
% 0.35/0.60 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( Newlist
% 0.35/0.60 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_not_mi_newnode_not_nil
% 0.35/0.60 thf(fact_4417_neg__eucl__rel__int__mult__2,axiom,
% 0.35/0.60 ! [B: int,A: int,Q2: int,R3: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 0.35/0.60 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.60 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % neg_eucl_rel_int_mult_2
% 0.35/0.60 thf(fact_4418_length__list__update,axiom,
% 0.35/0.60 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 0.35/0.60 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 0.35/0.60 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % length_list_update
% 0.35/0.60 thf(fact_4419_length__list__update,axiom,
% 0.35/0.60 ! [Xs2: list_o,I2: nat,X: $o] :
% 0.35/0.60 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 0.35/0.60 = ( size_size_list_o @ Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % length_list_update
% 0.35/0.60 thf(fact_4420_length__list__update,axiom,
% 0.35/0.60 ! [Xs2: list_nat,I2: nat,X: nat] :
% 0.35/0.60 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 0.35/0.60 = ( size_size_list_nat @ Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % length_list_update
% 0.35/0.60 thf(fact_4421_length__list__update,axiom,
% 0.35/0.60 ! [Xs2: list_int,I2: nat,X: int] :
% 0.35/0.60 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 0.35/0.60 = ( size_size_list_int @ Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % length_list_update
% 0.35/0.60 thf(fact_4422_option_Ocollapse,axiom,
% 0.35/0.60 ! [Option: option4927543243414619207at_nat] :
% 0.35/0.60 ( ( Option != none_P5556105721700978146at_nat )
% 0.35/0.60 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 0.35/0.60 = Option ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.collapse
% 0.35/0.60 thf(fact_4423_option_Ocollapse,axiom,
% 0.35/0.60 ! [Option: option_nat] :
% 0.35/0.60 ( ( Option != none_nat )
% 0.35/0.60 => ( ( some_nat @ ( the_nat @ Option ) )
% 0.35/0.60 = Option ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.collapse
% 0.35/0.60 thf(fact_4424_option_Ocollapse,axiom,
% 0.35/0.60 ! [Option: option_num] :
% 0.35/0.60 ( ( Option != none_num )
% 0.35/0.60 => ( ( some_num @ ( the_num @ Option ) )
% 0.35/0.60 = Option ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.collapse
% 0.35/0.60 thf(fact_4425_list__update__beyond,axiom,
% 0.35/0.60 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 0.35/0.60 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_beyond
% 0.35/0.60 thf(fact_4426_list__update__beyond,axiom,
% 0.35/0.60 ! [Xs2: list_o,I2: nat,X: $o] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 0.35/0.60 => ( ( list_update_o @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_beyond
% 0.35/0.60 thf(fact_4427_list__update__beyond,axiom,
% 0.35/0.60 ! [Xs2: list_nat,I2: nat,X: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 0.35/0.60 => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_beyond
% 0.35/0.60 thf(fact_4428_list__update__beyond,axiom,
% 0.35/0.60 ! [Xs2: list_int,I2: nat,X: int] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 0.35/0.60 => ( ( list_update_int @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_beyond
% 0.35/0.60 thf(fact_4429_set__encode__empty,axiom,
% 0.35/0.60 ( ( nat_set_encode @ bot_bot_set_nat )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % set_encode_empty
% 0.35/0.60 thf(fact_4430_nth__list__update__eq,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update_eq
% 0.35/0.60 thf(fact_4431_nth__list__update__eq,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_o,X: $o] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.60 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update_eq
% 0.35/0.60 thf(fact_4432_nth__list__update__eq,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_nat,X: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.60 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update_eq
% 0.35/0.60 thf(fact_4433_nth__list__update__eq,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_int,X: int] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.60 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update_eq
% 0.35/0.60 thf(fact_4434_set__swap,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.60 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.60 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) @ J2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 0.35/0.60 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_swap
% 0.35/0.60 thf(fact_4435_set__swap,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_o,J2: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.60 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.60 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J2 ) ) @ J2 @ ( nth_o @ Xs2 @ I2 ) ) )
% 0.35/0.60 = ( set_o2 @ Xs2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_swap
% 0.35/0.60 thf(fact_4436_set__swap,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_nat,J2: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.60 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.60 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J2 ) ) @ J2 @ ( nth_nat @ Xs2 @ I2 ) ) )
% 0.35/0.60 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_swap
% 0.35/0.60 thf(fact_4437_set__swap,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_int,J2: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.60 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.60 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J2 ) ) @ J2 @ ( nth_int @ Xs2 @ I2 ) ) )
% 0.35/0.60 = ( set_int2 @ Xs2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_swap
% 0.35/0.60 thf(fact_4438_unique__quotient,axiom,
% 0.35/0.60 ! [A: int,B: int,Q2: int,R3: int,Q4: int,R5: int] :
% 0.35/0.60 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.60 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R5 ) )
% 0.35/0.60 => ( Q2 = Q4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % unique_quotient
% 0.35/0.60 thf(fact_4439_unique__remainder,axiom,
% 0.35/0.60 ! [A: int,B: int,Q2: int,R3: int,Q4: int,R5: int] :
% 0.35/0.60 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.60 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R5 ) )
% 0.35/0.60 => ( R3 = R5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % unique_remainder
% 0.35/0.60 thf(fact_4440_zip__update,axiom,
% 0.35/0.60 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.35/0.60 ( ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ ( list_u1324408373059187874T_VEBT @ Ys @ I2 @ Y ) )
% 0.35/0.60 = ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) @ I2 @ ( produc537772716801021591T_VEBT @ X @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % zip_update
% 0.35/0.60 thf(fact_4441_zip__update,axiom,
% 0.35/0.60 ! [Xs2: list_Code_integer,I2: nat,X: code_integer,Ys: list_Code_integer,Y: code_integer] :
% 0.35/0.60 ( ( zip_Co3543743374963494515nteger @ ( list_u5447711078246177391nteger @ Xs2 @ I2 @ X ) @ ( list_u5447711078246177391nteger @ Ys @ I2 @ Y ) )
% 0.35/0.60 = ( list_u2254550707601501961nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) @ I2 @ ( produc1086072967326762835nteger @ X @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % zip_update
% 0.35/0.60 thf(fact_4442_zip__update,axiom,
% 0.35/0.60 ! [Xs2: list_P6011104703257516679at_nat,I2: nat,X: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,Y: product_prod_nat_nat] :
% 0.35/0.60 ( ( zip_Pr4664179122662387191at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) @ ( list_u6180841689913720943at_nat @ Ys @ I2 @ Y ) )
% 0.35/0.60 = ( list_u5003261594476800725at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) @ I2 @ ( produc6161850002892822231at_nat @ X @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % zip_update
% 0.35/0.60 thf(fact_4443_zip__update,axiom,
% 0.35/0.60 ! [Xs2: list_s1210847774152347623at_nat,I2: nat,X: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.35/0.60 ( ( zip_se5600341670672612855at_nat @ ( list_u8444657558853818831at_nat @ Xs2 @ I2 @ X ) @ ( list_u8444657558853818831at_nat @ Ys @ I2 @ Y ) )
% 0.35/0.60 = ( list_u4696772448584712917at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) @ I2 @ ( produc2922128104949294807at_nat @ X @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % zip_update
% 0.35/0.60 thf(fact_4444_zip__update,axiom,
% 0.35/0.60 ! [Xs2: list_nat,I2: nat,X: nat,Ys: list_nat,Y: nat] :
% 0.35/0.60 ( ( zip_nat_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ ( list_update_nat @ Ys @ I2 @ Y ) )
% 0.35/0.60 = ( list_u6180841689913720943at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) @ I2 @ ( product_Pair_nat_nat @ X @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % zip_update
% 0.35/0.60 thf(fact_4445_zip__update,axiom,
% 0.35/0.60 ! [Xs2: list_int,I2: nat,X: int,Ys: list_int,Y: int] :
% 0.35/0.60 ( ( zip_int_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ ( list_update_int @ Ys @ I2 @ Y ) )
% 0.35/0.60 = ( list_u3002344382305578791nt_int @ ( zip_int_int @ Xs2 @ Ys ) @ I2 @ ( product_Pair_int_int @ X @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % zip_update
% 0.35/0.60 thf(fact_4446_option_Osel,axiom,
% 0.35/0.60 ! [X2: product_prod_nat_nat] :
% 0.35/0.60 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 0.35/0.60 = X2 ) ).
% 0.35/0.60
% 0.35/0.60 % option.sel
% 0.35/0.60 thf(fact_4447_option_Osel,axiom,
% 0.35/0.60 ! [X2: nat] :
% 0.35/0.60 ( ( the_nat @ ( some_nat @ X2 ) )
% 0.35/0.60 = X2 ) ).
% 0.35/0.60
% 0.35/0.60 % option.sel
% 0.35/0.60 thf(fact_4448_option_Osel,axiom,
% 0.35/0.60 ! [X2: num] :
% 0.35/0.60 ( ( the_num @ ( some_num @ X2 ) )
% 0.35/0.60 = X2 ) ).
% 0.35/0.60
% 0.35/0.60 % option.sel
% 0.35/0.60 thf(fact_4449_option_Oexpand,axiom,
% 0.35/0.60 ! [Option: option_nat,Option2: option_nat] :
% 0.35/0.60 ( ( ( Option = none_nat )
% 0.35/0.60 = ( Option2 = none_nat ) )
% 0.35/0.60 => ( ( ( Option != none_nat )
% 0.35/0.60 => ( ( Option2 != none_nat )
% 0.35/0.60 => ( ( the_nat @ Option )
% 0.35/0.60 = ( the_nat @ Option2 ) ) ) )
% 0.35/0.60 => ( Option = Option2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.expand
% 0.35/0.60 thf(fact_4450_option_Oexpand,axiom,
% 0.35/0.60 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 0.35/0.60 ( ( ( Option = none_P5556105721700978146at_nat )
% 0.35/0.60 = ( Option2 = none_P5556105721700978146at_nat ) )
% 0.35/0.60 => ( ( ( Option != none_P5556105721700978146at_nat )
% 0.35/0.60 => ( ( Option2 != none_P5556105721700978146at_nat )
% 0.35/0.60 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 0.35/0.60 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 0.35/0.60 => ( Option = Option2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.expand
% 0.35/0.60 thf(fact_4451_option_Oexpand,axiom,
% 0.35/0.60 ! [Option: option_num,Option2: option_num] :
% 0.35/0.60 ( ( ( Option = none_num )
% 0.35/0.60 = ( Option2 = none_num ) )
% 0.35/0.60 => ( ( ( Option != none_num )
% 0.35/0.60 => ( ( Option2 != none_num )
% 0.35/0.60 => ( ( the_num @ Option )
% 0.35/0.60 = ( the_num @ Option2 ) ) ) )
% 0.35/0.60 => ( Option = Option2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.expand
% 0.35/0.60 thf(fact_4452_eucl__rel__int__by0,axiom,
% 0.35/0.60 ! [K2: int] : ( eucl_rel_int @ K2 @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % eucl_rel_int_by0
% 0.35/0.60 thf(fact_4453_div__int__unique,axiom,
% 0.35/0.60 ! [K2: int,L: int,Q2: int,R3: int] :
% 0.35/0.60 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.60 => ( ( divide_divide_int @ K2 @ L )
% 0.35/0.60 = Q2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % div_int_unique
% 0.35/0.60 thf(fact_4454_list__update__code_I3_J,axiom,
% 0.35/0.60 ! [X: nat,Xs2: list_nat,I2: nat,Y: nat] :
% 0.35/0.60 ( ( list_update_nat @ ( cons_nat @ X @ Xs2 ) @ ( suc @ I2 ) @ Y )
% 0.35/0.60 = ( cons_nat @ X @ ( list_update_nat @ Xs2 @ I2 @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_code(3)
% 0.35/0.60 thf(fact_4455_list__update__code_I3_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,I2: nat,Y: vEBT_VEBT] :
% 0.35/0.60 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( suc @ I2 ) @ Y )
% 0.35/0.60 = ( cons_VEBT_VEBT @ X @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_code(3)
% 0.35/0.60 thf(fact_4456_list__update__code_I2_J,axiom,
% 0.35/0.60 ! [X: nat,Xs2: list_nat,Y: nat] :
% 0.35/0.60 ( ( list_update_nat @ ( cons_nat @ X @ Xs2 ) @ zero_zero_nat @ Y )
% 0.35/0.60 = ( cons_nat @ Y @ Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_code(2)
% 0.35/0.60 thf(fact_4457_list__update__code_I2_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 0.35/0.60 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ zero_zero_nat @ Y )
% 0.35/0.60 = ( cons_VEBT_VEBT @ Y @ Xs2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_code(2)
% 0.35/0.60 thf(fact_4458_set__encode__eq,axiom,
% 0.35/0.60 ! [A4: set_nat,B5: set_nat] :
% 0.35/0.60 ( ( finite_finite_nat @ A4 )
% 0.35/0.60 => ( ( finite_finite_nat @ B5 )
% 0.35/0.60 => ( ( ( nat_set_encode @ A4 )
% 0.35/0.60 = ( nat_set_encode @ B5 ) )
% 0.35/0.60 = ( A4 = B5 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_encode_eq
% 0.35/0.60 thf(fact_4459_option_Oexhaust__sel,axiom,
% 0.35/0.60 ! [Option: option4927543243414619207at_nat] :
% 0.35/0.60 ( ( Option != none_P5556105721700978146at_nat )
% 0.35/0.60 => ( Option
% 0.35/0.60 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.exhaust_sel
% 0.35/0.60 thf(fact_4460_option_Oexhaust__sel,axiom,
% 0.35/0.60 ! [Option: option_nat] :
% 0.35/0.60 ( ( Option != none_nat )
% 0.35/0.60 => ( Option
% 0.35/0.60 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.exhaust_sel
% 0.35/0.60 thf(fact_4461_option_Oexhaust__sel,axiom,
% 0.35/0.60 ! [Option: option_num] :
% 0.35/0.60 ( ( Option != none_num )
% 0.35/0.60 => ( Option
% 0.35/0.60 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % option.exhaust_sel
% 0.35/0.60 thf(fact_4462_eucl__rel__int__dividesI,axiom,
% 0.35/0.60 ! [L: int,K2: int,Q2: int] :
% 0.35/0.60 ( ( L != zero_zero_int )
% 0.35/0.60 => ( ( K2
% 0.35/0.60 = ( times_times_int @ Q2 @ L ) )
% 0.35/0.60 => ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % eucl_rel_int_dividesI
% 0.35/0.60 thf(fact_4463_set__update__memI,axiom,
% 0.35/0.60 ! [N: nat,Xs2: list_complex,X: complex] :
% 0.35/0.60 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.35/0.60 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_update_memI
% 0.35/0.60 thf(fact_4464_set__update__memI,axiom,
% 0.35/0.60 ! [N: nat,Xs2: list_real,X: real] :
% 0.35/0.60 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.35/0.60 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_update_memI
% 0.35/0.60 thf(fact_4465_set__update__memI,axiom,
% 0.35/0.60 ! [N: nat,Xs2: list_set_nat,X: set_nat] :
% 0.35/0.60 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.35/0.60 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ N @ X ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_update_memI
% 0.35/0.60 thf(fact_4466_set__update__memI,axiom,
% 0.35/0.60 ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.60 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_update_memI
% 0.35/0.60 thf(fact_4467_set__update__memI,axiom,
% 0.35/0.60 ! [N: nat,Xs2: list_o,X: $o] :
% 0.35/0.60 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.60 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_update_memI
% 0.35/0.60 thf(fact_4468_set__update__memI,axiom,
% 0.35/0.60 ! [N: nat,Xs2: list_nat,X: nat] :
% 0.35/0.60 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.60 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_update_memI
% 0.35/0.60 thf(fact_4469_set__update__memI,axiom,
% 0.35/0.60 ! [N: nat,Xs2: list_int,X: int] :
% 0.35/0.60 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.60 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_update_memI
% 0.35/0.60 thf(fact_4470_list__update__same__conv,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.60 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 )
% 0.35/0.60 = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 0.35/0.60 = X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_same_conv
% 0.35/0.60 thf(fact_4471_list__update__same__conv,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_o,X: $o] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.60 => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 )
% 0.35/0.60 = ( ( nth_o @ Xs2 @ I2 )
% 0.35/0.60 = X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_same_conv
% 0.35/0.60 thf(fact_4472_list__update__same__conv,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_nat,X: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.60 => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 )
% 0.35/0.60 = ( ( nth_nat @ Xs2 @ I2 )
% 0.35/0.60 = X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_same_conv
% 0.35/0.60 thf(fact_4473_list__update__same__conv,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_int,X: int] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.60 => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 0.35/0.60 = Xs2 )
% 0.35/0.60 = ( ( nth_int @ Xs2 @ I2 )
% 0.35/0.60 = X ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % list_update_same_conv
% 0.35/0.60 thf(fact_4474_nth__list__update,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat,X: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.60 => ( ( ( I2 = J2 )
% 0.35/0.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J2 )
% 0.35/0.60 = X ) )
% 0.35/0.60 & ( ( I2 != J2 )
% 0.35/0.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J2 )
% 0.35/0.60 = ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update
% 0.35/0.60 thf(fact_4475_nth__list__update,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_o,X: $o,J2: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.60 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J2 )
% 0.35/0.60 = ( ( ( I2 = J2 )
% 0.35/0.60 => X )
% 0.35/0.60 & ( ( I2 != J2 )
% 0.35/0.60 => ( nth_o @ Xs2 @ J2 ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update
% 0.35/0.60 thf(fact_4476_nth__list__update,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_nat,J2: nat,X: nat] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.60 => ( ( ( I2 = J2 )
% 0.35/0.60 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J2 )
% 0.35/0.60 = X ) )
% 0.35/0.60 & ( ( I2 != J2 )
% 0.35/0.60 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J2 )
% 0.35/0.60 = ( nth_nat @ Xs2 @ J2 ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update
% 0.35/0.60 thf(fact_4477_nth__list__update,axiom,
% 0.35/0.60 ! [I2: nat,Xs2: list_int,J2: nat,X: int] :
% 0.35/0.60 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.60 => ( ( ( I2 = J2 )
% 0.35/0.60 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J2 )
% 0.35/0.60 = X ) )
% 0.35/0.60 & ( ( I2 != J2 )
% 0.35/0.60 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J2 )
% 0.35/0.60 = ( nth_int @ Xs2 @ J2 ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nth_list_update
% 0.35/0.60 thf(fact_4478_set__encode__inf,axiom,
% 0.35/0.60 ! [A4: set_nat] :
% 0.35/0.60 ( ~ ( finite_finite_nat @ A4 )
% 0.35/0.60 => ( ( nat_set_encode @ A4 )
% 0.35/0.60 = zero_zero_nat ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_encode_inf
% 0.35/0.60 thf(fact_4479_eucl__rel__int__iff,axiom,
% 0.35/0.60 ! [K2: int,L: int,Q2: int,R3: int] :
% 0.35/0.60 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.60 = ( ( K2
% 0.35/0.60 = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R3 ) )
% 0.35/0.60 & ( ( ord_less_int @ zero_zero_int @ L )
% 0.35/0.60 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.35/0.60 & ( ord_less_int @ R3 @ L ) ) )
% 0.35/0.60 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 0.35/0.60 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 0.35/0.60 => ( ( ord_less_int @ L @ R3 )
% 0.35/0.60 & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 0.35/0.60 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 0.35/0.60 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % eucl_rel_int_iff
% 0.35/0.60 thf(fact_4480_pos__eucl__rel__int__mult__2,axiom,
% 0.35/0.60 ! [B: int,A: int,Q2: int,R3: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.35/0.60 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.60 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % pos_eucl_rel_int_mult_2
% 0.35/0.60 thf(fact_4481_insert__simp__excp,axiom,
% 0.35/0.60 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( ord_less_nat @ X @ Mi )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( X != Ma )
% 0.35/0.60 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % insert_simp_excp
% 0.35/0.60 thf(fact_4482_insert__simp__norm,axiom,
% 0.35/0.60 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( ord_less_nat @ Mi @ X )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( X != Ma )
% 0.35/0.60 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % insert_simp_norm
% 0.35/0.60 thf(fact_4483_pred__less__length__list,axiom,
% 0.35/0.60 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ord_less_eq_nat @ X @ Ma )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % pred_less_length_list
% 0.35/0.60 thf(fact_4484_pred__lesseq__max,axiom,
% 0.35/0.60 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ord_less_eq_nat @ X @ Ma )
% 0.35/0.60 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % pred_lesseq_max
% 0.35/0.60 thf(fact_4485_succ__greatereq__min,axiom,
% 0.35/0.60 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Mi @ X )
% 0.35/0.60 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ none_nat
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % succ_greatereq_min
% 0.35/0.60 thf(fact_4486_succ__less__length__list,axiom,
% 0.35/0.60 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ord_less_eq_nat @ Mi @ X )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ none_nat
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % succ_less_length_list
% 0.35/0.60 thf(fact_4487_del__in__range,axiom,
% 0.35/0.60 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( ord_less_eq_nat @ Mi @ X )
% 0.35/0.60 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( X = Mi )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 = Ma ) )
% 0.35/0.60 & ( ( X != Mi )
% 0.35/0.60 => ( X = Ma ) ) )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( X = Mi )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 = Ma ) )
% 0.35/0.60 & ( ( X != Mi )
% 0.35/0.60 => ( X = Ma ) ) )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ Summary ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_in_range
% 0.35/0.60 thf(fact_4488_del__x__mi,axiom,
% 0.35/0.60 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat] :
% 0.35/0.60 ( ( ( X = Mi )
% 0.35/0.60 & ( ord_less_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( Xn
% 0.35/0.60 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ Xn
% 0.35/0.60 @ ( if_nat @ ( Xn = Ma )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ Xn
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_mi
% 0.35/0.60 thf(fact_4489_set__vebt_H__def,axiom,
% 0.35/0.60 ( vEBT_VEBT_set_vebt
% 0.35/0.60 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_vebt'_def
% 0.35/0.60 thf(fact_4490_pred__empty,axiom,
% 0.35/0.60 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.60 ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.60 => ( ( ( vEBT_vebt_pred @ T @ X )
% 0.35/0.60 = none_nat )
% 0.35/0.60 = ( ( collect_nat
% 0.35/0.60 @ ^ [Y4: nat] :
% 0.35/0.60 ( ( vEBT_vebt_member @ T @ Y4 )
% 0.35/0.60 & ( ord_less_nat @ Y4 @ X ) ) )
% 0.35/0.60 = bot_bot_set_nat ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % pred_empty
% 0.35/0.60 thf(fact_4491_succ__empty,axiom,
% 0.35/0.60 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 0.35/0.60 ( ( vEBT_invar_vebt @ T @ N )
% 0.35/0.60 => ( ( ( vEBT_vebt_succ @ T @ X )
% 0.35/0.60 = none_nat )
% 0.35/0.60 = ( ( collect_nat
% 0.35/0.60 @ ^ [Y4: nat] :
% 0.35/0.60 ( ( vEBT_vebt_member @ T @ Y4 )
% 0.35/0.60 & ( ord_less_nat @ X @ Y4 ) ) )
% 0.35/0.60 = bot_bot_set_nat ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % succ_empty
% 0.35/0.60 thf(fact_4492_max_Obounded__iff,axiom,
% 0.35/0.60 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 0.35/0.60 = ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.bounded_iff
% 0.35/0.60 thf(fact_4493_max_Obounded__iff,axiom,
% 0.35/0.60 ! [B: num,C2: num,A: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 0.35/0.60 = ( ( ord_less_eq_num @ B @ A )
% 0.35/0.60 & ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.bounded_iff
% 0.35/0.60 thf(fact_4494_max_Obounded__iff,axiom,
% 0.35/0.60 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 0.35/0.60 = ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.bounded_iff
% 0.35/0.60 thf(fact_4495_max_Obounded__iff,axiom,
% 0.35/0.60 ! [B: int,C2: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 0.35/0.60 = ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.bounded_iff
% 0.35/0.60 thf(fact_4496_max_Oabsorb2,axiom,
% 0.35/0.60 ! [A: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.60 => ( ( ord_max_rat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb2
% 0.35/0.60 thf(fact_4497_max_Oabsorb2,axiom,
% 0.35/0.60 ! [A: num,B: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ A @ B )
% 0.35/0.60 => ( ( ord_max_num @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb2
% 0.35/0.60 thf(fact_4498_max_Oabsorb2,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.60 => ( ( ord_max_nat @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb2
% 0.35/0.60 thf(fact_4499_max_Oabsorb2,axiom,
% 0.35/0.60 ! [A: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ A @ B )
% 0.35/0.60 => ( ( ord_max_int @ A @ B )
% 0.35/0.60 = B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb2
% 0.35/0.60 thf(fact_4500_max_Oabsorb1,axiom,
% 0.35/0.60 ! [B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ( ( ord_max_rat @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb1
% 0.35/0.60 thf(fact_4501_max_Oabsorb1,axiom,
% 0.35/0.60 ! [B: num,A: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ B @ A )
% 0.35/0.60 => ( ( ord_max_num @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb1
% 0.35/0.60 thf(fact_4502_max_Oabsorb1,axiom,
% 0.35/0.60 ! [B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ( ( ord_max_nat @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb1
% 0.35/0.60 thf(fact_4503_max_Oabsorb1,axiom,
% 0.35/0.60 ! [B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ( ( ord_max_int @ A @ B )
% 0.35/0.60 = A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb1
% 0.35/0.60 thf(fact_4504_max__bot,axiom,
% 0.35/0.60 ! [X: set_nat] :
% 0.35/0.60 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot
% 0.35/0.60 thf(fact_4505_max__bot,axiom,
% 0.35/0.60 ! [X: set_int] :
% 0.35/0.60 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot
% 0.35/0.60 thf(fact_4506_max__bot,axiom,
% 0.35/0.60 ! [X: set_real] :
% 0.35/0.60 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot
% 0.35/0.60 thf(fact_4507_max__bot,axiom,
% 0.35/0.60 ! [X: nat] :
% 0.35/0.60 ( ( ord_max_nat @ bot_bot_nat @ X )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot
% 0.35/0.60 thf(fact_4508_max__bot2,axiom,
% 0.35/0.60 ! [X: set_nat] :
% 0.35/0.60 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot2
% 0.35/0.60 thf(fact_4509_max__bot2,axiom,
% 0.35/0.60 ! [X: set_int] :
% 0.35/0.60 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot2
% 0.35/0.60 thf(fact_4510_max__bot2,axiom,
% 0.35/0.60 ! [X: set_real] :
% 0.35/0.60 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot2
% 0.35/0.60 thf(fact_4511_max__bot2,axiom,
% 0.35/0.60 ! [X: nat] :
% 0.35/0.60 ( ( ord_max_nat @ X @ bot_bot_nat )
% 0.35/0.60 = X ) ).
% 0.35/0.60
% 0.35/0.60 % max_bot2
% 0.35/0.60 thf(fact_4512_max__Suc__Suc,axiom,
% 0.35/0.60 ! [M2: nat,N: nat] :
% 0.35/0.60 ( ( ord_max_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.35/0.60 = ( suc @ ( ord_max_nat @ M2 @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_Suc_Suc
% 0.35/0.60 thf(fact_4513_max__nat_Oeq__neutr__iff,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( ( ord_max_nat @ A @ B )
% 0.35/0.60 = zero_zero_nat )
% 0.35/0.60 = ( ( A = zero_zero_nat )
% 0.35/0.60 & ( B = zero_zero_nat ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_nat.eq_neutr_iff
% 0.35/0.60 thf(fact_4514_max__nat_Oleft__neutral,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( ord_max_nat @ zero_zero_nat @ A )
% 0.35/0.60 = A ) ).
% 0.35/0.60
% 0.35/0.60 % max_nat.left_neutral
% 0.35/0.60 thf(fact_4515_max__nat_Oneutr__eq__iff,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( zero_zero_nat
% 0.35/0.60 = ( ord_max_nat @ A @ B ) )
% 0.35/0.60 = ( ( A = zero_zero_nat )
% 0.35/0.60 & ( B = zero_zero_nat ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_nat.neutr_eq_iff
% 0.35/0.60 thf(fact_4516_max__nat_Oright__neutral,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( ord_max_nat @ A @ zero_zero_nat )
% 0.35/0.60 = A ) ).
% 0.35/0.60
% 0.35/0.60 % max_nat.right_neutral
% 0.35/0.60 thf(fact_4517_max__0L,axiom,
% 0.35/0.60 ! [N: nat] :
% 0.35/0.60 ( ( ord_max_nat @ zero_zero_nat @ N )
% 0.35/0.60 = N ) ).
% 0.35/0.60
% 0.35/0.60 % max_0L
% 0.35/0.60 thf(fact_4518_max__0R,axiom,
% 0.35/0.60 ! [N: nat] :
% 0.35/0.60 ( ( ord_max_nat @ N @ zero_zero_nat )
% 0.35/0.60 = N ) ).
% 0.35/0.60
% 0.35/0.60 % max_0R
% 0.35/0.60 thf(fact_4519_finite__Collect__le__nat,axiom,
% 0.35/0.60 ! [K2: nat] :
% 0.35/0.60 ( finite_finite_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [N4: nat] : ( ord_less_eq_nat @ N4 @ K2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_Collect_le_nat
% 0.35/0.60 thf(fact_4520_max__number__of_I1_J,axiom,
% 0.35/0.60 ! [U: num,V2: num] :
% 0.35/0.60 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 0.35/0.60 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 0.35/0.60 = ( numera1916890842035813515d_enat @ V2 ) ) )
% 0.35/0.60 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 0.35/0.60 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 0.35/0.60 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_number_of(1)
% 0.35/0.60 thf(fact_4521_max__number__of_I1_J,axiom,
% 0.35/0.60 ! [U: num,V2: num] :
% 0.35/0.60 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.60 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.60 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_number_of(1)
% 0.35/0.60 thf(fact_4522_max__number__of_I1_J,axiom,
% 0.35/0.60 ! [U: num,V2: num] :
% 0.35/0.60 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.60 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.60 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_number_of(1)
% 0.35/0.60 thf(fact_4523_max__number__of_I1_J,axiom,
% 0.35/0.60 ! [U: num,V2: num] :
% 0.35/0.60 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 0.35/0.60 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_nat @ V2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 0.35/0.60 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_number_of(1)
% 0.35/0.60 thf(fact_4524_max__number__of_I1_J,axiom,
% 0.35/0.60 ! [U: num,V2: num] :
% 0.35/0.60 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.60 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.60 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.60 = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_number_of(1)
% 0.35/0.60 thf(fact_4525_max__0__1_I3_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 0.35/0.60 = ( numeral_numeral_rat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(3)
% 0.35/0.60 thf(fact_4526_max__0__1_I3_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 0.35/0.60 = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(3)
% 0.35/0.60 thf(fact_4527_max__0__1_I3_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 0.35/0.60 = ( numeral_numeral_real @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(3)
% 0.35/0.60 thf(fact_4528_max__0__1_I3_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 0.35/0.60 = ( numeral_numeral_nat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(3)
% 0.35/0.60 thf(fact_4529_max__0__1_I3_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 0.35/0.60 = ( numeral_numeral_int @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(3)
% 0.35/0.60 thf(fact_4530_max__0__1_I4_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 0.35/0.60 = ( numeral_numeral_rat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(4)
% 0.35/0.60 thf(fact_4531_max__0__1_I4_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 0.35/0.60 = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(4)
% 0.35/0.60 thf(fact_4532_max__0__1_I4_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 0.35/0.60 = ( numeral_numeral_real @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(4)
% 0.35/0.60 thf(fact_4533_max__0__1_I4_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 0.35/0.60 = ( numeral_numeral_nat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(4)
% 0.35/0.60 thf(fact_4534_max__0__1_I4_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 0.35/0.60 = ( numeral_numeral_int @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(4)
% 0.35/0.60 thf(fact_4535_max__0__1_I2_J,axiom,
% 0.35/0.60 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 0.35/0.60 = one_one_Code_integer ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(2)
% 0.35/0.60 thf(fact_4536_max__0__1_I2_J,axiom,
% 0.35/0.60 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 0.35/0.60 = one_one_real ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(2)
% 0.35/0.60 thf(fact_4537_max__0__1_I2_J,axiom,
% 0.35/0.60 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 0.35/0.60 = one_one_rat ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(2)
% 0.35/0.60 thf(fact_4538_max__0__1_I2_J,axiom,
% 0.35/0.60 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 0.35/0.60 = one_one_nat ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(2)
% 0.35/0.60 thf(fact_4539_max__0__1_I2_J,axiom,
% 0.35/0.60 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 0.35/0.60 = one_one_int ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(2)
% 0.35/0.60 thf(fact_4540_max__0__1_I1_J,axiom,
% 0.35/0.60 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 0.35/0.60 = one_one_Code_integer ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(1)
% 0.35/0.60 thf(fact_4541_max__0__1_I1_J,axiom,
% 0.35/0.60 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 0.35/0.60 = one_one_real ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(1)
% 0.35/0.60 thf(fact_4542_max__0__1_I1_J,axiom,
% 0.35/0.60 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 0.35/0.60 = one_one_rat ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(1)
% 0.35/0.60 thf(fact_4543_max__0__1_I1_J,axiom,
% 0.35/0.60 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 0.35/0.60 = one_one_nat ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(1)
% 0.35/0.60 thf(fact_4544_max__0__1_I1_J,axiom,
% 0.35/0.60 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 0.35/0.60 = one_one_int ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(1)
% 0.35/0.60 thf(fact_4545_max__0__1_I5_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 0.35/0.60 = ( numera6620942414471956472nteger @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(5)
% 0.35/0.60 thf(fact_4546_max__0__1_I5_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 0.35/0.60 = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(5)
% 0.35/0.60 thf(fact_4547_max__0__1_I5_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 0.35/0.60 = ( numeral_numeral_real @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(5)
% 0.35/0.60 thf(fact_4548_max__0__1_I5_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 0.35/0.60 = ( numeral_numeral_nat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(5)
% 0.35/0.60 thf(fact_4549_max__0__1_I5_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 0.35/0.60 = ( numeral_numeral_int @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(5)
% 0.35/0.60 thf(fact_4550_max__0__1_I6_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 0.35/0.60 = ( numera6620942414471956472nteger @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(6)
% 0.35/0.60 thf(fact_4551_max__0__1_I6_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 0.35/0.60 = ( numera1916890842035813515d_enat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(6)
% 0.35/0.60 thf(fact_4552_max__0__1_I6_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 0.35/0.60 = ( numeral_numeral_real @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(6)
% 0.35/0.60 thf(fact_4553_max__0__1_I6_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 0.35/0.60 = ( numeral_numeral_nat @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(6)
% 0.35/0.60 thf(fact_4554_max__0__1_I6_J,axiom,
% 0.35/0.60 ! [X: num] :
% 0.35/0.60 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 0.35/0.60 = ( numeral_numeral_int @ X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_0_1(6)
% 0.35/0.60 thf(fact_4555_card__Collect__le__nat,axiom,
% 0.35/0.60 ! [N: nat] :
% 0.35/0.60 ( ( finite_card_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [I: nat] : ( ord_less_eq_nat @ I @ N ) ) )
% 0.35/0.60 = ( suc @ N ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_Collect_le_nat
% 0.35/0.60 thf(fact_4556_del__x__not__mia,axiom,
% 0.35/0.60 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( ord_less_nat @ Mi @ X )
% 0.35/0.60 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ Mi
% 0.35/0.60 @ ( if_nat @ ( X = Ma )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ Mi
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_not_mia
% 0.35/0.60 thf(fact_4557_del__x__not__mi__new__node__nil,axiom,
% 0.35/0.60 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.35/0.60 ( ( ( ord_less_nat @ Mi @ X )
% 0.35/0.60 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( Newnode
% 0.35/0.60 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( Sn
% 0.35/0.60 = ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 => ( ( Newlist
% 0.35/0.60 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ Mi
% 0.35/0.60 @ ( if_nat @ ( X = Ma )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ Sn )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ Mi
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ Newlist
% 0.35/0.60 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_not_mi_new_node_nil
% 0.35/0.60 thf(fact_4558_del__x__not__mi,axiom,
% 0.35/0.60 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( ord_less_nat @ Mi @ X )
% 0.35/0.60 & ( ord_less_eq_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( Newnode
% 0.35/0.60 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 => ( ( Newlist
% 0.35/0.60 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ Mi
% 0.35/0.60 @ ( if_nat @ ( X = Ma )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ Mi
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ Newlist
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 0.35/0.60 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_not_mi
% 0.35/0.60 thf(fact_4559_del__x__mia,axiom,
% 0.35/0.60 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( X = Mi )
% 0.35/0.60 & ( ord_less_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 = Ma )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 = Ma )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ Summary ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_mia
% 0.35/0.60 thf(fact_4560_del__x__mi__lets__in__minNull,axiom,
% 0.35/0.60 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 0.35/0.60 ( ( ( X = Mi )
% 0.35/0.60 & ( ord_less_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( Xn
% 0.35/0.60 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( Newnode
% 0.35/0.60 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 => ( ( Newlist
% 0.35/0.60 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 0.35/0.60 => ( ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( Sn
% 0.35/0.60 = ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ Xn
% 0.35/0.60 @ ( if_nat @ ( Xn = Ma )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ Sn )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ Xn
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ Newlist
% 0.35/0.60 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_mi_lets_in_minNull
% 0.35/0.60 thf(fact_4561_del__x__mi__lets__in,axiom,
% 0.35/0.60 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 0.35/0.60 ( ( ( X = Mi )
% 0.35/0.60 & ( ord_less_nat @ X @ Ma ) )
% 0.35/0.60 => ( ( Mi != Ma )
% 0.35/0.60 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 0.35/0.60 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = H )
% 0.35/0.60 => ( ( Xn
% 0.35/0.60 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 0.35/0.60 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.60 = L )
% 0.35/0.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( ( Newnode
% 0.35/0.60 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 0.35/0.60 => ( ( Newlist
% 0.35/0.60 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 0.35/0.60 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ Xn
% 0.35/0.60 @ ( if_nat @ ( Xn = Ma )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ Xn
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ Deg
% 0.35/0.60 @ Newlist
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 0.35/0.60 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % del_x_mi_lets_in
% 0.35/0.60 thf(fact_4562_of__nat__max,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] :
% 0.35/0.60 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 0.35/0.60 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % of_nat_max
% 0.35/0.60 thf(fact_4563_of__nat__max,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] :
% 0.35/0.60 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 0.35/0.60 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % of_nat_max
% 0.35/0.60 thf(fact_4564_of__nat__max,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] :
% 0.35/0.60 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 0.35/0.60 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % of_nat_max
% 0.35/0.60 thf(fact_4565_max__def__raw,axiom,
% 0.35/0.60 ( ord_max_set_nat
% 0.35/0.60 = ( ^ [A5: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def_raw
% 0.35/0.60 thf(fact_4566_max__def__raw,axiom,
% 0.35/0.60 ( ord_max_rat
% 0.35/0.60 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def_raw
% 0.35/0.60 thf(fact_4567_max__def__raw,axiom,
% 0.35/0.60 ( ord_max_num
% 0.35/0.60 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def_raw
% 0.35/0.60 thf(fact_4568_max__def__raw,axiom,
% 0.35/0.60 ( ord_max_nat
% 0.35/0.60 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def_raw
% 0.35/0.60 thf(fact_4569_max__def__raw,axiom,
% 0.35/0.60 ( ord_max_int
% 0.35/0.60 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def_raw
% 0.35/0.60 thf(fact_4570_sup__nat__def,axiom,
% 0.35/0.60 sup_sup_nat = ord_max_nat ).
% 0.35/0.60
% 0.35/0.60 % sup_nat_def
% 0.35/0.60 thf(fact_4571_lambda__zero,axiom,
% 0.35/0.60 ( ( ^ [H2: complex] : zero_zero_complex )
% 0.35/0.60 = ( times_times_complex @ zero_zero_complex ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_zero
% 0.35/0.60 thf(fact_4572_lambda__zero,axiom,
% 0.35/0.60 ( ( ^ [H2: real] : zero_zero_real )
% 0.35/0.60 = ( times_times_real @ zero_zero_real ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_zero
% 0.35/0.60 thf(fact_4573_lambda__zero,axiom,
% 0.35/0.60 ( ( ^ [H2: rat] : zero_zero_rat )
% 0.35/0.60 = ( times_times_rat @ zero_zero_rat ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_zero
% 0.35/0.60 thf(fact_4574_lambda__zero,axiom,
% 0.35/0.60 ( ( ^ [H2: nat] : zero_zero_nat )
% 0.35/0.60 = ( times_times_nat @ zero_zero_nat ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_zero
% 0.35/0.60 thf(fact_4575_lambda__zero,axiom,
% 0.35/0.60 ( ( ^ [H2: int] : zero_zero_int )
% 0.35/0.60 = ( times_times_int @ zero_zero_int ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_zero
% 0.35/0.60 thf(fact_4576_lambda__one,axiom,
% 0.35/0.60 ( ( ^ [X4: code_integer] : X4 )
% 0.35/0.60 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_one
% 0.35/0.60 thf(fact_4577_lambda__one,axiom,
% 0.35/0.60 ( ( ^ [X4: complex] : X4 )
% 0.35/0.60 = ( times_times_complex @ one_one_complex ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_one
% 0.35/0.60 thf(fact_4578_lambda__one,axiom,
% 0.35/0.60 ( ( ^ [X4: real] : X4 )
% 0.35/0.60 = ( times_times_real @ one_one_real ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_one
% 0.35/0.60 thf(fact_4579_lambda__one,axiom,
% 0.35/0.60 ( ( ^ [X4: rat] : X4 )
% 0.35/0.60 = ( times_times_rat @ one_one_rat ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_one
% 0.35/0.60 thf(fact_4580_lambda__one,axiom,
% 0.35/0.60 ( ( ^ [X4: nat] : X4 )
% 0.35/0.60 = ( times_times_nat @ one_one_nat ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_one
% 0.35/0.60 thf(fact_4581_lambda__one,axiom,
% 0.35/0.60 ( ( ^ [X4: int] : X4 )
% 0.35/0.60 = ( times_times_int @ one_one_int ) ) ).
% 0.35/0.60
% 0.35/0.60 % lambda_one
% 0.35/0.60 thf(fact_4582_finite__M__bounded__by__nat,axiom,
% 0.35/0.60 ! [P2: nat > $o,I2: nat] :
% 0.35/0.60 ( finite_finite_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [K3: nat] :
% 0.35/0.60 ( ( P2 @ K3 )
% 0.35/0.60 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_M_bounded_by_nat
% 0.35/0.60 thf(fact_4583_finite__less__ub,axiom,
% 0.35/0.60 ! [F2: nat > nat,U: nat] :
% 0.35/0.60 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F2 @ N3 ) )
% 0.35/0.60 => ( finite_finite_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F2 @ N4 ) @ U ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_less_ub
% 0.35/0.60 thf(fact_4584_max_Omono,axiom,
% 0.35/0.60 ! [C2: rat,A: rat,D: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_rat @ D @ B )
% 0.35/0.60 => ( ord_less_eq_rat @ ( ord_max_rat @ C2 @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.mono
% 0.35/0.60 thf(fact_4585_max_Omono,axiom,
% 0.35/0.60 ! [C2: num,A: num,D: num,B: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_num @ D @ B )
% 0.35/0.60 => ( ord_less_eq_num @ ( ord_max_num @ C2 @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.mono
% 0.35/0.60 thf(fact_4586_max_Omono,axiom,
% 0.35/0.60 ! [C2: nat,A: nat,D: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_nat @ D @ B )
% 0.35/0.60 => ( ord_less_eq_nat @ ( ord_max_nat @ C2 @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.mono
% 0.35/0.60 thf(fact_4587_max_Omono,axiom,
% 0.35/0.60 ! [C2: int,A: int,D: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.60 => ( ( ord_less_eq_int @ D @ B )
% 0.35/0.60 => ( ord_less_eq_int @ ( ord_max_int @ C2 @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.mono
% 0.35/0.60 thf(fact_4588_max_OorderE,axiom,
% 0.35/0.60 ! [B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( ord_max_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderE
% 0.35/0.60 thf(fact_4589_max_OorderE,axiom,
% 0.35/0.60 ! [B: num,A: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( ord_max_num @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderE
% 0.35/0.60 thf(fact_4590_max_OorderE,axiom,
% 0.35/0.60 ! [B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( ord_max_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderE
% 0.35/0.60 thf(fact_4591_max_OorderE,axiom,
% 0.35/0.60 ! [B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ( A
% 0.35/0.60 = ( ord_max_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderE
% 0.35/0.60 thf(fact_4592_max_OorderI,axiom,
% 0.35/0.60 ! [A: rat,B: rat] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( ord_max_rat @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_rat @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderI
% 0.35/0.60 thf(fact_4593_max_OorderI,axiom,
% 0.35/0.60 ! [A: num,B: num] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( ord_max_num @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_num @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderI
% 0.35/0.60 thf(fact_4594_max_OorderI,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( ord_max_nat @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_nat @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderI
% 0.35/0.60 thf(fact_4595_max_OorderI,axiom,
% 0.35/0.60 ! [A: int,B: int] :
% 0.35/0.60 ( ( A
% 0.35/0.60 = ( ord_max_int @ A @ B ) )
% 0.35/0.60 => ( ord_less_eq_int @ B @ A ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.orderI
% 0.35/0.60 thf(fact_4596_max_OboundedE,axiom,
% 0.35/0.60 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedE
% 0.35/0.60 thf(fact_4597_max_OboundedE,axiom,
% 0.35/0.60 ! [B: num,C2: num,A: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_num @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedE
% 0.35/0.60 thf(fact_4598_max_OboundedE,axiom,
% 0.35/0.60 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedE
% 0.35/0.60 thf(fact_4599_max_OboundedE,axiom,
% 0.35/0.60 ! [B: int,C2: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 0.35/0.60 => ~ ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedE
% 0.35/0.60 thf(fact_4600_max_OboundedI,axiom,
% 0.35/0.60 ! [B: rat,A: rat,C2: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedI
% 0.35/0.60 thf(fact_4601_max_OboundedI,axiom,
% 0.35/0.60 ! [B: num,A: num,C2: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_num @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedI
% 0.35/0.60 thf(fact_4602_max_OboundedI,axiom,
% 0.35/0.60 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedI
% 0.35/0.60 thf(fact_4603_max_OboundedI,axiom,
% 0.35/0.60 ! [B: int,A: int,C2: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ B @ A )
% 0.35/0.60 => ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.boundedI
% 0.35/0.60 thf(fact_4604_max_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [B4: rat,A5: rat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( ord_max_rat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.order_iff
% 0.35/0.60 thf(fact_4605_max_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_num
% 0.35/0.60 = ( ^ [B4: num,A5: num] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( ord_max_num @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.order_iff
% 0.35/0.60 thf(fact_4606_max_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [B4: nat,A5: nat] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( ord_max_nat @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.order_iff
% 0.35/0.60 thf(fact_4607_max_Oorder__iff,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [B4: int,A5: int] :
% 0.35/0.60 ( A5
% 0.35/0.60 = ( ord_max_int @ A5 @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.order_iff
% 0.35/0.60 thf(fact_4608_max_Ocobounded1,axiom,
% 0.35/0.60 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded1
% 0.35/0.60 thf(fact_4609_max_Ocobounded1,axiom,
% 0.35/0.60 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded1
% 0.35/0.60 thf(fact_4610_max_Ocobounded1,axiom,
% 0.35/0.60 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded1
% 0.35/0.60 thf(fact_4611_max_Ocobounded1,axiom,
% 0.35/0.60 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded1
% 0.35/0.60 thf(fact_4612_max_Ocobounded2,axiom,
% 0.35/0.60 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded2
% 0.35/0.60 thf(fact_4613_max_Ocobounded2,axiom,
% 0.35/0.60 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded2
% 0.35/0.60 thf(fact_4614_max_Ocobounded2,axiom,
% 0.35/0.60 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded2
% 0.35/0.60 thf(fact_4615_max_Ocobounded2,axiom,
% 0.35/0.60 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.cobounded2
% 0.35/0.60 thf(fact_4616_le__max__iff__disj,axiom,
% 0.35/0.60 ! [Z3: rat,X: rat,Y: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ Z3 @ ( ord_max_rat @ X @ Y ) )
% 0.35/0.60 = ( ( ord_less_eq_rat @ Z3 @ X )
% 0.35/0.60 | ( ord_less_eq_rat @ Z3 @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_max_iff_disj
% 0.35/0.60 thf(fact_4617_le__max__iff__disj,axiom,
% 0.35/0.60 ! [Z3: num,X: num,Y: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ Z3 @ ( ord_max_num @ X @ Y ) )
% 0.35/0.60 = ( ( ord_less_eq_num @ Z3 @ X )
% 0.35/0.60 | ( ord_less_eq_num @ Z3 @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_max_iff_disj
% 0.35/0.60 thf(fact_4618_le__max__iff__disj,axiom,
% 0.35/0.60 ! [Z3: nat,X: nat,Y: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ Z3 @ ( ord_max_nat @ X @ Y ) )
% 0.35/0.60 = ( ( ord_less_eq_nat @ Z3 @ X )
% 0.35/0.60 | ( ord_less_eq_nat @ Z3 @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_max_iff_disj
% 0.35/0.60 thf(fact_4619_le__max__iff__disj,axiom,
% 0.35/0.60 ! [Z3: int,X: int,Y: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ Z3 @ ( ord_max_int @ X @ Y ) )
% 0.35/0.60 = ( ( ord_less_eq_int @ Z3 @ X )
% 0.35/0.60 | ( ord_less_eq_int @ Z3 @ Y ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % le_max_iff_disj
% 0.35/0.60 thf(fact_4620_max_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [B4: rat,A5: rat] :
% 0.35/0.60 ( ( ord_max_rat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff1
% 0.35/0.60 thf(fact_4621_max_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_num
% 0.35/0.60 = ( ^ [B4: num,A5: num] :
% 0.35/0.60 ( ( ord_max_num @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff1
% 0.35/0.60 thf(fact_4622_max_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [B4: nat,A5: nat] :
% 0.35/0.60 ( ( ord_max_nat @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff1
% 0.35/0.60 thf(fact_4623_max_Oabsorb__iff1,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [B4: int,A5: int] :
% 0.35/0.60 ( ( ord_max_int @ A5 @ B4 )
% 0.35/0.60 = A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff1
% 0.35/0.60 thf(fact_4624_max_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_rat
% 0.35/0.60 = ( ^ [A5: rat,B4: rat] :
% 0.35/0.60 ( ( ord_max_rat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff2
% 0.35/0.60 thf(fact_4625_max_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_num
% 0.35/0.60 = ( ^ [A5: num,B4: num] :
% 0.35/0.60 ( ( ord_max_num @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff2
% 0.35/0.60 thf(fact_4626_max_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [A5: nat,B4: nat] :
% 0.35/0.60 ( ( ord_max_nat @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff2
% 0.35/0.60 thf(fact_4627_max_Oabsorb__iff2,axiom,
% 0.35/0.60 ( ord_less_eq_int
% 0.35/0.60 = ( ^ [A5: int,B4: int] :
% 0.35/0.60 ( ( ord_max_int @ A5 @ B4 )
% 0.35/0.60 = B4 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.absorb_iff2
% 0.35/0.60 thf(fact_4628_max_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI1
% 0.35/0.60 thf(fact_4629_max_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: num,A: num,B: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI1
% 0.35/0.60 thf(fact_4630_max_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI1
% 0.35/0.60 thf(fact_4631_max_OcoboundedI1,axiom,
% 0.35/0.60 ! [C2: int,A: int,B: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ C2 @ A )
% 0.35/0.60 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI1
% 0.35/0.60 thf(fact_4632_max_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI2
% 0.35/0.60 thf(fact_4633_max_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: num,B: num,A: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI2
% 0.35/0.60 thf(fact_4634_max_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI2
% 0.35/0.60 thf(fact_4635_max_OcoboundedI2,axiom,
% 0.35/0.60 ! [C2: int,B: int,A: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ C2 @ B )
% 0.35/0.60 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max.coboundedI2
% 0.35/0.60 thf(fact_4636_max__absorb2,axiom,
% 0.35/0.60 ! [X: set_nat,Y: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.35/0.60 => ( ( ord_max_set_nat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb2
% 0.35/0.60 thf(fact_4637_max__absorb2,axiom,
% 0.35/0.60 ! [X: rat,Y: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ X @ Y )
% 0.35/0.60 => ( ( ord_max_rat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb2
% 0.35/0.60 thf(fact_4638_max__absorb2,axiom,
% 0.35/0.60 ! [X: num,Y: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ X @ Y )
% 0.35/0.60 => ( ( ord_max_num @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb2
% 0.35/0.60 thf(fact_4639_max__absorb2,axiom,
% 0.35/0.60 ! [X: nat,Y: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ X @ Y )
% 0.35/0.60 => ( ( ord_max_nat @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb2
% 0.35/0.60 thf(fact_4640_max__absorb2,axiom,
% 0.35/0.60 ! [X: int,Y: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ X @ Y )
% 0.35/0.60 => ( ( ord_max_int @ X @ Y )
% 0.35/0.60 = Y ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb2
% 0.35/0.60 thf(fact_4641_max__absorb1,axiom,
% 0.35/0.60 ! [Y: set_nat,X: set_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ Y @ X )
% 0.35/0.60 => ( ( ord_max_set_nat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb1
% 0.35/0.60 thf(fact_4642_max__absorb1,axiom,
% 0.35/0.60 ! [Y: rat,X: rat] :
% 0.35/0.60 ( ( ord_less_eq_rat @ Y @ X )
% 0.35/0.60 => ( ( ord_max_rat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb1
% 0.35/0.60 thf(fact_4643_max__absorb1,axiom,
% 0.35/0.60 ! [Y: num,X: num] :
% 0.35/0.60 ( ( ord_less_eq_num @ Y @ X )
% 0.35/0.60 => ( ( ord_max_num @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb1
% 0.35/0.60 thf(fact_4644_max__absorb1,axiom,
% 0.35/0.60 ! [Y: nat,X: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ Y @ X )
% 0.35/0.60 => ( ( ord_max_nat @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb1
% 0.35/0.60 thf(fact_4645_max__absorb1,axiom,
% 0.35/0.60 ! [Y: int,X: int] :
% 0.35/0.60 ( ( ord_less_eq_int @ Y @ X )
% 0.35/0.60 => ( ( ord_max_int @ X @ Y )
% 0.35/0.60 = X ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_absorb1
% 0.35/0.60 thf(fact_4646_max__def,axiom,
% 0.35/0.60 ( ord_max_set_nat
% 0.35/0.60 = ( ^ [A5: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def
% 0.35/0.60 thf(fact_4647_max__def,axiom,
% 0.35/0.60 ( ord_max_rat
% 0.35/0.60 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def
% 0.35/0.60 thf(fact_4648_max__def,axiom,
% 0.35/0.60 ( ord_max_num
% 0.35/0.60 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def
% 0.35/0.60 thf(fact_4649_max__def,axiom,
% 0.35/0.60 ( ord_max_nat
% 0.35/0.60 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def
% 0.35/0.60 thf(fact_4650_max__def,axiom,
% 0.35/0.60 ( ord_max_int
% 0.35/0.60 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_def
% 0.35/0.60 thf(fact_4651_max__add__distrib__left,axiom,
% 0.35/0.60 ! [X: real,Y: real,Z3: real] :
% 0.35/0.60 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z3 )
% 0.35/0.60 = ( ord_max_real @ ( plus_plus_real @ X @ Z3 ) @ ( plus_plus_real @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_left
% 0.35/0.60 thf(fact_4652_max__add__distrib__left,axiom,
% 0.35/0.60 ! [X: rat,Y: rat,Z3: rat] :
% 0.35/0.60 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 0.35/0.60 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z3 ) @ ( plus_plus_rat @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_left
% 0.35/0.60 thf(fact_4653_max__add__distrib__left,axiom,
% 0.35/0.60 ! [X: nat,Y: nat,Z3: nat] :
% 0.35/0.60 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z3 )
% 0.35/0.60 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z3 ) @ ( plus_plus_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_left
% 0.35/0.60 thf(fact_4654_max__add__distrib__left,axiom,
% 0.35/0.60 ! [X: int,Y: int,Z3: int] :
% 0.35/0.60 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 0.35/0.60 = ( ord_max_int @ ( plus_plus_int @ X @ Z3 ) @ ( plus_plus_int @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_left
% 0.35/0.60 thf(fact_4655_max__add__distrib__right,axiom,
% 0.35/0.60 ! [X: real,Y: real,Z3: real] :
% 0.35/0.60 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z3 ) )
% 0.35/0.60 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_right
% 0.35/0.60 thf(fact_4656_max__add__distrib__right,axiom,
% 0.35/0.60 ! [X: rat,Y: rat,Z3: rat] :
% 0.35/0.60 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z3 ) )
% 0.35/0.60 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_right
% 0.35/0.60 thf(fact_4657_max__add__distrib__right,axiom,
% 0.35/0.60 ! [X: nat,Y: nat,Z3: nat] :
% 0.35/0.60 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z3 ) )
% 0.35/0.60 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_right
% 0.35/0.60 thf(fact_4658_max__add__distrib__right,axiom,
% 0.35/0.60 ! [X: int,Y: int,Z3: int] :
% 0.35/0.60 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z3 ) )
% 0.35/0.60 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_add_distrib_right
% 0.35/0.60 thf(fact_4659_max__diff__distrib__left,axiom,
% 0.35/0.60 ! [X: rat,Y: rat,Z3: rat] :
% 0.35/0.60 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 0.35/0.60 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z3 ) @ ( minus_minus_rat @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_diff_distrib_left
% 0.35/0.60 thf(fact_4660_max__diff__distrib__left,axiom,
% 0.35/0.60 ! [X: int,Y: int,Z3: int] :
% 0.35/0.60 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 0.35/0.60 = ( ord_max_int @ ( minus_minus_int @ X @ Z3 ) @ ( minus_minus_int @ Y @ Z3 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % max_diff_distrib_left
% 0.35/0.60 thf(fact_4661_nat__add__max__left,axiom,
% 0.35/0.60 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.60 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N ) @ Q2 )
% 0.35/0.60 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nat_add_max_left
% 0.35/0.60 thf(fact_4662_nat__add__max__right,axiom,
% 0.35/0.60 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.60 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N @ Q2 ) )
% 0.35/0.60 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N ) @ ( plus_plus_nat @ M2 @ Q2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nat_add_max_right
% 0.35/0.60 thf(fact_4663_set__vebt__def,axiom,
% 0.35/0.60 ( vEBT_set_vebt
% 0.35/0.60 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % set_vebt_def
% 0.35/0.60 thf(fact_4664_nat__mult__max__left,axiom,
% 0.35/0.60 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.60 ( ( times_times_nat @ ( ord_max_nat @ M2 @ N ) @ Q2 )
% 0.35/0.60 = ( ord_max_nat @ ( times_times_nat @ M2 @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nat_mult_max_left
% 0.35/0.60 thf(fact_4665_nat__mult__max__right,axiom,
% 0.35/0.60 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.60 ( ( times_times_nat @ M2 @ ( ord_max_nat @ N @ Q2 ) )
% 0.35/0.60 = ( ord_max_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q2 ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nat_mult_max_right
% 0.35/0.60 thf(fact_4666_numeral__code_I2_J,axiom,
% 0.35/0.60 ! [N: num] :
% 0.35/0.60 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 0.35/0.60 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % numeral_code(2)
% 0.35/0.60 thf(fact_4667_numeral__code_I2_J,axiom,
% 0.35/0.60 ! [N: num] :
% 0.35/0.60 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 0.35/0.60 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % numeral_code(2)
% 0.35/0.60 thf(fact_4668_numeral__code_I2_J,axiom,
% 0.35/0.60 ! [N: num] :
% 0.35/0.60 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 0.35/0.60 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % numeral_code(2)
% 0.35/0.60 thf(fact_4669_numeral__code_I2_J,axiom,
% 0.35/0.60 ! [N: num] :
% 0.35/0.60 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 0.35/0.60 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % numeral_code(2)
% 0.35/0.60 thf(fact_4670_numeral__code_I2_J,axiom,
% 0.35/0.60 ! [N: num] :
% 0.35/0.60 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.35/0.60 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % numeral_code(2)
% 0.35/0.60 thf(fact_4671_numeral__code_I2_J,axiom,
% 0.35/0.60 ! [N: num] :
% 0.35/0.60 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 0.35/0.60 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % numeral_code(2)
% 0.35/0.60 thf(fact_4672_nat__leq__as__int,axiom,
% 0.35/0.60 ( ord_less_eq_nat
% 0.35/0.60 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % nat_leq_as_int
% 0.35/0.60 thf(fact_4673_power__numeral__even,axiom,
% 0.35/0.60 ! [Z3: complex,W2: num] :
% 0.35/0.60 ( ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 0.35/0.60 = ( times_times_complex @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % power_numeral_even
% 0.35/0.60 thf(fact_4674_power__numeral__even,axiom,
% 0.35/0.60 ! [Z3: real,W2: num] :
% 0.35/0.60 ( ( power_power_real @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 0.35/0.60 = ( times_times_real @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % power_numeral_even
% 0.35/0.60 thf(fact_4675_power__numeral__even,axiom,
% 0.35/0.60 ! [Z3: rat,W2: num] :
% 0.35/0.60 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 0.35/0.60 = ( times_times_rat @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % power_numeral_even
% 0.35/0.60 thf(fact_4676_power__numeral__even,axiom,
% 0.35/0.60 ! [Z3: nat,W2: num] :
% 0.35/0.60 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 0.35/0.60 = ( times_times_nat @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % power_numeral_even
% 0.35/0.60 thf(fact_4677_power__numeral__even,axiom,
% 0.35/0.60 ! [Z3: int,W2: num] :
% 0.35/0.60 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 0.35/0.60 = ( times_times_int @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % power_numeral_even
% 0.35/0.60 thf(fact_4678_card__less,axiom,
% 0.35/0.60 ! [M5: set_nat,I2: nat] :
% 0.35/0.60 ( ( member_nat @ zero_zero_nat @ M5 )
% 0.35/0.60 => ( ( finite_card_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [K3: nat] :
% 0.35/0.60 ( ( member_nat @ K3 @ M5 )
% 0.35/0.60 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 0.35/0.60 != zero_zero_nat ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_less
% 0.35/0.60 thf(fact_4679_card__less__Suc,axiom,
% 0.35/0.60 ! [M5: set_nat,I2: nat] :
% 0.35/0.60 ( ( member_nat @ zero_zero_nat @ M5 )
% 0.35/0.60 => ( ( suc
% 0.35/0.60 @ ( finite_card_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [K3: nat] :
% 0.35/0.60 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 0.35/0.60 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 0.35/0.60 = ( finite_card_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [K3: nat] :
% 0.35/0.60 ( ( member_nat @ K3 @ M5 )
% 0.35/0.60 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_less_Suc
% 0.35/0.60 thf(fact_4680_card__less__Suc2,axiom,
% 0.35/0.60 ! [M5: set_nat,I2: nat] :
% 0.35/0.60 ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 0.35/0.60 => ( ( finite_card_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [K3: nat] :
% 0.35/0.60 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 0.35/0.60 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 0.35/0.60 = ( finite_card_nat
% 0.35/0.60 @ ( collect_nat
% 0.35/0.60 @ ^ [K3: nat] :
% 0.35/0.60 ( ( member_nat @ K3 @ M5 )
% 0.35/0.60 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_less_Suc2
% 0.35/0.60 thf(fact_4681_nat__minus__add__max,axiom,
% 0.35/0.60 ! [N: nat,M2: nat] :
% 0.35/0.60 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M2 ) @ M2 )
% 0.35/0.60 = ( ord_max_nat @ N @ M2 ) ) ).
% 0.35/0.60
% 0.35/0.60 % nat_minus_add_max
% 0.35/0.60 thf(fact_4682_finite__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_complex,N: nat] :
% 0.35/0.60 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.60 => ( finite8712137658972009173omplex
% 0.35/0.60 @ ( collect_list_complex
% 0.35/0.60 @ ^ [Xs: list_complex] :
% 0.35/0.60 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_s3451745648224563538omplex @ Xs )
% 0.35/0.60 = N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_eq
% 0.35/0.60 thf(fact_4683_finite__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.35/0.60 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.35/0.60 => ( finite3004134309566078307T_VEBT
% 0.35/0.60 @ ( collec5608196760682091941T_VEBT
% 0.35/0.60 @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.60 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.35/0.60 = N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_eq
% 0.35/0.60 thf(fact_4684_finite__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_o,N: nat] :
% 0.35/0.60 ( ( finite_finite_o @ A4 )
% 0.35/0.60 => ( finite_finite_list_o
% 0.35/0.60 @ ( collect_list_o
% 0.35/0.60 @ ^ [Xs: list_o] :
% 0.35/0.60 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_size_list_o @ Xs )
% 0.35/0.60 = N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_eq
% 0.35/0.60 thf(fact_4685_finite__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_int,N: nat] :
% 0.35/0.60 ( ( finite_finite_int @ A4 )
% 0.35/0.60 => ( finite3922522038869484883st_int
% 0.35/0.60 @ ( collect_list_int
% 0.35/0.60 @ ^ [Xs: list_int] :
% 0.35/0.60 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_size_list_int @ Xs )
% 0.35/0.60 = N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_eq
% 0.35/0.60 thf(fact_4686_finite__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_nat,N: nat] :
% 0.35/0.60 ( ( finite_finite_nat @ A4 )
% 0.35/0.60 => ( finite8100373058378681591st_nat
% 0.35/0.60 @ ( collect_list_nat
% 0.35/0.60 @ ^ [Xs: list_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_size_list_nat @ Xs )
% 0.35/0.60 = N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_eq
% 0.35/0.60 thf(fact_4687_card__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_list_nat,N: nat] :
% 0.35/0.60 ( ( finite8100373058378681591st_nat @ A4 )
% 0.35/0.60 => ( ( finite7325466520557071688st_nat
% 0.35/0.60 @ ( collec5989764272469232197st_nat
% 0.35/0.60 @ ^ [Xs: list_list_nat] :
% 0.35/0.60 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_s3023201423986296836st_nat @ Xs )
% 0.35/0.60 = N ) ) ) )
% 0.35/0.60 = ( power_power_nat @ ( finite_card_list_nat @ A4 ) @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_lists_length_eq
% 0.35/0.60 thf(fact_4688_card__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_set_nat,N: nat] :
% 0.35/0.60 ( ( finite1152437895449049373et_nat @ A4 )
% 0.35/0.60 => ( ( finite5631907774883551598et_nat
% 0.35/0.60 @ ( collect_list_set_nat
% 0.35/0.60 @ ^ [Xs: list_set_nat] :
% 0.35/0.60 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_s3254054031482475050et_nat @ Xs )
% 0.35/0.60 = N ) ) ) )
% 0.35/0.60 = ( power_power_nat @ ( finite_card_set_nat @ A4 ) @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_lists_length_eq
% 0.35/0.60 thf(fact_4689_card__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_complex,N: nat] :
% 0.35/0.60 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.60 => ( ( finite5120063068150530198omplex
% 0.35/0.60 @ ( collect_list_complex
% 0.35/0.60 @ ^ [Xs: list_complex] :
% 0.35/0.60 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_s3451745648224563538omplex @ Xs )
% 0.35/0.60 = N ) ) ) )
% 0.35/0.60 = ( power_power_nat @ ( finite_card_complex @ A4 ) @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_lists_length_eq
% 0.35/0.60 thf(fact_4690_card__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.35/0.60 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.35/0.60 => ( ( finite5915292604075114978T_VEBT
% 0.35/0.60 @ ( collec5608196760682091941T_VEBT
% 0.35/0.60 @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.60 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.35/0.60 = N ) ) ) )
% 0.35/0.60 = ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_lists_length_eq
% 0.35/0.60 thf(fact_4691_card__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_o,N: nat] :
% 0.35/0.60 ( ( finite_finite_o @ A4 )
% 0.35/0.60 => ( ( finite_card_list_o
% 0.35/0.60 @ ( collect_list_o
% 0.35/0.60 @ ^ [Xs: list_o] :
% 0.35/0.60 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_size_list_o @ Xs )
% 0.35/0.60 = N ) ) ) )
% 0.35/0.60 = ( power_power_nat @ ( finite_card_o @ A4 ) @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_lists_length_eq
% 0.35/0.60 thf(fact_4692_card__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_int,N: nat] :
% 0.35/0.60 ( ( finite_finite_int @ A4 )
% 0.35/0.60 => ( ( finite_card_list_int
% 0.35/0.60 @ ( collect_list_int
% 0.35/0.60 @ ^ [Xs: list_int] :
% 0.35/0.60 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_size_list_int @ Xs )
% 0.35/0.60 = N ) ) ) )
% 0.35/0.60 = ( power_power_nat @ ( finite_card_int @ A4 ) @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_lists_length_eq
% 0.35/0.60 thf(fact_4693_card__lists__length__eq,axiom,
% 0.35/0.60 ! [A4: set_nat,N: nat] :
% 0.35/0.60 ( ( finite_finite_nat @ A4 )
% 0.35/0.60 => ( ( finite_card_list_nat
% 0.35/0.60 @ ( collect_list_nat
% 0.35/0.60 @ ^ [Xs: list_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ( size_size_list_nat @ Xs )
% 0.35/0.60 = N ) ) ) )
% 0.35/0.60 = ( power_power_nat @ ( finite_card_nat @ A4 ) @ N ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_lists_length_eq
% 0.35/0.60 thf(fact_4694_finite__lists__length__le,axiom,
% 0.35/0.60 ! [A4: set_complex,N: nat] :
% 0.35/0.60 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.60 => ( finite8712137658972009173omplex
% 0.35/0.60 @ ( collect_list_complex
% 0.35/0.60 @ ^ [Xs: list_complex] :
% 0.35/0.60 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_le
% 0.35/0.60 thf(fact_4695_finite__lists__length__le,axiom,
% 0.35/0.60 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.35/0.60 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.35/0.60 => ( finite3004134309566078307T_VEBT
% 0.35/0.60 @ ( collec5608196760682091941T_VEBT
% 0.35/0.60 @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.60 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_le
% 0.35/0.60 thf(fact_4696_finite__lists__length__le,axiom,
% 0.35/0.60 ! [A4: set_o,N: nat] :
% 0.35/0.60 ( ( finite_finite_o @ A4 )
% 0.35/0.60 => ( finite_finite_list_o
% 0.35/0.60 @ ( collect_list_o
% 0.35/0.60 @ ^ [Xs: list_o] :
% 0.35/0.60 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_le
% 0.35/0.60 thf(fact_4697_finite__lists__length__le,axiom,
% 0.35/0.60 ! [A4: set_int,N: nat] :
% 0.35/0.60 ( ( finite_finite_int @ A4 )
% 0.35/0.60 => ( finite3922522038869484883st_int
% 0.35/0.60 @ ( collect_list_int
% 0.35/0.60 @ ^ [Xs: list_int] :
% 0.35/0.60 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_le
% 0.35/0.60 thf(fact_4698_finite__lists__length__le,axiom,
% 0.35/0.60 ! [A4: set_nat,N: nat] :
% 0.35/0.60 ( ( finite_finite_nat @ A4 )
% 0.35/0.60 => ( finite8100373058378681591st_nat
% 0.35/0.60 @ ( collect_list_nat
% 0.35/0.60 @ ^ [Xs: list_nat] :
% 0.35/0.60 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 0.35/0.60 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_lists_length_le
% 0.35/0.60 thf(fact_4699_vebt__insert_Osimps_I5_J,axiom,
% 0.35/0.60 ! [Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.60 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_VEBT_VEBT
% 0.35/0.60 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 & ~ ( ( X = Mi )
% 0.35/0.60 | ( X = Ma ) ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_insert.simps(5)
% 0.35/0.60 thf(fact_4700_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 0.35/0.60 ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 0.35/0.60 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) @ X )
% 0.35/0.60 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.naive_member.simps(3)
% 0.35/0.60 thf(fact_4701_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 0.35/0.60 ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 0.35/0.60 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X )
% 0.35/0.60 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.membermima.simps(5)
% 0.35/0.60 thf(fact_4702_vebt__insert_Oelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.35/0.60 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 0.35/0.60 & ( ( Xa2 != one_one_nat )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) ) )
% 0.35/0.60 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) )
% 0.35/0.60 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) )
% 0.35/0.60 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( if_VEBT_VEBT
% 0.35/0.60 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 & ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 ) ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_insert.elims
% 0.35/0.60 thf(fact_4703_vebt__member_Osimps_I5_J,axiom,
% 0.35/0.60 ! [Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 0.35/0.60 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( ( X != Mi )
% 0.35/0.60 => ( ( X != Ma )
% 0.35/0.60 => ( ~ ( ord_less_nat @ X @ Mi )
% 0.35/0.60 & ( ~ ( ord_less_nat @ X @ Mi )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Ma @ X )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Ma @ X )
% 0.35/0.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_member.simps(5)
% 0.35/0.60 thf(fact_4704_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 0.35/0.60 ! [Mi: nat,Ma: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 0.35/0.60 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc ) @ X )
% 0.35/0.60 = ( ( X = Mi )
% 0.35/0.60 | ( X = Ma )
% 0.35/0.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.membermima.simps(4)
% 0.35/0.60 thf(fact_4705_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.60 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => A3 )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => B3 )
% 0.35/0.60 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.60 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 0.35/0.60 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [S: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 0.35/0.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.naive_member.elims(3)
% 0.35/0.60 thf(fact_4706_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.60 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => A3 )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => B3 )
% 0.35/0.60 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.60 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [S: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 0.35/0.60 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.naive_member.elims(2)
% 0.35/0.60 thf(fact_4707_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.60 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => A3 )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => B3 )
% 0.35/0.60 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.35/0.60 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 0.35/0.60 => Y )
% 0.35/0.60 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [S: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.naive_member.elims(1)
% 0.35/0.60 thf(fact_4708_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.60 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat] :
% 0.35/0.60 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 0.35/0.60 => ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 ) ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Vc2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 0.35/0.60 => ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 )
% 0.35/0.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 0.35/0.60 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Vd: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 0.35/0.60 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.membermima.elims(2)
% 0.35/0.60 thf(fact_4709_vebt__member_Oelims_I2_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.60 ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => A3 )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => B3 )
% 0.35/0.60 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ~ ( ( Xa2 != Mi2 )
% 0.35/0.60 => ( ( Xa2 != Ma2 )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_member.elims(2)
% 0.35/0.60 thf(fact_4710_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.60 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.60 => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.60 ( X
% 0.35/0.60 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.60 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat] :
% 0.35/0.60 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 0.35/0.60 => ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 ) ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Vc2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 0.35/0.60 => ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 )
% 0.35/0.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 0.35/0.60 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Vd: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 0.35/0.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.membermima.elims(3)
% 0.35/0.60 thf(fact_4711_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.60 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.60 => Y )
% 0.35/0.60 => ( ( ? [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.35/0.60 => Y )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat] :
% 0.35/0.60 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 ) ) ) ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Vc2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 )
% 0.35/0.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) )
% 0.35/0.60 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Vd: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % VEBT_internal.membermima.elims(1)
% 0.35/0.60 thf(fact_4712_vebt__member_Oelims_I3_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.60 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => A3 )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => B3 )
% 0.35/0.60 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.60 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.35/0.60 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.35/0.60 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( Xa2 != Mi2 )
% 0.35/0.60 => ( ( Xa2 != Ma2 )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_member.elims(3)
% 0.35/0.60 thf(fact_4713_vebt__member_Oelims_I1_J,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.60 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => A3 )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => B3 )
% 0.35/0.60 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 0.35/0.60 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.35/0.60 => Y )
% 0.35/0.60 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.35/0.60 => Y )
% 0.35/0.60 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.60 => Y )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 0.35/0.60 ( ? [Summary2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( ~ ( ( Xa2 != Mi2 )
% 0.35/0.60 => ( ( Xa2 != Ma2 )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_member.elims(1)
% 0.35/0.60 thf(fact_4714_vebt__pred_Osimps_I7_J,axiom,
% 0.35/0.60 ! [Ma: nat,X: nat,Mi: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( ord_less_nat @ Ma @ X )
% 0.35/0.60 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( some_nat @ Ma ) ) )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Ma @ X )
% 0.35/0.60 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_pred.simps(7)
% 0.35/0.60 thf(fact_4715_vebt__succ_Osimps_I6_J,axiom,
% 0.35/0.60 ! [X: nat,Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( ord_less_nat @ X @ Mi )
% 0.35/0.60 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( some_nat @ Mi ) ) )
% 0.35/0.60 & ( ~ ( ord_less_nat @ X @ Mi )
% 0.35/0.60 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ none_nat
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_succ.simps(6)
% 0.35/0.60 thf(fact_4716_vebt__delete_Osimps_I7_J,axiom,
% 0.35/0.60 ! [X: nat,Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.60 ( ( ( ( ord_less_nat @ X @ Mi )
% 0.35/0.60 | ( ord_less_nat @ Ma @ X ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) )
% 0.35/0.60 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 0.35/0.60 | ( ord_less_nat @ Ma @ X ) )
% 0.35/0.60 => ( ( ( ( X = Mi )
% 0.35/0.60 & ( X = Ma ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) )
% 0.35/0.60 & ( ~ ( ( X = Mi )
% 0.35/0.60 & ( X = Ma ) )
% 0.35/0.60 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 0.35/0.60 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 0.35/0.60 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( X = Mi )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 = Ma ) )
% 0.35/0.60 & ( ( X != Mi )
% 0.35/0.60 => ( X = Ma ) ) )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ ( suc @ ( suc @ Va3 ) )
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( X = Mi )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 0.35/0.60 = Ma ) )
% 0.35/0.60 & ( ( X != Mi )
% 0.35/0.60 => ( X = Ma ) ) )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma ) ) )
% 0.35/0.60 @ ( suc @ ( suc @ Va3 ) )
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ Summary ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_delete.simps(7)
% 0.35/0.60 thf(fact_4717_vebt__delete_Oelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.35/0.60 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 0.35/0.60 => ( ! [A3: $o] :
% 0.35/0.60 ( ? [B3: $o] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ( Xa2
% 0.35/0.60 = ( suc @ zero_zero_nat ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ? [N3: nat] :
% 0.35/0.60 ( Xa2
% 0.35/0.60 = ( suc @ ( suc @ N3 ) ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 0.35/0.60 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 0.35/0.60 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.60 => ( ( ( ( Xa2 = Mi2 )
% 0.35/0.60 & ( Xa2 = Ma2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 0.35/0.60 & ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 & ( Xa2 = Ma2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( Xa2 = Mi2 )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.60 = Ma2 ) )
% 0.35/0.60 & ( ( Xa2 != Mi2 )
% 0.35/0.60 => ( Xa2 = Ma2 ) ) )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma2 ) ) )
% 0.35/0.60 @ ( suc @ ( suc @ Va ) )
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( Xa2 = Mi2 )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.60 = Ma2 ) )
% 0.35/0.60 & ( ( Xa2 != Mi2 )
% 0.35/0.60 => ( Xa2 = Ma2 ) ) )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma2 ) ) )
% 0.35/0.60 @ ( suc @ ( suc @ Va ) )
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ Summary2 ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_delete.elims
% 0.35/0.60 thf(fact_4718_vebt__succ_Oelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.35/0.60 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ! [Uu2: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.60 => ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ~ ( ( B3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ one_one_nat ) ) )
% 0.35/0.60 & ( ~ B3
% 0.35/0.60 => ( Y = none_nat ) ) ) ) )
% 0.35/0.60 => ( ( ? [Uv2: $o,Uw: $o] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Leaf @ Uv2 @ Uw ) )
% 0.35/0.60 => ( ? [N3: nat] :
% 0.35/0.60 ( Xa2
% 0.35/0.60 = ( suc @ N3 ) )
% 0.35/0.60 => ( Y != none_nat ) ) )
% 0.35/0.60 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.35/0.60 => ( Y != none_nat ) )
% 0.35/0.60 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.35/0.60 => ( Y != none_nat ) )
% 0.35/0.60 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.35/0.60 => ( Y != none_nat ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ Mi2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ none_nat
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_succ.elims
% 0.35/0.60 thf(fact_4719_vebt__pred_Oelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.35/0.60 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.60 => ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ( Y != none_nat ) ) )
% 0.35/0.60 => ( ! [A3: $o] :
% 0.35/0.60 ( ? [Uw: $o] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.35/0.60 => ( ( Xa2
% 0.35/0.60 = ( suc @ zero_zero_nat ) )
% 0.35/0.60 => ~ ( ( A3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.60 & ( ~ A3
% 0.35/0.60 => ( Y = none_nat ) ) ) ) )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ? [Va: nat] :
% 0.35/0.60 ( Xa2
% 0.35/0.60 = ( suc @ ( suc @ Va ) ) )
% 0.35/0.60 => ~ ( ( B3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ one_one_nat ) ) )
% 0.35/0.60 & ( ~ B3
% 0.35/0.60 => ( ( A3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.60 & ( ~ A3
% 0.35/0.60 => ( Y = none_nat ) ) ) ) ) ) )
% 0.35/0.60 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) )
% 0.35/0.60 => ( Y != none_nat ) )
% 0.35/0.60 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.35/0.60 => ( Y != none_nat ) )
% 0.35/0.60 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.35/0.60 ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.35/0.60 => ( Y != none_nat ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ Ma2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_pred.elims
% 0.35/0.60 thf(fact_4720_finite__nth__roots,axiom,
% 0.35/0.60 ! [N: nat,C2: complex] :
% 0.35/0.60 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.60 => ( finite3207457112153483333omplex
% 0.35/0.60 @ ( collect_complex
% 0.35/0.60 @ ^ [Z4: complex] :
% 0.35/0.60 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.60 = C2 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_nth_roots
% 0.35/0.60 thf(fact_4721_card__roots__unity,axiom,
% 0.35/0.60 ! [N: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.60 => ( ord_less_eq_nat
% 0.35/0.60 @ ( finite_card_real
% 0.35/0.60 @ ( collect_real
% 0.35/0.60 @ ^ [Z4: real] :
% 0.35/0.60 ( ( power_power_real @ Z4 @ N )
% 0.35/0.60 = one_one_real ) ) )
% 0.35/0.60 @ N ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_roots_unity
% 0.35/0.60 thf(fact_4722_card__roots__unity,axiom,
% 0.35/0.60 ! [N: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.60 => ( ord_less_eq_nat
% 0.35/0.60 @ ( finite_card_complex
% 0.35/0.60 @ ( collect_complex
% 0.35/0.60 @ ^ [Z4: complex] :
% 0.35/0.60 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.60 = one_one_complex ) ) )
% 0.35/0.60 @ N ) ) ).
% 0.35/0.60
% 0.35/0.60 % card_roots_unity
% 0.35/0.60 thf(fact_4723_finite__roots__unity,axiom,
% 0.35/0.60 ! [N: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.60 => ( finite_finite_real
% 0.35/0.60 @ ( collect_real
% 0.35/0.60 @ ^ [Z4: real] :
% 0.35/0.60 ( ( power_power_real @ Z4 @ N )
% 0.35/0.60 = one_one_real ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_roots_unity
% 0.35/0.60 thf(fact_4724_finite__roots__unity,axiom,
% 0.35/0.60 ! [N: nat] :
% 0.35/0.60 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.60 => ( finite3207457112153483333omplex
% 0.35/0.60 @ ( collect_complex
% 0.35/0.60 @ ^ [Z4: complex] :
% 0.35/0.60 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.60 = one_one_complex ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % finite_roots_unity
% 0.35/0.60 thf(fact_4725_vebt__succ_Opelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.35/0.60 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.60 => ( ! [Uu2: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 0.35/0.60 => ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ( ( ( B3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ one_one_nat ) ) )
% 0.35/0.60 & ( ~ B3
% 0.35/0.60 => ( Y = none_nat ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.60 => ( ! [Uv2: $o,Uw: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ Uv2 @ Uw ) )
% 0.35/0.60 => ! [N3: nat] :
% 0.35/0.60 ( ( Xa2
% 0.35/0.60 = ( suc @ N3 ) )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw ) @ ( suc @ N3 ) ) ) ) ) )
% 0.35/0.60 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ Mi2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ none_nat
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_succ.pelims
% 0.35/0.60 thf(fact_4726_vebt__pred_Opelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 0.35/0.60 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.60 => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.60 => ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.60 => ( ! [A3: $o,Uw: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ Uw ) )
% 0.35/0.60 => ( ( Xa2
% 0.35/0.60 = ( suc @ zero_zero_nat ) )
% 0.35/0.60 => ( ( ( A3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.60 & ( ~ A3
% 0.35/0.60 => ( Y = none_nat ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ! [Va: nat] :
% 0.35/0.60 ( ( Xa2
% 0.35/0.60 = ( suc @ ( suc @ Va ) ) )
% 0.35/0.60 => ( ( ( B3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ one_one_nat ) ) )
% 0.35/0.60 & ( ~ B3
% 0.35/0.60 => ( ( A3
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ zero_zero_nat ) ) )
% 0.35/0.60 & ( ~ A3
% 0.35/0.60 => ( Y = none_nat ) ) ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 0.35/0.60 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 0.35/0.60 => ( ( Y = none_nat )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( some_nat @ Ma2 ) ) )
% 0.35/0.60 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 != none_nat )
% 0.35/0.60 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( if_option_nat
% 0.35/0.60 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 0.35/0.60 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ none_nat ) ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_pred.pelims
% 0.35/0.60 thf(fact_4727_vebt__delete_Opelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.35/0.60 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Leaf @ $false @ B3 ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ( Xa2
% 0.35/0.60 = ( suc @ zero_zero_nat ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ $false ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ! [N3: nat] :
% 0.35/0.60 ( ( Xa2
% 0.35/0.60 = ( suc @ ( suc @ N3 ) ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 0.35/0.60 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ Xa2 ) ) ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 0.35/0.60 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.60 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 0.35/0.60 => ( ( ( ( Xa2 = Mi2 )
% 0.35/0.60 & ( Xa2 = Ma2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 0.35/0.60 & ( ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 & ( Xa2 = Ma2 ) )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( Xa2 = Mi2 )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.60 = Ma2 ) )
% 0.35/0.60 & ( ( Xa2 != Mi2 )
% 0.35/0.60 => ( Xa2 = Ma2 ) ) )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 = none_nat )
% 0.35/0.60 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma2 ) ) )
% 0.35/0.60 @ ( suc @ ( suc @ Va ) )
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ ( vEBT_Node
% 0.35/0.60 @ ( some_P7363390416028606310at_nat
% 0.35/0.60 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 0.35/0.60 @ ( if_nat
% 0.35/0.60 @ ( ( ( Xa2 = Mi2 )
% 0.35/0.60 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 0.35/0.60 = Ma2 ) )
% 0.35/0.60 & ( ( Xa2 != Mi2 )
% 0.35/0.60 => ( Xa2 = Ma2 ) ) )
% 0.35/0.60 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 0.35/0.60 @ Ma2 ) ) )
% 0.35/0.60 @ ( suc @ ( suc @ Va ) )
% 0.35/0.60 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.60 @ Summary2 ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_delete.pelims
% 0.35/0.60 thf(fact_4728_vebt__insert_Opelims,axiom,
% 0.35/0.60 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.35/0.60 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 0.35/0.60 = Y )
% 0.35/0.60 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.60 => ( ! [A3: $o,B3: $o] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.60 => ( ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 0.35/0.60 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.60 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 0.35/0.60 & ( ( Xa2 != one_one_nat )
% 0.35/0.60 => ( Y
% 0.35/0.60 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ Xa2 ) ) ) )
% 0.35/0.60 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.60 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.60 ( ( X
% 0.35/0.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.60 => ( ( Y
% 0.35/0.60 = ( if_VEBT_VEBT
% 0.35/0.60 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.60 & ~ ( ( Xa2 = Mi2 )
% 0.35/0.60 | ( Xa2 = Ma2 ) ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 0.35/0.60 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 0.35/0.60 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % vebt_insert.pelims
% 0.35/0.60 thf(fact_4729_low__def,axiom,
% 0.35/0.60 ( vEBT_VEBT_low
% 0.35/0.60 = ( ^ [X4: nat,N4: nat] : ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % low_def
% 0.35/0.60 thf(fact_4730_mod__0,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % mod_0
% 0.35/0.60 thf(fact_4731_mod__0,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % mod_0
% 0.35/0.60 thf(fact_4732_mod__0,axiom,
% 0.35/0.60 ! [A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % mod_0
% 0.35/0.60 thf(fact_4733_mod__by__0,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 0.35/0.60 = A ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_0
% 0.35/0.60 thf(fact_4734_mod__by__0,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 0.35/0.60 = A ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_0
% 0.35/0.60 thf(fact_4735_mod__by__0,axiom,
% 0.35/0.60 ! [A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ A @ zero_z2226904508553997617atural )
% 0.35/0.60 = A ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_0
% 0.35/0.60 thf(fact_4736_mod__self,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ A @ A )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % mod_self
% 0.35/0.60 thf(fact_4737_mod__self,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ A @ A )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % mod_self
% 0.35/0.60 thf(fact_4738_mod__self,axiom,
% 0.35/0.60 ! [A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ A @ A )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % mod_self
% 0.35/0.60 thf(fact_4739_bits__mod__0,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_0
% 0.35/0.60 thf(fact_4740_bits__mod__0,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_0
% 0.35/0.60 thf(fact_4741_bits__mod__0,axiom,
% 0.35/0.60 ! [A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_0
% 0.35/0.60 thf(fact_4742_mod__mult__self2__is__0,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self2_is_0
% 0.35/0.60 thf(fact_4743_mod__mult__self2__is__0,axiom,
% 0.35/0.60 ! [A: int,B: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self2_is_0
% 0.35/0.60 thf(fact_4744_mod__mult__self2__is__0,axiom,
% 0.35/0.60 ! [A: code_natural,B: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self2_is_0
% 0.35/0.60 thf(fact_4745_mod__mult__self1__is__0,axiom,
% 0.35/0.60 ! [B: nat,A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self1_is_0
% 0.35/0.60 thf(fact_4746_mod__mult__self1__is__0,axiom,
% 0.35/0.60 ! [B: int,A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self1_is_0
% 0.35/0.60 thf(fact_4747_mod__mult__self1__is__0,axiom,
% 0.35/0.60 ! [B: code_natural,A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self1_is_0
% 0.35/0.60 thf(fact_4748_mod__by__1,axiom,
% 0.35/0.60 ! [A: code_integer] :
% 0.35/0.60 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.35/0.60 = zero_z3403309356797280102nteger ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_1
% 0.35/0.60 thf(fact_4749_mod__by__1,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_1
% 0.35/0.60 thf(fact_4750_mod__by__1,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ A @ one_one_int )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_1
% 0.35/0.60 thf(fact_4751_mod__by__1,axiom,
% 0.35/0.60 ! [A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_1
% 0.35/0.60 thf(fact_4752_bits__mod__by__1,axiom,
% 0.35/0.60 ! [A: code_integer] :
% 0.35/0.60 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 0.35/0.60 = zero_z3403309356797280102nteger ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_by_1
% 0.35/0.60 thf(fact_4753_bits__mod__by__1,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_by_1
% 0.35/0.60 thf(fact_4754_bits__mod__by__1,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ A @ one_one_int )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_by_1
% 0.35/0.60 thf(fact_4755_bits__mod__by__1,axiom,
% 0.35/0.60 ! [A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_by_1
% 0.35/0.60 thf(fact_4756_mod__div__trivial,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % mod_div_trivial
% 0.35/0.60 thf(fact_4757_mod__div__trivial,axiom,
% 0.35/0.60 ! [A: int,B: int] :
% 0.35/0.60 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % mod_div_trivial
% 0.35/0.60 thf(fact_4758_mod__div__trivial,axiom,
% 0.35/0.60 ! [A: code_natural,B: code_natural] :
% 0.35/0.60 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % mod_div_trivial
% 0.35/0.60 thf(fact_4759_bits__mod__div__trivial,axiom,
% 0.35/0.60 ! [A: nat,B: nat] :
% 0.35/0.60 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_div_trivial
% 0.35/0.60 thf(fact_4760_bits__mod__div__trivial,axiom,
% 0.35/0.60 ! [A: int,B: int] :
% 0.35/0.60 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 0.35/0.60 = zero_zero_int ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_div_trivial
% 0.35/0.60 thf(fact_4761_bits__mod__div__trivial,axiom,
% 0.35/0.60 ! [A: code_natural,B: code_natural] :
% 0.35/0.60 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 0.35/0.60 = zero_z2226904508553997617atural ) ).
% 0.35/0.60
% 0.35/0.60 % bits_mod_div_trivial
% 0.35/0.60 thf(fact_4762_mod__mult__self1,axiom,
% 0.35/0.60 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 0.35/0.60 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self1
% 0.35/0.60 thf(fact_4763_mod__mult__self1,axiom,
% 0.35/0.60 ! [A: int,C2: int,B: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 0.35/0.60 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self1
% 0.35/0.60 thf(fact_4764_mod__mult__self1,axiom,
% 0.35/0.60 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C2 @ B ) ) @ B )
% 0.35/0.60 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self1
% 0.35/0.60 thf(fact_4765_mod__mult__self2,axiom,
% 0.35/0.60 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 0.35/0.60 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self2
% 0.35/0.60 thf(fact_4766_mod__mult__self2,axiom,
% 0.35/0.60 ! [A: int,B: int,C2: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 0.35/0.60 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self2
% 0.35/0.60 thf(fact_4767_mod__mult__self2,axiom,
% 0.35/0.60 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C2 ) ) @ B )
% 0.35/0.60 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self2
% 0.35/0.60 thf(fact_4768_mod__mult__self3,axiom,
% 0.35/0.60 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 0.35/0.60 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self3
% 0.35/0.60 thf(fact_4769_mod__mult__self3,axiom,
% 0.35/0.60 ! [C2: int,B: int,A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 0.35/0.60 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self3
% 0.35/0.60 thf(fact_4770_mod__mult__self3,axiom,
% 0.35/0.60 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C2 @ B ) @ A ) @ B )
% 0.35/0.60 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self3
% 0.35/0.60 thf(fact_4771_mod__mult__self4,axiom,
% 0.35/0.60 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 0.35/0.60 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self4
% 0.35/0.60 thf(fact_4772_mod__mult__self4,axiom,
% 0.35/0.60 ! [B: int,C2: int,A: int] :
% 0.35/0.60 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 0.35/0.60 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self4
% 0.35/0.60 thf(fact_4773_mod__mult__self4,axiom,
% 0.35/0.60 ! [B: code_natural,C2: code_natural,A: code_natural] :
% 0.35/0.60 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C2 ) @ A ) @ B )
% 0.35/0.60 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod_mult_self4
% 0.35/0.60 thf(fact_4774_mod__by__Suc__0,axiom,
% 0.35/0.60 ! [M2: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 0.35/0.60 = zero_zero_nat ) ).
% 0.35/0.60
% 0.35/0.60 % mod_by_Suc_0
% 0.35/0.60 thf(fact_4775_Suc__mod__mult__self4,axiom,
% 0.35/0.60 ! [N: nat,K2: nat,M2: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K2 ) @ M2 ) ) @ N )
% 0.35/0.60 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.35/0.60
% 0.35/0.60 % Suc_mod_mult_self4
% 0.35/0.60 thf(fact_4776_Suc__mod__mult__self3,axiom,
% 0.35/0.60 ! [K2: nat,N: nat,M2: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K2 @ N ) @ M2 ) ) @ N )
% 0.35/0.60 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.35/0.60
% 0.35/0.60 % Suc_mod_mult_self3
% 0.35/0.60 thf(fact_4777_Suc__mod__mult__self2,axiom,
% 0.35/0.60 ! [M2: nat,N: nat,K2: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ N @ K2 ) ) ) @ N )
% 0.35/0.60 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.35/0.60
% 0.35/0.60 % Suc_mod_mult_self2
% 0.35/0.60 thf(fact_4778_Suc__mod__mult__self1,axiom,
% 0.35/0.60 ! [M2: nat,K2: nat,N: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ K2 @ N ) ) ) @ N )
% 0.35/0.60 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.35/0.60
% 0.35/0.60 % Suc_mod_mult_self1
% 0.35/0.60 thf(fact_4779_mod2__Suc__Suc,axiom,
% 0.35/0.60 ! [M2: nat] :
% 0.35/0.60 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60 = ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.60
% 0.35/0.60 % mod2_Suc_Suc
% 0.35/0.60 thf(fact_4780_Suc__times__numeral__mod__eq,axiom,
% 0.35/0.60 ! [K2: num,N: nat] :
% 0.35/0.60 ( ( ( numeral_numeral_nat @ K2 )
% 0.35/0.60 != one_one_nat )
% 0.35/0.60 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K2 ) @ N ) ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.60 = one_one_nat ) ) ).
% 0.35/0.60
% 0.35/0.60 % Suc_times_numeral_mod_eq
% 0.35/0.60 thf(fact_4781_not__mod__2__eq__0__eq__1,axiom,
% 0.35/0.60 ! [A: code_integer] :
% 0.35/0.60 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.60 != zero_z3403309356797280102nteger )
% 0.35/0.60 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.60 = one_one_Code_integer ) ) ).
% 0.35/0.60
% 0.35/0.60 % not_mod_2_eq_0_eq_1
% 0.35/0.60 thf(fact_4782_not__mod__2__eq__0__eq__1,axiom,
% 0.35/0.60 ! [A: nat] :
% 0.35/0.60 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60 != zero_zero_nat )
% 0.35/0.60 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.60 = one_one_nat ) ) ).
% 0.35/0.60
% 0.35/0.60 % not_mod_2_eq_0_eq_1
% 0.35/0.60 thf(fact_4783_not__mod__2__eq__0__eq__1,axiom,
% 0.35/0.60 ! [A: int] :
% 0.35/0.60 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.60 != zero_zero_int )
% 0.35/0.60 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.60 = one_one_int ) ) ).
% 0.35/0.60
% 0.35/0.60 % not_mod_2_eq_0_eq_1
% 0.35/0.60 thf(fact_4784_not__mod__2__eq__0__eq__1,axiom,
% 0.35/0.60 ! [A: code_natural] :
% 0.35/0.60 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.60 != zero_z2226904508553997617atural )
% 0.35/0.60 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.60 = one_one_Code_natural ) ) ).
% 0.35/0.60
% 0.35/0.60 % not_mod_2_eq_0_eq_1
% 0.35/0.60 thf(fact_4785_not__mod__2__eq__1__eq__0,axiom,
% 0.35/0.60 ! [A: code_integer] :
% 0.35/0.60 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.60 != one_one_Code_integer )
% 0.35/0.60 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.61 = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.61
% 0.35/0.61 % not_mod_2_eq_1_eq_0
% 0.35/0.61 thf(fact_4786_not__mod__2__eq__1__eq__0,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 != one_one_nat )
% 0.35/0.61 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % not_mod_2_eq_1_eq_0
% 0.35/0.61 thf(fact_4787_not__mod__2__eq__1__eq__0,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61 != one_one_int )
% 0.35/0.61 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61 = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % not_mod_2_eq_1_eq_0
% 0.35/0.61 thf(fact_4788_not__mod__2__eq__1__eq__0,axiom,
% 0.35/0.61 ! [A: code_natural] :
% 0.35/0.61 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.61 != one_one_Code_natural )
% 0.35/0.61 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.61 = zero_z2226904508553997617atural ) ) ).
% 0.35/0.61
% 0.35/0.61 % not_mod_2_eq_1_eq_0
% 0.35/0.61 thf(fact_4789_not__mod2__eq__Suc__0__eq__0,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 != ( suc @ zero_zero_nat ) )
% 0.35/0.61 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % not_mod2_eq_Suc_0_eq_0
% 0.35/0.61 thf(fact_4790_add__self__mod__2,axiom,
% 0.35/0.61 ! [M2: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 = zero_zero_nat ) ).
% 0.35/0.61
% 0.35/0.61 % add_self_mod_2
% 0.35/0.61 thf(fact_4791_mod2__gr__0,axiom,
% 0.35/0.61 ! [M2: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.61 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 = one_one_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod2_gr_0
% 0.35/0.61 thf(fact_4792_mod__mult__eq,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C2 ) @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_eq
% 0.35/0.61 thf(fact_4793_mod__mult__eq,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C2 ) @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_eq
% 0.35/0.61 thf(fact_4794_mod__mult__eq,axiom,
% 0.35/0.61 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 0.35/0.61 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 0.35/0.61 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_eq
% 0.35/0.61 thf(fact_4795_mod__mult__cong,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,A2: nat,B: nat,B2: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ A @ C2 )
% 0.35/0.61 = ( modulo_modulo_nat @ A2 @ C2 ) )
% 0.35/0.61 => ( ( ( modulo_modulo_nat @ B @ C2 )
% 0.35/0.61 = ( modulo_modulo_nat @ B2 @ C2 ) )
% 0.35/0.61 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_cong
% 0.35/0.61 thf(fact_4796_mod__mult__cong,axiom,
% 0.35/0.61 ! [A: int,C2: int,A2: int,B: int,B2: int] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ A @ C2 )
% 0.35/0.61 = ( modulo_modulo_int @ A2 @ C2 ) )
% 0.35/0.61 => ( ( ( modulo_modulo_int @ B @ C2 )
% 0.35/0.61 = ( modulo_modulo_int @ B2 @ C2 ) )
% 0.35/0.61 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_cong
% 0.35/0.61 thf(fact_4797_mod__mult__cong,axiom,
% 0.35/0.61 ! [A: code_natural,C2: code_natural,A2: code_natural,B: code_natural,B2: code_natural] :
% 0.35/0.61 ( ( ( modulo8411746178871703098atural @ A @ C2 )
% 0.35/0.61 = ( modulo8411746178871703098atural @ A2 @ C2 ) )
% 0.35/0.61 => ( ( ( modulo8411746178871703098atural @ B @ C2 )
% 0.35/0.61 = ( modulo8411746178871703098atural @ B2 @ C2 ) )
% 0.35/0.61 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 )
% 0.35/0.61 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_cong
% 0.35/0.61 thf(fact_4798_mod__mult__mult2,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.61 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_mult2
% 0.35/0.61 thf(fact_4799_mod__mult__mult2,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.35/0.61 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_mult2
% 0.35/0.61 thf(fact_4800_mod__mult__mult2,axiom,
% 0.35/0.61 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 0.35/0.61 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ C2 ) @ ( times_2397367101498566445atural @ B @ C2 ) )
% 0.35/0.61 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_mult2
% 0.35/0.61 thf(fact_4801_mult__mod__right,axiom,
% 0.35/0.61 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.61 ( ( times_times_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 = ( modulo_modulo_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_mod_right
% 0.35/0.61 thf(fact_4802_mult__mod__right,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( times_times_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 = ( modulo_modulo_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_mod_right
% 0.35/0.61 thf(fact_4803_mult__mod__right,axiom,
% 0.35/0.61 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( times_2397367101498566445atural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.35/0.61 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ C2 @ A ) @ ( times_2397367101498566445atural @ C2 @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_mod_right
% 0.35/0.61 thf(fact_4804_mod__mult__left__eq,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C2 ) @ B ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_left_eq
% 0.35/0.61 thf(fact_4805_mod__mult__left__eq,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C2 ) @ B ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_left_eq
% 0.35/0.61 thf(fact_4806_mod__mult__left__eq,axiom,
% 0.35/0.61 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 0.35/0.61 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ B ) @ C2 )
% 0.35/0.61 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_left_eq
% 0.35/0.61 thf(fact_4807_mod__mult__right__eq,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_right_eq
% 0.35/0.61 thf(fact_4808_mod__mult__right__eq,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 0.35/0.61 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_right_eq
% 0.35/0.61 thf(fact_4809_mod__mult__right__eq,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 0.35/0.61 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 0.35/0.61 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_right_eq
% 0.35/0.61 thf(fact_4810_mod__Suc__Suc__eq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) @ N )
% 0.35/0.61 = ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ N ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_Suc_Suc_eq
% 0.35/0.61 thf(fact_4811_mod__Suc__eq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) @ N )
% 0.35/0.61 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_Suc_eq
% 0.35/0.61 thf(fact_4812_mod__less__eq__dividend,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ M2 ) ).
% 0.35/0.61
% 0.35/0.61 % mod_less_eq_dividend
% 0.35/0.61 thf(fact_4813_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.61 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.35/0.61 thf(fact_4814_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.61 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 0.35/0.61 thf(fact_4815_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.35/0.61 ! [B: nat,A: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.61 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.35/0.61 thf(fact_4816_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.61 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 0.35/0.61 thf(fact_4817_mod__eq__self__iff__div__eq__0,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.61 = A )
% 0.35/0.61 = ( ( divide_divide_nat @ A @ B )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_eq_self_iff_div_eq_0
% 0.35/0.61 thf(fact_4818_mod__eq__self__iff__div__eq__0,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.61 = A )
% 0.35/0.61 = ( ( divide_divide_int @ A @ B )
% 0.35/0.61 = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_eq_self_iff_div_eq_0
% 0.35/0.61 thf(fact_4819_mod__eq__self__iff__div__eq__0,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( ( modulo8411746178871703098atural @ A @ B )
% 0.35/0.61 = A )
% 0.35/0.61 = ( ( divide5121882707175180666atural @ A @ B )
% 0.35/0.61 = zero_z2226904508553997617atural ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_eq_self_iff_div_eq_0
% 0.35/0.61 thf(fact_4820_cong__exp__iff__simps_I9_J,axiom,
% 0.35/0.61 ! [M2: num,Q2: num,N: num] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.61 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.61 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(9)
% 0.35/0.61 thf(fact_4821_cong__exp__iff__simps_I9_J,axiom,
% 0.35/0.61 ! [M2: num,Q2: num,N: num] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.61 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.61 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(9)
% 0.35/0.61 thf(fact_4822_cong__exp__iff__simps_I4_J,axiom,
% 0.35/0.61 ! [M2: num,N: num] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ one ) )
% 0.35/0.61 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(4)
% 0.35/0.61 thf(fact_4823_cong__exp__iff__simps_I4_J,axiom,
% 0.35/0.61 ! [M2: num,N: num] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ one ) )
% 0.35/0.61 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(4)
% 0.35/0.61 thf(fact_4824_mod__eqE,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ A @ C2 )
% 0.35/0.61 = ( modulo_modulo_int @ B @ C2 ) )
% 0.35/0.61 => ~ ! [D5: int] :
% 0.35/0.61 ( B
% 0.35/0.61 != ( plus_plus_int @ A @ ( times_times_int @ C2 @ D5 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_eqE
% 0.35/0.61 thf(fact_4825_mod__Suc,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] :
% 0.35/0.61 ( ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 0.35/0.61 = N )
% 0.35/0.61 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 0.35/0.61 = zero_zero_nat ) )
% 0.35/0.61 & ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 0.35/0.61 != N )
% 0.35/0.61 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 0.35/0.61 = ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_Suc
% 0.35/0.61 thf(fact_4826_mod__induct,axiom,
% 0.35/0.61 ! [P2: nat > $o,N: nat,P: nat,M2: nat] :
% 0.35/0.61 ( ( P2 @ N )
% 0.35/0.61 => ( ( ord_less_nat @ N @ P )
% 0.35/0.61 => ( ( ord_less_nat @ M2 @ P )
% 0.35/0.61 => ( ! [N3: nat] :
% 0.35/0.61 ( ( ord_less_nat @ N3 @ P )
% 0.35/0.61 => ( ( P2 @ N3 )
% 0.35/0.61 => ( P2 @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P ) ) ) )
% 0.35/0.61 => ( P2 @ M2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_induct
% 0.35/0.61 thf(fact_4827_mod__less__divisor,axiom,
% 0.35/0.61 ! [N: nat,M2: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ord_less_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_less_divisor
% 0.35/0.61 thf(fact_4828_gcd__nat__induct,axiom,
% 0.35/0.61 ! [P2: nat > nat > $o,M2: nat,N: nat] :
% 0.35/0.61 ( ! [M: nat] : ( P2 @ M @ zero_zero_nat )
% 0.35/0.61 => ( ! [M: nat,N3: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.61 => ( ( P2 @ N3 @ ( modulo_modulo_nat @ M @ N3 ) )
% 0.35/0.61 => ( P2 @ M @ N3 ) ) )
% 0.35/0.61 => ( P2 @ M2 @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % gcd_nat_induct
% 0.35/0.61 thf(fact_4829_mod__Suc__le__divisor,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ ( suc @ N ) ) @ N ) ).
% 0.35/0.61
% 0.35/0.61 % mod_Suc_le_divisor
% 0.35/0.61 thf(fact_4830_mod__eq__0D,axiom,
% 0.35/0.61 ! [M2: nat,D: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ M2 @ D )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 => ? [Q3: nat] :
% 0.35/0.61 ( M2
% 0.35/0.61 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_eq_0D
% 0.35/0.61 thf(fact_4831_mod__geq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] :
% 0.35/0.61 ( ~ ( ord_less_nat @ M2 @ N )
% 0.35/0.61 => ( ( modulo_modulo_nat @ M2 @ N )
% 0.35/0.61 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_geq
% 0.35/0.61 thf(fact_4832_le__mod__geq,axiom,
% 0.35/0.61 ! [N: nat,M2: nat] :
% 0.35/0.61 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.61 => ( ( modulo_modulo_nat @ M2 @ N )
% 0.35/0.61 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % le_mod_geq
% 0.35/0.61 thf(fact_4833_nat__mod__eq__iff,axiom,
% 0.35/0.61 ! [X: nat,N: nat,Y: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ X @ N )
% 0.35/0.61 = ( modulo_modulo_nat @ Y @ N ) )
% 0.35/0.61 = ( ? [Q1: nat,Q22: nat] :
% 0.35/0.61 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 0.35/0.61 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nat_mod_eq_iff
% 0.35/0.61 thf(fact_4834_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.61 => ( ( ord_less_nat @ A @ B )
% 0.35/0.61 => ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.61 = A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.mod_less
% 0.35/0.61 thf(fact_4835_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.61 => ( ( ord_less_int @ A @ B )
% 0.35/0.61 => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.61 = A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.mod_less
% 0.35/0.61 thf(fact_4836_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.35/0.61 ! [B: nat,A: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.35/0.61 thf(fact_4837_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.61 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 0.35/0.61 thf(fact_4838_cong__exp__iff__simps_I2_J,axiom,
% 0.35/0.61 ! [N: num,Q2: num] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(2)
% 0.35/0.61 thf(fact_4839_cong__exp__iff__simps_I2_J,axiom,
% 0.35/0.61 ! [N: num,Q2: num] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 = zero_zero_int )
% 0.35/0.61 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.61 = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(2)
% 0.35/0.61 thf(fact_4840_cong__exp__iff__simps_I1_J,axiom,
% 0.35/0.61 ! [N: num] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 0.35/0.61 = zero_zero_nat ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(1)
% 0.35/0.61 thf(fact_4841_cong__exp__iff__simps_I1_J,axiom,
% 0.35/0.61 ! [N: num] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 0.35/0.61 = zero_zero_int ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(1)
% 0.35/0.61 thf(fact_4842_cong__exp__iff__simps_I6_J,axiom,
% 0.35/0.61 ! [Q2: num,N: num] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(6)
% 0.35/0.61 thf(fact_4843_cong__exp__iff__simps_I6_J,axiom,
% 0.35/0.61 ! [Q2: num,N: num] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(6)
% 0.35/0.61 thf(fact_4844_cong__exp__iff__simps_I8_J,axiom,
% 0.35/0.61 ! [M2: num,Q2: num] :
% 0.35/0.61 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(8)
% 0.35/0.61 thf(fact_4845_cong__exp__iff__simps_I8_J,axiom,
% 0.35/0.61 ! [M2: num,Q2: num] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.61 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % cong_exp_iff_simps(8)
% 0.35/0.61 thf(fact_4846_div__mult1__eq,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.35/0.61 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_mult1_eq
% 0.35/0.61 thf(fact_4847_div__mult1__eq,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_mult1_eq
% 0.35/0.61 thf(fact_4848_div__mult1__eq,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 0.35/0.61 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C2 ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_mult1_eq
% 0.35/0.61 thf(fact_4849_cancel__div__mod__rules_I2_J,axiom,
% 0.35/0.61 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.61 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 0.35/0.61 = ( plus_plus_nat @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % cancel_div_mod_rules(2)
% 0.35/0.61 thf(fact_4850_cancel__div__mod__rules_I2_J,axiom,
% 0.35/0.61 ! [B: int,A: int,C2: int] :
% 0.35/0.61 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 0.35/0.61 = ( plus_plus_int @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % cancel_div_mod_rules(2)
% 0.35/0.61 thf(fact_4851_cancel__div__mod__rules_I2_J,axiom,
% 0.35/0.61 ! [B: code_natural,A: code_natural,C2: code_natural] :
% 0.35/0.61 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % cancel_div_mod_rules(2)
% 0.35/0.61 thf(fact_4852_cancel__div__mod__rules_I1_J,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 0.35/0.61 = ( plus_plus_nat @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % cancel_div_mod_rules(1)
% 0.35/0.61 thf(fact_4853_cancel__div__mod__rules_I1_J,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 0.35/0.61 = ( plus_plus_int @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % cancel_div_mod_rules(1)
% 0.35/0.61 thf(fact_4854_cancel__div__mod__rules_I1_J,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 0.35/0.61 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % cancel_div_mod_rules(1)
% 0.35/0.61 thf(fact_4855_mod__div__decomp,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( A
% 0.35/0.61 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_div_decomp
% 0.35/0.61 thf(fact_4856_mod__div__decomp,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( A
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_div_decomp
% 0.35/0.61 thf(fact_4857_mod__div__decomp,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( A
% 0.35/0.61 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_div_decomp
% 0.35/0.61 thf(fact_4858_div__mult__mod__eq,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % div_mult_mod_eq
% 0.35/0.61 thf(fact_4859_div__mult__mod__eq,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % div_mult_mod_eq
% 0.35/0.61 thf(fact_4860_div__mult__mod__eq,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % div_mult_mod_eq
% 0.35/0.61 thf(fact_4861_mod__div__mult__eq,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mod_div_mult_eq
% 0.35/0.61 thf(fact_4862_mod__div__mult__eq,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mod_div_mult_eq
% 0.35/0.61 thf(fact_4863_mod__div__mult__eq,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mod_div_mult_eq
% 0.35/0.61 thf(fact_4864_mod__mult__div__eq,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_div_eq
% 0.35/0.61 thf(fact_4865_mod__mult__div__eq,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_div_eq
% 0.35/0.61 thf(fact_4866_mod__mult__div__eq,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult_div_eq
% 0.35/0.61 thf(fact_4867_mult__div__mod__eq,axiom,
% 0.35/0.61 ! [B: nat,A: nat] :
% 0.35/0.61 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mult_div_mod_eq
% 0.35/0.61 thf(fact_4868_mult__div__mod__eq,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mult_div_mod_eq
% 0.35/0.61 thf(fact_4869_mult__div__mod__eq,axiom,
% 0.35/0.61 ! [B: code_natural,A: code_natural] :
% 0.35/0.61 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.35/0.61 = A ) ).
% 0.35/0.61
% 0.35/0.61 % mult_div_mod_eq
% 0.35/0.61 thf(fact_4870_minus__div__mult__eq__mod,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 0.35/0.61 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_div_mult_eq_mod
% 0.35/0.61 thf(fact_4871_minus__div__mult__eq__mod,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 0.35/0.61 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_div_mult_eq_mod
% 0.35/0.61 thf(fact_4872_minus__div__mult__eq__mod,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 0.35/0.61 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_div_mult_eq_mod
% 0.35/0.61 thf(fact_4873_minus__mod__eq__div__mult,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mod_eq_div_mult
% 0.35/0.61 thf(fact_4874_minus__mod__eq__div__mult,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mod_eq_div_mult
% 0.35/0.61 thf(fact_4875_minus__mod__eq__div__mult,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.35/0.61 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mod_eq_div_mult
% 0.35/0.61 thf(fact_4876_minus__mod__eq__mult__div,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mod_eq_mult_div
% 0.35/0.61 thf(fact_4877_minus__mod__eq__mult__div,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mod_eq_mult_div
% 0.35/0.61 thf(fact_4878_minus__mod__eq__mult__div,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.35/0.61 = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mod_eq_mult_div
% 0.35/0.61 thf(fact_4879_minus__mult__div__eq__mod,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 0.35/0.61 = ( modulo_modulo_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mult_div_eq_mod
% 0.35/0.61 thf(fact_4880_minus__mult__div__eq__mod,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 0.35/0.61 = ( modulo_modulo_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mult_div_eq_mod
% 0.35/0.61 thf(fact_4881_minus__mult__div__eq__mod,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 0.35/0.61 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % minus_mult_div_eq_mod
% 0.35/0.61 thf(fact_4882_mod__le__divisor,axiom,
% 0.35/0.61 ! [N: nat,M2: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_le_divisor
% 0.35/0.61 thf(fact_4883_div__less__mono,axiom,
% 0.35/0.61 ! [A4: nat,B5: nat,N: nat] :
% 0.35/0.61 ( ( ord_less_nat @ A4 @ B5 )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( ( modulo_modulo_nat @ A4 @ N )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 => ( ( ( modulo_modulo_nat @ B5 @ N )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B5 @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_less_mono
% 0.35/0.61 thf(fact_4884_nat__mod__eq__lemma,axiom,
% 0.35/0.61 ! [X: nat,N: nat,Y: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ X @ N )
% 0.35/0.61 = ( modulo_modulo_nat @ Y @ N ) )
% 0.35/0.61 => ( ( ord_less_eq_nat @ Y @ X )
% 0.35/0.61 => ? [Q3: nat] :
% 0.35/0.61 ( X
% 0.35/0.61 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nat_mod_eq_lemma
% 0.35/0.61 thf(fact_4885_mod__eq__nat2E,axiom,
% 0.35/0.61 ! [M2: nat,Q2: nat,N: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 0.35/0.61 = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.35/0.61 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.61 => ~ ! [S: nat] :
% 0.35/0.61 ( N
% 0.35/0.61 != ( plus_plus_nat @ M2 @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_eq_nat2E
% 0.35/0.61 thf(fact_4886_mod__eq__nat1E,axiom,
% 0.35/0.61 ! [M2: nat,Q2: nat,N: nat] :
% 0.35/0.61 ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 0.35/0.61 = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.35/0.61 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.61 => ~ ! [S: nat] :
% 0.35/0.61 ( M2
% 0.35/0.61 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_eq_nat1E
% 0.35/0.61 thf(fact_4887_mod__mult2__eq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ M2 @ ( times_times_nat @ N @ Q2 ) )
% 0.35/0.61 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M2 @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M2 @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult2_eq
% 0.35/0.61 thf(fact_4888_div__mod__decomp,axiom,
% 0.35/0.61 ! [A4: nat,N: nat] :
% 0.35/0.61 ( A4
% 0.35/0.61 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A4 @ N ) @ N ) @ ( modulo_modulo_nat @ A4 @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_mod_decomp
% 0.35/0.61 thf(fact_4889_modulo__nat__def,axiom,
% 0.35/0.61 ( modulo_modulo_nat
% 0.35/0.61 = ( ^ [M6: nat,N4: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N4 ) @ N4 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % modulo_nat_def
% 0.35/0.61 thf(fact_4890_mod__mult2__eq_H,axiom,
% 0.35/0.61 ! [A: code_natural,M2: nat,N: nat] :
% 0.35/0.61 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N ) ) )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult2_eq'
% 0.35/0.61 thf(fact_4891_mod__mult2__eq_H,axiom,
% 0.35/0.61 ! [A: int,M2: nat,N: nat] :
% 0.35/0.61 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult2_eq'
% 0.35/0.61 thf(fact_4892_mod__mult2__eq_H,axiom,
% 0.35/0.61 ! [A: nat,M2: nat,N: nat] :
% 0.35/0.61 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 0.35/0.61 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_mult2_eq'
% 0.35/0.61 thf(fact_4893_split__mod,axiom,
% 0.35/0.61 ! [P2: nat > $o,M2: nat,N: nat] :
% 0.35/0.61 ( ( P2 @ ( modulo_modulo_nat @ M2 @ N ) )
% 0.35/0.61 = ( ( ( N = zero_zero_nat )
% 0.35/0.61 => ( P2 @ M2 ) )
% 0.35/0.61 & ( ( N != zero_zero_nat )
% 0.35/0.61 => ! [I: nat,J: nat] :
% 0.35/0.61 ( ( ord_less_nat @ J @ N )
% 0.35/0.61 => ( ( M2
% 0.35/0.61 = ( plus_plus_nat @ ( times_times_nat @ N @ I ) @ J ) )
% 0.35/0.61 => ( P2 @ J ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % split_mod
% 0.35/0.61 thf(fact_4894_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.35/0.61 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 0.35/0.61 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.61 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.35/0.61 thf(fact_4895_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.35/0.61 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 0.35/0.61 thf(fact_4896_Suc__times__mod__eq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] :
% 0.35/0.61 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 0.35/0.61 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N ) ) @ M2 )
% 0.35/0.61 = one_one_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % Suc_times_mod_eq
% 0.35/0.61 thf(fact_4897_nth__rotate1,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.61 => ( ( nth_VEBT_VEBT @ ( rotate1_VEBT_VEBT @ Xs2 ) @ N )
% 0.35/0.61 = ( nth_VEBT_VEBT @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nth_rotate1
% 0.35/0.61 thf(fact_4898_nth__rotate1,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_o] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.61 => ( ( nth_o @ ( rotate1_o @ Xs2 ) @ N )
% 0.35/0.61 = ( nth_o @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nth_rotate1
% 0.35/0.61 thf(fact_4899_nth__rotate1,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_nat] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.61 => ( ( nth_nat @ ( rotate1_nat @ Xs2 ) @ N )
% 0.35/0.61 = ( nth_nat @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nth_rotate1
% 0.35/0.61 thf(fact_4900_nth__rotate1,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_int] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.61 => ( ( nth_int @ ( rotate1_int @ Xs2 ) @ N )
% 0.35/0.61 = ( nth_int @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nth_rotate1
% 0.35/0.61 thf(fact_4901_divmod__digit__0_I2_J,axiom,
% 0.35/0.61 ! [B: nat,A: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.61 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.61 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 0.35/0.61 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_0(2)
% 0.35/0.61 thf(fact_4902_divmod__digit__0_I2_J,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.61 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.61 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 0.35/0.61 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_0(2)
% 0.35/0.61 thf(fact_4903_bits__stable__imp__add__self,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 = A )
% 0.35/0.61 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % bits_stable_imp_add_self
% 0.35/0.61 thf(fact_4904_bits__stable__imp__add__self,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.61 = A )
% 0.35/0.61 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.35/0.61 = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % bits_stable_imp_add_self
% 0.35/0.61 thf(fact_4905_bits__stable__imp__add__self,axiom,
% 0.35/0.61 ! [A: code_natural] :
% 0.35/0.61 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.61 = A )
% 0.35/0.61 => ( ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 0.35/0.61 = zero_z2226904508553997617atural ) ) ).
% 0.35/0.61
% 0.35/0.61 % bits_stable_imp_add_self
% 0.35/0.61 thf(fact_4906_verit__le__mono__div,axiom,
% 0.35/0.61 ! [A4: nat,B5: nat,N: nat] :
% 0.35/0.61 ( ( ord_less_nat @ A4 @ B5 )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ord_less_eq_nat
% 0.35/0.61 @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 0.35/0.61 @ ( if_nat
% 0.35/0.61 @ ( ( modulo_modulo_nat @ B5 @ N )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 @ one_one_nat
% 0.35/0.61 @ zero_zero_nat ) )
% 0.35/0.61 @ ( divide_divide_nat @ B5 @ N ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % verit_le_mono_div
% 0.35/0.61 thf(fact_4907_divmod__digit__0_I1_J,axiom,
% 0.35/0.61 ! [B: nat,A: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.61 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.61 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.61 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_0(1)
% 0.35/0.61 thf(fact_4908_divmod__digit__0_I1_J,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.61 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.61 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.61 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_0(1)
% 0.35/0.61 thf(fact_4909_mult__exp__mod__exp__eq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat,A: nat] :
% 0.35/0.61 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.61 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_exp_mod_exp_eq
% 0.35/0.61 thf(fact_4910_mult__exp__mod__exp__eq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat,A: int] :
% 0.35/0.61 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.61 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_exp_mod_exp_eq
% 0.35/0.61 thf(fact_4911_mult__exp__mod__exp__eq,axiom,
% 0.35/0.61 ! [M2: nat,N: nat,A: code_natural] :
% 0.35/0.61 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.61 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_exp_mod_exp_eq
% 0.35/0.61 thf(fact_4912_mod__double__modulus,axiom,
% 0.35/0.61 ! [M2: nat,X: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.61 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 0.35/0.61 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.61 = ( modulo_modulo_nat @ X @ M2 ) )
% 0.35/0.61 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.61 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_double_modulus
% 0.35/0.61 thf(fact_4913_mod__double__modulus,axiom,
% 0.35/0.61 ! [M2: int,X: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ M2 )
% 0.35/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.61 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.61 = ( modulo_modulo_int @ X @ M2 ) )
% 0.35/0.61 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 0.35/0.61 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_double_modulus
% 0.35/0.61 thf(fact_4914_divmod__digit__1_I2_J,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.61 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.61 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.61 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_1(2)
% 0.35/0.61 thf(fact_4915_divmod__digit__1_I2_J,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.61 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.61 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.61 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 0.35/0.61 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_1(2)
% 0.35/0.61 thf(fact_4916_unset__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: nat] :
% 0.35/0.61 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unset_bit_Suc
% 0.35/0.61 thf(fact_4917_unset__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: code_natural] :
% 0.35/0.61 ( ( bit_se7083795435491715335atural @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unset_bit_Suc
% 0.35/0.61 thf(fact_4918_unset__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: int] :
% 0.35/0.61 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unset_bit_Suc
% 0.35/0.61 thf(fact_4919_set__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: nat] :
% 0.35/0.61 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % set_bit_Suc
% 0.35/0.61 thf(fact_4920_set__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: code_natural] :
% 0.35/0.61 ( ( bit_se1617098188084679374atural @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % set_bit_Suc
% 0.35/0.61 thf(fact_4921_set__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: int] :
% 0.35/0.61 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % set_bit_Suc
% 0.35/0.61 thf(fact_4922_card__roots__unity__eq,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( finite_card_complex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [Z4: complex] :
% 0.35/0.61 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.61 = one_one_complex ) ) )
% 0.35/0.61 = N ) ) ).
% 0.35/0.61
% 0.35/0.61 % card_roots_unity_eq
% 0.35/0.61 thf(fact_4923_card__nth__roots,axiom,
% 0.35/0.61 ! [C2: complex,N: nat] :
% 0.35/0.61 ( ( C2 != zero_zero_complex )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( finite_card_complex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [Z4: complex] :
% 0.35/0.61 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.61 = C2 ) ) )
% 0.35/0.61 = N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % card_nth_roots
% 0.35/0.61 thf(fact_4924_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_s3445333598471063425nteger @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr2304437835452373666nteger @ ( produc8792966785426426881nteger @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) @ ( nth_Code_integer @ Ys @ ( modulo_modulo_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4925_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4926_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4927_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4928_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4929_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4930_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4931_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4932_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_o,Ys: list_int] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4933_product__nth,axiom,
% 0.35/0.61 ! [N: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 0.35/0.61 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 0.35/0.61 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N )
% 0.35/0.61 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % product_nth
% 0.35/0.61 thf(fact_4934_divmod__digit__1_I1_J,axiom,
% 0.35/0.61 ! [A: code_integer,B: code_integer] :
% 0.35/0.61 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.61 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 0.35/0.61 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.61 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 0.35/0.61 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_1(1)
% 0.35/0.61 thf(fact_4935_divmod__digit__1_I1_J,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 0.35/0.61 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.61 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 0.35/0.61 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_1(1)
% 0.35/0.61 thf(fact_4936_divmod__digit__1_I1_J,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.61 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.61 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 0.35/0.61 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 0.35/0.61 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % divmod_digit_1(1)
% 0.35/0.61 thf(fact_4937_VEBT__internal_Oinsert_H_Opelims,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 0.35/0.61 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 0.35/0.61 = Y )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [A3: $o,B3: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.61 => ( ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.35/0.61 => ( Y
% 0.35/0.61 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 0.35/0.61 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 0.35/0.61 => ( Y
% 0.35/0.61 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % VEBT_internal.insert'.pelims
% 0.35/0.61 thf(fact_4938_vebt__member_Opelims_I1_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.61 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.61 = Y )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [A3: $o,B3: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.61 => A3 )
% 0.35/0.61 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.61 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.61 => B3 )
% 0.35/0.61 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.35/0.61 => ( ~ Y
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ Xa2 ) ) ) )
% 0.35/0.61 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.35/0.61 => ( ~ Y
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.61 => ( ~ Y
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( ( Xa2 != Mi2 )
% 0.35/0.61 => ( ( Xa2 != Ma2 )
% 0.35/0.61 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.61 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.61 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.61 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % vebt_member.pelims(1)
% 0.35/0.61 thf(fact_4939_vebt__member_Opelims_I3_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.61 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [A3: $o,B3: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.35/0.61 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.61 => A3 )
% 0.35/0.61 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.61 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.61 => B3 )
% 0.35/0.61 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.61 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ Xa2 ) ) )
% 0.35/0.61 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) )
% 0.35/0.61 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 0.35/0.61 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 0.35/0.61 => ( ( Xa2 != Mi2 )
% 0.35/0.61 => ( ( Xa2 != Ma2 )
% 0.35/0.61 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.61 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.61 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.61 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % vebt_member.pelims(3)
% 0.35/0.61 thf(fact_4940_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.61 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.61 = Y )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [A3: $o,B3: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.61 => A3 )
% 0.35/0.61 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.61 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.61 => B3 )
% 0.35/0.61 & ( Xa2 = one_one_nat ) ) ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 0.35/0.61 => ( ~ Y
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Xa2 ) ) ) )
% 0.35/0.61 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % VEBT_internal.naive_member.pelims(1)
% 0.35/0.61 thf(fact_4941_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.61 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [A3: $o,B3: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.35/0.61 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.61 => A3 )
% 0.35/0.61 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.61 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.61 => B3 )
% 0.35/0.61 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.61 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) )
% 0.35/0.61 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % VEBT_internal.naive_member.pelims(2)
% 0.35/0.61 thf(fact_4942_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.61 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [A3: $o,B3: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.35/0.61 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.61 => A3 )
% 0.35/0.61 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.61 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.61 => B3 )
% 0.35/0.61 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.61 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Xa2 ) ) )
% 0.35/0.61 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) )
% 0.35/0.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % VEBT_internal.naive_member.pelims(3)
% 0.35/0.61 thf(fact_4943_vebt__member_Opelims_I2_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.61 ( ( vEBT_vebt_member @ X @ Xa2 )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [A3: $o,B3: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 0.35/0.61 => ~ ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.61 => A3 )
% 0.35/0.61 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.61 => ( ( ( Xa2 = one_one_nat )
% 0.35/0.61 => B3 )
% 0.35/0.61 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 0.35/0.61 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 0.35/0.61 => ~ ( ( Xa2 != Mi2 )
% 0.35/0.61 => ( ( Xa2 != Ma2 )
% 0.35/0.61 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.61 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 0.35/0.61 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.61 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 0.35/0.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % vebt_member.pelims(2)
% 0.35/0.61 thf(fact_4944_zmod__numeral__Bit0,axiom,
% 0.35/0.61 ! [V2: num,W2: num] :
% 0.35/0.61 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.35/0.61 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zmod_numeral_Bit0
% 0.35/0.61 thf(fact_4945_zmod__le__nonneg__dividend,axiom,
% 0.35/0.61 ! [M2: int,K2: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 0.35/0.61 => ( ord_less_eq_int @ ( modulo_modulo_int @ M2 @ K2 ) @ M2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % zmod_le_nonneg_dividend
% 0.35/0.61 thf(fact_4946_zmod__eq__0__iff,axiom,
% 0.35/0.61 ! [M2: int,D: int] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ M2 @ D )
% 0.35/0.61 = zero_zero_int )
% 0.35/0.61 = ( ? [Q5: int] :
% 0.35/0.61 ( M2
% 0.35/0.61 = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zmod_eq_0_iff
% 0.35/0.61 thf(fact_4947_zmod__eq__0D,axiom,
% 0.35/0.61 ! [M2: int,D: int] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ M2 @ D )
% 0.35/0.61 = zero_zero_int )
% 0.35/0.61 => ? [Q3: int] :
% 0.35/0.61 ( M2
% 0.35/0.61 = ( times_times_int @ D @ Q3 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zmod_eq_0D
% 0.35/0.61 thf(fact_4948_zmod__int,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zmod_int
% 0.35/0.61 thf(fact_4949_mod__int__unique,axiom,
% 0.35/0.61 ! [K2: int,L: int,Q2: int,R3: int] :
% 0.35/0.61 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.61 => ( ( modulo_modulo_int @ K2 @ L )
% 0.35/0.61 = R3 ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_int_unique
% 0.35/0.61 thf(fact_4950_neg__mod__conj,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( ord_less_int @ B @ zero_zero_int )
% 0.35/0.61 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 0.35/0.61 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % neg_mod_conj
% 0.35/0.61 thf(fact_4951_pos__mod__conj,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % pos_mod_conj
% 0.35/0.61 thf(fact_4952_zmod__trivial__iff,axiom,
% 0.35/0.61 ! [I2: int,K2: int] :
% 0.35/0.61 ( ( ( modulo_modulo_int @ I2 @ K2 )
% 0.35/0.61 = I2 )
% 0.35/0.61 = ( ( K2 = zero_zero_int )
% 0.35/0.61 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 0.35/0.61 & ( ord_less_int @ I2 @ K2 ) )
% 0.35/0.61 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 0.35/0.61 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zmod_trivial_iff
% 0.35/0.61 thf(fact_4953_div__mod__decomp__int,axiom,
% 0.35/0.61 ! [A4: int,N: int] :
% 0.35/0.61 ( A4
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A4 @ N ) @ N ) @ ( modulo_modulo_int @ A4 @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_mod_decomp_int
% 0.35/0.61 thf(fact_4954_eucl__rel__int,axiom,
% 0.35/0.61 ! [K2: int,L: int] : ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K2 @ L ) @ ( modulo_modulo_int @ K2 @ L ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % eucl_rel_int
% 0.35/0.61 thf(fact_4955_mod__pos__geq,axiom,
% 0.35/0.61 ! [L: int,K2: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ L )
% 0.35/0.61 => ( ( ord_less_eq_int @ L @ K2 )
% 0.35/0.61 => ( ( modulo_modulo_int @ K2 @ L )
% 0.35/0.61 = ( modulo_modulo_int @ ( minus_minus_int @ K2 @ L ) @ L ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mod_pos_geq
% 0.35/0.61 thf(fact_4956_int__mod__pos__eq,axiom,
% 0.35/0.61 ! [A: int,B: int,Q2: int,R3: int] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 0.35/0.61 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 0.35/0.61 => ( ( ord_less_int @ R3 @ B )
% 0.35/0.61 => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.61 = R3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % int_mod_pos_eq
% 0.35/0.61 thf(fact_4957_int__mod__neg__eq,axiom,
% 0.35/0.61 ! [A: int,B: int,Q2: int,R3: int] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 0.35/0.61 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 0.35/0.61 => ( ( ord_less_int @ B @ R3 )
% 0.35/0.61 => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.61 = R3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % int_mod_neg_eq
% 0.35/0.61 thf(fact_4958_split__zmod,axiom,
% 0.35/0.61 ! [P2: int > $o,N: int,K2: int] :
% 0.35/0.61 ( ( P2 @ ( modulo_modulo_int @ N @ K2 ) )
% 0.35/0.61 = ( ( ( K2 = zero_zero_int )
% 0.35/0.61 => ( P2 @ N ) )
% 0.35/0.61 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.61 => ! [I: int,J: int] :
% 0.35/0.61 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 0.35/0.61 & ( ord_less_int @ J @ K2 )
% 0.35/0.61 & ( N
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 0.35/0.61 => ( P2 @ J ) ) )
% 0.35/0.61 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 0.35/0.61 => ! [I: int,J: int] :
% 0.35/0.61 ( ( ( ord_less_int @ K2 @ J )
% 0.35/0.61 & ( ord_less_eq_int @ J @ zero_zero_int )
% 0.35/0.61 & ( N
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 0.35/0.61 => ( P2 @ J ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % split_zmod
% 0.35/0.61 thf(fact_4959_zmod__zmult2__eq,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 0.35/0.61 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zmod_zmult2_eq
% 0.35/0.61 thf(fact_4960_split__pos__lemma,axiom,
% 0.35/0.61 ! [K2: int,P2: int > int > $o,N: int] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ K2 )
% 0.35/0.61 => ( ( P2 @ ( divide_divide_int @ N @ K2 ) @ ( modulo_modulo_int @ N @ K2 ) )
% 0.35/0.61 = ( ! [I: int,J: int] :
% 0.35/0.61 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 0.35/0.61 & ( ord_less_int @ J @ K2 )
% 0.35/0.61 & ( N
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 0.35/0.61 => ( P2 @ I @ J ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % split_pos_lemma
% 0.35/0.61 thf(fact_4961_split__neg__lemma,axiom,
% 0.35/0.61 ! [K2: int,P2: int > int > $o,N: int] :
% 0.35/0.61 ( ( ord_less_int @ K2 @ zero_zero_int )
% 0.35/0.61 => ( ( P2 @ ( divide_divide_int @ N @ K2 ) @ ( modulo_modulo_int @ N @ K2 ) )
% 0.35/0.61 = ( ! [I: int,J: int] :
% 0.35/0.61 ( ( ( ord_less_int @ K2 @ J )
% 0.35/0.61 & ( ord_less_eq_int @ J @ zero_zero_int )
% 0.35/0.61 & ( N
% 0.35/0.61 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 0.35/0.61 => ( P2 @ I @ J ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % split_neg_lemma
% 0.35/0.61 thf(fact_4962_pos__zmod__mult__2,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.61 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % pos_zmod_mult_2
% 0.35/0.61 thf(fact_4963_neg__zmod__mult__2,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.61 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 0.35/0.61 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % neg_zmod_mult_2
% 0.35/0.61 thf(fact_4964_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.61 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.61 = Y )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.61 => ( ~ Y
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.35/0.61 => ( ~ Y
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) ) )
% 0.35/0.61 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( ( Xa2 = Mi2 )
% 0.35/0.61 | ( Xa2 = Ma2 ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( ( Xa2 = Mi2 )
% 0.35/0.61 | ( Xa2 = Ma2 )
% 0.35/0.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) ) ) )
% 0.35/0.61 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 0.35/0.61 => ( ( Y
% 0.35/0.61 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % VEBT_internal.membermima.pelims(1)
% 0.35/0.61 thf(fact_4965_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.61 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 0.35/0.61 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 0.35/0.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) )
% 0.35/0.61 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 0.35/0.61 => ( ( Xa2 = Mi2 )
% 0.35/0.61 | ( Xa2 = Ma2 ) ) ) )
% 0.35/0.61 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 0.35/0.61 => ( ( Xa2 = Mi2 )
% 0.35/0.61 | ( Xa2 = Ma2 )
% 0.35/0.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 0.35/0.61 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) )
% 0.35/0.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % VEBT_internal.membermima.pelims(3)
% 0.35/0.61 thf(fact_4966_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 0.35/0.61 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.61 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.61 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 0.35/0.61 => ~ ( ( Xa2 = Mi2 )
% 0.35/0.61 | ( Xa2 = Ma2 ) ) ) )
% 0.35/0.61 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 0.35/0.61 => ~ ( ( Xa2 = Mi2 )
% 0.35/0.61 | ( Xa2 = Ma2 )
% 0.35/0.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 0.35/0.61 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 0.35/0.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) )
% 0.35/0.61 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 0.35/0.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % VEBT_internal.membermima.pelims(2)
% 0.35/0.61 thf(fact_4967_arcosh__1,axiom,
% 0.35/0.61 ( ( arcosh_real @ one_one_real )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % arcosh_1
% 0.35/0.61 thf(fact_4968_lemma__termdiff3,axiom,
% 0.35/0.61 ! [H: real,Z3: real,K5: real,N: nat] :
% 0.35/0.61 ( ( H != zero_zero_real )
% 0.35/0.61 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z3 ) @ K5 )
% 0.35/0.61 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z3 @ H ) ) @ K5 )
% 0.35/0.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ N ) @ ( power_power_real @ Z3 @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % lemma_termdiff3
% 0.35/0.61 thf(fact_4969_lemma__termdiff3,axiom,
% 0.35/0.61 ! [H: complex,Z3: complex,K5: real,N: nat] :
% 0.35/0.61 ( ( H != zero_zero_complex )
% 0.35/0.61 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z3 ) @ K5 )
% 0.35/0.61 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z3 @ H ) ) @ K5 )
% 0.35/0.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ N ) @ ( power_power_complex @ Z3 @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % lemma_termdiff3
% 0.35/0.61 thf(fact_4970_flip__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: nat] :
% 0.35/0.61 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % flip_bit_Suc
% 0.35/0.61 thf(fact_4971_flip__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: int] :
% 0.35/0.61 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % flip_bit_Suc
% 0.35/0.61 thf(fact_4972_flip__bit__Suc,axiom,
% 0.35/0.61 ! [N: nat,A: code_natural] :
% 0.35/0.61 ( ( bit_se168947363167071951atural @ ( suc @ N ) @ A )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % flip_bit_Suc
% 0.35/0.61 thf(fact_4973_artanh__0,axiom,
% 0.35/0.61 ( ( artanh_real @ zero_zero_real )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % artanh_0
% 0.35/0.61 thf(fact_4974_norm__mult__numeral1,axiom,
% 0.35/0.61 ! [W2: num,A: real] :
% 0.35/0.61 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ A ) )
% 0.35/0.61 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_numeral1
% 0.35/0.61 thf(fact_4975_norm__mult__numeral1,axiom,
% 0.35/0.61 ! [W2: num,A: complex] :
% 0.35/0.61 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ A ) )
% 0.35/0.61 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_numeral1
% 0.35/0.61 thf(fact_4976_norm__mult__numeral2,axiom,
% 0.35/0.61 ! [A: real,W2: num] :
% 0.35/0.61 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.61 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_numeral2
% 0.35/0.61 thf(fact_4977_norm__mult__numeral2,axiom,
% 0.35/0.61 ! [A: complex,W2: num] :
% 0.35/0.61 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.35/0.61 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_numeral2
% 0.35/0.61 thf(fact_4978_norm__le__zero__iff,axiom,
% 0.35/0.61 ! [X: real] :
% 0.35/0.61 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 0.35/0.61 = ( X = zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_le_zero_iff
% 0.35/0.61 thf(fact_4979_norm__le__zero__iff,axiom,
% 0.35/0.61 ! [X: complex] :
% 0.35/0.61 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 0.35/0.61 = ( X = zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_le_zero_iff
% 0.35/0.61 thf(fact_4980_zero__less__norm__iff,axiom,
% 0.35/0.61 ! [X: real] :
% 0.35/0.61 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 0.35/0.61 = ( X != zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_less_norm_iff
% 0.35/0.61 thf(fact_4981_zero__less__norm__iff,axiom,
% 0.35/0.61 ! [X: complex] :
% 0.35/0.61 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 0.35/0.61 = ( X != zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_less_norm_iff
% 0.35/0.61 thf(fact_4982_norm__zero,axiom,
% 0.35/0.61 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % norm_zero
% 0.35/0.61 thf(fact_4983_norm__zero,axiom,
% 0.35/0.61 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % norm_zero
% 0.35/0.61 thf(fact_4984_norm__eq__zero,axiom,
% 0.35/0.61 ! [X: real] :
% 0.35/0.61 ( ( ( real_V7735802525324610683m_real @ X )
% 0.35/0.61 = zero_zero_real )
% 0.35/0.61 = ( X = zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_eq_zero
% 0.35/0.61 thf(fact_4985_norm__eq__zero,axiom,
% 0.35/0.61 ! [X: complex] :
% 0.35/0.61 ( ( ( real_V1022390504157884413omplex @ X )
% 0.35/0.61 = zero_zero_real )
% 0.35/0.61 = ( X = zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_eq_zero
% 0.35/0.61 thf(fact_4986_norm__power__diff,axiom,
% 0.35/0.61 ! [Z3: real,W2: real,M2: nat] :
% 0.35/0.61 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z3 ) @ one_one_real )
% 0.35/0.61 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W2 ) @ one_one_real )
% 0.35/0.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z3 @ M2 ) @ ( power_power_real @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z3 @ W2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_power_diff
% 0.35/0.61 thf(fact_4987_norm__power__diff,axiom,
% 0.35/0.61 ! [Z3: complex,W2: complex,M2: nat] :
% 0.35/0.61 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z3 ) @ one_one_real )
% 0.35/0.61 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W2 ) @ one_one_real )
% 0.35/0.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z3 @ M2 ) @ ( power_power_complex @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z3 @ W2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_power_diff
% 0.35/0.61 thf(fact_4988_norm__mult,axiom,
% 0.35/0.61 ! [X: real,Y: real] :
% 0.35/0.61 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 0.35/0.61 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult
% 0.35/0.61 thf(fact_4989_norm__mult,axiom,
% 0.35/0.61 ! [X: complex,Y: complex] :
% 0.35/0.61 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 0.35/0.61 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult
% 0.35/0.61 thf(fact_4990_nonzero__norm__divide,axiom,
% 0.35/0.61 ! [B: real,A: real] :
% 0.35/0.61 ( ( B != zero_zero_real )
% 0.35/0.61 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.61 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nonzero_norm_divide
% 0.35/0.61 thf(fact_4991_nonzero__norm__divide,axiom,
% 0.35/0.61 ! [B: complex,A: complex] :
% 0.35/0.61 ( ( B != zero_zero_complex )
% 0.35/0.61 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.61 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nonzero_norm_divide
% 0.35/0.61 thf(fact_4992_power__eq__imp__eq__norm,axiom,
% 0.35/0.61 ! [W2: real,N: nat,Z3: real] :
% 0.35/0.61 ( ( ( power_power_real @ W2 @ N )
% 0.35/0.61 = ( power_power_real @ Z3 @ N ) )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( real_V7735802525324610683m_real @ W2 )
% 0.35/0.61 = ( real_V7735802525324610683m_real @ Z3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_eq_imp_eq_norm
% 0.35/0.61 thf(fact_4993_power__eq__imp__eq__norm,axiom,
% 0.35/0.61 ! [W2: complex,N: nat,Z3: complex] :
% 0.35/0.61 ( ( ( power_power_complex @ W2 @ N )
% 0.35/0.61 = ( power_power_complex @ Z3 @ N ) )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( real_V1022390504157884413omplex @ W2 )
% 0.35/0.61 = ( real_V1022390504157884413omplex @ Z3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_eq_imp_eq_norm
% 0.35/0.61 thf(fact_4994_norm__mult__less,axiom,
% 0.35/0.61 ! [X: real,R3: real,Y: real,S2: real] :
% 0.35/0.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R3 )
% 0.35/0.61 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 0.35/0.61 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R3 @ S2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_less
% 0.35/0.61 thf(fact_4995_norm__mult__less,axiom,
% 0.35/0.61 ! [X: complex,R3: real,Y: complex,S2: real] :
% 0.35/0.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R3 )
% 0.35/0.61 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 0.35/0.61 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R3 @ S2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_less
% 0.35/0.61 thf(fact_4996_norm__mult__ineq,axiom,
% 0.35/0.61 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_ineq
% 0.35/0.61 thf(fact_4997_norm__mult__ineq,axiom,
% 0.35/0.61 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % norm_mult_ineq
% 0.35/0.61 thf(fact_4998_power__eq__1__iff,axiom,
% 0.35/0.61 ! [W2: real,N: nat] :
% 0.35/0.61 ( ( ( power_power_real @ W2 @ N )
% 0.35/0.61 = one_one_real )
% 0.35/0.61 => ( ( ( real_V7735802525324610683m_real @ W2 )
% 0.35/0.61 = one_one_real )
% 0.35/0.61 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_eq_1_iff
% 0.35/0.61 thf(fact_4999_power__eq__1__iff,axiom,
% 0.35/0.61 ! [W2: complex,N: nat] :
% 0.35/0.61 ( ( ( power_power_complex @ W2 @ N )
% 0.35/0.61 = one_one_complex )
% 0.35/0.61 => ( ( ( real_V1022390504157884413omplex @ W2 )
% 0.35/0.61 = one_one_real )
% 0.35/0.61 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_eq_1_iff
% 0.35/0.61 thf(fact_5000_arsinh__0,axiom,
% 0.35/0.61 ( ( arsinh_real @ zero_zero_real )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % arsinh_0
% 0.35/0.61 thf(fact_5001_vebt__buildup_Oelims,axiom,
% 0.35/0.61 ! [X: nat,Y: vEBT_VEBT] :
% 0.35/0.61 ( ( ( vEBT_vebt_buildup @ X )
% 0.35/0.61 = Y )
% 0.35/0.61 => ( ( ( X = zero_zero_nat )
% 0.35/0.61 => ( Y
% 0.35/0.61 != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.35/0.61 => ( ( ( X
% 0.35/0.61 = ( suc @ zero_zero_nat ) )
% 0.35/0.61 => ( Y
% 0.35/0.61 != ( vEBT_Leaf @ $false @ $false ) ) )
% 0.35/0.61 => ~ ! [Va: nat] :
% 0.35/0.61 ( ( X
% 0.35/0.61 = ( suc @ ( suc @ Va ) ) )
% 0.35/0.61 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.61 => ( Y
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.61 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.61 => ( Y
% 0.35/0.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % vebt_buildup.elims
% 0.35/0.61 thf(fact_5002_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_real,X: real > code_integer,Y: real > code_integer] :
% 0.35/0.61 ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5003_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 0.35/0.61 ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5004_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_int,X: int > code_integer,Y: int > code_integer] :
% 0.35/0.61 ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5005_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_complex,X: complex > code_integer,Y: complex > code_integer] :
% 0.35/0.61 ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_Code_integer ) ) ) )
% 0.35/0.61 => ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_Code_integer ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5006_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 0.35/0.61 ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5007_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 0.35/0.61 ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5008_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 0.35/0.61 ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5009_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 0.35/0.61 ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_complex ) ) ) )
% 0.35/0.61 => ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5010_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_real,X: real > real,Y: real > real] :
% 0.35/0.61 ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_real ) ) ) )
% 0.35/0.61 => ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_real ) ) ) )
% 0.35/0.61 => ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( times_times_real @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_real ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5011_prod_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 0.35/0.61 ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != one_one_real ) ) ) )
% 0.35/0.61 => ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != one_one_real ) ) ) )
% 0.35/0.61 => ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( times_times_real @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != one_one_real ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % prod.finite_Collect_op
% 0.35/0.61 thf(fact_5012_sum__gp,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,X: complex] :
% 0.35/0.61 ( ( ( ord_less_nat @ N @ M2 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = zero_zero_complex ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ N @ M2 )
% 0.35/0.61 => ( ( ( X = one_one_complex )
% 0.35/0.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 0.35/0.61 & ( ( X != one_one_complex )
% 0.35/0.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_gp
% 0.35/0.61 thf(fact_5013_sum__gp,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,X: rat] :
% 0.35/0.61 ( ( ( ord_less_nat @ N @ M2 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = zero_zero_rat ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ N @ M2 )
% 0.35/0.61 => ( ( ( X = one_one_rat )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 0.35/0.61 & ( ( X != one_one_rat )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_gp
% 0.35/0.61 thf(fact_5014_sum__gp,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,X: real] :
% 0.35/0.61 ( ( ( ord_less_nat @ N @ M2 )
% 0.35/0.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = zero_zero_real ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ N @ M2 )
% 0.35/0.61 => ( ( ( X = one_one_real )
% 0.35/0.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 0.35/0.61 & ( ( X != one_one_real )
% 0.35/0.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.61 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_gp
% 0.35/0.61 thf(fact_5015_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 0.35/0.61 ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5016_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 0.35/0.61 ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5017_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 0.35/0.61 ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5018_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 0.35/0.61 ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_complex ) ) ) )
% 0.35/0.61 => ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_complex ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5019_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_real,X: real > real,Y: real > real] :
% 0.35/0.61 ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5020_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 0.35/0.61 ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5021_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_int,X: int > real,Y: int > real] :
% 0.35/0.61 ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( finite_finite_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( ( member_int @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5022_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_complex,X: complex > real,Y: complex > real] :
% 0.35/0.61 ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_real ) ) ) )
% 0.35/0.61 => ( finite3207457112153483333omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [I: complex] :
% 0.35/0.61 ( ( member_complex @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5023_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_real,X: real > rat,Y: real > rat] :
% 0.35/0.61 ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_rat ) ) ) )
% 0.35/0.61 => ( ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_rat ) ) ) )
% 0.35/0.61 => ( finite_finite_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [I: real] :
% 0.35/0.61 ( ( member_real @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5024_sum_Ofinite__Collect__op,axiom,
% 0.35/0.61 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 0.35/0.61 ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( X @ I )
% 0.35/0.61 != zero_zero_rat ) ) ) )
% 0.35/0.61 => ( ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( Y @ I )
% 0.35/0.61 != zero_zero_rat ) ) ) )
% 0.35/0.61 => ( finite_finite_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( ( member_nat @ I @ I5 )
% 0.35/0.61 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 0.35/0.61 != zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.finite_Collect_op
% 0.35/0.61 thf(fact_5025_geometric__deriv__sums,axiom,
% 0.35/0.61 ! [Z3: real] :
% 0.35/0.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z3 ) @ one_one_real )
% 0.35/0.61 => ( sums_real
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) @ ( power_power_real @ Z3 @ N4 ) )
% 0.35/0.61 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % geometric_deriv_sums
% 0.35/0.61 thf(fact_5026_geometric__deriv__sums,axiom,
% 0.35/0.61 ! [Z3: complex] :
% 0.35/0.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z3 ) @ one_one_real )
% 0.35/0.61 => ( sums_complex
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N4 ) ) @ ( power_power_complex @ Z3 @ N4 ) )
% 0.35/0.61 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % geometric_deriv_sums
% 0.35/0.61 thf(fact_5027_pochhammer__double,axiom,
% 0.35/0.61 ! [Z3: complex,N: nat] :
% 0.35/0.61 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z3 @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_double
% 0.35/0.61 thf(fact_5028_pochhammer__double,axiom,
% 0.35/0.61 ! [Z3: rat,N: nat] :
% 0.35/0.61 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_double
% 0.35/0.61 thf(fact_5029_pochhammer__double,axiom,
% 0.35/0.61 ! [Z3: real,N: nat] :
% 0.35/0.61 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z3 @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_double
% 0.35/0.61 thf(fact_5030_dvd__0__right,axiom,
% 0.35/0.61 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_right
% 0.35/0.61 thf(fact_5031_dvd__0__right,axiom,
% 0.35/0.61 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_right
% 0.35/0.61 thf(fact_5032_dvd__0__right,axiom,
% 0.35/0.61 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_right
% 0.35/0.61 thf(fact_5033_dvd__0__right,axiom,
% 0.35/0.61 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_right
% 0.35/0.61 thf(fact_5034_dvd__0__right,axiom,
% 0.35/0.61 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_right
% 0.35/0.61 thf(fact_5035_dvd__0__left__iff,axiom,
% 0.35/0.61 ! [A: complex] :
% 0.35/0.61 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.35/0.61 = ( A = zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left_iff
% 0.35/0.61 thf(fact_5036_dvd__0__left__iff,axiom,
% 0.35/0.61 ! [A: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.35/0.61 = ( A = zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left_iff
% 0.35/0.61 thf(fact_5037_dvd__0__left__iff,axiom,
% 0.35/0.61 ! [A: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.35/0.61 = ( A = zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left_iff
% 0.35/0.61 thf(fact_5038_dvd__0__left__iff,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.35/0.61 = ( A = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left_iff
% 0.35/0.61 thf(fact_5039_dvd__0__left__iff,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.35/0.61 = ( A = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left_iff
% 0.35/0.61 thf(fact_5040_dvd__add__triv__right__iff,axiom,
% 0.35/0.61 ! [A: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 0.35/0.61 = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_right_iff
% 0.35/0.61 thf(fact_5041_dvd__add__triv__right__iff,axiom,
% 0.35/0.61 ! [A: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 0.35/0.61 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_right_iff
% 0.35/0.61 thf(fact_5042_dvd__add__triv__right__iff,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_right_iff
% 0.35/0.61 thf(fact_5043_dvd__add__triv__right__iff,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_right_iff
% 0.35/0.61 thf(fact_5044_dvd__add__triv__left__iff,axiom,
% 0.35/0.61 ! [A: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 0.35/0.61 = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_left_iff
% 0.35/0.61 thf(fact_5045_dvd__add__triv__left__iff,axiom,
% 0.35/0.61 ! [A: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.61 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_left_iff
% 0.35/0.61 thf(fact_5046_dvd__add__triv__left__iff,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_left_iff
% 0.35/0.61 thf(fact_5047_dvd__add__triv__left__iff,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_triv_left_iff
% 0.35/0.61 thf(fact_5048_div__dvd__div,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ A @ C2 )
% 0.35/0.61 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C2 @ A ) )
% 0.35/0.61 = ( dvd_dvd_nat @ B @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_dvd_div
% 0.35/0.61 thf(fact_5049_div__dvd__div,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ A @ C2 )
% 0.35/0.61 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C2 @ A ) )
% 0.35/0.61 = ( dvd_dvd_int @ B @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_dvd_div
% 0.35/0.61 thf(fact_5050_nat__dvd__1__iff__1,axiom,
% 0.35/0.61 ! [M2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 0.35/0.61 = ( M2 = one_one_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % nat_dvd_1_iff_1
% 0.35/0.61 thf(fact_5051_sum_Oneutral__const,axiom,
% 0.35/0.61 ! [A4: set_nat] :
% 0.35/0.61 ( ( groups3542108847815614940at_nat
% 0.35/0.61 @ ^ [Uu3: nat] : zero_zero_nat
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_nat ) ).
% 0.35/0.61
% 0.35/0.61 % sum.neutral_const
% 0.35/0.61 thf(fact_5052_sum_Oneutral__const,axiom,
% 0.35/0.61 ! [A4: set_int] :
% 0.35/0.61 ( ( groups4538972089207619220nt_int
% 0.35/0.61 @ ^ [Uu3: int] : zero_zero_int
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_int ) ).
% 0.35/0.61
% 0.35/0.61 % sum.neutral_const
% 0.35/0.61 thf(fact_5053_sum_Oneutral__const,axiom,
% 0.35/0.61 ! [A4: set_nat] :
% 0.35/0.61 ( ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [Uu3: nat] : zero_zero_real
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % sum.neutral_const
% 0.35/0.61 thf(fact_5054_dvd__times__right__cancel__iff,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( A != zero_zero_nat )
% 0.35/0.61 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C2 @ A ) )
% 0.35/0.61 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_times_right_cancel_iff
% 0.35/0.61 thf(fact_5055_dvd__times__right__cancel__iff,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( A != zero_zero_int )
% 0.35/0.61 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C2 @ A ) )
% 0.35/0.61 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_times_right_cancel_iff
% 0.35/0.61 thf(fact_5056_dvd__times__left__cancel__iff,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( A != zero_zero_nat )
% 0.35/0.61 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_times_left_cancel_iff
% 0.35/0.61 thf(fact_5057_dvd__times__left__cancel__iff,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( A != zero_zero_int )
% 0.35/0.61 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_times_left_cancel_iff
% 0.35/0.61 thf(fact_5058_dvd__mult__cancel__right,axiom,
% 0.35/0.61 ! [A: complex,C2: complex,B: complex] :
% 0.35/0.61 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ B @ C2 ) )
% 0.35/0.61 = ( ( C2 = zero_zero_complex )
% 0.35/0.61 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_right
% 0.35/0.61 thf(fact_5059_dvd__mult__cancel__right,axiom,
% 0.35/0.61 ! [A: real,C2: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 0.35/0.61 = ( ( C2 = zero_zero_real )
% 0.35/0.61 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_right
% 0.35/0.61 thf(fact_5060_dvd__mult__cancel__right,axiom,
% 0.35/0.61 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 0.35/0.61 = ( ( C2 = zero_zero_rat )
% 0.35/0.61 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_right
% 0.35/0.61 thf(fact_5061_dvd__mult__cancel__right,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 0.35/0.61 = ( ( C2 = zero_zero_int )
% 0.35/0.61 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_right
% 0.35/0.61 thf(fact_5062_dvd__mult__cancel__left,axiom,
% 0.35/0.61 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.61 ( ( dvd_dvd_complex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 0.35/0.61 = ( ( C2 = zero_zero_complex )
% 0.35/0.61 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_left
% 0.35/0.61 thf(fact_5063_dvd__mult__cancel__left,axiom,
% 0.35/0.61 ! [C2: real,A: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 0.35/0.61 = ( ( C2 = zero_zero_real )
% 0.35/0.61 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_left
% 0.35/0.61 thf(fact_5064_dvd__mult__cancel__left,axiom,
% 0.35/0.61 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 0.35/0.61 = ( ( C2 = zero_zero_rat )
% 0.35/0.61 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_left
% 0.35/0.61 thf(fact_5065_dvd__mult__cancel__left,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.35/0.61 = ( ( C2 = zero_zero_int )
% 0.35/0.61 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_cancel_left
% 0.35/0.61 thf(fact_5066_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.61 ! [A: real,B: real,C2: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C2 @ A ) ) )
% 0.35/0.61 = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_right_iff
% 0.35/0.61 thf(fact_5067_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.61 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C2 @ A ) ) )
% 0.35/0.61 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_right_iff
% 0.35/0.61 thf(fact_5068_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C2 @ A ) ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_right_iff
% 0.35/0.61 thf(fact_5069_dvd__add__times__triv__right__iff,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C2 @ A ) ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_right_iff
% 0.35/0.61 thf(fact_5070_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.61 ! [A: real,C2: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C2 @ A ) @ B ) )
% 0.35/0.61 = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_left_iff
% 0.35/0.61 thf(fact_5071_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.61 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C2 @ A ) @ B ) )
% 0.35/0.61 = ( dvd_dvd_rat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_left_iff
% 0.35/0.61 thf(fact_5072_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C2 @ A ) @ B ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_left_iff
% 0.35/0.61 thf(fact_5073_dvd__add__times__triv__left__iff,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C2 @ A ) @ B ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_times_triv_left_iff
% 0.35/0.61 thf(fact_5074_unit__prod,axiom,
% 0.35/0.61 ! [A: code_integer,B: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.61 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.61 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_prod
% 0.35/0.61 thf(fact_5075_unit__prod,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.61 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.61 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_prod
% 0.35/0.61 thf(fact_5076_unit__prod,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.61 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.61 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_prod
% 0.35/0.61 thf(fact_5077_dvd__div__mult__self,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.35/0.61 = B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_mult_self
% 0.35/0.61 thf(fact_5078_dvd__div__mult__self,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.35/0.61 = B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_mult_self
% 0.35/0.61 thf(fact_5079_dvd__mult__div__cancel,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 0.35/0.61 = B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_div_cancel
% 0.35/0.61 thf(fact_5080_dvd__mult__div__cancel,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 0.35/0.61 = B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_div_cancel
% 0.35/0.61 thf(fact_5081_div__add,axiom,
% 0.35/0.61 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.61 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 0.35/0.61 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C2 ) @ ( divide_divide_nat @ B @ C2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_add
% 0.35/0.61 thf(fact_5082_div__add,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.61 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 0.35/0.61 = ( plus_plus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_add
% 0.35/0.61 thf(fact_5083_unit__div,axiom,
% 0.35/0.61 ! [A: code_integer,B: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.61 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.61 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div
% 0.35/0.61 thf(fact_5084_unit__div,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.61 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.61 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div
% 0.35/0.61 thf(fact_5085_unit__div,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.61 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.61 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div
% 0.35/0.61 thf(fact_5086_unit__div__1__unit,axiom,
% 0.35/0.61 ! [A: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.61 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_1_unit
% 0.35/0.61 thf(fact_5087_unit__div__1__unit,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.61 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_1_unit
% 0.35/0.61 thf(fact_5088_unit__div__1__unit,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.61 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_1_unit
% 0.35/0.61 thf(fact_5089_unit__div__1__div__1,axiom,
% 0.35/0.61 ! [A: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.61 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.35/0.61 = A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_1_div_1
% 0.35/0.61 thf(fact_5090_unit__div__1__div__1,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.61 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.35/0.61 = A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_1_div_1
% 0.35/0.61 thf(fact_5091_unit__div__1__div__1,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.61 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 0.35/0.61 = A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_1_div_1
% 0.35/0.61 thf(fact_5092_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: nat > complex] :
% 0.35/0.61 ( ( groups2073611262835488442omplex @ G2 @ bot_bot_set_nat )
% 0.35/0.61 = zero_zero_complex ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5093_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: nat > rat] :
% 0.35/0.61 ( ( groups2906978787729119204at_rat @ G2 @ bot_bot_set_nat )
% 0.35/0.61 = zero_zero_rat ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5094_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: nat > int] :
% 0.35/0.61 ( ( groups3539618377306564664at_int @ G2 @ bot_bot_set_nat )
% 0.35/0.61 = zero_zero_int ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5095_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: int > complex] :
% 0.35/0.61 ( ( groups3049146728041665814omplex @ G2 @ bot_bot_set_int )
% 0.35/0.61 = zero_zero_complex ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5096_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: int > real] :
% 0.35/0.61 ( ( groups8778361861064173332t_real @ G2 @ bot_bot_set_int )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5097_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: int > rat] :
% 0.35/0.61 ( ( groups3906332499630173760nt_rat @ G2 @ bot_bot_set_int )
% 0.35/0.61 = zero_zero_rat ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5098_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: int > nat] :
% 0.35/0.61 ( ( groups4541462559716669496nt_nat @ G2 @ bot_bot_set_int )
% 0.35/0.61 = zero_zero_nat ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5099_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: real > complex] :
% 0.35/0.61 ( ( groups5754745047067104278omplex @ G2 @ bot_bot_set_real )
% 0.35/0.61 = zero_zero_complex ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5100_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: real > real] :
% 0.35/0.61 ( ( groups8097168146408367636l_real @ G2 @ bot_bot_set_real )
% 0.35/0.61 = zero_zero_real ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5101_sum_Oempty,axiom,
% 0.35/0.61 ! [G2: real > rat] :
% 0.35/0.61 ( ( groups1300246762558778688al_rat @ G2 @ bot_bot_set_real )
% 0.35/0.61 = zero_zero_rat ) ).
% 0.35/0.61
% 0.35/0.61 % sum.empty
% 0.35/0.61 thf(fact_5102_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_nat,G2: nat > complex] :
% 0.35/0.61 ( ~ ( finite_finite_nat @ A4 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex @ G2 @ A4 )
% 0.35/0.61 = zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5103_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > complex] :
% 0.35/0.61 ( ~ ( finite_finite_int @ A4 )
% 0.35/0.61 => ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 0.35/0.61 = zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5104_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_complex,G2: complex > complex] :
% 0.35/0.61 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.35/0.61 => ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 0.35/0.61 = zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5105_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > real] :
% 0.35/0.61 ( ~ ( finite_finite_int @ A4 )
% 0.35/0.61 => ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 0.35/0.61 = zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5106_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_complex,G2: complex > real] :
% 0.35/0.61 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.35/0.61 => ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 0.35/0.61 = zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5107_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_nat,G2: nat > rat] :
% 0.35/0.61 ( ~ ( finite_finite_nat @ A4 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat @ G2 @ A4 )
% 0.35/0.61 = zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5108_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > rat] :
% 0.35/0.61 ( ~ ( finite_finite_int @ A4 )
% 0.35/0.61 => ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 0.35/0.61 = zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5109_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_complex,G2: complex > rat] :
% 0.35/0.61 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.35/0.61 => ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 0.35/0.61 = zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5110_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > nat] :
% 0.35/0.61 ( ~ ( finite_finite_int @ A4 )
% 0.35/0.61 => ( ( groups4541462559716669496nt_nat @ G2 @ A4 )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5111_sum_Oinfinite,axiom,
% 0.35/0.61 ! [A4: set_complex,G2: complex > nat] :
% 0.35/0.61 ( ~ ( finite3207457112153483333omplex @ A4 )
% 0.35/0.61 => ( ( groups5693394587270226106ex_nat @ G2 @ A4 )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.infinite
% 0.35/0.61 thf(fact_5112_sum__eq__0__iff,axiom,
% 0.35/0.61 ! [F3: set_int,F2: int > nat] :
% 0.35/0.61 ( ( finite_finite_int @ F3 )
% 0.35/0.61 => ( ( ( groups4541462559716669496nt_nat @ F2 @ F3 )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 = ( ! [X4: int] :
% 0.35/0.61 ( ( member_int @ X4 @ F3 )
% 0.35/0.61 => ( ( F2 @ X4 )
% 0.35/0.61 = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_eq_0_iff
% 0.35/0.61 thf(fact_5113_sum__eq__0__iff,axiom,
% 0.35/0.61 ! [F3: set_complex,F2: complex > nat] :
% 0.35/0.61 ( ( finite3207457112153483333omplex @ F3 )
% 0.35/0.61 => ( ( ( groups5693394587270226106ex_nat @ F2 @ F3 )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 = ( ! [X4: complex] :
% 0.35/0.61 ( ( member_complex @ X4 @ F3 )
% 0.35/0.61 => ( ( F2 @ X4 )
% 0.35/0.61 = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_eq_0_iff
% 0.35/0.61 thf(fact_5114_sum__eq__0__iff,axiom,
% 0.35/0.61 ! [F3: set_nat,F2: nat > nat] :
% 0.35/0.61 ( ( finite_finite_nat @ F3 )
% 0.35/0.61 => ( ( ( groups3542108847815614940at_nat @ F2 @ F3 )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 = ( ! [X4: nat] :
% 0.35/0.61 ( ( member_nat @ X4 @ F3 )
% 0.35/0.61 => ( ( F2 @ X4 )
% 0.35/0.61 = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_eq_0_iff
% 0.35/0.61 thf(fact_5115_div__diff,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.61 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 0.35/0.61 = ( minus_minus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_diff
% 0.35/0.61 thf(fact_5116_dvd__imp__mod__0,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( modulo_modulo_nat @ B @ A )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_imp_mod_0
% 0.35/0.61 thf(fact_5117_dvd__imp__mod__0,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( modulo_modulo_int @ B @ A )
% 0.35/0.61 = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_imp_mod_0
% 0.35/0.61 thf(fact_5118_dvd__imp__mod__0,axiom,
% 0.35/0.61 ! [A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( dvd_dvd_Code_natural @ A @ B )
% 0.35/0.61 => ( ( modulo8411746178871703098atural @ B @ A )
% 0.35/0.61 = zero_z2226904508553997617atural ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_imp_mod_0
% 0.35/0.61 thf(fact_5119_dvd__1__left,axiom,
% 0.35/0.61 ! [K2: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K2 ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_1_left
% 0.35/0.61 thf(fact_5120_dvd__1__iff__1,axiom,
% 0.35/0.61 ! [M2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 0.35/0.61 = ( M2
% 0.35/0.61 = ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_1_iff_1
% 0.35/0.61 thf(fact_5121_nat__mult__dvd__cancel__disj,axiom,
% 0.35/0.61 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.35/0.61 = ( ( K2 = zero_zero_nat )
% 0.35/0.61 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % nat_mult_dvd_cancel_disj
% 0.35/0.61 thf(fact_5122_pochhammer__0,axiom,
% 0.35/0.61 ! [A: code_integer] :
% 0.35/0.61 ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 0.35/0.61 = one_one_Code_integer ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_0
% 0.35/0.61 thf(fact_5123_pochhammer__0,axiom,
% 0.35/0.61 ! [A: complex] :
% 0.35/0.61 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 0.35/0.61 = one_one_complex ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_0
% 0.35/0.61 thf(fact_5124_pochhammer__0,axiom,
% 0.35/0.61 ! [A: real] :
% 0.35/0.61 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 0.35/0.61 = one_one_real ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_0
% 0.35/0.61 thf(fact_5125_pochhammer__0,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 0.35/0.61 = one_one_nat ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_0
% 0.35/0.61 thf(fact_5126_pochhammer__0,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 0.35/0.61 = one_one_int ) ).
% 0.35/0.61
% 0.35/0.61 % pochhammer_0
% 0.35/0.61 thf(fact_5127_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_real,A: real,B: real > complex] :
% 0.35/0.61 ( ( finite_finite_real @ S3 )
% 0.35/0.61 => ( ( ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups5754745047067104278omplex
% 0.35/0.61 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups5754745047067104278omplex
% 0.35/0.61 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5128_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_nat,A: nat,B: nat > complex] :
% 0.35/0.61 ( ( finite_finite_nat @ S3 )
% 0.35/0.61 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5129_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_int,A: int,B: int > complex] :
% 0.35/0.61 ( ( finite_finite_int @ S3 )
% 0.35/0.61 => ( ( ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3049146728041665814omplex
% 0.35/0.61 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3049146728041665814omplex
% 0.35/0.61 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5130_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_complex,A: complex,B: complex > complex] :
% 0.35/0.61 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.61 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups7754918857620584856omplex
% 0.35/0.61 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups7754918857620584856omplex
% 0.35/0.61 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5131_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_real,A: real,B: real > real] :
% 0.35/0.61 ( ( finite_finite_real @ S3 )
% 0.35/0.61 => ( ( ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups8097168146408367636l_real
% 0.35/0.61 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups8097168146408367636l_real
% 0.35/0.61 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_real ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5132_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_int,A: int,B: int > real] :
% 0.35/0.61 ( ( finite_finite_int @ S3 )
% 0.35/0.61 => ( ( ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups8778361861064173332t_real
% 0.35/0.61 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups8778361861064173332t_real
% 0.35/0.61 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_real ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5133_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_complex,A: complex,B: complex > real] :
% 0.35/0.61 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.61 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups5808333547571424918x_real
% 0.35/0.61 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups5808333547571424918x_real
% 0.35/0.61 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_real ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5134_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_real,A: real,B: real > rat] :
% 0.35/0.61 ( ( finite_finite_real @ S3 )
% 0.35/0.61 => ( ( ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups1300246762558778688al_rat
% 0.35/0.61 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups1300246762558778688al_rat
% 0.35/0.61 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5135_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_nat,A: nat,B: nat > rat] :
% 0.35/0.61 ( ( finite_finite_nat @ S3 )
% 0.35/0.61 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5136_sum_Odelta,axiom,
% 0.35/0.61 ! [S3: set_int,A: int,B: int > rat] :
% 0.35/0.61 ( ( finite_finite_int @ S3 )
% 0.35/0.61 => ( ( ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3906332499630173760nt_rat
% 0.35/0.61 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3906332499630173760nt_rat
% 0.35/0.61 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta
% 0.35/0.61 thf(fact_5137_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_real,A: real,B: real > complex] :
% 0.35/0.61 ( ( finite_finite_real @ S3 )
% 0.35/0.61 => ( ( ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups5754745047067104278omplex
% 0.35/0.61 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups5754745047067104278omplex
% 0.35/0.61 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5138_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_nat,A: nat,B: nat > complex] :
% 0.35/0.61 ( ( finite_finite_nat @ S3 )
% 0.35/0.61 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5139_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_int,A: int,B: int > complex] :
% 0.35/0.61 ( ( finite_finite_int @ S3 )
% 0.35/0.61 => ( ( ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3049146728041665814omplex
% 0.35/0.61 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3049146728041665814omplex
% 0.35/0.61 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5140_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_complex,A: complex,B: complex > complex] :
% 0.35/0.61 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.61 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups7754918857620584856omplex
% 0.35/0.61 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups7754918857620584856omplex
% 0.35/0.61 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5141_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_real,A: real,B: real > real] :
% 0.35/0.61 ( ( finite_finite_real @ S3 )
% 0.35/0.61 => ( ( ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups8097168146408367636l_real
% 0.35/0.61 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups8097168146408367636l_real
% 0.35/0.61 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_real ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5142_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_int,A: int,B: int > real] :
% 0.35/0.61 ( ( finite_finite_int @ S3 )
% 0.35/0.61 => ( ( ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups8778361861064173332t_real
% 0.35/0.61 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups8778361861064173332t_real
% 0.35/0.61 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_real ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5143_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_complex,A: complex,B: complex > real] :
% 0.35/0.61 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.61 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups5808333547571424918x_real
% 0.35/0.61 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.61 => ( ( groups5808333547571424918x_real
% 0.35/0.61 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_real ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5144_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_real,A: real,B: real > rat] :
% 0.35/0.61 ( ( finite_finite_real @ S3 )
% 0.35/0.61 => ( ( ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups1300246762558778688al_rat
% 0.35/0.61 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.61 => ( ( groups1300246762558778688al_rat
% 0.35/0.61 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5145_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_nat,A: nat,B: nat > rat] :
% 0.35/0.61 ( ( finite_finite_nat @ S3 )
% 0.35/0.61 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5146_sum_Odelta_H,axiom,
% 0.35/0.61 ! [S3: set_int,A: int,B: int > rat] :
% 0.35/0.61 ( ( finite_finite_int @ S3 )
% 0.35/0.61 => ( ( ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3906332499630173760nt_rat
% 0.35/0.61 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = ( B @ A ) ) )
% 0.35/0.61 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.61 => ( ( groups3906332499630173760nt_rat
% 0.35/0.61 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 0.35/0.61 @ S3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.delta'
% 0.35/0.61 thf(fact_5147_unit__mult__div__div,axiom,
% 0.35/0.61 ! [A: code_integer,B: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.61 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 0.35/0.61 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_mult_div_div
% 0.35/0.61 thf(fact_5148_unit__mult__div__div,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.61 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 0.35/0.61 = ( divide_divide_nat @ B @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_mult_div_div
% 0.35/0.61 thf(fact_5149_unit__mult__div__div,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.61 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 0.35/0.61 = ( divide_divide_int @ B @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_mult_div_div
% 0.35/0.61 thf(fact_5150_unit__div__mult__self,axiom,
% 0.35/0.61 ! [A: code_integer,B: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.61 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 0.35/0.61 = B ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_mult_self
% 0.35/0.61 thf(fact_5151_unit__div__mult__self,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.61 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 0.35/0.61 = B ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_mult_self
% 0.35/0.61 thf(fact_5152_unit__div__mult__self,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.61 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 0.35/0.61 = B ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_div_mult_self
% 0.35/0.61 thf(fact_5153_pow__divides__pow__iff,axiom,
% 0.35/0.61 ! [N: nat,A: nat,B: nat] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % pow_divides_pow_iff
% 0.35/0.61 thf(fact_5154_pow__divides__pow__iff,axiom,
% 0.35/0.61 ! [N: nat,A: int,B: int] :
% 0.35/0.61 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % pow_divides_pow_iff
% 0.35/0.61 thf(fact_5155_sum__constant,axiom,
% 0.35/0.61 ! [Y: rat,A4: set_nat] :
% 0.35/0.61 ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [X4: nat] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5156_sum__constant,axiom,
% 0.35/0.61 ! [Y: rat,A4: set_complex] :
% 0.35/0.61 ( ( groups5058264527183730370ex_rat
% 0.35/0.61 @ ^ [X4: complex] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5157_sum__constant,axiom,
% 0.35/0.61 ! [Y: rat,A4: set_int] :
% 0.35/0.61 ( ( groups3906332499630173760nt_rat
% 0.35/0.61 @ ^ [X4: int] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5158_sum__constant,axiom,
% 0.35/0.61 ! [Y: real,A4: set_complex] :
% 0.35/0.61 ( ( groups5808333547571424918x_real
% 0.35/0.61 @ ^ [X4: complex] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5159_sum__constant,axiom,
% 0.35/0.61 ! [Y: real,A4: set_int] :
% 0.35/0.61 ( ( groups8778361861064173332t_real
% 0.35/0.61 @ ^ [X4: int] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5160_sum__constant,axiom,
% 0.35/0.61 ! [Y: int,A4: set_nat] :
% 0.35/0.61 ( ( groups3539618377306564664at_int
% 0.35/0.61 @ ^ [X4: nat] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5161_sum__constant,axiom,
% 0.35/0.61 ! [Y: int,A4: set_complex] :
% 0.35/0.61 ( ( groups5690904116761175830ex_int
% 0.35/0.61 @ ^ [X4: complex] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5162_sum__constant,axiom,
% 0.35/0.61 ! [Y: nat,A4: set_complex] :
% 0.35/0.61 ( ( groups5693394587270226106ex_nat
% 0.35/0.61 @ ^ [X4: complex] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5163_sum__constant,axiom,
% 0.35/0.61 ! [Y: nat,A4: set_int] :
% 0.35/0.61 ( ( groups4541462559716669496nt_nat
% 0.35/0.61 @ ^ [X4: int] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5164_sum__constant,axiom,
% 0.35/0.61 ! [Y: nat,A4: set_nat] :
% 0.35/0.61 ( ( groups3542108847815614940at_nat
% 0.35/0.61 @ ^ [X4: nat] : Y
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_constant
% 0.35/0.61 thf(fact_5165_even__mult__iff,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 0.35/0.61 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_mult_iff
% 0.35/0.61 thf(fact_5166_even__mult__iff,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 0.35/0.61 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_mult_iff
% 0.35/0.61 thf(fact_5167_even__Suc__Suc__iff,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 0.35/0.61 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_Suc_Suc_iff
% 0.35/0.61 thf(fact_5168_even__Suc,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 0.35/0.61 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_Suc
% 0.35/0.61 thf(fact_5169_powser__sums__zero__iff,axiom,
% 0.35/0.61 ! [A: nat > complex,X: complex] :
% 0.35/0.61 ( ( sums_complex
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 0.35/0.61 @ X )
% 0.35/0.61 = ( ( A @ zero_zero_nat )
% 0.35/0.61 = X ) ) ).
% 0.35/0.61
% 0.35/0.61 % powser_sums_zero_iff
% 0.35/0.61 thf(fact_5170_powser__sums__zero__iff,axiom,
% 0.35/0.61 ! [A: nat > real,X: real] :
% 0.35/0.61 ( ( sums_real
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 0.35/0.61 @ X )
% 0.35/0.61 = ( ( A @ zero_zero_nat )
% 0.35/0.61 = X ) ) ).
% 0.35/0.61
% 0.35/0.61 % powser_sums_zero_iff
% 0.35/0.61 thf(fact_5171_even__Suc__div__two,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_Suc_div_two
% 0.35/0.61 thf(fact_5172_odd__Suc__div__two,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.61 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % odd_Suc_div_two
% 0.35/0.61 thf(fact_5173_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,G2: nat > complex] :
% 0.35/0.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = zero_zero_complex ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.cl_ivl_Suc
% 0.35/0.61 thf(fact_5174_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,G2: nat > rat] :
% 0.35/0.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = zero_zero_rat ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.cl_ivl_Suc
% 0.35/0.61 thf(fact_5175_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,G2: nat > int] :
% 0.35/0.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = zero_zero_int ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.cl_ivl_Suc
% 0.35/0.61 thf(fact_5176_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,G2: nat > nat] :
% 0.35/0.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = zero_zero_nat ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.cl_ivl_Suc
% 0.35/0.61 thf(fact_5177_sum_Ocl__ivl__Suc,axiom,
% 0.35/0.61 ! [N: nat,M2: nat,G2: nat > real] :
% 0.35/0.61 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = zero_zero_real ) )
% 0.35/0.61 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.61 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.61 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.cl_ivl_Suc
% 0.35/0.61 thf(fact_5178_sum__zero__power,axiom,
% 0.35/0.61 ! [A4: set_nat,C2: nat > complex] :
% 0.35/0.61 ( ( ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( C2 @ zero_zero_nat ) ) )
% 0.35/0.61 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_complex ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_zero_power
% 0.35/0.61 thf(fact_5179_sum__zero__power,axiom,
% 0.35/0.61 ! [A4: set_nat,C2: nat > rat] :
% 0.35/0.61 ( ( ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( C2 @ zero_zero_nat ) ) )
% 0.35/0.61 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_rat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_zero_power
% 0.35/0.61 thf(fact_5180_sum__zero__power,axiom,
% 0.35/0.61 ! [A4: set_nat,C2: nat > real] :
% 0.35/0.61 ( ( ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( C2 @ zero_zero_nat ) ) )
% 0.35/0.61 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_real ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_zero_power
% 0.35/0.61 thf(fact_5181_zero__le__power__eq__numeral,axiom,
% 0.35/0.61 ! [A: real,W2: num] :
% 0.35/0.61 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.35/0.61 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_le_power_eq_numeral
% 0.35/0.61 thf(fact_5182_zero__le__power__eq__numeral,axiom,
% 0.35/0.61 ! [A: rat,W2: num] :
% 0.35/0.61 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.35/0.61 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_le_power_eq_numeral
% 0.35/0.61 thf(fact_5183_zero__le__power__eq__numeral,axiom,
% 0.35/0.61 ! [A: int,W2: num] :
% 0.35/0.61 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.35/0.61 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_le_power_eq_numeral
% 0.35/0.61 thf(fact_5184_even__power,axiom,
% 0.35/0.61 ! [A: nat,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 0.35/0.61 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_power
% 0.35/0.61 thf(fact_5185_even__power,axiom,
% 0.35/0.61 ! [A: int,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 0.35/0.61 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_power
% 0.35/0.61 thf(fact_5186_power__less__zero__eq,axiom,
% 0.35/0.61 ! [A: real,N: nat] :
% 0.35/0.61 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.35/0.61 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_less_zero_eq
% 0.35/0.61 thf(fact_5187_power__less__zero__eq,axiom,
% 0.35/0.61 ! [A: rat,N: nat] :
% 0.35/0.61 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.35/0.61 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_less_zero_eq
% 0.35/0.61 thf(fact_5188_power__less__zero__eq,axiom,
% 0.35/0.61 ! [A: int,N: nat] :
% 0.35/0.61 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.35/0.61 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_less_zero_eq
% 0.35/0.61 thf(fact_5189_power__less__zero__eq__numeral,axiom,
% 0.35/0.61 ! [A: real,W2: num] :
% 0.35/0.61 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 0.35/0.61 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_less_zero_eq_numeral
% 0.35/0.61 thf(fact_5190_power__less__zero__eq__numeral,axiom,
% 0.35/0.61 ! [A: rat,W2: num] :
% 0.35/0.61 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 0.35/0.61 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_less_zero_eq_numeral
% 0.35/0.61 thf(fact_5191_power__less__zero__eq__numeral,axiom,
% 0.35/0.61 ! [A: int,W2: num] :
% 0.35/0.61 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 0.35/0.61 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_less_zero_eq_numeral
% 0.35/0.61 thf(fact_5192_odd__Suc__minus__one,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 0.35/0.61 = N ) ) ).
% 0.35/0.61
% 0.35/0.61 % odd_Suc_minus_one
% 0.35/0.61 thf(fact_5193_sum__zero__power_H,axiom,
% 0.35/0.61 ! [A4: set_nat,C2: nat > complex,D: nat > complex] :
% 0.35/0.61 ( ( ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [I: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) ) @ ( D @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( divide1717551699836669952omplex @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.35/0.61 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [I: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) ) @ ( D @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_complex ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_zero_power'
% 0.35/0.61 thf(fact_5194_sum__zero__power_H,axiom,
% 0.35/0.61 ! [A4: set_nat,C2: nat > rat,D: nat > rat] :
% 0.35/0.61 ( ( ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( divide_divide_rat @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.35/0.61 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_rat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_zero_power'
% 0.35/0.61 thf(fact_5195_sum__zero__power_H,axiom,
% 0.35/0.61 ! [A4: set_nat,C2: nat > real,D: nat > real] :
% 0.35/0.61 ( ( ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [I: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) ) @ ( D @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = ( divide_divide_real @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 0.35/0.61 & ( ~ ( ( finite_finite_nat @ A4 )
% 0.35/0.61 & ( member_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.61 => ( ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [I: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) ) @ ( D @ I ) )
% 0.35/0.61 @ A4 )
% 0.35/0.61 = zero_zero_real ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_zero_power'
% 0.35/0.61 thf(fact_5196_odd__two__times__div__two__succ,axiom,
% 0.35/0.61 ! [A: code_integer] :
% 0.35/0.61 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 0.35/0.61 = A ) ) ).
% 0.35/0.61
% 0.35/0.61 % odd_two_times_div_two_succ
% 0.35/0.61 thf(fact_5197_odd__two__times__div__two__succ,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 0.35/0.61 = A ) ) ).
% 0.35/0.61
% 0.35/0.61 % odd_two_times_div_two_succ
% 0.35/0.61 thf(fact_5198_odd__two__times__div__two__succ,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 0.35/0.61 = A ) ) ).
% 0.35/0.61
% 0.35/0.61 % odd_two_times_div_two_succ
% 0.35/0.61 thf(fact_5199_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 0.35/0.61 = ( N = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % semiring_parity_class.even_mask_iff
% 0.35/0.61 thf(fact_5200_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 0.35/0.61 = ( N = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % semiring_parity_class.even_mask_iff
% 0.35/0.61 thf(fact_5201_semiring__parity__class_Oeven__mask__iff,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 0.35/0.61 = ( N = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % semiring_parity_class.even_mask_iff
% 0.35/0.61 thf(fact_5202_zero__less__power__eq__numeral,axiom,
% 0.35/0.61 ! [A: real,W2: num] :
% 0.35/0.61 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.35/0.61 = ( ( ( numeral_numeral_nat @ W2 )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( A != zero_zero_real ) )
% 0.35/0.61 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_less_power_eq_numeral
% 0.35/0.61 thf(fact_5203_zero__less__power__eq__numeral,axiom,
% 0.35/0.61 ! [A: rat,W2: num] :
% 0.35/0.61 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.35/0.61 = ( ( ( numeral_numeral_nat @ W2 )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( A != zero_zero_rat ) )
% 0.35/0.61 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_less_power_eq_numeral
% 0.35/0.61 thf(fact_5204_zero__less__power__eq__numeral,axiom,
% 0.35/0.61 ! [A: int,W2: num] :
% 0.35/0.61 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 0.35/0.61 = ( ( ( numeral_numeral_nat @ W2 )
% 0.35/0.61 = zero_zero_nat )
% 0.35/0.61 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( A != zero_zero_int ) )
% 0.35/0.61 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % zero_less_power_eq_numeral
% 0.35/0.61 thf(fact_5205_odd__two__times__div__two__nat,axiom,
% 0.35/0.61 ! [N: nat] :
% 0.35/0.61 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.61 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.61 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % odd_two_times_div_two_nat
% 0.35/0.61 thf(fact_5206_power__le__zero__eq__numeral,axiom,
% 0.35/0.61 ! [A: real,W2: num] :
% 0.35/0.61 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 0.35/0.61 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.35/0.61 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( A = zero_zero_real ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_le_zero_eq_numeral
% 0.35/0.61 thf(fact_5207_power__le__zero__eq__numeral,axiom,
% 0.35/0.61 ! [A: rat,W2: num] :
% 0.35/0.61 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 0.35/0.61 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.35/0.61 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_le_zero_eq_numeral
% 0.35/0.61 thf(fact_5208_power__le__zero__eq__numeral,axiom,
% 0.35/0.61 ! [A: int,W2: num] :
% 0.35/0.61 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 0.35/0.61 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.35/0.61 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 0.35/0.61 & ( A = zero_zero_int ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % power_le_zero_eq_numeral
% 0.35/0.61 thf(fact_5209_even__succ__div__exp,axiom,
% 0.35/0.61 ! [A: code_integer,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_succ_div_exp
% 0.35/0.61 thf(fact_5210_even__succ__div__exp,axiom,
% 0.35/0.61 ! [A: nat,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_succ_div_exp
% 0.35/0.61 thf(fact_5211_even__succ__div__exp,axiom,
% 0.35/0.61 ! [A: int,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_succ_div_exp
% 0.35/0.61 thf(fact_5212_even__succ__mod__exp,axiom,
% 0.35/0.61 ! [A: code_integer,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_succ_mod_exp
% 0.35/0.61 thf(fact_5213_even__succ__mod__exp,axiom,
% 0.35/0.61 ! [A: nat,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_succ_mod_exp
% 0.35/0.61 thf(fact_5214_even__succ__mod__exp,axiom,
% 0.35/0.61 ! [A: int,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_succ_mod_exp
% 0.35/0.61 thf(fact_5215_even__succ__mod__exp,axiom,
% 0.35/0.61 ! [A: code_natural,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.35/0.61 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.61 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.61 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % even_succ_mod_exp
% 0.35/0.61 thf(fact_5216_sum_Oneutral,axiom,
% 0.35/0.61 ! [A4: set_nat,G2: nat > nat] :
% 0.35/0.61 ( ! [X3: nat] :
% 0.35/0.61 ( ( member_nat @ X3 @ A4 )
% 0.35/0.61 => ( ( G2 @ X3 )
% 0.35/0.61 = zero_zero_nat ) )
% 0.35/0.61 => ( ( groups3542108847815614940at_nat @ G2 @ A4 )
% 0.35/0.61 = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.neutral
% 0.35/0.61 thf(fact_5217_sum_Oneutral,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > int] :
% 0.35/0.61 ( ! [X3: int] :
% 0.35/0.61 ( ( member_int @ X3 @ A4 )
% 0.35/0.61 => ( ( G2 @ X3 )
% 0.35/0.61 = zero_zero_int ) )
% 0.35/0.61 => ( ( groups4538972089207619220nt_int @ G2 @ A4 )
% 0.35/0.61 = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.neutral
% 0.35/0.61 thf(fact_5218_sum_Oneutral,axiom,
% 0.35/0.61 ! [A4: set_nat,G2: nat > real] :
% 0.35/0.61 ( ! [X3: nat] :
% 0.35/0.61 ( ( member_nat @ X3 @ A4 )
% 0.35/0.61 => ( ( G2 @ X3 )
% 0.35/0.61 = zero_zero_real ) )
% 0.35/0.61 => ( ( groups6591440286371151544t_real @ G2 @ A4 )
% 0.35/0.61 = zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.neutral
% 0.35/0.61 thf(fact_5219_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: complex > complex,A4: set_complex] :
% 0.35/0.61 ( ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 0.35/0.61 != zero_zero_complex )
% 0.35/0.61 => ~ ! [A3: complex] :
% 0.35/0.61 ( ( member_complex @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5220_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: real > complex,A4: set_real] :
% 0.35/0.61 ( ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 0.35/0.61 != zero_zero_complex )
% 0.35/0.61 => ~ ! [A3: real] :
% 0.35/0.61 ( ( member_real @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5221_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: nat > complex,A4: set_nat] :
% 0.35/0.61 ( ( ( groups2073611262835488442omplex @ G2 @ A4 )
% 0.35/0.61 != zero_zero_complex )
% 0.35/0.61 => ~ ! [A3: nat] :
% 0.35/0.61 ( ( member_nat @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5222_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: int > complex,A4: set_int] :
% 0.35/0.61 ( ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 0.35/0.61 != zero_zero_complex )
% 0.35/0.61 => ~ ! [A3: int] :
% 0.35/0.61 ( ( member_int @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_complex ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5223_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: complex > real,A4: set_complex] :
% 0.35/0.61 ( ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 0.35/0.61 != zero_zero_real )
% 0.35/0.61 => ~ ! [A3: complex] :
% 0.35/0.61 ( ( member_complex @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_real ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5224_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: real > real,A4: set_real] :
% 0.35/0.61 ( ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 0.35/0.61 != zero_zero_real )
% 0.35/0.61 => ~ ! [A3: real] :
% 0.35/0.61 ( ( member_real @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_real ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5225_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: int > real,A4: set_int] :
% 0.35/0.61 ( ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 0.35/0.61 != zero_zero_real )
% 0.35/0.61 => ~ ! [A3: int] :
% 0.35/0.61 ( ( member_int @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_real ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5226_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: complex > rat,A4: set_complex] :
% 0.35/0.61 ( ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 0.35/0.61 != zero_zero_rat )
% 0.35/0.61 => ~ ! [A3: complex] :
% 0.35/0.61 ( ( member_complex @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5227_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: real > rat,A4: set_real] :
% 0.35/0.61 ( ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 0.35/0.61 != zero_zero_rat )
% 0.35/0.61 => ~ ! [A3: real] :
% 0.35/0.61 ( ( member_real @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5228_sum_Onot__neutral__contains__not__neutral,axiom,
% 0.35/0.61 ! [G2: nat > rat,A4: set_nat] :
% 0.35/0.61 ( ( ( groups2906978787729119204at_rat @ G2 @ A4 )
% 0.35/0.61 != zero_zero_rat )
% 0.35/0.61 => ~ ! [A3: nat] :
% 0.35/0.61 ( ( member_nat @ A3 @ A4 )
% 0.35/0.61 => ( ( G2 @ A3 )
% 0.35/0.61 = zero_zero_rat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.not_neutral_contains_not_neutral
% 0.35/0.61 thf(fact_5229_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_complex,F2: complex > rat,G2: complex > rat] :
% 0.35/0.61 ( ! [I3: complex] :
% 0.35/0.61 ( ( member_complex @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ K5 ) @ ( groups5058264527183730370ex_rat @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5230_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_real,F2: real > rat,G2: real > rat] :
% 0.35/0.61 ( ! [I3: real] :
% 0.35/0.61 ( ( member_real @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ K5 ) @ ( groups1300246762558778688al_rat @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5231_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_nat,F2: nat > rat,G2: nat > rat] :
% 0.35/0.61 ( ! [I3: nat] :
% 0.35/0.61 ( ( member_nat @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ K5 ) @ ( groups2906978787729119204at_rat @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5232_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_int,F2: int > rat,G2: int > rat] :
% 0.35/0.61 ( ! [I3: int] :
% 0.35/0.61 ( ( member_int @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ K5 ) @ ( groups3906332499630173760nt_rat @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5233_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_complex,F2: complex > nat,G2: complex > nat] :
% 0.35/0.61 ( ! [I3: complex] :
% 0.35/0.61 ( ( member_complex @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ K5 ) @ ( groups5693394587270226106ex_nat @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5234_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_real,F2: real > nat,G2: real > nat] :
% 0.35/0.61 ( ! [I3: real] :
% 0.35/0.61 ( ( member_real @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ K5 ) @ ( groups1935376822645274424al_nat @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5235_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_int,F2: int > nat,G2: int > nat] :
% 0.35/0.61 ( ! [I3: int] :
% 0.35/0.61 ( ( member_int @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ K5 ) @ ( groups4541462559716669496nt_nat @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5236_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_complex,F2: complex > int,G2: complex > int] :
% 0.35/0.61 ( ! [I3: complex] :
% 0.35/0.61 ( ( member_complex @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F2 @ K5 ) @ ( groups5690904116761175830ex_int @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5237_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_real,F2: real > int,G2: real > int] :
% 0.35/0.61 ( ! [I3: real] :
% 0.35/0.61 ( ( member_real @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F2 @ K5 ) @ ( groups1932886352136224148al_int @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5238_sum__mono,axiom,
% 0.35/0.61 ! [K5: set_nat,F2: nat > int,G2: nat > int] :
% 0.35/0.61 ( ! [I3: nat] :
% 0.35/0.61 ( ( member_nat @ I3 @ K5 )
% 0.35/0.61 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ K5 ) @ ( groups3539618377306564664at_int @ G2 @ K5 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono
% 0.35/0.61 thf(fact_5239_sum__distrib__left,axiom,
% 0.35/0.61 ! [R3: nat,F2: nat > nat,A4: set_nat] :
% 0.35/0.61 ( ( times_times_nat @ R3 @ ( groups3542108847815614940at_nat @ F2 @ A4 ) )
% 0.35/0.61 = ( groups3542108847815614940at_nat
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_nat @ R3 @ ( F2 @ N4 ) )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_distrib_left
% 0.35/0.61 thf(fact_5240_sum__distrib__left,axiom,
% 0.35/0.61 ! [R3: int,F2: int > int,A4: set_int] :
% 0.35/0.61 ( ( times_times_int @ R3 @ ( groups4538972089207619220nt_int @ F2 @ A4 ) )
% 0.35/0.61 = ( groups4538972089207619220nt_int
% 0.35/0.61 @ ^ [N4: int] : ( times_times_int @ R3 @ ( F2 @ N4 ) )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_distrib_left
% 0.35/0.61 thf(fact_5241_sum__distrib__left,axiom,
% 0.35/0.61 ! [R3: real,F2: nat > real,A4: set_nat] :
% 0.35/0.61 ( ( times_times_real @ R3 @ ( groups6591440286371151544t_real @ F2 @ A4 ) )
% 0.35/0.61 = ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_real @ R3 @ ( F2 @ N4 ) )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_distrib_left
% 0.35/0.61 thf(fact_5242_sum__distrib__right,axiom,
% 0.35/0.61 ! [F2: nat > nat,A4: set_nat,R3: nat] :
% 0.35/0.61 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ R3 )
% 0.35/0.61 = ( groups3542108847815614940at_nat
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_nat @ ( F2 @ N4 ) @ R3 )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_distrib_right
% 0.35/0.61 thf(fact_5243_sum__distrib__right,axiom,
% 0.35/0.61 ! [F2: int > int,A4: set_int,R3: int] :
% 0.35/0.61 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) @ R3 )
% 0.35/0.61 = ( groups4538972089207619220nt_int
% 0.35/0.61 @ ^ [N4: int] : ( times_times_int @ ( F2 @ N4 ) @ R3 )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_distrib_right
% 0.35/0.61 thf(fact_5244_sum__distrib__right,axiom,
% 0.35/0.61 ! [F2: nat > real,A4: set_nat,R3: real] :
% 0.35/0.61 ( ( times_times_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ R3 )
% 0.35/0.61 = ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ R3 )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_distrib_right
% 0.35/0.61 thf(fact_5245_sum__product,axiom,
% 0.35/0.61 ! [F2: nat > nat,A4: set_nat,G2: nat > nat,B5: set_nat] :
% 0.35/0.61 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ B5 ) )
% 0.35/0.61 = ( groups3542108847815614940at_nat
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( groups3542108847815614940at_nat
% 0.35/0.61 @ ^ [J: nat] : ( times_times_nat @ ( F2 @ I ) @ ( G2 @ J ) )
% 0.35/0.61 @ B5 )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_product
% 0.35/0.61 thf(fact_5246_sum__product,axiom,
% 0.35/0.61 ! [F2: int > int,A4: set_int,G2: int > int,B5: set_int] :
% 0.35/0.61 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) @ ( groups4538972089207619220nt_int @ G2 @ B5 ) )
% 0.35/0.61 = ( groups4538972089207619220nt_int
% 0.35/0.61 @ ^ [I: int] :
% 0.35/0.61 ( groups4538972089207619220nt_int
% 0.35/0.61 @ ^ [J: int] : ( times_times_int @ ( F2 @ I ) @ ( G2 @ J ) )
% 0.35/0.61 @ B5 )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_product
% 0.35/0.61 thf(fact_5247_sum__product,axiom,
% 0.35/0.61 ! [F2: nat > real,A4: set_nat,G2: nat > real,B5: set_nat] :
% 0.35/0.61 ( ( times_times_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ ( groups6591440286371151544t_real @ G2 @ B5 ) )
% 0.35/0.61 = ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [I: nat] :
% 0.35/0.61 ( groups6591440286371151544t_real
% 0.35/0.61 @ ^ [J: nat] : ( times_times_real @ ( F2 @ I ) @ ( G2 @ J ) )
% 0.35/0.61 @ B5 )
% 0.35/0.61 @ A4 ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_product
% 0.35/0.61 thf(fact_5248_dvd__antisym,axiom,
% 0.35/0.61 ! [M2: nat,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ M2 @ N )
% 0.35/0.61 => ( ( dvd_dvd_nat @ N @ M2 )
% 0.35/0.61 => ( M2 = N ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_antisym
% 0.35/0.61 thf(fact_5249_dvd__trans,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ B @ C2 )
% 0.35/0.61 => ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_trans
% 0.35/0.61 thf(fact_5250_dvd__trans,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ B @ C2 )
% 0.35/0.61 => ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_trans
% 0.35/0.61 thf(fact_5251_dvd__refl,axiom,
% 0.35/0.61 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_refl
% 0.35/0.61 thf(fact_5252_dvd__refl,axiom,
% 0.35/0.61 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_refl
% 0.35/0.61 thf(fact_5253_dvd__field__iff,axiom,
% 0.35/0.61 ( dvd_dvd_complex
% 0.35/0.61 = ( ^ [A5: complex,B4: complex] :
% 0.35/0.61 ( ( A5 = zero_zero_complex )
% 0.35/0.61 => ( B4 = zero_zero_complex ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_field_iff
% 0.35/0.61 thf(fact_5254_dvd__field__iff,axiom,
% 0.35/0.61 ( dvd_dvd_real
% 0.35/0.61 = ( ^ [A5: real,B4: real] :
% 0.35/0.61 ( ( A5 = zero_zero_real )
% 0.35/0.61 => ( B4 = zero_zero_real ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_field_iff
% 0.35/0.61 thf(fact_5255_dvd__field__iff,axiom,
% 0.35/0.61 ( dvd_dvd_rat
% 0.35/0.61 = ( ^ [A5: rat,B4: rat] :
% 0.35/0.61 ( ( A5 = zero_zero_rat )
% 0.35/0.61 => ( B4 = zero_zero_rat ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_field_iff
% 0.35/0.61 thf(fact_5256_dvd__0__left,axiom,
% 0.35/0.61 ! [A: complex] :
% 0.35/0.61 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 0.35/0.61 => ( A = zero_zero_complex ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left
% 0.35/0.61 thf(fact_5257_dvd__0__left,axiom,
% 0.35/0.61 ! [A: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 0.35/0.61 => ( A = zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left
% 0.35/0.61 thf(fact_5258_dvd__0__left,axiom,
% 0.35/0.61 ! [A: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 0.35/0.61 => ( A = zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left
% 0.35/0.61 thf(fact_5259_dvd__0__left,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.35/0.61 => ( A = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left
% 0.35/0.61 thf(fact_5260_dvd__0__left,axiom,
% 0.35/0.61 ! [A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 0.35/0.61 => ( A = zero_zero_int ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_0_left
% 0.35/0.61 thf(fact_5261_dvd__productE,axiom,
% 0.35/0.61 ! [P: nat,A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ P @ ( times_times_nat @ A @ B ) )
% 0.35/0.61 => ~ ! [X3: nat,Y3: nat] :
% 0.35/0.61 ( ( P
% 0.35/0.61 = ( times_times_nat @ X3 @ Y3 ) )
% 0.35/0.61 => ( ( dvd_dvd_nat @ X3 @ A )
% 0.35/0.61 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_productE
% 0.35/0.61 thf(fact_5262_dvd__productE,axiom,
% 0.35/0.61 ! [P: int,A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ P @ ( times_times_int @ A @ B ) )
% 0.35/0.61 => ~ ! [X3: int,Y3: int] :
% 0.35/0.61 ( ( P
% 0.35/0.61 = ( times_times_int @ X3 @ Y3 ) )
% 0.35/0.61 => ( ( dvd_dvd_int @ X3 @ A )
% 0.35/0.61 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_productE
% 0.35/0.61 thf(fact_5263_division__decomp,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.61 => ? [B9: nat,C5: nat] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( times_times_nat @ B9 @ C5 ) )
% 0.35/0.61 & ( dvd_dvd_nat @ B9 @ B )
% 0.35/0.61 & ( dvd_dvd_nat @ C5 @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % division_decomp
% 0.35/0.61 thf(fact_5264_division__decomp,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.61 => ? [B9: int,C5: int] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( times_times_int @ B9 @ C5 ) )
% 0.35/0.61 & ( dvd_dvd_int @ B9 @ B )
% 0.35/0.61 & ( dvd_dvd_int @ C5 @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % division_decomp
% 0.35/0.61 thf(fact_5265_dvdE,axiom,
% 0.35/0.61 ! [B: real,A: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ B @ A )
% 0.35/0.61 => ~ ! [K: real] :
% 0.35/0.61 ( A
% 0.35/0.61 != ( times_times_real @ B @ K ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdE
% 0.35/0.61 thf(fact_5266_dvdE,axiom,
% 0.35/0.61 ! [B: rat,A: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ B @ A )
% 0.35/0.61 => ~ ! [K: rat] :
% 0.35/0.61 ( A
% 0.35/0.61 != ( times_times_rat @ B @ K ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdE
% 0.35/0.61 thf(fact_5267_dvdE,axiom,
% 0.35/0.61 ! [B: nat,A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.61 => ~ ! [K: nat] :
% 0.35/0.61 ( A
% 0.35/0.61 != ( times_times_nat @ B @ K ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdE
% 0.35/0.61 thf(fact_5268_dvdE,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ B @ A )
% 0.35/0.61 => ~ ! [K: int] :
% 0.35/0.61 ( A
% 0.35/0.61 != ( times_times_int @ B @ K ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdE
% 0.35/0.61 thf(fact_5269_dvdI,axiom,
% 0.35/0.61 ! [A: real,B: real,K2: real] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( times_times_real @ B @ K2 ) )
% 0.35/0.61 => ( dvd_dvd_real @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdI
% 0.35/0.61 thf(fact_5270_dvdI,axiom,
% 0.35/0.61 ! [A: rat,B: rat,K2: rat] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( times_times_rat @ B @ K2 ) )
% 0.35/0.61 => ( dvd_dvd_rat @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdI
% 0.35/0.61 thf(fact_5271_dvdI,axiom,
% 0.35/0.61 ! [A: nat,B: nat,K2: nat] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( times_times_nat @ B @ K2 ) )
% 0.35/0.61 => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdI
% 0.35/0.61 thf(fact_5272_dvdI,axiom,
% 0.35/0.61 ! [A: int,B: int,K2: int] :
% 0.35/0.61 ( ( A
% 0.35/0.61 = ( times_times_int @ B @ K2 ) )
% 0.35/0.61 => ( dvd_dvd_int @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvdI
% 0.35/0.61 thf(fact_5273_dvd__def,axiom,
% 0.35/0.61 ( dvd_dvd_real
% 0.35/0.61 = ( ^ [B4: real,A5: real] :
% 0.35/0.61 ? [K3: real] :
% 0.35/0.61 ( A5
% 0.35/0.61 = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_def
% 0.35/0.61 thf(fact_5274_dvd__def,axiom,
% 0.35/0.61 ( dvd_dvd_rat
% 0.35/0.61 = ( ^ [B4: rat,A5: rat] :
% 0.35/0.61 ? [K3: rat] :
% 0.35/0.61 ( A5
% 0.35/0.61 = ( times_times_rat @ B4 @ K3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_def
% 0.35/0.61 thf(fact_5275_dvd__def,axiom,
% 0.35/0.61 ( dvd_dvd_nat
% 0.35/0.61 = ( ^ [B4: nat,A5: nat] :
% 0.35/0.61 ? [K3: nat] :
% 0.35/0.61 ( A5
% 0.35/0.61 = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_def
% 0.35/0.61 thf(fact_5276_dvd__def,axiom,
% 0.35/0.61 ( dvd_dvd_int
% 0.35/0.61 = ( ^ [B4: int,A5: int] :
% 0.35/0.61 ? [K3: int] :
% 0.35/0.61 ( A5
% 0.35/0.61 = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_def
% 0.35/0.61 thf(fact_5277_dvd__mult,axiom,
% 0.35/0.61 ! [A: real,C2: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult
% 0.35/0.61 thf(fact_5278_dvd__mult,axiom,
% 0.35/0.61 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult
% 0.35/0.61 thf(fact_5279_dvd__mult,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult
% 0.35/0.61 thf(fact_5280_dvd__mult,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult
% 0.35/0.61 thf(fact_5281_dvd__mult2,axiom,
% 0.35/0.61 ! [A: real,B: real,C2: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ B )
% 0.35/0.61 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult2
% 0.35/0.61 thf(fact_5282_dvd__mult2,axiom,
% 0.35/0.61 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ B )
% 0.35/0.61 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult2
% 0.35/0.61 thf(fact_5283_dvd__mult2,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult2
% 0.35/0.61 thf(fact_5284_dvd__mult2,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult2
% 0.35/0.61 thf(fact_5285_dvd__mult__left,axiom,
% 0.35/0.61 ! [A: real,B: real,C2: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_real @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_left
% 0.35/0.61 thf(fact_5286_dvd__mult__left,axiom,
% 0.35/0.61 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_rat @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_left
% 0.35/0.61 thf(fact_5287_dvd__mult__left,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_nat @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_left
% 0.35/0.61 thf(fact_5288_dvd__mult__left,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_int @ A @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_left
% 0.35/0.61 thf(fact_5289_dvd__triv__left,axiom,
% 0.35/0.61 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_left
% 0.35/0.61 thf(fact_5290_dvd__triv__left,axiom,
% 0.35/0.61 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_left
% 0.35/0.61 thf(fact_5291_dvd__triv__left,axiom,
% 0.35/0.61 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_left
% 0.35/0.61 thf(fact_5292_dvd__triv__left,axiom,
% 0.35/0.61 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_left
% 0.35/0.61 thf(fact_5293_mult__dvd__mono,axiom,
% 0.35/0.61 ! [A: real,B: real,C2: real,D: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_real @ C2 @ D )
% 0.35/0.61 => ( dvd_dvd_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_dvd_mono
% 0.35/0.61 thf(fact_5294_mult__dvd__mono,axiom,
% 0.35/0.61 ! [A: rat,B: rat,C2: rat,D: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_rat @ C2 @ D )
% 0.35/0.61 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_dvd_mono
% 0.35/0.61 thf(fact_5295_mult__dvd__mono,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat,D: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ C2 @ D )
% 0.35/0.61 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_dvd_mono
% 0.35/0.61 thf(fact_5296_mult__dvd__mono,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int,D: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ D )
% 0.35/0.61 => ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % mult_dvd_mono
% 0.35/0.61 thf(fact_5297_dvd__mult__right,axiom,
% 0.35/0.61 ! [A: real,B: real,C2: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_real @ B @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_right
% 0.35/0.61 thf(fact_5298_dvd__mult__right,axiom,
% 0.35/0.61 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_rat @ B @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_right
% 0.35/0.61 thf(fact_5299_dvd__mult__right,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_nat @ B @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_right
% 0.35/0.61 thf(fact_5300_dvd__mult__right,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.35/0.61 => ( dvd_dvd_int @ B @ C2 ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mult_right
% 0.35/0.61 thf(fact_5301_dvd__triv__right,axiom,
% 0.35/0.61 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_right
% 0.35/0.61 thf(fact_5302_dvd__triv__right,axiom,
% 0.35/0.61 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_right
% 0.35/0.61 thf(fact_5303_dvd__triv__right,axiom,
% 0.35/0.61 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_right
% 0.35/0.61 thf(fact_5304_dvd__triv__right,axiom,
% 0.35/0.61 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_triv_right
% 0.35/0.61 thf(fact_5305_dvd__add__right__iff,axiom,
% 0.35/0.61 ! [A: real,B: real,C2: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_real @ A @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_right_iff
% 0.35/0.61 thf(fact_5306_dvd__add__right__iff,axiom,
% 0.35/0.61 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_rat @ A @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_right_iff
% 0.35/0.61 thf(fact_5307_dvd__add__right__iff,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_right_iff
% 0.35/0.61 thf(fact_5308_dvd__add__right__iff,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_right_iff
% 0.35/0.61 thf(fact_5309_dvd__add__left__iff,axiom,
% 0.35/0.61 ! [A: real,C2: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ C2 )
% 0.35/0.61 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_left_iff
% 0.35/0.61 thf(fact_5310_dvd__add__left__iff,axiom,
% 0.35/0.61 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ C2 )
% 0.35/0.61 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_left_iff
% 0.35/0.61 thf(fact_5311_dvd__add__left__iff,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ C2 )
% 0.35/0.61 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_left_iff
% 0.35/0.61 thf(fact_5312_dvd__add__left__iff,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ C2 )
% 0.35/0.61 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add_left_iff
% 0.35/0.61 thf(fact_5313_dvd__add,axiom,
% 0.35/0.61 ! [A: real,B: real,C2: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_real @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add
% 0.35/0.61 thf(fact_5314_dvd__add,axiom,
% 0.35/0.61 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_rat @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add
% 0.35/0.61 thf(fact_5315_dvd__add,axiom,
% 0.35/0.61 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add
% 0.35/0.61 thf(fact_5316_dvd__add,axiom,
% 0.35/0.61 ! [A: int,B: int,C2: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ A @ C2 )
% 0.35/0.61 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_add
% 0.35/0.61 thf(fact_5317_dvd__unit__imp__unit,axiom,
% 0.35/0.61 ! [A: code_integer,B: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.61 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_unit_imp_unit
% 0.35/0.61 thf(fact_5318_dvd__unit__imp__unit,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.61 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_unit_imp_unit
% 0.35/0.61 thf(fact_5319_dvd__unit__imp__unit,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ A @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.61 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_unit_imp_unit
% 0.35/0.61 thf(fact_5320_unit__imp__dvd,axiom,
% 0.35/0.61 ! [B: code_integer,A: code_integer] :
% 0.35/0.61 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.61 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_imp_dvd
% 0.35/0.61 thf(fact_5321_unit__imp__dvd,axiom,
% 0.35/0.61 ! [B: nat,A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.61 => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_imp_dvd
% 0.35/0.61 thf(fact_5322_unit__imp__dvd,axiom,
% 0.35/0.61 ! [B: int,A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.61 => ( dvd_dvd_int @ B @ A ) ) ).
% 0.35/0.61
% 0.35/0.61 % unit_imp_dvd
% 0.35/0.61 thf(fact_5323_one__dvd,axiom,
% 0.35/0.61 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 0.35/0.61
% 0.35/0.61 % one_dvd
% 0.35/0.61 thf(fact_5324_one__dvd,axiom,
% 0.35/0.61 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 0.35/0.61
% 0.35/0.61 % one_dvd
% 0.35/0.61 thf(fact_5325_one__dvd,axiom,
% 0.35/0.61 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 0.35/0.61
% 0.35/0.61 % one_dvd
% 0.35/0.61 thf(fact_5326_one__dvd,axiom,
% 0.35/0.61 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.35/0.61
% 0.35/0.61 % one_dvd
% 0.35/0.61 thf(fact_5327_one__dvd,axiom,
% 0.35/0.61 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 0.35/0.61
% 0.35/0.61 % one_dvd
% 0.35/0.61 thf(fact_5328_dvd__diff,axiom,
% 0.35/0.61 ! [X: rat,Y: rat,Z3: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ X @ Y )
% 0.35/0.61 => ( ( dvd_dvd_rat @ X @ Z3 )
% 0.35/0.61 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_diff
% 0.35/0.61 thf(fact_5329_dvd__diff,axiom,
% 0.35/0.61 ! [X: int,Y: int,Z3: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ X @ Y )
% 0.35/0.61 => ( ( dvd_dvd_int @ X @ Z3 )
% 0.35/0.61 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z3 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_diff
% 0.35/0.61 thf(fact_5330_div__div__div__same,axiom,
% 0.35/0.61 ! [D: nat,B: nat,A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ D @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.61 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 0.35/0.61 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_div_div_same
% 0.35/0.61 thf(fact_5331_div__div__div__same,axiom,
% 0.35/0.61 ! [D: int,B: int,A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ D @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.61 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 0.35/0.61 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % div_div_div_same
% 0.35/0.61 thf(fact_5332_dvd__div__eq__cancel,axiom,
% 0.35/0.61 ! [A: complex,C2: complex,B: complex] :
% 0.35/0.61 ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 0.35/0.61 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.61 => ( ( dvd_dvd_complex @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_complex @ C2 @ B )
% 0.35/0.61 => ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_cancel
% 0.35/0.61 thf(fact_5333_dvd__div__eq__cancel,axiom,
% 0.35/0.61 ! [A: real,C2: real,B: real] :
% 0.35/0.61 ( ( ( divide_divide_real @ A @ C2 )
% 0.35/0.61 = ( divide_divide_real @ B @ C2 ) )
% 0.35/0.61 => ( ( dvd_dvd_real @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_real @ C2 @ B )
% 0.35/0.61 => ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_cancel
% 0.35/0.61 thf(fact_5334_dvd__div__eq__cancel,axiom,
% 0.35/0.61 ! [A: rat,C2: rat,B: rat] :
% 0.35/0.61 ( ( ( divide_divide_rat @ A @ C2 )
% 0.35/0.61 = ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.61 => ( ( dvd_dvd_rat @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_rat @ C2 @ B )
% 0.35/0.61 => ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_cancel
% 0.35/0.61 thf(fact_5335_dvd__div__eq__cancel,axiom,
% 0.35/0.61 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.61 ( ( ( divide_divide_nat @ A @ C2 )
% 0.35/0.61 = ( divide_divide_nat @ B @ C2 ) )
% 0.35/0.61 => ( ( dvd_dvd_nat @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.61 => ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_cancel
% 0.35/0.61 thf(fact_5336_dvd__div__eq__cancel,axiom,
% 0.35/0.61 ! [A: int,C2: int,B: int] :
% 0.35/0.61 ( ( ( divide_divide_int @ A @ C2 )
% 0.35/0.61 = ( divide_divide_int @ B @ C2 ) )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.61 => ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_cancel
% 0.35/0.61 thf(fact_5337_dvd__div__eq__iff,axiom,
% 0.35/0.61 ! [C2: complex,A: complex,B: complex] :
% 0.35/0.61 ( ( dvd_dvd_complex @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_complex @ C2 @ B )
% 0.35/0.61 => ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 0.35/0.61 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.61 = ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_iff
% 0.35/0.61 thf(fact_5338_dvd__div__eq__iff,axiom,
% 0.35/0.61 ! [C2: real,A: real,B: real] :
% 0.35/0.61 ( ( dvd_dvd_real @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_real @ C2 @ B )
% 0.35/0.61 => ( ( ( divide_divide_real @ A @ C2 )
% 0.35/0.61 = ( divide_divide_real @ B @ C2 ) )
% 0.35/0.61 = ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_iff
% 0.35/0.61 thf(fact_5339_dvd__div__eq__iff,axiom,
% 0.35/0.61 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.61 ( ( dvd_dvd_rat @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_rat @ C2 @ B )
% 0.35/0.61 => ( ( ( divide_divide_rat @ A @ C2 )
% 0.35/0.61 = ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.61 = ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_iff
% 0.35/0.61 thf(fact_5340_dvd__div__eq__iff,axiom,
% 0.35/0.61 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.61 => ( ( ( divide_divide_nat @ A @ C2 )
% 0.35/0.61 = ( divide_divide_nat @ B @ C2 ) )
% 0.35/0.61 = ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_iff
% 0.35/0.61 thf(fact_5341_dvd__div__eq__iff,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ C2 @ A )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.61 => ( ( ( divide_divide_int @ A @ C2 )
% 0.35/0.61 = ( divide_divide_int @ B @ C2 ) )
% 0.35/0.61 = ( A = B ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_div_eq_iff
% 0.35/0.61 thf(fact_5342_gcd__nat_Oextremum,axiom,
% 0.35/0.61 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.35/0.61
% 0.35/0.61 % gcd_nat.extremum
% 0.35/0.61 thf(fact_5343_gcd__nat_Oextremum__strict,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.35/0.61 & ( zero_zero_nat != A ) ) ).
% 0.35/0.61
% 0.35/0.61 % gcd_nat.extremum_strict
% 0.35/0.61 thf(fact_5344_gcd__nat_Oextremum__unique,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.35/0.61 = ( A = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % gcd_nat.extremum_unique
% 0.35/0.61 thf(fact_5345_gcd__nat_Onot__eq__extremum,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( A != zero_zero_nat )
% 0.35/0.61 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 0.35/0.61 & ( A != zero_zero_nat ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % gcd_nat.not_eq_extremum
% 0.35/0.61 thf(fact_5346_gcd__nat_Oextremum__uniqueI,axiom,
% 0.35/0.61 ! [A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.35/0.61 => ( A = zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % gcd_nat.extremum_uniqueI
% 0.35/0.61 thf(fact_5347_dvd__mod__imp__dvd,axiom,
% 0.35/0.61 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 => ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.61 => ( dvd_dvd_nat @ C2 @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mod_imp_dvd
% 0.35/0.61 thf(fact_5348_dvd__mod__imp__dvd,axiom,
% 0.35/0.61 ! [C2: int,A: int,B: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.61 => ( dvd_dvd_int @ C2 @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mod_imp_dvd
% 0.35/0.61 thf(fact_5349_dvd__mod__imp__dvd,axiom,
% 0.35/0.61 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 0.35/0.61 ( ( dvd_dvd_Code_natural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.35/0.61 => ( ( dvd_dvd_Code_natural @ C2 @ B )
% 0.35/0.61 => ( dvd_dvd_Code_natural @ C2 @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mod_imp_dvd
% 0.35/0.61 thf(fact_5350_dvd__mod__iff,axiom,
% 0.35/0.61 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.61 => ( ( dvd_dvd_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 0.35/0.61 = ( dvd_dvd_nat @ C2 @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mod_iff
% 0.35/0.61 thf(fact_5351_dvd__mod__iff,axiom,
% 0.35/0.61 ! [C2: int,B: int,A: int] :
% 0.35/0.61 ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.61 => ( ( dvd_dvd_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 0.35/0.61 = ( dvd_dvd_int @ C2 @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mod_iff
% 0.35/0.61 thf(fact_5352_dvd__mod__iff,axiom,
% 0.35/0.61 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 0.35/0.61 ( ( dvd_dvd_Code_natural @ C2 @ B )
% 0.35/0.61 => ( ( dvd_dvd_Code_natural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 0.35/0.61 = ( dvd_dvd_Code_natural @ C2 @ A ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_mod_iff
% 0.35/0.61 thf(fact_5353_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_complex,F2: complex > real] :
% 0.35/0.61 ( ! [X3: complex] :
% 0.35/0.61 ( ( member_complex @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5354_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_real,F2: real > real] :
% 0.35/0.61 ( ! [X3: real] :
% 0.35/0.61 ( ( member_real @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5355_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_int,F2: int > real] :
% 0.35/0.61 ( ! [X3: int] :
% 0.35/0.61 ( ( member_int @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5356_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_complex,F2: complex > rat] :
% 0.35/0.61 ( ! [X3: complex] :
% 0.35/0.61 ( ( member_complex @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5357_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_real,F2: real > rat] :
% 0.35/0.61 ( ! [X3: real] :
% 0.35/0.61 ( ( member_real @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5358_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_nat,F2: nat > rat] :
% 0.35/0.61 ( ! [X3: nat] :
% 0.35/0.61 ( ( member_nat @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5359_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_int,F2: int > rat] :
% 0.35/0.61 ( ! [X3: int] :
% 0.35/0.61 ( ( member_int @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5360_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_complex,F2: complex > nat] :
% 0.35/0.61 ( ! [X3: complex] :
% 0.35/0.61 ( ( member_complex @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5361_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_real,F2: real > nat] :
% 0.35/0.61 ( ! [X3: real] :
% 0.35/0.61 ( ( member_real @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5362_sum__nonneg,axiom,
% 0.35/0.61 ! [A4: set_int,F2: int > nat] :
% 0.35/0.61 ( ! [X3: int] :
% 0.35/0.61 ( ( member_int @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonneg
% 0.35/0.61 thf(fact_5363_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_complex,F2: complex > real] :
% 0.35/0.61 ( ! [X3: complex] :
% 0.35/0.61 ( ( member_complex @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 0.35/0.61 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5364_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_real,F2: real > real] :
% 0.35/0.61 ( ! [X3: real] :
% 0.35/0.61 ( ( member_real @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 0.35/0.61 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5365_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_int,F2: int > real] :
% 0.35/0.61 ( ! [X3: int] :
% 0.35/0.61 ( ( member_int @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 0.35/0.61 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5366_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_complex,F2: complex > rat] :
% 0.35/0.61 ( ! [X3: complex] :
% 0.35/0.61 ( ( member_complex @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5367_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_real,F2: real > rat] :
% 0.35/0.61 ( ! [X3: real] :
% 0.35/0.61 ( ( member_real @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5368_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_nat,F2: nat > rat] :
% 0.35/0.61 ( ! [X3: nat] :
% 0.35/0.61 ( ( member_nat @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5369_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_int,F2: int > rat] :
% 0.35/0.61 ( ! [X3: int] :
% 0.35/0.61 ( ( member_int @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 0.35/0.61 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5370_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_complex,F2: complex > nat] :
% 0.35/0.61 ( ! [X3: complex] :
% 0.35/0.61 ( ( member_complex @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 0.35/0.61 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5371_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_real,F2: real > nat] :
% 0.35/0.61 ( ! [X3: real] :
% 0.35/0.61 ( ( member_real @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 0.35/0.61 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5372_sum__nonpos,axiom,
% 0.35/0.61 ! [A4: set_int,F2: int > nat] :
% 0.35/0.61 ( ! [X3: int] :
% 0.35/0.61 ( ( member_int @ X3 @ A4 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 0.35/0.61 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_nonpos
% 0.35/0.61 thf(fact_5373_dvd__diff__nat,axiom,
% 0.35/0.61 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.61 ( ( dvd_dvd_nat @ K2 @ M2 )
% 0.35/0.61 => ( ( dvd_dvd_nat @ K2 @ N )
% 0.35/0.61 => ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % dvd_diff_nat
% 0.35/0.61 thf(fact_5374_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: real > rat,I5: set_real,G2: real > rat,I2: real] :
% 0.35/0.61 ( ( ( groups1300246762558778688al_rat @ F2 @ I5 )
% 0.35/0.61 = ( groups1300246762558778688al_rat @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: real] :
% 0.35/0.61 ( ( member_real @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_real @ I2 @ I5 )
% 0.35/0.61 => ( ( finite_finite_real @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5375_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: nat > rat,I5: set_nat,G2: nat > rat,I2: nat] :
% 0.35/0.61 ( ( ( groups2906978787729119204at_rat @ F2 @ I5 )
% 0.35/0.61 = ( groups2906978787729119204at_rat @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: nat] :
% 0.35/0.61 ( ( member_nat @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_nat @ I2 @ I5 )
% 0.35/0.61 => ( ( finite_finite_nat @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5376_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: int > rat,I5: set_int,G2: int > rat,I2: int] :
% 0.35/0.61 ( ( ( groups3906332499630173760nt_rat @ F2 @ I5 )
% 0.35/0.61 = ( groups3906332499630173760nt_rat @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: int] :
% 0.35/0.61 ( ( member_int @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_int @ I2 @ I5 )
% 0.35/0.61 => ( ( finite_finite_int @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5377_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: complex > rat,I5: set_complex,G2: complex > rat,I2: complex] :
% 0.35/0.61 ( ( ( groups5058264527183730370ex_rat @ F2 @ I5 )
% 0.35/0.61 = ( groups5058264527183730370ex_rat @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: complex] :
% 0.35/0.61 ( ( member_complex @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.61 => ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5378_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: real > nat,I5: set_real,G2: real > nat,I2: real] :
% 0.35/0.61 ( ( ( groups1935376822645274424al_nat @ F2 @ I5 )
% 0.35/0.61 = ( groups1935376822645274424al_nat @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: real] :
% 0.35/0.61 ( ( member_real @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_real @ I2 @ I5 )
% 0.35/0.61 => ( ( finite_finite_real @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5379_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: int > nat,I5: set_int,G2: int > nat,I2: int] :
% 0.35/0.61 ( ( ( groups4541462559716669496nt_nat @ F2 @ I5 )
% 0.35/0.61 = ( groups4541462559716669496nt_nat @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: int] :
% 0.35/0.61 ( ( member_int @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_int @ I2 @ I5 )
% 0.35/0.61 => ( ( finite_finite_int @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5380_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: complex > nat,I5: set_complex,G2: complex > nat,I2: complex] :
% 0.35/0.61 ( ( ( groups5693394587270226106ex_nat @ F2 @ I5 )
% 0.35/0.61 = ( groups5693394587270226106ex_nat @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: complex] :
% 0.35/0.61 ( ( member_complex @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.61 => ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5381_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: real > int,I5: set_real,G2: real > int,I2: real] :
% 0.35/0.61 ( ( ( groups1932886352136224148al_int @ F2 @ I5 )
% 0.35/0.61 = ( groups1932886352136224148al_int @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: real] :
% 0.35/0.61 ( ( member_real @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_real @ I2 @ I5 )
% 0.35/0.61 => ( ( finite_finite_real @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5382_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: nat > int,I5: set_nat,G2: nat > int,I2: nat] :
% 0.35/0.61 ( ( ( groups3539618377306564664at_int @ F2 @ I5 )
% 0.35/0.61 = ( groups3539618377306564664at_int @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: nat] :
% 0.35/0.61 ( ( member_nat @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_nat @ I2 @ I5 )
% 0.35/0.61 => ( ( finite_finite_nat @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5383_sum__mono__inv,axiom,
% 0.35/0.61 ! [F2: complex > int,I5: set_complex,G2: complex > int,I2: complex] :
% 0.35/0.61 ( ( ( groups5690904116761175830ex_int @ F2 @ I5 )
% 0.35/0.61 = ( groups5690904116761175830ex_int @ G2 @ I5 ) )
% 0.35/0.61 => ( ! [I3: complex] :
% 0.35/0.61 ( ( member_complex @ I3 @ I5 )
% 0.35/0.61 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 0.35/0.61 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.61 => ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.61 => ( ( F2 @ I2 )
% 0.35/0.61 = ( G2 @ I2 ) ) ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_mono_inv
% 0.35/0.61 thf(fact_5384_sum__cong__Suc,axiom,
% 0.35/0.61 ! [A4: set_nat,F2: nat > nat,G2: nat > nat] :
% 0.35/0.61 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 0.35/0.61 => ( ! [X3: nat] :
% 0.35/0.61 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 0.35/0.61 => ( ( F2 @ ( suc @ X3 ) )
% 0.35/0.61 = ( G2 @ ( suc @ X3 ) ) ) )
% 0.35/0.61 => ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 0.35/0.61 = ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_cong_Suc
% 0.35/0.61 thf(fact_5385_sum__cong__Suc,axiom,
% 0.35/0.61 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 0.35/0.61 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 0.35/0.61 => ( ! [X3: nat] :
% 0.35/0.61 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 0.35/0.61 => ( ( F2 @ ( suc @ X3 ) )
% 0.35/0.61 = ( G2 @ ( suc @ X3 ) ) ) )
% 0.35/0.61 => ( ( groups6591440286371151544t_real @ F2 @ A4 )
% 0.35/0.61 = ( groups6591440286371151544t_real @ G2 @ A4 ) ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum_cong_Suc
% 0.35/0.61 thf(fact_5386_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_real,G2: real > complex,P2: real > $o] :
% 0.35/0.61 ( ( finite_finite_real @ A4 )
% 0.35/0.61 => ( ( groups5754745047067104278omplex @ G2
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [X4: real] :
% 0.35/0.61 ( ( member_real @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups5754745047067104278omplex
% 0.35/0.61 @ ^ [X4: real] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5387_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_nat,G2: nat > complex,P2: nat > $o] :
% 0.35/0.61 ( ( finite_finite_nat @ A4 )
% 0.35/0.61 => ( ( groups2073611262835488442omplex @ G2
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [X4: nat] :
% 0.35/0.61 ( ( member_nat @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups2073611262835488442omplex
% 0.35/0.61 @ ^ [X4: nat] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5388_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > complex,P2: int > $o] :
% 0.35/0.61 ( ( finite_finite_int @ A4 )
% 0.35/0.61 => ( ( groups3049146728041665814omplex @ G2
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [X4: int] :
% 0.35/0.61 ( ( member_int @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups3049146728041665814omplex
% 0.35/0.61 @ ^ [X4: int] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5389_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_complex,G2: complex > complex,P2: complex > $o] :
% 0.35/0.61 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.61 => ( ( groups7754918857620584856omplex @ G2
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [X4: complex] :
% 0.35/0.61 ( ( member_complex @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups7754918857620584856omplex
% 0.35/0.61 @ ^ [X4: complex] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5390_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_real,G2: real > real,P2: real > $o] :
% 0.35/0.61 ( ( finite_finite_real @ A4 )
% 0.35/0.61 => ( ( groups8097168146408367636l_real @ G2
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [X4: real] :
% 0.35/0.61 ( ( member_real @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups8097168146408367636l_real
% 0.35/0.61 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5391_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > real,P2: int > $o] :
% 0.35/0.61 ( ( finite_finite_int @ A4 )
% 0.35/0.61 => ( ( groups8778361861064173332t_real @ G2
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [X4: int] :
% 0.35/0.61 ( ( member_int @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups8778361861064173332t_real
% 0.35/0.61 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5392_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_complex,G2: complex > real,P2: complex > $o] :
% 0.35/0.61 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.61 => ( ( groups5808333547571424918x_real @ G2
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [X4: complex] :
% 0.35/0.61 ( ( member_complex @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups5808333547571424918x_real
% 0.35/0.61 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5393_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_real,G2: real > rat,P2: real > $o] :
% 0.35/0.61 ( ( finite_finite_real @ A4 )
% 0.35/0.61 => ( ( groups1300246762558778688al_rat @ G2
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [X4: real] :
% 0.35/0.61 ( ( member_real @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups1300246762558778688al_rat
% 0.35/0.61 @ ^ [X4: real] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5394_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_nat,G2: nat > rat,P2: nat > $o] :
% 0.35/0.61 ( ( finite_finite_nat @ A4 )
% 0.35/0.61 => ( ( groups2906978787729119204at_rat @ G2
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [X4: nat] :
% 0.35/0.61 ( ( member_nat @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups2906978787729119204at_rat
% 0.35/0.61 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5395_sum_Ointer__filter,axiom,
% 0.35/0.61 ! [A4: set_int,G2: int > rat,P2: int > $o] :
% 0.35/0.61 ( ( finite_finite_int @ A4 )
% 0.35/0.61 => ( ( groups3906332499630173760nt_rat @ G2
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [X4: int] :
% 0.35/0.61 ( ( member_int @ X4 @ A4 )
% 0.35/0.61 & ( P2 @ X4 ) ) ) )
% 0.35/0.61 = ( groups3906332499630173760nt_rat
% 0.35/0.61 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 0.35/0.61 @ A4 ) ) ) ).
% 0.35/0.61
% 0.35/0.61 % sum.inter_filter
% 0.35/0.61 thf(fact_5396_subset__divisors__dvd,axiom,
% 0.35/0.61 ! [A: complex,B: complex] :
% 0.35/0.61 ( ( ord_le211207098394363844omplex
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 0.35/0.61 @ ( collect_complex
% 0.35/0.61 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 0.35/0.61 = ( dvd_dvd_complex @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % subset_divisors_dvd
% 0.35/0.61 thf(fact_5397_subset__divisors__dvd,axiom,
% 0.35/0.61 ! [A: real,B: real] :
% 0.35/0.61 ( ( ord_less_eq_set_real
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 0.35/0.61 @ ( collect_real
% 0.35/0.61 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 0.35/0.61 = ( dvd_dvd_real @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % subset_divisors_dvd
% 0.35/0.61 thf(fact_5398_subset__divisors__dvd,axiom,
% 0.35/0.61 ! [A: int,B: int] :
% 0.35/0.61 ( ( ord_less_eq_set_int
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 0.35/0.61 @ ( collect_int
% 0.35/0.61 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 0.35/0.61 = ( dvd_dvd_int @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % subset_divisors_dvd
% 0.35/0.61 thf(fact_5399_subset__divisors__dvd,axiom,
% 0.35/0.61 ! [A: nat,B: nat] :
% 0.35/0.61 ( ( ord_less_eq_set_nat
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 0.35/0.61 @ ( collect_nat
% 0.35/0.61 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 0.35/0.61 = ( dvd_dvd_nat @ A @ B ) ) ).
% 0.35/0.61
% 0.35/0.61 % subset_divisors_dvd
% 0.35/0.61 thf(fact_5400_strict__subset__divisors__dvd,axiom,
% 0.35/0.61 ! [A: complex,B: complex] :
% 0.35/0.61 ( ( ord_less_set_complex
% 0.35/0.62 @ ( collect_complex
% 0.35/0.62 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 0.35/0.62 @ ( collect_complex
% 0.35/0.62 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 0.35/0.62 = ( ( dvd_dvd_complex @ A @ B )
% 0.35/0.62 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % strict_subset_divisors_dvd
% 0.35/0.62 thf(fact_5401_strict__subset__divisors__dvd,axiom,
% 0.35/0.62 ! [A: real,B: real] :
% 0.35/0.62 ( ( ord_less_set_real
% 0.35/0.62 @ ( collect_real
% 0.35/0.62 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 0.35/0.62 @ ( collect_real
% 0.35/0.62 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 0.35/0.62 = ( ( dvd_dvd_real @ A @ B )
% 0.35/0.62 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % strict_subset_divisors_dvd
% 0.35/0.62 thf(fact_5402_strict__subset__divisors__dvd,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( ord_less_set_nat
% 0.35/0.62 @ ( collect_nat
% 0.35/0.62 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 0.35/0.62 @ ( collect_nat
% 0.35/0.62 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 0.35/0.62 = ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.62 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % strict_subset_divisors_dvd
% 0.35/0.62 thf(fact_5403_strict__subset__divisors__dvd,axiom,
% 0.35/0.62 ! [A: int,B: int] :
% 0.35/0.62 ( ( ord_less_set_int
% 0.35/0.62 @ ( collect_int
% 0.35/0.62 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 0.35/0.62 @ ( collect_int
% 0.35/0.62 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 0.35/0.62 = ( ( dvd_dvd_int @ A @ B )
% 0.35/0.62 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % strict_subset_divisors_dvd
% 0.35/0.62 thf(fact_5404_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_int,T: set_int,G2: int > real,I2: int > int,F2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ( finite_finite_int @ T )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: int] :
% 0.35/0.62 ( ( member_int @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ S2 ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5405_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_int,T: set_complex,G2: complex > real,I2: complex > int,F2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: complex] :
% 0.35/0.62 ( ( member_complex @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ S2 ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5406_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_complex,T: set_int,G2: int > real,I2: int > complex,F2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ( finite_finite_int @ T )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: int] :
% 0.35/0.62 ( ( member_int @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ S2 ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5407_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_complex,T: set_complex,G2: complex > real,I2: complex > complex,F2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: complex] :
% 0.35/0.62 ( ( member_complex @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ S2 ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5408_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_nat,T: set_nat,G2: nat > rat,I2: nat > nat,F2: nat > rat] :
% 0.35/0.62 ( ( finite_finite_nat @ S2 )
% 0.35/0.62 => ( ( finite_finite_nat @ T )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: nat] :
% 0.35/0.62 ( ( member_nat @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups2906978787729119204at_rat @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5409_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_nat,T: set_int,G2: int > rat,I2: int > nat,F2: nat > rat] :
% 0.35/0.62 ( ( finite_finite_nat @ S2 )
% 0.35/0.62 => ( ( finite_finite_int @ T )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: int] :
% 0.35/0.62 ( ( member_int @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5410_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_nat,T: set_complex,G2: complex > rat,I2: complex > nat,F2: nat > rat] :
% 0.35/0.62 ( ( finite_finite_nat @ S2 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: complex] :
% 0.35/0.62 ( ( member_complex @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5411_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_int,T: set_nat,G2: nat > rat,I2: nat > int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ( finite_finite_nat @ T )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: nat] :
% 0.35/0.62 ( ( member_nat @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups2906978787729119204at_rat @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5412_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_int,T: set_int,G2: int > rat,I2: int > int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ( finite_finite_int @ T )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: int] :
% 0.35/0.62 ( ( member_int @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5413_sum__le__included,axiom,
% 0.35/0.62 ! [S2: set_int,T: set_complex,G2: complex > rat,I2: complex > int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ T )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ T )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S2 )
% 0.35/0.62 => ? [Xa: complex] :
% 0.35/0.62 ( ( member_complex @ Xa @ T )
% 0.35/0.62 & ( ( I2 @ Xa )
% 0.35/0.62 = X3 )
% 0.35/0.62 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G2 @ T ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_le_included
% 0.35/0.62 thf(fact_5414_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups8097168146408367636l_real @ F2 @ A4 )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 = ( ! [X4: real] :
% 0.35/0.62 ( ( member_real @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5415_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups8778361861064173332t_real @ F2 @ A4 )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 = ( ! [X4: int] :
% 0.35/0.62 ( ( member_int @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5416_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups5808333547571424918x_real @ F2 @ A4 )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 = ( ! [X4: complex] :
% 0.35/0.62 ( ( member_complex @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5417_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups1300246762558778688al_rat @ F2 @ A4 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 = ( ! [X4: real] :
% 0.35/0.62 ( ( member_real @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5418_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > rat] :
% 0.35/0.62 ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups2906978787729119204at_rat @ F2 @ A4 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 = ( ! [X4: nat] :
% 0.35/0.62 ( ( member_nat @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5419_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups3906332499630173760nt_rat @ F2 @ A4 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 = ( ! [X4: int] :
% 0.35/0.62 ( ( member_int @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5420_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups5058264527183730370ex_rat @ F2 @ A4 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 = ( ! [X4: complex] :
% 0.35/0.62 ( ( member_complex @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5421_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups1935376822645274424al_nat @ F2 @ A4 )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 = ( ! [X4: real] :
% 0.35/0.62 ( ( member_real @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5422_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 = ( ! [X4: int] :
% 0.35/0.62 ( ( member_int @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5423_sum__nonneg__eq__0__iff,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 = ( ! [X4: complex] :
% 0.35/0.62 ( ( member_complex @ X4 @ A4 )
% 0.35/0.62 => ( ( F2 @ X4 )
% 0.35/0.62 = zero_zero_nat ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_eq_0_iff
% 0.35/0.62 thf(fact_5424_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > real,G2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: int] :
% 0.35/0.62 ( ( member_int @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_real @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5425_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: complex] :
% 0.35/0.62 ( ( member_complex @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_real @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5426_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 0.35/0.62 ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: nat] :
% 0.35/0.62 ( ( member_nat @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( groups2906978787729119204at_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5427_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: int] :
% 0.35/0.62 ( ( member_int @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5428_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: complex] :
% 0.35/0.62 ( ( member_complex @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5429_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > nat,G2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: int] :
% 0.35/0.62 ( ( member_int @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5430_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: complex] :
% 0.35/0.62 ( ( member_complex @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5431_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > int,G2: nat > int] :
% 0.35/0.62 ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: nat] :
% 0.35/0.62 ( ( member_nat @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_int @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A4 ) @ ( groups3539618377306564664at_int @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5432_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > int,G2: complex > int] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: complex] :
% 0.35/0.62 ( ( member_complex @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_int @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F2 @ A4 ) @ ( groups5690904116761175830ex_int @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5433_sum__strict__mono__ex1,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > nat,G2: nat > nat] :
% 0.35/0.62 ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( ? [X5: nat] :
% 0.35/0.62 ( ( member_nat @ X5 @ A4 )
% 0.35/0.62 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 0.35/0.62 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono_ex1
% 0.35/0.62 thf(fact_5434_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: complex > complex > $o,S3: set_nat,H: nat > complex,G2: nat > complex] :
% 0.35/0.62 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 0.35/0.62 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite_finite_nat @ S3 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups2073611262835488442omplex @ H @ S3 ) @ ( groups2073611262835488442omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5435_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: complex > complex > $o,S3: set_int,H: int > complex,G2: int > complex] :
% 0.35/0.62 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 0.35/0.62 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ S3 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups3049146728041665814omplex @ H @ S3 ) @ ( groups3049146728041665814omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5436_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: complex > complex > $o,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 0.35/0.62 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 0.35/0.62 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups7754918857620584856omplex @ H @ S3 ) @ ( groups7754918857620584856omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5437_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: real > real > $o,S3: set_int,H: int > real,G2: int > real] :
% 0.35/0.62 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 0.35/0.62 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ S3 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups8778361861064173332t_real @ H @ S3 ) @ ( groups8778361861064173332t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5438_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: real > real > $o,S3: set_complex,H: complex > real,G2: complex > real] :
% 0.35/0.62 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 0.35/0.62 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups5808333547571424918x_real @ H @ S3 ) @ ( groups5808333547571424918x_real @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5439_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: rat > rat > $o,S3: set_nat,H: nat > rat,G2: nat > rat] :
% 0.35/0.62 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.35/0.62 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite_finite_nat @ S3 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups2906978787729119204at_rat @ H @ S3 ) @ ( groups2906978787729119204at_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5440_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: rat > rat > $o,S3: set_int,H: int > rat,G2: int > rat] :
% 0.35/0.62 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.35/0.62 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ S3 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups3906332499630173760nt_rat @ H @ S3 ) @ ( groups3906332499630173760nt_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5441_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: rat > rat > $o,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 0.35/0.62 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 0.35/0.62 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups5058264527183730370ex_rat @ H @ S3 ) @ ( groups5058264527183730370ex_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5442_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: nat > nat > $o,S3: set_int,H: int > nat,G2: int > nat] :
% 0.35/0.62 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 0.35/0.62 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ S3 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups4541462559716669496nt_nat @ H @ S3 ) @ ( groups4541462559716669496nt_nat @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5443_sum_Orelated,axiom,
% 0.35/0.62 ! [R2: nat > nat > $o,S3: set_complex,H: complex > nat,G2: complex > nat] :
% 0.35/0.62 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 0.35/0.62 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 0.35/0.62 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.62 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.62 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.62 => ( R2 @ ( groups5693394587270226106ex_nat @ H @ S3 ) @ ( groups5693394587270226106ex_nat @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.related
% 0.35/0.62 thf(fact_5444_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_real,T4: set_real,S3: set_real,I2: real > real,J2: real > real,T5: set_real,G2: real > complex,H: real > complex] :
% 0.35/0.62 ( ( finite_finite_real @ S5 )
% 0.35/0.62 => ( ( finite_finite_real @ T4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5445_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_real,T4: set_int,S3: set_real,I2: int > real,J2: real > int,T5: set_int,G2: real > complex,H: int > complex] :
% 0.35/0.62 ( ( finite_finite_real @ S5 )
% 0.35/0.62 => ( ( finite_finite_int @ T4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.35/0.62 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5446_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_real,T4: set_complex,S3: set_real,I2: complex > real,J2: real > complex,T5: set_complex,G2: real > complex,H: complex > complex] :
% 0.35/0.62 ( ( finite_finite_real @ S5 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.35/0.62 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5447_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_int,T4: set_real,S3: set_int,I2: real > int,J2: int > real,T5: set_real,G2: int > complex,H: real > complex] :
% 0.35/0.62 ( ( finite_finite_int @ S5 )
% 0.35/0.62 => ( ( finite_finite_real @ T4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 0.35/0.62 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5448_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_int,T4: set_int,S3: set_int,I2: int > int,J2: int > int,T5: set_int,G2: int > complex,H: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ S5 )
% 0.35/0.62 => ( ( finite_finite_int @ T4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 0.35/0.62 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.35/0.62 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5449_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_int,T4: set_complex,S3: set_int,I2: complex > int,J2: int > complex,T5: set_complex,G2: int > complex,H: complex > complex] :
% 0.35/0.62 ( ( finite_finite_int @ S5 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 0.35/0.62 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.35/0.62 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5450_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_complex,T4: set_real,S3: set_complex,I2: real > complex,J2: complex > real,T5: set_real,G2: complex > complex,H: real > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S5 )
% 0.35/0.62 => ( ( finite_finite_real @ T4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 0.35/0.62 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5451_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_complex,T4: set_int,S3: set_complex,I2: int > complex,J2: complex > int,T5: set_int,G2: complex > complex,H: int > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S5 )
% 0.35/0.62 => ( ( finite_finite_int @ T4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 0.35/0.62 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 0.35/0.62 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5452_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_complex,T4: set_complex,S3: set_complex,I2: complex > complex,J2: complex > complex,T5: set_complex,G2: complex > complex,H: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S5 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ T4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 0.35/0.62 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 0.35/0.62 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5453_sum_Oreindex__bij__witness__not__neutral,axiom,
% 0.35/0.62 ! [S5: set_real,T4: set_real,S3: set_real,I2: real > real,J2: real > real,T5: set_real,G2: real > real,H: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ S5 )
% 0.35/0.62 => ( ( finite_finite_real @ T4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( ( I2 @ ( J2 @ A3 ) )
% 0.35/0.62 = A3 ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 0.35/0.62 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( ( J2 @ ( I2 @ B3 ) )
% 0.35/0.62 = B3 ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 0.35/0.62 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S5 )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ T4 )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ S3 )
% 0.35/0.62 => ( ( H @ ( J2 @ A3 ) )
% 0.35/0.62 = ( G2 @ A3 ) ) )
% 0.35/0.62 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.reindex_bij_witness_not_neutral
% 0.35/0.62 thf(fact_5454_not__is__unit__0,axiom,
% 0.35/0.62 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 0.35/0.62
% 0.35/0.62 % not_is_unit_0
% 0.35/0.62 thf(fact_5455_not__is__unit__0,axiom,
% 0.35/0.62 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 0.35/0.62
% 0.35/0.62 % not_is_unit_0
% 0.35/0.62 thf(fact_5456_not__is__unit__0,axiom,
% 0.35/0.62 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 0.35/0.62
% 0.35/0.62 % not_is_unit_0
% 0.35/0.62 thf(fact_5457_dvd__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: complex,A: complex] :
% 0.35/0.62 ( ( dvd_dvd_complex @ B @ A )
% 0.35/0.62 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.35/0.62 = zero_zero_complex )
% 0.35/0.62 = ( A = zero_zero_complex ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_eq_0_iff
% 0.35/0.62 thf(fact_5458_dvd__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: real,A: real] :
% 0.35/0.62 ( ( dvd_dvd_real @ B @ A )
% 0.35/0.62 => ( ( ( divide_divide_real @ A @ B )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 = ( A = zero_zero_real ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_eq_0_iff
% 0.35/0.62 thf(fact_5459_dvd__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: rat,A: rat] :
% 0.35/0.62 ( ( dvd_dvd_rat @ B @ A )
% 0.35/0.62 => ( ( ( divide_divide_rat @ A @ B )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 = ( A = zero_zero_rat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_eq_0_iff
% 0.35/0.62 thf(fact_5460_dvd__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.62 => ( ( ( divide_divide_nat @ A @ B )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 = ( A = zero_zero_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_eq_0_iff
% 0.35/0.62 thf(fact_5461_dvd__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ A )
% 0.35/0.62 => ( ( ( divide_divide_int @ A @ B )
% 0.35/0.62 = zero_zero_int )
% 0.35/0.62 = ( A = zero_zero_int ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_eq_0_iff
% 0.35/0.62 thf(fact_5462_unit__mult__right__cancel,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 0.35/0.62 = ( times_3573771949741848930nteger @ C2 @ A ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_mult_right_cancel
% 0.35/0.62 thf(fact_5463_unit__mult__right__cancel,axiom,
% 0.35/0.62 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 => ( ( ( times_times_nat @ B @ A )
% 0.35/0.62 = ( times_times_nat @ C2 @ A ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_mult_right_cancel
% 0.35/0.62 thf(fact_5464_unit__mult__right__cancel,axiom,
% 0.35/0.62 ! [A: int,B: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 => ( ( ( times_times_int @ B @ A )
% 0.35/0.62 = ( times_times_int @ C2 @ A ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_mult_right_cancel
% 0.35/0.62 thf(fact_5465_unit__mult__left__cancel,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 0.35/0.62 = ( times_3573771949741848930nteger @ A @ C2 ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_mult_left_cancel
% 0.35/0.62 thf(fact_5466_unit__mult__left__cancel,axiom,
% 0.35/0.62 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 => ( ( ( times_times_nat @ A @ B )
% 0.35/0.62 = ( times_times_nat @ A @ C2 ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_mult_left_cancel
% 0.35/0.62 thf(fact_5467_unit__mult__left__cancel,axiom,
% 0.35/0.62 ! [A: int,B: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 => ( ( ( times_times_int @ A @ B )
% 0.35/0.62 = ( times_times_int @ A @ C2 ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_mult_left_cancel
% 0.35/0.62 thf(fact_5468_mult__unit__dvd__iff_H,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_Code_integer @ B @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mult_unit_dvd_iff'
% 0.35/0.62 thf(fact_5469_mult__unit__dvd__iff_H,axiom,
% 0.35/0.62 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mult_unit_dvd_iff'
% 0.35/0.62 thf(fact_5470_mult__unit__dvd__iff_H,axiom,
% 0.35/0.62 ! [A: int,B: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mult_unit_dvd_iff'
% 0.35/0.62 thf(fact_5471_dvd__mult__unit__iff_H,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 0.35/0.62 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_unit_iff'
% 0.35/0.62 thf(fact_5472_dvd__mult__unit__iff_H,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.62 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_unit_iff'
% 0.35/0.62 thf(fact_5473_dvd__mult__unit__iff_H,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.62 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_unit_iff'
% 0.35/0.62 thf(fact_5474_mult__unit__dvd__iff,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mult_unit_dvd_iff
% 0.35/0.62 thf(fact_5475_mult__unit__dvd__iff,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mult_unit_dvd_iff
% 0.35/0.62 thf(fact_5476_mult__unit__dvd__iff,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mult_unit_dvd_iff
% 0.35/0.62 thf(fact_5477_dvd__mult__unit__iff,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 0.35/0.62 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_unit_iff
% 0.35/0.62 thf(fact_5478_dvd__mult__unit__iff,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C2 @ B ) )
% 0.35/0.62 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_unit_iff
% 0.35/0.62 thf(fact_5479_dvd__mult__unit__iff,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C2 @ B ) )
% 0.35/0.62 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_unit_iff
% 0.35/0.62 thf(fact_5480_is__unit__mult__iff,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 0.35/0.62 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_mult_iff
% 0.35/0.62 thf(fact_5481_is__unit__mult__iff,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 0.35/0.62 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_mult_iff
% 0.35/0.62 thf(fact_5482_is__unit__mult__iff,axiom,
% 0.35/0.62 ! [A: int,B: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 0.35/0.62 = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_mult_iff
% 0.35/0.62 thf(fact_5483_dvd__div__mult,axiom,
% 0.35/0.62 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.62 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C2 ) @ A )
% 0.35/0.62 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_mult
% 0.35/0.62 thf(fact_5484_dvd__div__mult,axiom,
% 0.35/0.62 ! [C2: int,B: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.62 => ( ( times_times_int @ ( divide_divide_int @ B @ C2 ) @ A )
% 0.35/0.62 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_mult
% 0.35/0.62 thf(fact_5485_div__mult__swap,axiom,
% 0.35/0.62 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.62 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_mult_swap
% 0.35/0.62 thf(fact_5486_div__mult__swap,axiom,
% 0.35/0.62 ! [C2: int,B: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.62 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_mult_swap
% 0.35/0.62 thf(fact_5487_div__div__eq__right,axiom,
% 0.35/0.62 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.62 => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.62 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 0.35/0.62 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_div_eq_right
% 0.35/0.62 thf(fact_5488_div__div__eq__right,axiom,
% 0.35/0.62 ! [C2: int,B: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.62 => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.62 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 0.35/0.62 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_div_eq_right
% 0.35/0.62 thf(fact_5489_dvd__div__mult2__eq,axiom,
% 0.35/0.62 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C2 ) @ A )
% 0.35/0.62 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_mult2_eq
% 0.35/0.62 thf(fact_5490_dvd__div__mult2__eq,axiom,
% 0.35/0.62 ! [B: int,C2: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ ( times_times_int @ B @ C2 ) @ A )
% 0.35/0.62 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_mult2_eq
% 0.35/0.62 thf(fact_5491_dvd__mult__imp__div,axiom,
% 0.35/0.62 ! [A: nat,C2: nat,B: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ B )
% 0.35/0.62 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_imp_div
% 0.35/0.62 thf(fact_5492_dvd__mult__imp__div,axiom,
% 0.35/0.62 ! [A: int,C2: int,B: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ B )
% 0.35/0.62 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_imp_div
% 0.35/0.62 thf(fact_5493_div__mult__div__if__dvd,axiom,
% 0.35/0.62 ! [B: nat,A: nat,D: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.62 => ( ( dvd_dvd_nat @ D @ C2 )
% 0.35/0.62 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C2 @ D ) )
% 0.35/0.62 = ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_mult_div_if_dvd
% 0.35/0.62 thf(fact_5494_div__mult__div__if__dvd,axiom,
% 0.35/0.62 ! [B: int,A: int,D: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ A )
% 0.35/0.62 => ( ( dvd_dvd_int @ D @ C2 )
% 0.35/0.62 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C2 @ D ) )
% 0.35/0.62 = ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_mult_div_if_dvd
% 0.35/0.62 thf(fact_5495_unit__div__cancel,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 0.35/0.62 = ( divide6298287555418463151nteger @ C2 @ A ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_cancel
% 0.35/0.62 thf(fact_5496_unit__div__cancel,axiom,
% 0.35/0.62 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 => ( ( ( divide_divide_nat @ B @ A )
% 0.35/0.62 = ( divide_divide_nat @ C2 @ A ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_cancel
% 0.35/0.62 thf(fact_5497_unit__div__cancel,axiom,
% 0.35/0.62 ! [A: int,B: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 => ( ( ( divide_divide_int @ B @ A )
% 0.35/0.62 = ( divide_divide_int @ C2 @ A ) )
% 0.35/0.62 = ( B = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_cancel
% 0.35/0.62 thf(fact_5498_div__unit__dvd__iff,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_unit_dvd_iff
% 0.35/0.62 thf(fact_5499_div__unit__dvd__iff,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_unit_dvd_iff
% 0.35/0.62 thf(fact_5500_div__unit__dvd__iff,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_unit_dvd_iff
% 0.35/0.62 thf(fact_5501_dvd__div__unit__iff,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C2 @ B ) )
% 0.35/0.62 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_unit_iff
% 0.35/0.62 thf(fact_5502_dvd__div__unit__iff,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C2 @ B ) )
% 0.35/0.62 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_unit_iff
% 0.35/0.62 thf(fact_5503_dvd__div__unit__iff,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C2 @ B ) )
% 0.35/0.62 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_unit_iff
% 0.35/0.62 thf(fact_5504_mod__eq__0__iff__dvd,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 = ( dvd_dvd_nat @ B @ A ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_eq_0_iff_dvd
% 0.35/0.62 thf(fact_5505_mod__eq__0__iff__dvd,axiom,
% 0.35/0.62 ! [A: int,B: int] :
% 0.35/0.62 ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62 = zero_zero_int )
% 0.35/0.62 = ( dvd_dvd_int @ B @ A ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_eq_0_iff_dvd
% 0.35/0.62 thf(fact_5506_mod__eq__0__iff__dvd,axiom,
% 0.35/0.62 ! [A: code_natural,B: code_natural] :
% 0.35/0.62 ( ( ( modulo8411746178871703098atural @ A @ B )
% 0.35/0.62 = zero_z2226904508553997617atural )
% 0.35/0.62 = ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_eq_0_iff_dvd
% 0.35/0.62 thf(fact_5507_dvd__eq__mod__eq__0,axiom,
% 0.35/0.62 ( dvd_dvd_nat
% 0.35/0.62 = ( ^ [A5: nat,B4: nat] :
% 0.35/0.62 ( ( modulo_modulo_nat @ B4 @ A5 )
% 0.35/0.62 = zero_zero_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_eq_mod_eq_0
% 0.35/0.62 thf(fact_5508_dvd__eq__mod__eq__0,axiom,
% 0.35/0.62 ( dvd_dvd_int
% 0.35/0.62 = ( ^ [A5: int,B4: int] :
% 0.35/0.62 ( ( modulo_modulo_int @ B4 @ A5 )
% 0.35/0.62 = zero_zero_int ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_eq_mod_eq_0
% 0.35/0.62 thf(fact_5509_dvd__eq__mod__eq__0,axiom,
% 0.35/0.62 ( dvd_dvd_Code_natural
% 0.35/0.62 = ( ^ [A5: code_natural,B4: code_natural] :
% 0.35/0.62 ( ( modulo8411746178871703098atural @ B4 @ A5 )
% 0.35/0.62 = zero_z2226904508553997617atural ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_eq_mod_eq_0
% 0.35/0.62 thf(fact_5510_mod__0__imp__dvd,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 => ( dvd_dvd_nat @ B @ A ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_0_imp_dvd
% 0.35/0.62 thf(fact_5511_mod__0__imp__dvd,axiom,
% 0.35/0.62 ! [A: int,B: int] :
% 0.35/0.62 ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62 = zero_zero_int )
% 0.35/0.62 => ( dvd_dvd_int @ B @ A ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_0_imp_dvd
% 0.35/0.62 thf(fact_5512_mod__0__imp__dvd,axiom,
% 0.35/0.62 ! [A: code_natural,B: code_natural] :
% 0.35/0.62 ( ( ( modulo8411746178871703098atural @ A @ B )
% 0.35/0.62 = zero_z2226904508553997617atural )
% 0.35/0.62 => ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_0_imp_dvd
% 0.35/0.62 thf(fact_5513_dvd__power__le,axiom,
% 0.35/0.62 ! [X: nat,Y: nat,N: nat,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ X @ Y )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ M2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power_le
% 0.35/0.62 thf(fact_5514_dvd__power__le,axiom,
% 0.35/0.62 ! [X: real,Y: real,N: nat,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_real @ X @ Y )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ M2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power_le
% 0.35/0.62 thf(fact_5515_dvd__power__le,axiom,
% 0.35/0.62 ! [X: int,Y: int,N: nat,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_int @ X @ Y )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ M2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power_le
% 0.35/0.62 thf(fact_5516_dvd__power__le,axiom,
% 0.35/0.62 ! [X: complex,Y: complex,N: nat,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_complex @ X @ Y )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ M2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power_le
% 0.35/0.62 thf(fact_5517_power__le__dvd,axiom,
% 0.35/0.62 ! [A: nat,N: nat,B: nat,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 0.35/0.62 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % power_le_dvd
% 0.35/0.62 thf(fact_5518_power__le__dvd,axiom,
% 0.35/0.62 ! [A: real,N: nat,B: real,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 0.35/0.62 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % power_le_dvd
% 0.35/0.62 thf(fact_5519_power__le__dvd,axiom,
% 0.35/0.62 ! [A: int,N: nat,B: int,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 0.35/0.62 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % power_le_dvd
% 0.35/0.62 thf(fact_5520_power__le__dvd,axiom,
% 0.35/0.62 ! [A: complex,N: nat,B: complex,M2: nat] :
% 0.35/0.62 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 0.35/0.62 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % power_le_dvd
% 0.35/0.62 thf(fact_5521_le__imp__power__dvd,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,A: nat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % le_imp_power_dvd
% 0.35/0.62 thf(fact_5522_le__imp__power__dvd,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,A: real] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % le_imp_power_dvd
% 0.35/0.62 thf(fact_5523_le__imp__power__dvd,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,A: int] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % le_imp_power_dvd
% 0.35/0.62 thf(fact_5524_le__imp__power__dvd,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,A: complex] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % le_imp_power_dvd
% 0.35/0.62 thf(fact_5525_dvd__minus__mod,axiom,
% 0.35/0.62 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_minus_mod
% 0.35/0.62 thf(fact_5526_dvd__minus__mod,axiom,
% 0.35/0.62 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_minus_mod
% 0.35/0.62 thf(fact_5527_dvd__minus__mod,axiom,
% 0.35/0.62 ! [B: code_natural,A: code_natural] : ( dvd_dvd_Code_natural @ B @ ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_minus_mod
% 0.35/0.62 thf(fact_5528_dvd__pos__nat,axiom,
% 0.35/0.62 ! [N: nat,M2: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.62 => ( ( dvd_dvd_nat @ M2 @ N )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_pos_nat
% 0.35/0.62 thf(fact_5529_nat__dvd__not__less,axiom,
% 0.35/0.62 ! [M2: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.62 => ( ( ord_less_nat @ M2 @ N )
% 0.35/0.62 => ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % nat_dvd_not_less
% 0.35/0.62 thf(fact_5530_pochhammer__pos,axiom,
% 0.35/0.62 ! [X: real,N: nat] :
% 0.35/0.62 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_pos
% 0.35/0.62 thf(fact_5531_pochhammer__pos,axiom,
% 0.35/0.62 ! [X: rat,N: nat] :
% 0.35/0.62 ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_pos
% 0.35/0.62 thf(fact_5532_pochhammer__pos,axiom,
% 0.35/0.62 ! [X: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_pos
% 0.35/0.62 thf(fact_5533_pochhammer__pos,axiom,
% 0.35/0.62 ! [X: int,N: nat] :
% 0.35/0.62 ( ( ord_less_int @ zero_zero_int @ X )
% 0.35/0.62 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_pos
% 0.35/0.62 thf(fact_5534_dvd__minus__self,axiom,
% 0.35/0.62 ! [M2: nat,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) )
% 0.35/0.62 = ( ( ord_less_nat @ N @ M2 )
% 0.35/0.62 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_minus_self
% 0.35/0.62 thf(fact_5535_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_real,F2: real > real,I2: real] :
% 0.35/0.62 ( ( finite_finite_real @ S2 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups8097168146408367636l_real @ F2 @ S2 )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 => ( ( member_real @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5536_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_int,F2: int > real,I2: int] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups8778361861064173332t_real @ F2 @ S2 )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 => ( ( member_int @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5537_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_complex,F2: complex > real,I2: complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups5808333547571424918x_real @ F2 @ S2 )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 => ( ( member_complex @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5538_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_real,F2: real > rat,I2: real] :
% 0.35/0.62 ( ( finite_finite_real @ S2 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups1300246762558778688al_rat @ F2 @ S2 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 => ( ( member_real @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5539_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_nat,F2: nat > rat,I2: nat] :
% 0.35/0.62 ( ( finite_finite_nat @ S2 )
% 0.35/0.62 => ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups2906978787729119204at_rat @ F2 @ S2 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 => ( ( member_nat @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5540_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_int,F2: int > rat,I2: int] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups3906332499630173760nt_rat @ F2 @ S2 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 => ( ( member_int @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5541_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_complex,F2: complex > rat,I2: complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups5058264527183730370ex_rat @ F2 @ S2 )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 => ( ( member_complex @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5542_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_real,F2: real > nat,I2: real] :
% 0.35/0.62 ( ( finite_finite_real @ S2 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups1935376822645274424al_nat @ F2 @ S2 )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 => ( ( member_real @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5543_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_int,F2: int > nat,I2: int] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups4541462559716669496nt_nat @ F2 @ S2 )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 => ( ( member_int @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5544_sum__nonneg__0,axiom,
% 0.35/0.62 ! [S2: set_complex,F2: complex > nat,I2: complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups5693394587270226106ex_nat @ F2 @ S2 )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 => ( ( member_complex @ I2 @ S2 )
% 0.35/0.62 => ( ( F2 @ I2 )
% 0.35/0.62 = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_0
% 0.35/0.62 thf(fact_5545_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_real,F2: real > real,B5: real,I2: real] :
% 0.35/0.62 ( ( finite_finite_real @ S2 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups8097168146408367636l_real @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_real @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5546_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_int,F2: int > real,B5: real,I2: int] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups8778361861064173332t_real @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_int @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5547_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_complex,F2: complex > real,B5: real,I2: complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups5808333547571424918x_real @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_complex @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5548_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_real,F2: real > rat,B5: rat,I2: real] :
% 0.35/0.62 ( ( finite_finite_real @ S2 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups1300246762558778688al_rat @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_real @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5549_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_nat,F2: nat > rat,B5: rat,I2: nat] :
% 0.35/0.62 ( ( finite_finite_nat @ S2 )
% 0.35/0.62 => ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups2906978787729119204at_rat @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_nat @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5550_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_int,F2: int > rat,B5: rat,I2: int] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups3906332499630173760nt_rat @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_int @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5551_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_complex,F2: complex > rat,B5: rat,I2: complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups5058264527183730370ex_rat @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_complex @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5552_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_real,F2: real > nat,B5: nat,I2: real] :
% 0.35/0.62 ( ( finite_finite_real @ S2 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups1935376822645274424al_nat @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_real @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5553_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_int,F2: int > nat,B5: nat,I2: int] :
% 0.35/0.62 ( ( finite_finite_int @ S2 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups4541462559716669496nt_nat @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_int @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5554_sum__nonneg__leq__bound,axiom,
% 0.35/0.62 ! [S2: set_complex,F2: complex > nat,B5: nat,I2: complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ S2 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ( ( groups5693394587270226106ex_nat @ F2 @ S2 )
% 0.35/0.62 = B5 )
% 0.35/0.62 => ( ( member_complex @ I2 @ S2 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_nonneg_leq_bound
% 0.35/0.62 thf(fact_5555_less__eq__dvd__minus,axiom,
% 0.35/0.62 ! [M2: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( ( dvd_dvd_nat @ M2 @ N )
% 0.35/0.62 = ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % less_eq_dvd_minus
% 0.35/0.62 thf(fact_5556_dvd__diffD1,axiom,
% 0.35/0.62 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.62 => ( ( dvd_dvd_nat @ K2 @ M2 )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( dvd_dvd_nat @ K2 @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_diffD1
% 0.35/0.62 thf(fact_5557_dvd__diffD,axiom,
% 0.35/0.62 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 0.35/0.62 => ( ( dvd_dvd_nat @ K2 @ N )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( dvd_dvd_nat @ K2 @ M2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_diffD
% 0.35/0.62 thf(fact_5558_pochhammer__eq__0__mono,axiom,
% 0.35/0.62 ! [A: complex,N: nat,M2: nat] :
% 0.35/0.62 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 0.35/0.62 = zero_zero_complex )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 0.35/0.62 = zero_zero_complex ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_eq_0_mono
% 0.35/0.62 thf(fact_5559_pochhammer__eq__0__mono,axiom,
% 0.35/0.62 ! [A: real,N: nat,M2: nat] :
% 0.35/0.62 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 0.35/0.62 = zero_zero_real ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_eq_0_mono
% 0.35/0.62 thf(fact_5560_pochhammer__eq__0__mono,axiom,
% 0.35/0.62 ! [A: rat,N: nat,M2: nat] :
% 0.35/0.62 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 0.35/0.62 = zero_zero_rat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_eq_0_mono
% 0.35/0.62 thf(fact_5561_pochhammer__neq__0__mono,axiom,
% 0.35/0.62 ! [A: complex,M2: nat,N: nat] :
% 0.35/0.62 ( ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 0.35/0.62 != zero_zero_complex )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 0.35/0.62 != zero_zero_complex ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_neq_0_mono
% 0.35/0.62 thf(fact_5562_pochhammer__neq__0__mono,axiom,
% 0.35/0.62 ! [A: real,M2: nat,N: nat] :
% 0.35/0.62 ( ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 0.35/0.62 != zero_zero_real )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.35/0.62 != zero_zero_real ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_neq_0_mono
% 0.35/0.62 thf(fact_5563_pochhammer__neq__0__mono,axiom,
% 0.35/0.62 ! [A: rat,M2: nat,N: nat] :
% 0.35/0.62 ( ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 0.35/0.62 != zero_zero_rat )
% 0.35/0.62 => ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.35/0.62 != zero_zero_rat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_neq_0_mono
% 0.35/0.62 thf(fact_5564_bezout__add__nat,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ? [D5: nat,X3: nat,Y3: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ D5 @ A )
% 0.35/0.62 & ( dvd_dvd_nat @ D5 @ B )
% 0.35/0.62 & ( ( ( times_times_nat @ A @ X3 )
% 0.35/0.62 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D5 ) )
% 0.35/0.62 | ( ( times_times_nat @ B @ X3 )
% 0.35/0.62 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % bezout_add_nat
% 0.35/0.62 thf(fact_5565_bezout__lemma__nat,axiom,
% 0.35/0.62 ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ D @ A )
% 0.35/0.62 => ( ( dvd_dvd_nat @ D @ B )
% 0.35/0.62 => ( ( ( ( times_times_nat @ A @ X )
% 0.35/0.62 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 0.35/0.62 | ( ( times_times_nat @ B @ X )
% 0.35/0.62 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 0.35/0.62 => ? [X3: nat,Y3: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ D @ A )
% 0.35/0.62 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 0.35/0.62 & ( ( ( times_times_nat @ A @ X3 )
% 0.35/0.62 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 0.35/0.62 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 0.35/0.62 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % bezout_lemma_nat
% 0.35/0.62 thf(fact_5566_bezout1__nat,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ? [D5: nat,X3: nat,Y3: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ D5 @ A )
% 0.35/0.62 & ( dvd_dvd_nat @ D5 @ B )
% 0.35/0.62 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 0.35/0.62 = D5 )
% 0.35/0.62 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 0.35/0.62 = D5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % bezout1_nat
% 0.35/0.62 thf(fact_5567_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > complex,B5: set_real] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 0.35/0.62 = ( groups5754745047067104278omplex
% 0.35/0.62 @ ^ [X4: real] : ( if_complex @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5568_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_int,G2: int > complex,B5: set_int] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.62 = ( groups3049146728041665814omplex
% 0.35/0.62 @ ^ [X4: int] : ( if_complex @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5569_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_complex,G2: complex > complex,B5: set_complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( groups7754918857620584856omplex
% 0.35/0.62 @ ^ [X4: complex] : ( if_complex @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5570_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > real,B5: set_real] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups8097168146408367636l_real @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 0.35/0.62 = ( groups8097168146408367636l_real
% 0.35/0.62 @ ^ [X4: real] : ( if_real @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5571_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_int,G2: int > real,B5: set_int] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.62 = ( groups8778361861064173332t_real
% 0.35/0.62 @ ^ [X4: int] : ( if_real @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5572_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_complex,G2: complex > real,B5: set_complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( groups5808333547571424918x_real
% 0.35/0.62 @ ^ [X4: complex] : ( if_real @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5573_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > rat,B5: set_real] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups1300246762558778688al_rat @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 0.35/0.62 = ( groups1300246762558778688al_rat
% 0.35/0.62 @ ^ [X4: real] : ( if_rat @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5574_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_int,G2: int > rat,B5: set_int] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.62 = ( groups3906332499630173760nt_rat
% 0.35/0.62 @ ^ [X4: int] : ( if_rat @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5575_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_complex,G2: complex > rat,B5: set_complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( groups5058264527183730370ex_rat
% 0.35/0.62 @ ^ [X4: complex] : ( if_rat @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5576_sum_Ointer__restrict,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > nat,B5: set_real] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups1935376822645274424al_nat @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 0.35/0.62 = ( groups1935376822645274424al_nat
% 0.35/0.62 @ ^ [X4: real] : ( if_nat @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_nat )
% 0.35/0.62 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.inter_restrict
% 0.35/0.62 thf(fact_5577_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > complex] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2
% 0.35/0.62 @ ( minus_minus_set_real @ A4
% 0.35/0.62 @ ( collect_real
% 0.35/0.62 @ ^ [X4: real] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_complex ) ) ) )
% 0.35/0.62 = ( groups5754745047067104278omplex @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5578_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_int,G2: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2
% 0.35/0.62 @ ( minus_minus_set_int @ A4
% 0.35/0.62 @ ( collect_int
% 0.35/0.62 @ ^ [X4: int] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_complex ) ) ) )
% 0.35/0.62 = ( groups3049146728041665814omplex @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5579_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_complex,G2: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2
% 0.35/0.62 @ ( minus_811609699411566653omplex @ A4
% 0.35/0.62 @ ( collect_complex
% 0.35/0.62 @ ^ [X4: complex] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_complex ) ) ) )
% 0.35/0.62 = ( groups7754918857620584856omplex @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5580_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups8097168146408367636l_real @ G2
% 0.35/0.62 @ ( minus_minus_set_real @ A4
% 0.35/0.62 @ ( collect_real
% 0.35/0.62 @ ^ [X4: real] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_real ) ) ) )
% 0.35/0.62 = ( groups8097168146408367636l_real @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5581_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_int,G2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2
% 0.35/0.62 @ ( minus_minus_set_int @ A4
% 0.35/0.62 @ ( collect_int
% 0.35/0.62 @ ^ [X4: int] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_real ) ) ) )
% 0.35/0.62 = ( groups8778361861064173332t_real @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5582_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_complex,G2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2
% 0.35/0.62 @ ( minus_811609699411566653omplex @ A4
% 0.35/0.62 @ ( collect_complex
% 0.35/0.62 @ ^ [X4: complex] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_real ) ) ) )
% 0.35/0.62 = ( groups5808333547571424918x_real @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5583_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups1300246762558778688al_rat @ G2
% 0.35/0.62 @ ( minus_minus_set_real @ A4
% 0.35/0.62 @ ( collect_real
% 0.35/0.62 @ ^ [X4: real] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_rat ) ) ) )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5584_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_int,G2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2
% 0.35/0.62 @ ( minus_minus_set_int @ A4
% 0.35/0.62 @ ( collect_int
% 0.35/0.62 @ ^ [X4: int] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_rat ) ) ) )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5585_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_complex,G2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2
% 0.35/0.62 @ ( minus_811609699411566653omplex @ A4
% 0.35/0.62 @ ( collect_complex
% 0.35/0.62 @ ^ [X4: complex] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_rat ) ) ) )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5586_sum_Osetdiff__irrelevant,axiom,
% 0.35/0.62 ! [A4: set_real,G2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( groups1935376822645274424al_nat @ G2
% 0.35/0.62 @ ( minus_minus_set_real @ A4
% 0.35/0.62 @ ( collect_real
% 0.35/0.62 @ ^ [X4: real] :
% 0.35/0.62 ( ( G2 @ X4 )
% 0.35/0.62 = zero_zero_nat ) ) ) )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ G2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.setdiff_irrelevant
% 0.35/0.62 thf(fact_5587_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.62 ! [G2: nat > nat,M2: nat,N: nat] :
% 0.35/0.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 0.35/0.62 = ( groups3542108847815614940at_nat
% 0.35/0.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.shift_bounds_cl_Suc_ivl
% 0.35/0.62 thf(fact_5588_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.62 ! [G2: nat > real,M2: nat,N: nat] :
% 0.35/0.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 0.35/0.62 = ( groups6591440286371151544t_real
% 0.35/0.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.shift_bounds_cl_Suc_ivl
% 0.35/0.62 thf(fact_5589_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.62 ! [G2: nat > nat,M2: nat,K2: nat,N: nat] :
% 0.35/0.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 0.35/0.62 = ( groups3542108847815614940at_nat
% 0.35/0.62 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 0.35/0.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.shift_bounds_cl_nat_ivl
% 0.35/0.62 thf(fact_5590_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.62 ! [G2: nat > real,M2: nat,K2: nat,N: nat] :
% 0.35/0.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 0.35/0.62 = ( groups6591440286371151544t_real
% 0.35/0.62 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 0.35/0.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.shift_bounds_cl_nat_ivl
% 0.35/0.62 thf(fact_5591_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_real,I2: real,F2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ I5 )
% 0.35/0.62 => ( ( member_real @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5592_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_int,I2: int,F2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ I5 )
% 0.35/0.62 => ( ( member_int @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5593_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_complex,I2: complex,F2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.62 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5594_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_real,I2: real,F2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ I5 )
% 0.35/0.62 => ( ( member_real @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5595_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_nat,I2: nat,F2: nat > rat] :
% 0.35/0.62 ( ( finite_finite_nat @ I5 )
% 0.35/0.62 => ( ( member_nat @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5596_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_int,I2: int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ I5 )
% 0.35/0.62 => ( ( member_int @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5597_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_complex,I2: complex,F2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.62 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5598_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_real,I2: real,F2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ I5 )
% 0.35/0.62 => ( ( member_real @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5599_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_int,I2: int,F2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ I5 )
% 0.35/0.62 => ( ( member_int @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5600_sum__pos2,axiom,
% 0.35/0.62 ! [I5: set_complex,I2: complex,F2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.62 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos2
% 0.35/0.62 thf(fact_5601_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_complex,F2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_complex )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5602_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_int,F2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_int )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5603_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_real,F2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_real )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5604_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_complex,F2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_complex )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5605_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_nat,F2: nat > rat] :
% 0.35/0.62 ( ( finite_finite_nat @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_nat )
% 0.35/0.62 => ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5606_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_int )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5607_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_real,F2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_real )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5608_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_complex,F2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_complex )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5609_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_int,F2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_int )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5610_sum__pos,axiom,
% 0.35/0.62 ! [I5: set_real,F2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ I5 )
% 0.35/0.62 => ( ( I5 != bot_bot_set_real )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ I5 )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ I5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_pos
% 0.35/0.62 thf(fact_5611_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_real,K5: real,F2: real > real] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5612_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_complex,K5: real,F2: complex > real] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5613_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_int,K5: real,F2: int > real] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5614_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_real,K5: rat,F2: real > rat] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5615_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_nat,K5: rat,F2: nat > rat] :
% 0.35/0.62 ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5616_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_complex,K5: rat,F2: complex > rat] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5617_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_int,K5: rat,F2: int > rat] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5618_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_real,K5: nat,F2: real > nat] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5619_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_complex,K5: nat,F2: complex > nat] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5620_sum__bounded__below,axiom,
% 0.35/0.62 ! [A4: set_int,K5: nat,F2: int > nat] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_below
% 0.35/0.62 thf(fact_5621_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > real,K5: real] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5622_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > real,K5: real] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5623_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > real,K5: real] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5624_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5625_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5626_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5627_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5628_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > nat,K5: nat] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5629_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > nat,K5: nat] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5630_sum__bounded__above,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > nat,K5: nat] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above
% 0.35/0.62 thf(fact_5631_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,G2: real > complex,H: real > complex] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ T5 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5632_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > complex,H: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ T5 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5633_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > complex,H: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ T5 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5634_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,G2: real > real,H: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups8097168146408367636l_real @ G2 @ T5 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5635_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > real,H: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ T5 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5636_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > real,H: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ T5 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5637_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,G2: real > rat,H: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups1300246762558778688al_rat @ G2 @ T5 )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5638_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > rat,H: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ T5 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5639_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > rat,H: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ T5 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5640_sum_Omono__neutral__cong__right,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,G2: real > nat,H: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups1935376822645274424al_nat @ G2 @ T5 )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ H @ S3 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_right
% 0.35/0.62 thf(fact_5641_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > complex,G2: real > complex] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5642_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,H: int > complex,G2: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5643_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5644_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > real,G2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5645_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,H: int > real,G2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5646_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,H: complex > real,G2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5647_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > rat,G2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups1300246762558778688al_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5648_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,H: int > rat,G2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5649_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5650_sum_Omono__neutral__cong__left,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > nat,G2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ S3 )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups1935376822645274424al_nat @ G2 @ S3 )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ H @ T5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong_left
% 0.35/0.62 thf(fact_5651_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ T5 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5652_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ T5 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5653_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ T5 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5654_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ T5 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5655_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ T5 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5656_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ T5 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5657_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( groups4541462559716669496nt_nat @ G2 @ T5 )
% 0.35/0.62 = ( groups4541462559716669496nt_nat @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5658_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( groups5693394587270226106ex_nat @ G2 @ T5 )
% 0.35/0.62 = ( groups5693394587270226106ex_nat @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5659_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > int] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_int ) )
% 0.35/0.62 => ( ( groups5690904116761175830ex_int @ G2 @ T5 )
% 0.35/0.62 = ( groups5690904116761175830ex_int @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5660_sum_Omono__neutral__right,axiom,
% 0.35/0.62 ! [T5: set_nat,S3: set_nat,G2: nat > complex] :
% 0.35/0.62 ( ( finite_finite_nat @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups2073611262835488442omplex @ G2 @ T5 )
% 0.35/0.62 = ( groups2073611262835488442omplex @ G2 @ S3 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_right
% 0.35/0.62 thf(fact_5661_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5662_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5663_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5664_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5665_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5666_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5667_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,G2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( groups4541462559716669496nt_nat @ G2 @ S3 )
% 0.35/0.62 = ( groups4541462559716669496nt_nat @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5668_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( groups5693394587270226106ex_nat @ G2 @ S3 )
% 0.35/0.62 = ( groups5693394587270226106ex_nat @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5669_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,G2: complex > int] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_int ) )
% 0.35/0.62 => ( ( groups5690904116761175830ex_int @ G2 @ S3 )
% 0.35/0.62 = ( groups5690904116761175830ex_int @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5670_sum_Omono__neutral__left,axiom,
% 0.35/0.62 ! [T5: set_nat,S3: set_nat,G2: nat > complex] :
% 0.35/0.62 ( ( finite_finite_nat @ T5 )
% 0.35/0.62 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups2073611262835488442omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups2073611262835488442omplex @ G2 @ T5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_left
% 0.35/0.62 thf(fact_5671_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > complex,H: real > complex] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( ( groups5754745047067104278omplex @ G2 @ C4 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ C4 ) )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5672_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > complex,H: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( ( groups3049146728041665814omplex @ G2 @ C4 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ C4 ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5673_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > complex,H: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( ( groups7754918857620584856omplex @ G2 @ C4 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ C4 ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5674_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > real,H: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( ( groups8097168146408367636l_real @ G2 @ C4 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ C4 ) )
% 0.35/0.62 => ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5675_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > real,H: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( ( groups8778361861064173332t_real @ G2 @ C4 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ H @ C4 ) )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5676_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > real,H: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( ( groups5808333547571424918x_real @ G2 @ C4 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ H @ C4 ) )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5677_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > rat,H: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( ( groups1300246762558778688al_rat @ G2 @ C4 )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ H @ C4 ) )
% 0.35/0.62 => ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5678_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > rat,H: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( ( groups3906332499630173760nt_rat @ G2 @ C4 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ H @ C4 ) )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5679_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > rat,H: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( ( groups5058264527183730370ex_rat @ G2 @ C4 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ H @ C4 ) )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5680_sum_Osame__carrierI,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > nat,H: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( ( groups1935376822645274424al_nat @ G2 @ C4 )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ H @ C4 ) )
% 0.35/0.62 => ( ( groups1935376822645274424al_nat @ G2 @ A4 )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrierI
% 0.35/0.62 thf(fact_5681_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > complex,H: real > complex] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ B5 ) )
% 0.35/0.62 = ( ( groups5754745047067104278omplex @ G2 @ C4 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5682_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > complex,H: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ B5 ) )
% 0.35/0.62 = ( ( groups3049146728041665814omplex @ G2 @ C4 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5683_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > complex,H: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ B5 ) )
% 0.35/0.62 = ( ( groups7754918857620584856omplex @ G2 @ C4 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5684_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > real,H: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ B5 ) )
% 0.35/0.62 = ( ( groups8097168146408367636l_real @ G2 @ C4 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5685_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > real,H: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ H @ B5 ) )
% 0.35/0.62 = ( ( groups8778361861064173332t_real @ G2 @ C4 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5686_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > real,H: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ H @ B5 ) )
% 0.35/0.62 = ( ( groups5808333547571424918x_real @ G2 @ C4 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5687_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > rat,H: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ H @ B5 ) )
% 0.35/0.62 = ( ( groups1300246762558778688al_rat @ G2 @ C4 )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5688_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > rat,H: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: int] :
% 0.35/0.62 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ H @ B5 ) )
% 0.35/0.62 = ( ( groups3906332499630173760nt_rat @ G2 @ C4 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5689_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > rat,H: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: complex] :
% 0.35/0.62 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ H @ B5 ) )
% 0.35/0.62 = ( ( groups5058264527183730370ex_rat @ G2 @ C4 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5690_sum_Osame__carrier,axiom,
% 0.35/0.62 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > nat,H: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 0.35/0.62 => ( ! [A3: real] :
% 0.35/0.62 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 0.35/0.62 => ( ( G2 @ A3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 0.35/0.62 => ( ( H @ B3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( ( groups1935376822645274424al_nat @ G2 @ A4 )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ H @ B5 ) )
% 0.35/0.62 = ( ( groups1935376822645274424al_nat @ G2 @ C4 )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.same_carrier
% 0.35/0.62 thf(fact_5691_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > complex,G2: real > complex] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( finite_finite_real @ S3 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5692_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,H: int > complex,G2: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( finite_finite_int @ S3 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5693_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 0.35/0.62 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5694_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > real,G2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( finite_finite_real @ S3 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 0.35/0.62 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5695_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,H: int > real,G2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( finite_finite_int @ S3 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 0.35/0.62 = ( groups8778361861064173332t_real @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5696_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,H: complex > real,G2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 0.35/0.62 = ( groups5808333547571424918x_real @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5697_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > rat,G2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( finite_finite_real @ S3 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups1300246762558778688al_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups1300246762558778688al_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5698_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_int,S3: set_int,H: int > rat,G2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ T5 )
% 0.35/0.62 => ( ( finite_finite_int @ S3 )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups3906332499630173760nt_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5699_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_complex,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 0.35/0.62 = ( groups5058264527183730370ex_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5700_sum_Omono__neutral__cong,axiom,
% 0.35/0.62 ! [T5: set_real,S3: set_real,H: real > nat,G2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ T5 )
% 0.35/0.62 => ( ( finite_finite_real @ S3 )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 0.35/0.62 => ( ( H @ I3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ I3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = ( H @ X3 ) ) )
% 0.35/0.62 => ( ( groups1935376822645274424al_nat @ G2 @ S3 )
% 0.35/0.62 = ( groups1935376822645274424al_nat @ H @ T5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.mono_neutral_cong
% 0.35/0.62 thf(fact_5701_unity__coeff__ex,axiom,
% 0.35/0.62 ! [P2: complex > $o,L: complex] :
% 0.35/0.62 ( ( ? [X4: complex] : ( P2 @ ( times_times_complex @ L @ X4 ) ) )
% 0.35/0.62 = ( ? [X4: complex] :
% 0.35/0.62 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X4 @ zero_zero_complex ) )
% 0.35/0.62 & ( P2 @ X4 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unity_coeff_ex
% 0.35/0.62 thf(fact_5702_unity__coeff__ex,axiom,
% 0.35/0.62 ! [P2: real > $o,L: real] :
% 0.35/0.62 ( ( ? [X4: real] : ( P2 @ ( times_times_real @ L @ X4 ) ) )
% 0.35/0.62 = ( ? [X4: real] :
% 0.35/0.62 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X4 @ zero_zero_real ) )
% 0.35/0.62 & ( P2 @ X4 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unity_coeff_ex
% 0.35/0.62 thf(fact_5703_unity__coeff__ex,axiom,
% 0.35/0.62 ! [P2: rat > $o,L: rat] :
% 0.35/0.62 ( ( ? [X4: rat] : ( P2 @ ( times_times_rat @ L @ X4 ) ) )
% 0.35/0.62 = ( ? [X4: rat] :
% 0.35/0.62 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X4 @ zero_zero_rat ) )
% 0.35/0.62 & ( P2 @ X4 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unity_coeff_ex
% 0.35/0.62 thf(fact_5704_unity__coeff__ex,axiom,
% 0.35/0.62 ! [P2: nat > $o,L: nat] :
% 0.35/0.62 ( ( ? [X4: nat] : ( P2 @ ( times_times_nat @ L @ X4 ) ) )
% 0.35/0.62 = ( ? [X4: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X4 @ zero_zero_nat ) )
% 0.35/0.62 & ( P2 @ X4 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unity_coeff_ex
% 0.35/0.62 thf(fact_5705_unity__coeff__ex,axiom,
% 0.35/0.62 ! [P2: int > $o,L: int] :
% 0.35/0.62 ( ( ? [X4: int] : ( P2 @ ( times_times_int @ L @ X4 ) ) )
% 0.35/0.62 = ( ? [X4: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X4 @ zero_zero_int ) )
% 0.35/0.62 & ( P2 @ X4 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unity_coeff_ex
% 0.35/0.62 thf(fact_5706_unit__dvdE,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.62 => ! [C: code_integer] :
% 0.35/0.62 ( B
% 0.35/0.62 != ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_dvdE
% 0.35/0.62 thf(fact_5707_unit__dvdE,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 => ~ ( ( A != zero_zero_nat )
% 0.35/0.62 => ! [C: nat] :
% 0.35/0.62 ( B
% 0.35/0.62 != ( times_times_nat @ A @ C ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_dvdE
% 0.35/0.62 thf(fact_5708_unit__dvdE,axiom,
% 0.35/0.62 ! [A: int,B: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 => ~ ( ( A != zero_zero_int )
% 0.35/0.62 => ! [C: int] :
% 0.35/0.62 ( B
% 0.35/0.62 != ( times_times_int @ A @ C ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_dvdE
% 0.35/0.62 thf(fact_5709_dvd__div__div__eq__mult,axiom,
% 0.35/0.62 ! [A: nat,C2: nat,B: nat,D: nat] :
% 0.35/0.62 ( ( A != zero_zero_nat )
% 0.35/0.62 => ( ( C2 != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.62 => ( ( dvd_dvd_nat @ C2 @ D )
% 0.35/0.62 => ( ( ( divide_divide_nat @ B @ A )
% 0.35/0.62 = ( divide_divide_nat @ D @ C2 ) )
% 0.35/0.62 = ( ( times_times_nat @ B @ C2 )
% 0.35/0.62 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_div_eq_mult
% 0.35/0.62 thf(fact_5710_dvd__div__div__eq__mult,axiom,
% 0.35/0.62 ! [A: int,C2: int,B: int,D: int] :
% 0.35/0.62 ( ( A != zero_zero_int )
% 0.35/0.62 => ( ( C2 != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ A @ B )
% 0.35/0.62 => ( ( dvd_dvd_int @ C2 @ D )
% 0.35/0.62 => ( ( ( divide_divide_int @ B @ A )
% 0.35/0.62 = ( divide_divide_int @ D @ C2 ) )
% 0.35/0.62 = ( ( times_times_int @ B @ C2 )
% 0.35/0.62 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_div_eq_mult
% 0.35/0.62 thf(fact_5711_dvd__div__iff__mult,axiom,
% 0.35/0.62 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.62 ( ( C2 != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ C2 @ B )
% 0.35/0.62 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 0.35/0.62 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_iff_mult
% 0.35/0.62 thf(fact_5712_dvd__div__iff__mult,axiom,
% 0.35/0.62 ! [C2: int,B: int,A: int] :
% 0.35/0.62 ( ( C2 != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ C2 @ B )
% 0.35/0.62 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 0.35/0.62 = ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_iff_mult
% 0.35/0.62 thf(fact_5713_div__dvd__iff__mult,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( B != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C2 @ B ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_dvd_iff_mult
% 0.35/0.62 thf(fact_5714_div__dvd__iff__mult,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( B != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.62 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 0.35/0.62 = ( dvd_dvd_int @ A @ ( times_times_int @ C2 @ B ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_dvd_iff_mult
% 0.35/0.62 thf(fact_5715_dvd__div__eq__mult,axiom,
% 0.35/0.62 ! [A: nat,B: nat,C2: nat] :
% 0.35/0.62 ( ( A != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ A @ B )
% 0.35/0.62 => ( ( ( divide_divide_nat @ B @ A )
% 0.35/0.62 = C2 )
% 0.35/0.62 = ( B
% 0.35/0.62 = ( times_times_nat @ C2 @ A ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_eq_mult
% 0.35/0.62 thf(fact_5716_dvd__div__eq__mult,axiom,
% 0.35/0.62 ! [A: int,B: int,C2: int] :
% 0.35/0.62 ( ( A != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ A @ B )
% 0.35/0.62 => ( ( ( divide_divide_int @ B @ A )
% 0.35/0.62 = C2 )
% 0.35/0.62 = ( B
% 0.35/0.62 = ( times_times_int @ C2 @ A ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_div_eq_mult
% 0.35/0.62 thf(fact_5717_unit__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.35/0.62 = zero_z3403309356797280102nteger )
% 0.35/0.62 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_eq_0_iff
% 0.35/0.62 thf(fact_5718_unit__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( ( divide_divide_nat @ A @ B )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 = ( A = zero_zero_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_eq_0_iff
% 0.35/0.62 thf(fact_5719_unit__div__eq__0__iff,axiom,
% 0.35/0.62 ! [B: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( ( divide_divide_int @ A @ B )
% 0.35/0.62 = zero_zero_int )
% 0.35/0.62 = ( A = zero_zero_int ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_eq_0_iff
% 0.35/0.62 thf(fact_5720_inf__period_I4_J,axiom,
% 0.35/0.62 ! [D: real,D3: real,T: real] :
% 0.35/0.62 ( ( dvd_dvd_real @ D @ D3 )
% 0.35/0.62 => ! [X5: real,K4: real] :
% 0.35/0.62 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 0.35/0.62 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % inf_period(4)
% 0.35/0.62 thf(fact_5721_inf__period_I4_J,axiom,
% 0.35/0.62 ! [D: rat,D3: rat,T: rat] :
% 0.35/0.62 ( ( dvd_dvd_rat @ D @ D3 )
% 0.35/0.62 => ! [X5: rat,K4: rat] :
% 0.35/0.62 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 0.35/0.62 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % inf_period(4)
% 0.35/0.62 thf(fact_5722_inf__period_I4_J,axiom,
% 0.35/0.62 ! [D: int,D3: int,T: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ D @ D3 )
% 0.35/0.62 => ! [X5: int,K4: int] :
% 0.35/0.62 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 0.35/0.62 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % inf_period(4)
% 0.35/0.62 thf(fact_5723_inf__period_I3_J,axiom,
% 0.35/0.62 ! [D: real,D3: real,T: real] :
% 0.35/0.62 ( ( dvd_dvd_real @ D @ D3 )
% 0.35/0.62 => ! [X5: real,K4: real] :
% 0.35/0.62 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 0.35/0.62 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % inf_period(3)
% 0.35/0.62 thf(fact_5724_inf__period_I3_J,axiom,
% 0.35/0.62 ! [D: rat,D3: rat,T: rat] :
% 0.35/0.62 ( ( dvd_dvd_rat @ D @ D3 )
% 0.35/0.62 => ! [X5: rat,K4: rat] :
% 0.35/0.62 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 0.35/0.62 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % inf_period(3)
% 0.35/0.62 thf(fact_5725_inf__period_I3_J,axiom,
% 0.35/0.62 ! [D: int,D3: int,T: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ D @ D3 )
% 0.35/0.62 => ! [X5: int,K4: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 0.35/0.62 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % inf_period(3)
% 0.35/0.62 thf(fact_5726_unit__eq__div1,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 0.35/0.62 = C2 )
% 0.35/0.62 = ( A
% 0.35/0.62 = ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_eq_div1
% 0.35/0.62 thf(fact_5727_unit__eq__div1,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( ( divide_divide_nat @ A @ B )
% 0.35/0.62 = C2 )
% 0.35/0.62 = ( A
% 0.35/0.62 = ( times_times_nat @ C2 @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_eq_div1
% 0.35/0.62 thf(fact_5728_unit__eq__div1,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( ( divide_divide_int @ A @ B )
% 0.35/0.62 = C2 )
% 0.35/0.62 = ( A
% 0.35/0.62 = ( times_times_int @ C2 @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_eq_div1
% 0.35/0.62 thf(fact_5729_unit__eq__div2,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( A
% 0.35/0.62 = ( divide6298287555418463151nteger @ C2 @ B ) )
% 0.35/0.62 = ( ( times_3573771949741848930nteger @ A @ B )
% 0.35/0.62 = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_eq_div2
% 0.35/0.62 thf(fact_5730_unit__eq__div2,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( A
% 0.35/0.62 = ( divide_divide_nat @ C2 @ B ) )
% 0.35/0.62 = ( ( times_times_nat @ A @ B )
% 0.35/0.62 = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_eq_div2
% 0.35/0.62 thf(fact_5731_unit__eq__div2,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( A
% 0.35/0.62 = ( divide_divide_int @ C2 @ B ) )
% 0.35/0.62 = ( ( times_times_int @ A @ B )
% 0.35/0.62 = C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_eq_div2
% 0.35/0.62 thf(fact_5732_div__mult__unit2,axiom,
% 0.35/0.62 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.62 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 0.35/0.62 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_mult_unit2
% 0.35/0.62 thf(fact_5733_div__mult__unit2,axiom,
% 0.35/0.62 ! [C2: nat,B: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ B @ A )
% 0.35/0.62 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_mult_unit2
% 0.35/0.62 thf(fact_5734_div__mult__unit2,axiom,
% 0.35/0.62 ! [C2: int,B: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ B @ A )
% 0.35/0.62 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div_mult_unit2
% 0.35/0.62 thf(fact_5735_unit__div__commute,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 )
% 0.35/0.62 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_commute
% 0.35/0.62 thf(fact_5736_unit__div__commute,axiom,
% 0.35/0.62 ! [B: nat,A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 0.35/0.62 = ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_commute
% 0.35/0.62 thf(fact_5737_unit__div__commute,axiom,
% 0.35/0.62 ! [B: int,A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 0.35/0.62 = ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ B ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_commute
% 0.35/0.62 thf(fact_5738_unit__div__mult__swap,axiom,
% 0.35/0.62 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 0.35/0.62 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C2 ) )
% 0.35/0.62 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_mult_swap
% 0.35/0.62 thf(fact_5739_unit__div__mult__swap,axiom,
% 0.35/0.62 ! [C2: nat,A: nat,B: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 0.35/0.62 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_mult_swap
% 0.35/0.62 thf(fact_5740_unit__div__mult__swap,axiom,
% 0.35/0.62 ! [C2: int,A: int,B: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 0.35/0.62 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_div_mult_swap
% 0.35/0.62 thf(fact_5741_is__unit__div__mult2__eq,axiom,
% 0.35/0.62 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 0.35/0.62 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 0.35/0.62 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult2_eq
% 0.35/0.62 thf(fact_5742_is__unit__div__mult2__eq,axiom,
% 0.35/0.62 ! [B: nat,C2: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 0.35/0.62 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult2_eq
% 0.35/0.62 thf(fact_5743_is__unit__div__mult2__eq,axiom,
% 0.35/0.62 ! [B: int,C2: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ C2 @ one_one_int )
% 0.35/0.62 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 0.35/0.62 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult2_eq
% 0.35/0.62 thf(fact_5744_is__unit__power__iff,axiom,
% 0.35/0.62 ! [A: code_integer,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 0.35/0.62 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_power_iff
% 0.35/0.62 thf(fact_5745_is__unit__power__iff,axiom,
% 0.35/0.62 ! [A: nat,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 0.35/0.62 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_power_iff
% 0.35/0.62 thf(fact_5746_is__unit__power__iff,axiom,
% 0.35/0.62 ! [A: int,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 0.35/0.62 = ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_power_iff
% 0.35/0.62 thf(fact_5747_unit__imp__mod__eq__0,axiom,
% 0.35/0.62 ! [B: code_integer,A: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( modulo364778990260209775nteger @ A @ B )
% 0.35/0.62 = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_imp_mod_eq_0
% 0.35/0.62 thf(fact_5748_unit__imp__mod__eq__0,axiom,
% 0.35/0.62 ! [B: nat,A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( modulo_modulo_nat @ A @ B )
% 0.35/0.62 = zero_zero_nat ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_imp_mod_eq_0
% 0.35/0.62 thf(fact_5749_unit__imp__mod__eq__0,axiom,
% 0.35/0.62 ! [B: int,A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( modulo_modulo_int @ A @ B )
% 0.35/0.62 = zero_zero_int ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_imp_mod_eq_0
% 0.35/0.62 thf(fact_5750_unit__imp__mod__eq__0,axiom,
% 0.35/0.62 ! [B: code_natural,A: code_natural] :
% 0.35/0.62 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 0.35/0.62 => ( ( modulo8411746178871703098atural @ A @ B )
% 0.35/0.62 = zero_z2226904508553997617atural ) ) ).
% 0.35/0.62
% 0.35/0.62 % unit_imp_mod_eq_0
% 0.35/0.62 thf(fact_5751_pochhammer__nonneg,axiom,
% 0.35/0.62 ! [X: real,N: nat] :
% 0.35/0.62 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_nonneg
% 0.35/0.62 thf(fact_5752_pochhammer__nonneg,axiom,
% 0.35/0.62 ! [X: rat,N: nat] :
% 0.35/0.62 ( ( ord_less_rat @ zero_zero_rat @ X )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_nonneg
% 0.35/0.62 thf(fact_5753_pochhammer__nonneg,axiom,
% 0.35/0.62 ! [X: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_nonneg
% 0.35/0.62 thf(fact_5754_pochhammer__nonneg,axiom,
% 0.35/0.62 ! [X: int,N: nat] :
% 0.35/0.62 ( ( ord_less_int @ zero_zero_int @ X )
% 0.35/0.62 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_nonneg
% 0.35/0.62 thf(fact_5755_dvd__imp__le,axiom,
% 0.35/0.62 ! [K2: nat,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ K2 @ N )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.62 => ( ord_less_eq_nat @ K2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_imp_le
% 0.35/0.62 thf(fact_5756_dvd__mult__cancel,axiom,
% 0.35/0.62 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.62 => ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_cancel
% 0.35/0.62 thf(fact_5757_nat__mult__dvd__cancel1,axiom,
% 0.35/0.62 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 0.35/0.62 = ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % nat_mult_dvd_cancel1
% 0.35/0.62 thf(fact_5758_pochhammer__0__left,axiom,
% 0.35/0.62 ! [N: nat] :
% 0.35/0.62 ( ( ( N = zero_zero_nat )
% 0.35/0.62 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 0.35/0.62 = one_one_Code_integer ) )
% 0.35/0.62 & ( ( N != zero_zero_nat )
% 0.35/0.62 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 0.35/0.62 = zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_0_left
% 0.35/0.62 thf(fact_5759_pochhammer__0__left,axiom,
% 0.35/0.62 ! [N: nat] :
% 0.35/0.62 ( ( ( N = zero_zero_nat )
% 0.35/0.62 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 0.35/0.62 = one_one_complex ) )
% 0.35/0.62 & ( ( N != zero_zero_nat )
% 0.35/0.62 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 0.35/0.62 = zero_zero_complex ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_0_left
% 0.35/0.62 thf(fact_5760_pochhammer__0__left,axiom,
% 0.35/0.62 ! [N: nat] :
% 0.35/0.62 ( ( ( N = zero_zero_nat )
% 0.35/0.62 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 0.35/0.62 = one_one_real ) )
% 0.35/0.62 & ( ( N != zero_zero_nat )
% 0.35/0.62 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 0.35/0.62 = zero_zero_real ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_0_left
% 0.35/0.62 thf(fact_5761_pochhammer__0__left,axiom,
% 0.35/0.62 ! [N: nat] :
% 0.35/0.62 ( ( ( N = zero_zero_nat )
% 0.35/0.62 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.35/0.62 = one_one_rat ) )
% 0.35/0.62 & ( ( N != zero_zero_nat )
% 0.35/0.62 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 0.35/0.62 = zero_zero_rat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_0_left
% 0.35/0.62 thf(fact_5762_pochhammer__0__left,axiom,
% 0.35/0.62 ! [N: nat] :
% 0.35/0.62 ( ( ( N = zero_zero_nat )
% 0.35/0.62 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.35/0.62 = one_one_nat ) )
% 0.35/0.62 & ( ( N != zero_zero_nat )
% 0.35/0.62 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 0.35/0.62 = zero_zero_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_0_left
% 0.35/0.62 thf(fact_5763_pochhammer__0__left,axiom,
% 0.35/0.62 ! [N: nat] :
% 0.35/0.62 ( ( ( N = zero_zero_nat )
% 0.35/0.62 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.35/0.62 = one_one_int ) )
% 0.35/0.62 & ( ( N != zero_zero_nat )
% 0.35/0.62 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 0.35/0.62 = zero_zero_int ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_0_left
% 0.35/0.62 thf(fact_5764_bezout__add__strong__nat,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( A != zero_zero_nat )
% 0.35/0.62 => ? [D5: nat,X3: nat,Y3: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ D5 @ A )
% 0.35/0.62 & ( dvd_dvd_nat @ D5 @ B )
% 0.35/0.62 & ( ( times_times_nat @ A @ X3 )
% 0.35/0.62 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % bezout_add_strong_nat
% 0.35/0.62 thf(fact_5765_mod__greater__zero__iff__not__dvd,axiom,
% 0.35/0.62 ! [M2: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ N ) )
% 0.35/0.62 = ( ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_greater_zero_iff_not_dvd
% 0.35/0.62 thf(fact_5766_mod__eq__dvd__iff__nat,axiom,
% 0.35/0.62 ! [N: nat,M2: nat,Q2: nat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.62 => ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 0.35/0.62 = ( modulo_modulo_nat @ N @ Q2 ) )
% 0.35/0.62 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_eq_dvd_iff_nat
% 0.35/0.62 thf(fact_5767_sum__power__add,axiom,
% 0.35/0.62 ! [X: complex,M2: nat,I5: set_nat] :
% 0.35/0.62 ( ( groups2073611262835488442omplex
% 0.35/0.62 @ ^ [I: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M2 @ I ) )
% 0.35/0.62 @ I5 )
% 0.35/0.62 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_power_add
% 0.35/0.62 thf(fact_5768_sum__power__add,axiom,
% 0.35/0.62 ! [X: rat,M2: nat,I5: set_nat] :
% 0.35/0.62 ( ( groups2906978787729119204at_rat
% 0.35/0.62 @ ^ [I: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M2 @ I ) )
% 0.35/0.62 @ I5 )
% 0.35/0.62 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_power_add
% 0.35/0.62 thf(fact_5769_sum__power__add,axiom,
% 0.35/0.62 ! [X: int,M2: nat,I5: set_nat] :
% 0.35/0.62 ( ( groups3539618377306564664at_int
% 0.35/0.62 @ ^ [I: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M2 @ I ) )
% 0.35/0.62 @ I5 )
% 0.35/0.62 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_power_add
% 0.35/0.62 thf(fact_5770_sum__power__add,axiom,
% 0.35/0.62 ! [X: real,M2: nat,I5: set_nat] :
% 0.35/0.62 ( ( groups6591440286371151544t_real
% 0.35/0.62 @ ^ [I: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M2 @ I ) )
% 0.35/0.62 @ I5 )
% 0.35/0.62 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I5 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_power_add
% 0.35/0.62 thf(fact_5771_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,F2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( groups8097168146408367636l_real @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5772_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_int,A4: set_int,F2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5773_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_complex,A4: set_complex,F2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5774_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,F2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( groups1300246762558778688al_rat @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5775_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_int,A4: set_int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5776_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_complex,A4: set_complex,F2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5777_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,F2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5778_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_int,A4: set_int,F2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: int] :
% 0.35/0.62 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5779_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_complex,A4: set_complex,F2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: complex] :
% 0.35/0.62 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5780_sum__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,F2: real > int] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ! [B3: real] :
% 0.35/0.62 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ B3 ) ) )
% 0.35/0.62 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( groups1932886352136224148al_int @ F2 @ B5 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_mono2
% 0.35/0.62 thf(fact_5781_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_int,B5: set_int,G2: int > complex] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups3049146728041665814omplex @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_complex @ ( groups3049146728041665814omplex @ G2 @ A4 ) @ ( groups3049146728041665814omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5782_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_complex,B5: set_complex,G2: complex > complex] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups7754918857620584856omplex @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G2 @ A4 ) @ ( groups7754918857620584856omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5783_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_int,B5: set_int,G2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( groups8778361861064173332t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G2 @ A4 ) @ ( groups8778361861064173332t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5784_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_real ) )
% 0.35/0.62 => ( ( groups5808333547571424918x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G2 @ A4 ) @ ( groups5808333547571424918x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5785_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A4 ) @ ( groups3906332499630173760nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5786_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_rat ) )
% 0.35/0.62 => ( ( groups5058264527183730370ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G2 @ A4 ) @ ( groups5058264527183730370ex_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5787_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5788_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_nat ) )
% 0.35/0.62 => ( ( groups5693394587270226106ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5789_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_int ) )
% 0.35/0.62 => ( ( groups5690904116761175830ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G2 @ A4 ) @ ( groups5690904116761175830ex_int @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5790_sum_Ounion__inter__neutral,axiom,
% 0.35/0.62 ! [A4: set_nat,B5: set_nat,G2: nat > complex] :
% 0.35/0.62 ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ( finite_finite_nat @ B5 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.35/0.62 => ( ( G2 @ X3 )
% 0.35/0.62 = zero_zero_complex ) )
% 0.35/0.62 => ( ( groups2073611262835488442omplex @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.62 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G2 @ A4 ) @ ( groups2073611262835488442omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.union_inter_neutral
% 0.35/0.62 thf(fact_5791_sum_OatLeastAtMost__rev,axiom,
% 0.35/0.62 ! [G2: nat > nat,N: nat,M2: nat] :
% 0.35/0.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 0.35/0.62 = ( groups3542108847815614940at_nat
% 0.35/0.62 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 0.35/0.62 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeastAtMost_rev
% 0.35/0.62 thf(fact_5792_sum_OatLeastAtMost__rev,axiom,
% 0.35/0.62 ! [G2: nat > real,N: nat,M2: nat] :
% 0.35/0.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 0.35/0.62 = ( groups6591440286371151544t_real
% 0.35/0.62 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 0.35/0.62 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeastAtMost_rev
% 0.35/0.62 thf(fact_5793_finite__divisors__nat,axiom,
% 0.35/0.62 ! [M2: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.62 => ( finite_finite_nat
% 0.35/0.62 @ ( collect_nat
% 0.35/0.62 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % finite_divisors_nat
% 0.35/0.62 thf(fact_5794_powser__sums__zero,axiom,
% 0.35/0.62 ! [A: nat > complex] :
% 0.35/0.62 ( sums_complex
% 0.35/0.62 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 0.35/0.62 @ ( A @ zero_zero_nat ) ) ).
% 0.35/0.62
% 0.35/0.62 % powser_sums_zero
% 0.35/0.62 thf(fact_5795_powser__sums__zero,axiom,
% 0.35/0.62 ! [A: nat > real] :
% 0.35/0.62 ( sums_real
% 0.35/0.62 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 0.35/0.62 @ ( A @ zero_zero_nat ) ) ).
% 0.35/0.62
% 0.35/0.62 % powser_sums_zero
% 0.35/0.62 thf(fact_5796_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.62 ! [F2: nat > complex,K2: nat] :
% 0.35/0.62 ( ( ( F2 @ zero_zero_nat )
% 0.35/0.62 = zero_zero_complex )
% 0.35/0.62 => ( ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 0.35/0.62 = ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_shift_lb_Suc0_0
% 0.35/0.62 thf(fact_5797_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.62 ! [F2: nat > rat,K2: nat] :
% 0.35/0.62 ( ( ( F2 @ zero_zero_nat )
% 0.35/0.62 = zero_zero_rat )
% 0.35/0.62 => ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 0.35/0.62 = ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_shift_lb_Suc0_0
% 0.35/0.62 thf(fact_5798_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.62 ! [F2: nat > int,K2: nat] :
% 0.35/0.62 ( ( ( F2 @ zero_zero_nat )
% 0.35/0.62 = zero_zero_int )
% 0.35/0.62 => ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 0.35/0.62 = ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_shift_lb_Suc0_0
% 0.35/0.62 thf(fact_5799_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.62 ! [F2: nat > nat,K2: nat] :
% 0.35/0.62 ( ( ( F2 @ zero_zero_nat )
% 0.35/0.62 = zero_zero_nat )
% 0.35/0.62 => ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 0.35/0.62 = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_shift_lb_Suc0_0
% 0.35/0.62 thf(fact_5800_sum__shift__lb__Suc0__0,axiom,
% 0.35/0.62 ! [F2: nat > real,K2: nat] :
% 0.35/0.62 ( ( ( F2 @ zero_zero_nat )
% 0.35/0.62 = zero_zero_real )
% 0.35/0.62 => ( ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 0.35/0.62 = ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_shift_lb_Suc0_0
% 0.35/0.62 thf(fact_5801_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.62 ! [G2: nat > rat,N: nat] :
% 0.35/0.62 ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast0_atMost_Suc
% 0.35/0.62 thf(fact_5802_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.62 ! [G2: nat > int,N: nat] :
% 0.35/0.62 ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast0_atMost_Suc
% 0.35/0.62 thf(fact_5803_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.62 ! [G2: nat > nat,N: nat] :
% 0.35/0.62 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast0_atMost_Suc
% 0.35/0.62 thf(fact_5804_sum_OatLeast0__atMost__Suc,axiom,
% 0.35/0.62 ! [G2: nat > real,N: nat] :
% 0.35/0.62 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast0_atMost_Suc
% 0.35/0.62 thf(fact_5805_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > rat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.62 = ( plus_plus_rat @ ( G2 @ M2 ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast_Suc_atMost
% 0.35/0.62 thf(fact_5806_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > int] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.62 = ( plus_plus_int @ ( G2 @ M2 ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast_Suc_atMost
% 0.35/0.62 thf(fact_5807_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > nat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.62 = ( plus_plus_nat @ ( G2 @ M2 ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast_Suc_atMost
% 0.35/0.62 thf(fact_5808_sum_OatLeast__Suc__atMost,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > real] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.62 = ( plus_plus_real @ ( G2 @ M2 ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.atLeast_Suc_atMost
% 0.35/0.62 thf(fact_5809_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > rat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.62 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_rat @ ( G2 @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.nat_ivl_Suc'
% 0.35/0.62 thf(fact_5810_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > int] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.62 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_int @ ( G2 @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.nat_ivl_Suc'
% 0.35/0.62 thf(fact_5811_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > nat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.62 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_nat @ ( G2 @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.nat_ivl_Suc'
% 0.35/0.62 thf(fact_5812_sum_Onat__ivl__Suc_H,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > real] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.62 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_real @ ( G2 @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum.nat_ivl_Suc'
% 0.35/0.62 thf(fact_5813_even__zero,axiom,
% 0.35/0.62 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 0.35/0.62
% 0.35/0.62 % even_zero
% 0.35/0.62 thf(fact_5814_even__zero,axiom,
% 0.35/0.62 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 0.35/0.62
% 0.35/0.62 % even_zero
% 0.35/0.62 thf(fact_5815_is__unitE,axiom,
% 0.35/0.62 ! [A: code_integer,C2: code_integer] :
% 0.35/0.62 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 0.35/0.62 => ~ ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.62 => ! [B3: code_integer] :
% 0.35/0.62 ( ( B3 != zero_z3403309356797280102nteger )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 0.35/0.62 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 0.35/0.62 = B3 )
% 0.35/0.62 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 0.35/0.62 = A )
% 0.35/0.62 => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 0.35/0.62 = one_one_Code_integer )
% 0.35/0.62 => ( ( divide6298287555418463151nteger @ C2 @ A )
% 0.35/0.62 != ( times_3573771949741848930nteger @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unitE
% 0.35/0.62 thf(fact_5816_is__unitE,axiom,
% 0.35/0.62 ! [A: nat,C2: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.35/0.62 => ~ ( ( A != zero_zero_nat )
% 0.35/0.62 => ! [B3: nat] :
% 0.35/0.62 ( ( B3 != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 0.35/0.62 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 0.35/0.62 = B3 )
% 0.35/0.62 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 0.35/0.62 = A )
% 0.35/0.62 => ( ( ( times_times_nat @ A @ B3 )
% 0.35/0.62 = one_one_nat )
% 0.35/0.62 => ( ( divide_divide_nat @ C2 @ A )
% 0.35/0.62 != ( times_times_nat @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unitE
% 0.35/0.62 thf(fact_5817_is__unitE,axiom,
% 0.35/0.62 ! [A: int,C2: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ A @ one_one_int )
% 0.35/0.62 => ~ ( ( A != zero_zero_int )
% 0.35/0.62 => ! [B3: int] :
% 0.35/0.62 ( ( B3 != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 0.35/0.62 => ( ( ( divide_divide_int @ one_one_int @ A )
% 0.35/0.62 = B3 )
% 0.35/0.62 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 0.35/0.62 = A )
% 0.35/0.62 => ( ( ( times_times_int @ A @ B3 )
% 0.35/0.62 = one_one_int )
% 0.35/0.62 => ( ( divide_divide_int @ C2 @ A )
% 0.35/0.62 != ( times_times_int @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unitE
% 0.35/0.62 thf(fact_5818_is__unit__div__mult__cancel__left,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer] :
% 0.35/0.62 ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.35/0.62 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult_cancel_left
% 0.35/0.62 thf(fact_5819_is__unit__div__mult__cancel__left,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( A != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 0.35/0.62 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult_cancel_left
% 0.35/0.62 thf(fact_5820_is__unit__div__mult__cancel__left,axiom,
% 0.35/0.62 ! [A: int,B: int] :
% 0.35/0.62 ( ( A != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 0.35/0.62 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult_cancel_left
% 0.35/0.62 thf(fact_5821_is__unit__div__mult__cancel__right,axiom,
% 0.35/0.62 ! [A: code_integer,B: code_integer] :
% 0.35/0.62 ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 0.35/0.62 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 0.35/0.62 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult_cancel_right
% 0.35/0.62 thf(fact_5822_is__unit__div__mult__cancel__right,axiom,
% 0.35/0.62 ! [A: nat,B: nat] :
% 0.35/0.62 ( ( A != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 0.35/0.62 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 0.35/0.62 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult_cancel_right
% 0.35/0.62 thf(fact_5823_is__unit__div__mult__cancel__right,axiom,
% 0.35/0.62 ! [A: int,B: int] :
% 0.35/0.62 ( ( A != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ B @ one_one_int )
% 0.35/0.62 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 0.35/0.62 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % is_unit_div_mult_cancel_right
% 0.35/0.62 thf(fact_5824_evenE,axiom,
% 0.35/0.62 ! [A: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.62 => ~ ! [B3: nat] :
% 0.35/0.62 ( A
% 0.35/0.62 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % evenE
% 0.35/0.62 thf(fact_5825_evenE,axiom,
% 0.35/0.62 ! [A: int] :
% 0.35/0.62 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.62 => ~ ! [B3: int] :
% 0.35/0.62 ( A
% 0.35/0.62 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % evenE
% 0.35/0.62 thf(fact_5826_dvd__power__iff,axiom,
% 0.35/0.62 ! [X: code_integer,M2: nat,N: nat] :
% 0.35/0.62 ( ( X != zero_z3403309356797280102nteger )
% 0.35/0.62 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.35/0.62 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 0.35/0.62 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power_iff
% 0.35/0.62 thf(fact_5827_dvd__power__iff,axiom,
% 0.35/0.62 ! [X: nat,M2: nat,N: nat] :
% 0.35/0.62 ( ( X != zero_zero_nat )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N ) )
% 0.35/0.62 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 0.35/0.62 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power_iff
% 0.35/0.62 thf(fact_5828_dvd__power__iff,axiom,
% 0.35/0.62 ! [X: int,M2: nat,N: nat] :
% 0.35/0.62 ( ( X != zero_zero_int )
% 0.35/0.62 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N ) )
% 0.35/0.62 = ( ( dvd_dvd_int @ X @ one_one_int )
% 0.35/0.62 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power_iff
% 0.35/0.62 thf(fact_5829_dvd__power,axiom,
% 0.35/0.62 ! [N: nat,X: code_integer] :
% 0.35/0.62 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.62 | ( X = one_one_Code_integer ) )
% 0.35/0.62 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power
% 0.35/0.62 thf(fact_5830_dvd__power,axiom,
% 0.35/0.62 ! [N: nat,X: nat] :
% 0.35/0.62 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.62 | ( X = one_one_nat ) )
% 0.35/0.62 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power
% 0.35/0.62 thf(fact_5831_dvd__power,axiom,
% 0.35/0.62 ! [N: nat,X: real] :
% 0.35/0.62 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.62 | ( X = one_one_real ) )
% 0.35/0.62 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power
% 0.35/0.62 thf(fact_5832_dvd__power,axiom,
% 0.35/0.62 ! [N: nat,X: int] :
% 0.35/0.62 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.62 | ( X = one_one_int ) )
% 0.35/0.62 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power
% 0.35/0.62 thf(fact_5833_dvd__power,axiom,
% 0.35/0.62 ! [N: nat,X: complex] :
% 0.35/0.62 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.62 | ( X = one_one_complex ) )
% 0.35/0.62 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_power
% 0.35/0.62 thf(fact_5834_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,B: real,F2: real > real] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( groups8097168146408367636l_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5835_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_int,A4: set_int,B: int,F2: int > real] :
% 0.35/0.62 ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.62 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5836_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > real] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.62 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5837_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,B: real,F2: real > rat] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( groups1300246762558778688al_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5838_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_int,A4: set_int,B: int,F2: int > rat] :
% 0.35/0.62 ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.62 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5839_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > rat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.62 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5840_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,B: real,F2: real > nat] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5841_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_int,A4: set_int,B: int,F2: int > nat] :
% 0.35/0.62 ( ( finite_finite_int @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.62 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5842_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > nat] :
% 0.35/0.62 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.62 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.62 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5843_sum__strict__mono2,axiom,
% 0.35/0.62 ! [B5: set_real,A4: set_real,B: real,F2: real > int] :
% 0.35/0.62 ( ( finite_finite_real @ B5 )
% 0.35/0.62 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.62 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.62 => ( ( ord_less_int @ zero_zero_int @ ( F2 @ B ) )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ B5 )
% 0.35/0.62 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ord_less_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( groups1932886352136224148al_int @ F2 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_strict_mono2
% 0.35/0.62 thf(fact_5844_member__le__sum,axiom,
% 0.35/0.62 ! [I2: complex,A4: set_complex,F2: complex > real] :
% 0.35/0.62 ( ( member_complex @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5845_member__le__sum,axiom,
% 0.35/0.62 ! [I2: int,A4: set_int,F2: int > real] :
% 0.35/0.62 ( ( member_int @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5846_member__le__sum,axiom,
% 0.35/0.62 ! [I2: real,A4: set_real,F2: real > real] :
% 0.35/0.62 ( ( member_real @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 0.35/0.62 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5847_member__le__sum,axiom,
% 0.35/0.62 ! [I2: complex,A4: set_complex,F2: complex > rat] :
% 0.35/0.62 ( ( member_complex @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5848_member__le__sum,axiom,
% 0.35/0.62 ! [I2: int,A4: set_int,F2: int > rat] :
% 0.35/0.62 ( ( member_int @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5849_member__le__sum,axiom,
% 0.35/0.62 ! [I2: real,A4: set_real,F2: real > rat] :
% 0.35/0.62 ( ( member_real @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5850_member__le__sum,axiom,
% 0.35/0.62 ! [I2: nat,A4: set_nat,F2: nat > rat] :
% 0.35/0.62 ( ( member_nat @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: nat] :
% 0.35/0.62 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 0.35/0.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5851_member__le__sum,axiom,
% 0.35/0.62 ! [I2: complex,A4: set_complex,F2: complex > nat] :
% 0.35/0.62 ( ( member_complex @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: complex] :
% 0.35/0.62 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5852_member__le__sum,axiom,
% 0.35/0.62 ! [I2: int,A4: set_int,F2: int > nat] :
% 0.35/0.62 ( ( member_int @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: int] :
% 0.35/0.62 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5853_member__le__sum,axiom,
% 0.35/0.62 ! [I2: real,A4: set_real,F2: real > nat] :
% 0.35/0.62 ( ( member_real @ I2 @ A4 )
% 0.35/0.62 => ( ! [X3: real] :
% 0.35/0.62 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 0.35/0.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.62 => ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % member_le_sum
% 0.35/0.62 thf(fact_5854_div2__even__ext__nat,axiom,
% 0.35/0.62 ! [X: nat,Y: nat] :
% 0.35/0.62 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.62 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.62 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 0.35/0.62 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 0.35/0.62 => ( X = Y ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % div2_even_ext_nat
% 0.35/0.62 thf(fact_5855_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5856_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5857_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5858_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 0.35/0.62 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5859_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > real,K5: real] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 0.35/0.62 => ( ord_less_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5860_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > real,K5: real] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.35/0.62 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5861_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > real,K5: real] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 0.35/0.62 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5862_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > int,K5: int] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 0.35/0.62 => ( ord_less_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5863_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > int,K5: int] :
% 0.35/0.62 ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 0.35/0.62 => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5864_sum__bounded__above__strict,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > int,K5: int] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 0.35/0.62 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 0.35/0.62 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_strict
% 0.35/0.62 thf(fact_5865_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > real,K5: real] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_complex )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5866_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > real,K5: real] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_int )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5867_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > real,K5: real] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_real )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5868_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: complex] :
% 0.35/0.62 ( ( member_complex @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_complex )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5869_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_nat )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5870_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_int,F2: int > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: int] :
% 0.35/0.62 ( ( member_int @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite_finite_int @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_int )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5871_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_real,F2: real > rat,K5: rat] :
% 0.35/0.62 ( ! [I3: real] :
% 0.35/0.62 ( ( member_real @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite_finite_real @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_real )
% 0.35/0.62 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5872_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_nat,F2: nat > real,K5: real] :
% 0.35/0.62 ( ! [I3: nat] :
% 0.35/0.62 ( ( member_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite_finite_nat @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_nat )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5873_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_list_nat,F2: list_nat > real,K5: real] :
% 0.35/0.62 ( ! [I3: list_nat] :
% 0.35/0.62 ( ( member_list_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_list_nat @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite8100373058378681591st_nat @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_list_nat )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups8399112307953289288t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5874_sum__bounded__above__divide,axiom,
% 0.35/0.62 ! [A4: set_set_nat,F2: set_nat > real,K5: real] :
% 0.35/0.62 ( ! [I3: set_nat] :
% 0.35/0.62 ( ( member_set_nat @ I3 @ A4 )
% 0.35/0.62 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_set_nat @ A4 ) ) ) ) )
% 0.35/0.62 => ( ( finite1152437895449049373et_nat @ A4 )
% 0.35/0.62 => ( ( A4 != bot_bot_set_set_nat )
% 0.35/0.62 => ( ord_less_eq_real @ ( groups5107569545109728110t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % sum_bounded_above_divide
% 0.35/0.62 thf(fact_5875_pochhammer__rec,axiom,
% 0.35/0.62 ! [A: code_integer,N: nat] :
% 0.35/0.62 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec
% 0.35/0.62 thf(fact_5876_pochhammer__rec,axiom,
% 0.35/0.62 ! [A: complex,N: nat] :
% 0.35/0.62 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec
% 0.35/0.62 thf(fact_5877_pochhammer__rec,axiom,
% 0.35/0.62 ! [A: real,N: nat] :
% 0.35/0.62 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec
% 0.35/0.62 thf(fact_5878_pochhammer__rec,axiom,
% 0.35/0.62 ! [A: rat,N: nat] :
% 0.35/0.62 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec
% 0.35/0.62 thf(fact_5879_pochhammer__rec,axiom,
% 0.35/0.62 ! [A: nat,N: nat] :
% 0.35/0.62 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec
% 0.35/0.62 thf(fact_5880_pochhammer__rec,axiom,
% 0.35/0.62 ! [A: int,N: nat] :
% 0.35/0.62 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec
% 0.35/0.62 thf(fact_5881_dvd__mult__cancel1,axiom,
% 0.35/0.62 ! [M2: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N ) @ M2 )
% 0.35/0.62 = ( N = one_one_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_cancel1
% 0.35/0.62 thf(fact_5882_dvd__mult__cancel2,axiom,
% 0.35/0.62 ! [M2: nat,N: nat] :
% 0.35/0.62 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.62 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M2 ) @ M2 )
% 0.35/0.62 = ( N = one_one_nat ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_mult_cancel2
% 0.35/0.62 thf(fact_5883_pochhammer__rec_H,axiom,
% 0.35/0.62 ! [Z3: rat,N: nat] :
% 0.35/0.62 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec'
% 0.35/0.62 thf(fact_5884_pochhammer__rec_H,axiom,
% 0.35/0.62 ! [Z3: real,N: nat] :
% 0.35/0.62 ( ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z3 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec'
% 0.35/0.62 thf(fact_5885_pochhammer__rec_H,axiom,
% 0.35/0.62 ! [Z3: int,N: nat] :
% 0.35/0.62 ( ( comm_s4660882817536571857er_int @ Z3 @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z3 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec'
% 0.35/0.62 thf(fact_5886_pochhammer__rec_H,axiom,
% 0.35/0.62 ! [Z3: nat,N: nat] :
% 0.35/0.62 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z3 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_rec'
% 0.35/0.62 thf(fact_5887_pochhammer__Suc,axiom,
% 0.35/0.62 ! [A: rat,N: nat] :
% 0.35/0.62 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_Suc
% 0.35/0.62 thf(fact_5888_pochhammer__Suc,axiom,
% 0.35/0.62 ! [A: real,N: nat] :
% 0.35/0.62 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_Suc
% 0.35/0.62 thf(fact_5889_pochhammer__Suc,axiom,
% 0.35/0.62 ! [A: int,N: nat] :
% 0.35/0.62 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_Suc
% 0.35/0.62 thf(fact_5890_pochhammer__Suc,axiom,
% 0.35/0.62 ! [A: nat,N: nat] :
% 0.35/0.62 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.62 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_Suc
% 0.35/0.62 thf(fact_5891_dvd__minus__add,axiom,
% 0.35/0.62 ! [Q2: nat,N: nat,R3: nat,M2: nat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ Q2 @ N )
% 0.35/0.62 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R3 @ M2 ) )
% 0.35/0.62 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ Q2 ) )
% 0.35/0.62 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R3 @ M2 ) @ Q2 ) ) ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % dvd_minus_add
% 0.35/0.62 thf(fact_5892_power__dvd__imp__le,axiom,
% 0.35/0.62 ! [I2: nat,M2: nat,N: nat] :
% 0.35/0.62 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M2 ) @ ( power_power_nat @ I2 @ N ) )
% 0.35/0.62 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 0.35/0.62 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % power_dvd_imp_le
% 0.35/0.62 thf(fact_5893_pochhammer__product_H,axiom,
% 0.35/0.62 ! [Z3: rat,N: nat,M2: nat] :
% 0.35/0.62 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.62 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N ) ) @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_product'
% 0.35/0.62 thf(fact_5894_pochhammer__product_H,axiom,
% 0.35/0.62 ! [Z3: real,N: nat,M2: nat] :
% 0.35/0.62 ( ( comm_s7457072308508201937r_real @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.62 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N ) ) @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_product'
% 0.35/0.62 thf(fact_5895_pochhammer__product_H,axiom,
% 0.35/0.62 ! [Z3: int,N: nat,M2: nat] :
% 0.35/0.62 ( ( comm_s4660882817536571857er_int @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.62 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N ) ) @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_product'
% 0.35/0.62 thf(fact_5896_pochhammer__product_H,axiom,
% 0.35/0.62 ! [Z3: nat,N: nat,M2: nat] :
% 0.35/0.62 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 0.35/0.62 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N ) ) @ M2 ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % pochhammer_product'
% 0.35/0.62 thf(fact_5897_mod__nat__eqI,axiom,
% 0.35/0.62 ! [R3: nat,N: nat,M2: nat] :
% 0.35/0.62 ( ( ord_less_nat @ R3 @ N )
% 0.35/0.62 => ( ( ord_less_eq_nat @ R3 @ M2 )
% 0.35/0.62 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M2 @ R3 ) )
% 0.35/0.62 => ( ( modulo_modulo_nat @ M2 @ N )
% 0.35/0.62 = R3 ) ) ) ) ).
% 0.35/0.62
% 0.35/0.62 % mod_nat_eqI
% 0.35/0.62 thf(fact_5898_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.62 ! [M2: nat,N: nat,G2: nat > rat] :
% 0.35/0.62 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.62 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.62 = ( plus_plus_rat @ ( G2 @ M2 )
% 0.35/0.62 @ ( groups2906978787729119204at_rat
% 0.35/0.62 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.62 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.Suc_reindex_ivl
% 0.35/0.63 thf(fact_5899_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_int @ ( G2 @ M2 )
% 0.35/0.63 @ ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.Suc_reindex_ivl
% 0.35/0.63 thf(fact_5900_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_nat @ ( G2 @ M2 )
% 0.35/0.63 @ ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.Suc_reindex_ivl
% 0.35/0.63 thf(fact_5901_sum_OSuc__reindex__ivl,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_real @ ( G2 @ M2 )
% 0.35/0.63 @ ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.Suc_reindex_ivl
% 0.35/0.63 thf(fact_5902_sum__Suc__diff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > rat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.63 => ( ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( minus_minus_rat @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc_diff
% 0.35/0.63 thf(fact_5903_sum__Suc__diff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.63 => ( ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( minus_minus_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc_diff
% 0.35/0.63 thf(fact_5904_sum__Suc__diff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.63 => ( ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( minus_minus_real @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc_diff
% 0.35/0.63 thf(fact_5905_sum__norm__bound,axiom,
% 0.35/0.63 ! [S3: set_real,F2: real > complex,K5: real] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ S3 )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ S3 ) ) @ K5 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_norm_bound
% 0.35/0.63 thf(fact_5906_sum__norm__bound,axiom,
% 0.35/0.63 ! [S3: set_nat,F2: nat > complex,K5: real] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ S3 )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S3 ) ) @ K5 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_norm_bound
% 0.35/0.63 thf(fact_5907_sum__norm__bound,axiom,
% 0.35/0.63 ! [S3: set_complex,F2: complex > complex,K5: real] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ S3 )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ S3 ) ) @ K5 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_norm_bound
% 0.35/0.63 thf(fact_5908_sum__norm__bound,axiom,
% 0.35/0.63 ! [S3: set_int,F2: int > complex,K5: real] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ S3 )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ S3 ) ) @ K5 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_norm_bound
% 0.35/0.63 thf(fact_5909_sum__norm__bound,axiom,
% 0.35/0.63 ! [S3: set_list_nat,F2: list_nat > complex,K5: real] :
% 0.35/0.63 ( ! [X3: list_nat] :
% 0.35/0.63 ( ( member_list_nat @ X3 @ S3 )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6529277132148336714omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_list_nat @ S3 ) ) @ K5 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_norm_bound
% 0.35/0.63 thf(fact_5910_sum__norm__bound,axiom,
% 0.35/0.63 ! [S3: set_set_nat,F2: set_nat > complex,K5: real] :
% 0.35/0.63 ( ! [X3: set_nat] :
% 0.35/0.63 ( ( member_set_nat @ X3 @ S3 )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_set_nat @ S3 ) ) @ K5 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_norm_bound
% 0.35/0.63 thf(fact_5911_sum__norm__bound,axiom,
% 0.35/0.63 ! [S3: set_nat,F2: nat > real,K5: real] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ S3 )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F2 @ X3 ) ) @ K5 ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S3 ) ) @ K5 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_norm_bound
% 0.35/0.63 thf(fact_5912_sum_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > rat,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.ub_add_nat
% 0.35/0.63 thf(fact_5913_sum_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > int,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.ub_add_nat
% 0.35/0.63 thf(fact_5914_sum_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > nat,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.ub_add_nat
% 0.35/0.63 thf(fact_5915_sum_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > real,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.ub_add_nat
% 0.35/0.63 thf(fact_5916_even__two__times__div__two,axiom,
% 0.35/0.63 ! [A: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.63 = A ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_two_times_div_two
% 0.35/0.63 thf(fact_5917_even__two__times__div__two,axiom,
% 0.35/0.63 ! [A: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 0.35/0.63 = A ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_two_times_div_two
% 0.35/0.63 thf(fact_5918_even__iff__mod__2__eq__zero,axiom,
% 0.35/0.63 ! [A: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63 = zero_zero_nat ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_iff_mod_2_eq_zero
% 0.35/0.63 thf(fact_5919_even__iff__mod__2__eq__zero,axiom,
% 0.35/0.63 ! [A: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.63 = zero_zero_int ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_iff_mod_2_eq_zero
% 0.35/0.63 thf(fact_5920_even__iff__mod__2__eq__zero,axiom,
% 0.35/0.63 ! [A: code_natural] :
% 0.35/0.63 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.63 = zero_z2226904508553997617atural ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_iff_mod_2_eq_zero
% 0.35/0.63 thf(fact_5921_power__mono__odd,axiom,
% 0.35/0.63 ! [N: nat,A: real,B: real] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ( ord_less_eq_real @ A @ B )
% 0.35/0.63 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % power_mono_odd
% 0.35/0.63 thf(fact_5922_power__mono__odd,axiom,
% 0.35/0.63 ! [N: nat,A: rat,B: rat] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.63 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % power_mono_odd
% 0.35/0.63 thf(fact_5923_power__mono__odd,axiom,
% 0.35/0.63 ! [N: nat,A: int,B: int] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ( ord_less_eq_int @ A @ B )
% 0.35/0.63 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % power_mono_odd
% 0.35/0.63 thf(fact_5924_odd__pos,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % odd_pos
% 0.35/0.63 thf(fact_5925_dvd__power__iff__le,axiom,
% 0.35/0.63 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 0.35/0.63 => ( ( dvd_dvd_nat @ ( power_power_nat @ K2 @ M2 ) @ ( power_power_nat @ K2 @ N ) )
% 0.35/0.63 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dvd_power_iff_le
% 0.35/0.63 thf(fact_5926_even__unset__bit__iff,axiom,
% 0.35/0.63 ! [M2: nat,A: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M2 @ A ) )
% 0.35/0.63 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 | ( M2 = zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_unset_bit_iff
% 0.35/0.63 thf(fact_5927_even__unset__bit__iff,axiom,
% 0.35/0.63 ! [M2: nat,A: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M2 @ A ) )
% 0.35/0.63 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 | ( M2 = zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_unset_bit_iff
% 0.35/0.63 thf(fact_5928_set__encode__def,axiom,
% 0.35/0.63 ( nat_set_encode
% 0.35/0.63 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % set_encode_def
% 0.35/0.63 thf(fact_5929_even__set__bit__iff,axiom,
% 0.35/0.63 ! [M2: nat,A: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M2 @ A ) )
% 0.35/0.63 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 & ( M2 != zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_set_bit_iff
% 0.35/0.63 thf(fact_5930_even__set__bit__iff,axiom,
% 0.35/0.63 ! [M2: nat,A: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M2 @ A ) )
% 0.35/0.63 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 & ( M2 != zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_set_bit_iff
% 0.35/0.63 thf(fact_5931_even__flip__bit__iff,axiom,
% 0.35/0.63 ! [M2: nat,A: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M2 @ A ) )
% 0.35/0.63 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 != ( M2 = zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_flip_bit_iff
% 0.35/0.63 thf(fact_5932_even__flip__bit__iff,axiom,
% 0.35/0.63 ! [M2: nat,A: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M2 @ A ) )
% 0.35/0.63 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 != ( M2 = zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_flip_bit_iff
% 0.35/0.63 thf(fact_5933_pochhammer__product,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,Z3: rat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( comm_s4028243227959126397er_rat @ Z3 @ N )
% 0.35/0.63 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ M2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_product
% 0.35/0.63 thf(fact_5934_pochhammer__product,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,Z3: real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( comm_s7457072308508201937r_real @ Z3 @ N )
% 0.35/0.63 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ M2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_product
% 0.35/0.63 thf(fact_5935_pochhammer__product,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,Z3: int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( comm_s4660882817536571857er_int @ Z3 @ N )
% 0.35/0.63 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_product
% 0.35/0.63 thf(fact_5936_pochhammer__product,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,Z3: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( comm_s4663373288045622133er_nat @ Z3 @ N )
% 0.35/0.63 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_product
% 0.35/0.63 thf(fact_5937_oddE,axiom,
% 0.35/0.63 ! [A: code_integer] :
% 0.35/0.63 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ~ ! [B3: code_integer] :
% 0.35/0.63 ( A
% 0.35/0.63 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % oddE
% 0.35/0.63 thf(fact_5938_oddE,axiom,
% 0.35/0.63 ! [A: nat] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ~ ! [B3: nat] :
% 0.35/0.63 ( A
% 0.35/0.63 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % oddE
% 0.35/0.63 thf(fact_5939_oddE,axiom,
% 0.35/0.63 ! [A: int] :
% 0.35/0.63 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ~ ! [B3: int] :
% 0.35/0.63 ( A
% 0.35/0.63 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % oddE
% 0.35/0.63 thf(fact_5940_mod2__eq__if,axiom,
% 0.35/0.63 ! [A: code_integer] :
% 0.35/0.63 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.63 = zero_z3403309356797280102nteger ) )
% 0.35/0.63 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.63 = one_one_Code_integer ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % mod2_eq_if
% 0.35/0.63 thf(fact_5941_mod2__eq__if,axiom,
% 0.35/0.63 ! [A: nat] :
% 0.35/0.63 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63 = zero_zero_nat ) )
% 0.35/0.63 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63 = one_one_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % mod2_eq_if
% 0.35/0.63 thf(fact_5942_mod2__eq__if,axiom,
% 0.35/0.63 ! [A: int] :
% 0.35/0.63 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.63 = zero_zero_int ) )
% 0.35/0.63 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.63 = one_one_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % mod2_eq_if
% 0.35/0.63 thf(fact_5943_mod2__eq__if,axiom,
% 0.35/0.63 ! [A: code_natural] :
% 0.35/0.63 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.63 = zero_z2226904508553997617atural ) )
% 0.35/0.63 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.63 = one_one_Code_natural ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % mod2_eq_if
% 0.35/0.63 thf(fact_5944_parity__cases,axiom,
% 0.35/0.63 ! [A: code_integer] :
% 0.35/0.63 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.63 != zero_z3403309356797280102nteger ) )
% 0.35/0.63 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.63 != one_one_Code_integer ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % parity_cases
% 0.35/0.63 thf(fact_5945_parity__cases,axiom,
% 0.35/0.63 ! [A: nat] :
% 0.35/0.63 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63 != zero_zero_nat ) )
% 0.35/0.63 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63 != one_one_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % parity_cases
% 0.35/0.63 thf(fact_5946_parity__cases,axiom,
% 0.35/0.63 ! [A: int] :
% 0.35/0.63 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.63 != zero_zero_int ) )
% 0.35/0.63 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.63 != one_one_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % parity_cases
% 0.35/0.63 thf(fact_5947_parity__cases,axiom,
% 0.35/0.63 ! [A: code_natural] :
% 0.35/0.63 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.63 != zero_z2226904508553997617atural ) )
% 0.35/0.63 => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 0.35/0.63 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 0.35/0.63 != one_one_Code_natural ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % parity_cases
% 0.35/0.63 thf(fact_5948_zero__le__even__power,axiom,
% 0.35/0.63 ! [N: nat,A: real] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_even_power
% 0.35/0.63 thf(fact_5949_zero__le__even__power,axiom,
% 0.35/0.63 ! [N: nat,A: rat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_even_power
% 0.35/0.63 thf(fact_5950_zero__le__even__power,axiom,
% 0.35/0.63 ! [N: nat,A: int] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_even_power
% 0.35/0.63 thf(fact_5951_zero__le__odd__power,axiom,
% 0.35/0.63 ! [N: nat,A: real] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.35/0.63 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_odd_power
% 0.35/0.63 thf(fact_5952_zero__le__odd__power,axiom,
% 0.35/0.63 ! [N: nat,A: rat] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.35/0.63 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_odd_power
% 0.35/0.63 thf(fact_5953_zero__le__odd__power,axiom,
% 0.35/0.63 ! [N: nat,A: int] :
% 0.35/0.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.35/0.63 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_odd_power
% 0.35/0.63 thf(fact_5954_zero__le__power__eq,axiom,
% 0.35/0.63 ! [A: real,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.35/0.63 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_power_eq
% 0.35/0.63 thf(fact_5955_zero__le__power__eq,axiom,
% 0.35/0.63 ! [A: rat,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.35/0.63 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_power_eq
% 0.35/0.63 thf(fact_5956_zero__le__power__eq,axiom,
% 0.35/0.63 ! [A: int,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.35/0.63 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_le_power_eq
% 0.35/0.63 thf(fact_5957_sum__natinterval__diff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > complex] :
% 0.35/0.63 ( ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups2073611262835488442omplex
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_complex @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( minus_minus_complex @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.63 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups2073611262835488442omplex
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_complex @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = zero_zero_complex ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_natinterval_diff
% 0.35/0.63 thf(fact_5958_sum__natinterval__diff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > rat] :
% 0.35/0.63 ( ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( minus_minus_rat @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.63 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = zero_zero_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_natinterval_diff
% 0.35/0.63 thf(fact_5959_sum__natinterval__diff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > int] :
% 0.35/0.63 ( ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( minus_minus_int @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.63 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = zero_zero_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_natinterval_diff
% 0.35/0.63 thf(fact_5960_sum__natinterval__diff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > real] :
% 0.35/0.63 ( ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( minus_minus_real @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 0.35/0.63 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = zero_zero_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_natinterval_diff
% 0.35/0.63 thf(fact_5961_sum__telescope_H_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > rat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 0.35/0.63 = ( minus_minus_rat @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_telescope''
% 0.35/0.63 thf(fact_5962_sum__telescope_H_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 0.35/0.63 = ( minus_minus_int @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_telescope''
% 0.35/0.63 thf(fact_5963_sum__telescope_H_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,F2: nat > real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 0.35/0.63 = ( minus_minus_real @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_telescope''
% 0.35/0.63 thf(fact_5964_even__set__encode__iff,axiom,
% 0.35/0.63 ! [A4: set_nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 0.35/0.63 = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_set_encode_iff
% 0.35/0.63 thf(fact_5965_zero__less__power__eq,axiom,
% 0.35/0.63 ! [A: real,N: nat] :
% 0.35/0.63 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 0.35/0.63 = ( ( N = zero_zero_nat )
% 0.35/0.63 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( A != zero_zero_real ) )
% 0.35/0.63 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_less_power_eq
% 0.35/0.63 thf(fact_5966_zero__less__power__eq,axiom,
% 0.35/0.63 ! [A: rat,N: nat] :
% 0.35/0.63 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 0.35/0.63 = ( ( N = zero_zero_nat )
% 0.35/0.63 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( A != zero_zero_rat ) )
% 0.35/0.63 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_less_power_eq
% 0.35/0.63 thf(fact_5967_zero__less__power__eq,axiom,
% 0.35/0.63 ! [A: int,N: nat] :
% 0.35/0.63 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 0.35/0.63 = ( ( N = zero_zero_nat )
% 0.35/0.63 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( A != zero_zero_int ) )
% 0.35/0.63 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zero_less_power_eq
% 0.35/0.63 thf(fact_5968_sum__gp__multiplied,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,X: code_integer] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_multiplied
% 0.35/0.63 thf(fact_5969_sum__gp__multiplied,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,X: complex] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_multiplied
% 0.35/0.63 thf(fact_5970_sum__gp__multiplied,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,X: rat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_multiplied
% 0.35/0.63 thf(fact_5971_sum__gp__multiplied,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,X: int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( minus_minus_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_multiplied
% 0.35/0.63 thf(fact_5972_sum__gp__multiplied,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,X: real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_multiplied
% 0.35/0.63 thf(fact_5973_sum_Oin__pairs,axiom,
% 0.35/0.63 ! [G2: nat > rat,M2: nat,N: nat] :
% 0.35/0.63 ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.63 = ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.in_pairs
% 0.35/0.63 thf(fact_5974_sum_Oin__pairs,axiom,
% 0.35/0.63 ! [G2: nat > int,M2: nat,N: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.63 = ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.in_pairs
% 0.35/0.63 thf(fact_5975_sum_Oin__pairs,axiom,
% 0.35/0.63 ! [G2: nat > nat,M2: nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.63 = ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.in_pairs
% 0.35/0.63 thf(fact_5976_sum_Oin__pairs,axiom,
% 0.35/0.63 ! [G2: nat > real,M2: nat,N: nat] :
% 0.35/0.63 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.63 = ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.in_pairs
% 0.35/0.63 thf(fact_5977_even__mask__div__iff_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mask_div_iff'
% 0.35/0.63 thf(fact_5978_even__mask__div__iff_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mask_div_iff'
% 0.35/0.63 thf(fact_5979_even__mask__div__iff_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mask_div_iff'
% 0.35/0.63 thf(fact_5980_power__le__zero__eq,axiom,
% 0.35/0.63 ! [A: real,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 0.35/0.63 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.63 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.35/0.63 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( A = zero_zero_real ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % power_le_zero_eq
% 0.35/0.63 thf(fact_5981_power__le__zero__eq,axiom,
% 0.35/0.63 ! [A: rat,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 0.35/0.63 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.63 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.35/0.63 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( A = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % power_le_zero_eq
% 0.35/0.63 thf(fact_5982_power__le__zero__eq,axiom,
% 0.35/0.63 ! [A: int,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 0.35/0.63 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.63 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.35/0.63 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 & ( A = zero_zero_int ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % power_le_zero_eq
% 0.35/0.63 thf(fact_5983_mask__eq__sum__exp__nat,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.63 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.63 @ ( collect_nat
% 0.35/0.63 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % mask_eq_sum_exp_nat
% 0.35/0.63 thf(fact_5984_gauss__sum__nat,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [X4: nat] : X4
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % gauss_sum_nat
% 0.35/0.63 thf(fact_5985_even__mod__4__div__2,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.63 = ( suc @ zero_zero_nat ) )
% 0.35/0.63 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mod_4_div_2
% 0.35/0.63 thf(fact_5986_even__mask__div__iff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 = zero_z3403309356797280102nteger )
% 0.35/0.63 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mask_div_iff
% 0.35/0.63 thf(fact_5987_even__mask__div__iff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 = zero_zero_nat )
% 0.35/0.63 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mask_div_iff
% 0.35/0.63 thf(fact_5988_even__mask__div__iff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 = zero_zero_int )
% 0.35/0.63 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mask_div_iff
% 0.35/0.63 thf(fact_5989_double__gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum
% 0.35/0.63 thf(fact_5990_double__gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum
% 0.35/0.63 thf(fact_5991_double__gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum
% 0.35/0.63 thf(fact_5992_double__gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum
% 0.35/0.63 thf(fact_5993_double__gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum
% 0.35/0.63 thf(fact_5994_double__gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum
% 0.35/0.63 thf(fact_5995_double__gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum
% 0.35/0.63 thf(fact_5996_double__arith__series,axiom,
% 0.35/0.63 ! [A: code_integer,D: code_integer,N: nat] :
% 0.35/0.63 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 0.35/0.63 @ ( groups7501900531339628137nteger
% 0.35/0.63 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_arith_series
% 0.35/0.63 thf(fact_5997_double__arith__series,axiom,
% 0.35/0.63 ! [A: rat,D: rat,N: nat] :
% 0.35/0.63 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.35/0.63 @ ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_arith_series
% 0.35/0.63 thf(fact_5998_double__arith__series,axiom,
% 0.35/0.63 ! [A: extended_enat,D: extended_enat,N: nat] :
% 0.35/0.63 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 0.35/0.63 @ ( groups7108830773950497114d_enat
% 0.35/0.63 @ ^ [I: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ D ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_arith_series
% 0.35/0.63 thf(fact_5999_double__arith__series,axiom,
% 0.35/0.63 ! [A: complex,D: complex,N: nat] :
% 0.35/0.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.35/0.63 @ ( groups2073611262835488442omplex
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_arith_series
% 0.35/0.63 thf(fact_6000_double__arith__series,axiom,
% 0.35/0.63 ! [A: int,D: int,N: nat] :
% 0.35/0.63 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.35/0.63 @ ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_arith_series
% 0.35/0.63 thf(fact_6001_double__arith__series,axiom,
% 0.35/0.63 ! [A: nat,D: nat,N: nat] :
% 0.35/0.63 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 0.35/0.63 @ ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_arith_series
% 0.35/0.63 thf(fact_6002_double__arith__series,axiom,
% 0.35/0.63 ! [A: real,D: real,N: nat] :
% 0.35/0.63 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.35/0.63 @ ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_arith_series
% 0.35/0.63 thf(fact_6003_arith__series__nat,axiom,
% 0.35/0.63 ! [A: nat,D: nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % arith_series_nat
% 0.35/0.63 thf(fact_6004_Sum__Icc__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [X4: nat] : X4
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Sum_Icc_nat
% 0.35/0.63 thf(fact_6005_Bernoulli__inequality__even,axiom,
% 0.35/0.63 ! [N: nat,X: real] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Bernoulli_inequality_even
% 0.35/0.63 thf(fact_6006_gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % gauss_sum
% 0.35/0.63 thf(fact_6007_gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % gauss_sum
% 0.35/0.63 thf(fact_6008_gauss__sum,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % gauss_sum
% 0.35/0.63 thf(fact_6009_arith__series,axiom,
% 0.35/0.63 ! [A: code_integer,D: code_integer,N: nat] :
% 0.35/0.63 ( ( groups7501900531339628137nteger
% 0.35/0.63 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % arith_series
% 0.35/0.63 thf(fact_6010_arith__series,axiom,
% 0.35/0.63 ! [A: int,D: int,N: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % arith_series
% 0.35/0.63 thf(fact_6011_arith__series,axiom,
% 0.35/0.63 ! [A: nat,D: nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.63 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % arith_series
% 0.35/0.63 thf(fact_6012_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.63 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6013_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6014_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.63 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6015_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.63 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6016_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6017_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6018_double__gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % double_gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6019_even__mult__exp__div__exp__iff,axiom,
% 0.35/0.63 ! [A: nat,M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ( ord_less_nat @ N @ M2 )
% 0.35/0.63 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 = zero_zero_nat )
% 0.35/0.63 | ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mult_exp_div_exp_iff
% 0.35/0.63 thf(fact_6020_even__mult__exp__div__exp__iff,axiom,
% 0.35/0.63 ! [A: int,M2: nat,N: nat] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.63 = ( ( ord_less_nat @ N @ M2 )
% 0.35/0.63 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.63 = zero_zero_int )
% 0.35/0.63 | ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % even_mult_exp_div_exp_iff
% 0.35/0.63 thf(fact_6021_sum__gp__offset,axiom,
% 0.35/0.63 ! [X: complex,M2: nat,N: nat] :
% 0.35/0.63 ( ( ( X = one_one_complex )
% 0.35/0.63 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 0.35/0.63 & ( ( X != one_one_complex )
% 0.35/0.63 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_offset
% 0.35/0.63 thf(fact_6022_sum__gp__offset,axiom,
% 0.35/0.63 ! [X: rat,M2: nat,N: nat] :
% 0.35/0.63 ( ( ( X = one_one_rat )
% 0.35/0.63 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 0.35/0.63 & ( ( X != one_one_rat )
% 0.35/0.63 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_offset
% 0.35/0.63 thf(fact_6023_sum__gp__offset,axiom,
% 0.35/0.63 ! [X: real,M2: nat,N: nat] :
% 0.35/0.63 ( ( ( X = one_one_real )
% 0.35/0.63 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 0.35/0.63 & ( ( X != one_one_real )
% 0.35/0.63 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.63 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_gp_offset
% 0.35/0.63 thf(fact_6024_vebt__buildup_Osimps_I3_J,axiom,
% 0.35/0.63 ! [Va3: nat] :
% 0.35/0.63 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 0.35/0.63 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 0.35/0.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.63 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 0.35/0.63 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 0.35/0.63 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % vebt_buildup.simps(3)
% 0.35/0.63 thf(fact_6025_gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.63 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6026_gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.63 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6027_gauss__sum__from__Suc__0,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.63 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % gauss_sum_from_Suc_0
% 0.35/0.63 thf(fact_6028_power__half__series,axiom,
% 0.35/0.63 ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N4 ) )
% 0.35/0.63 @ one_one_real ) ).
% 0.35/0.63
% 0.35/0.63 % power_half_series
% 0.35/0.63 thf(fact_6029_sums__zero,axiom,
% 0.35/0.63 ( sums_complex
% 0.35/0.63 @ ^ [N4: nat] : zero_zero_complex
% 0.35/0.63 @ zero_zero_complex ) ).
% 0.35/0.63
% 0.35/0.63 % sums_zero
% 0.35/0.63 thf(fact_6030_sums__zero,axiom,
% 0.35/0.63 ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : zero_zero_real
% 0.35/0.63 @ zero_zero_real ) ).
% 0.35/0.63
% 0.35/0.63 % sums_zero
% 0.35/0.63 thf(fact_6031_sums__zero,axiom,
% 0.35/0.63 ( sums_nat
% 0.35/0.63 @ ^ [N4: nat] : zero_zero_nat
% 0.35/0.63 @ zero_zero_nat ) ).
% 0.35/0.63
% 0.35/0.63 % sums_zero
% 0.35/0.63 thf(fact_6032_sums__zero,axiom,
% 0.35/0.63 ( sums_int
% 0.35/0.63 @ ^ [N4: nat] : zero_zero_int
% 0.35/0.63 @ zero_zero_int ) ).
% 0.35/0.63
% 0.35/0.63 % sums_zero
% 0.35/0.63 thf(fact_6033_powser__sums__if,axiom,
% 0.35/0.63 ! [M2: nat,Z3: complex] :
% 0.35/0.63 ( sums_complex
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_complex @ ( if_complex @ ( N4 = M2 ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z3 @ N4 ) )
% 0.35/0.63 @ ( power_power_complex @ Z3 @ M2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % powser_sums_if
% 0.35/0.63 thf(fact_6034_powser__sums__if,axiom,
% 0.35/0.63 ! [M2: nat,Z3: real] :
% 0.35/0.63 ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_real @ ( if_real @ ( N4 = M2 ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z3 @ N4 ) )
% 0.35/0.63 @ ( power_power_real @ Z3 @ M2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % powser_sums_if
% 0.35/0.63 thf(fact_6035_powser__sums__if,axiom,
% 0.35/0.63 ! [M2: nat,Z3: int] :
% 0.35/0.63 ( sums_int
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_int @ ( if_int @ ( N4 = M2 ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z3 @ N4 ) )
% 0.35/0.63 @ ( power_power_int @ Z3 @ M2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % powser_sums_if
% 0.35/0.63 thf(fact_6036_sums__If__finite__set,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > complex] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( sums_complex
% 0.35/0.63 @ ^ [R: nat] : ( if_complex @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_complex )
% 0.35/0.63 @ ( groups2073611262835488442omplex @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite_set
% 0.35/0.63 thf(fact_6037_sums__If__finite__set,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > int] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( sums_int
% 0.35/0.63 @ ^ [R: nat] : ( if_int @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_int )
% 0.35/0.63 @ ( groups3539618377306564664at_int @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite_set
% 0.35/0.63 thf(fact_6038_sums__If__finite__set,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( sums_nat
% 0.35/0.63 @ ^ [R: nat] : ( if_nat @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_nat )
% 0.35/0.63 @ ( groups3542108847815614940at_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite_set
% 0.35/0.63 thf(fact_6039_sums__If__finite__set,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( sums_real
% 0.35/0.63 @ ^ [R: nat] : ( if_real @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_real )
% 0.35/0.63 @ ( groups6591440286371151544t_real @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite_set
% 0.35/0.63 thf(fact_6040_sums__If__finite,axiom,
% 0.35/0.63 ! [P2: nat > $o,F2: nat > complex] :
% 0.35/0.63 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.35/0.63 => ( sums_complex
% 0.35/0.63 @ ^ [R: nat] : ( if_complex @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_complex )
% 0.35/0.63 @ ( groups2073611262835488442omplex @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite
% 0.35/0.63 thf(fact_6041_sums__If__finite,axiom,
% 0.35/0.63 ! [P2: nat > $o,F2: nat > int] :
% 0.35/0.63 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.35/0.63 => ( sums_int
% 0.35/0.63 @ ^ [R: nat] : ( if_int @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_int )
% 0.35/0.63 @ ( groups3539618377306564664at_int @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite
% 0.35/0.63 thf(fact_6042_sums__If__finite,axiom,
% 0.35/0.63 ! [P2: nat > $o,F2: nat > nat] :
% 0.35/0.63 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.35/0.63 => ( sums_nat
% 0.35/0.63 @ ^ [R: nat] : ( if_nat @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_nat )
% 0.35/0.63 @ ( groups3542108847815614940at_nat @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite
% 0.35/0.63 thf(fact_6043_sums__If__finite,axiom,
% 0.35/0.63 ! [P2: nat > $o,F2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 0.35/0.63 => ( sums_real
% 0.35/0.63 @ ^ [R: nat] : ( if_real @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_real )
% 0.35/0.63 @ ( groups6591440286371151544t_real @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_If_finite
% 0.35/0.63 thf(fact_6044_sums__finite,axiom,
% 0.35/0.63 ! [N6: set_nat,F2: nat > complex] :
% 0.35/0.63 ( ( finite_finite_nat @ N6 )
% 0.35/0.63 => ( ! [N3: nat] :
% 0.35/0.63 ( ~ ( member_nat @ N3 @ N6 )
% 0.35/0.63 => ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_complex ) )
% 0.35/0.63 => ( sums_complex @ F2 @ ( groups2073611262835488442omplex @ F2 @ N6 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_finite
% 0.35/0.63 thf(fact_6045_sums__finite,axiom,
% 0.35/0.63 ! [N6: set_nat,F2: nat > int] :
% 0.35/0.63 ( ( finite_finite_nat @ N6 )
% 0.35/0.63 => ( ! [N3: nat] :
% 0.35/0.63 ( ~ ( member_nat @ N3 @ N6 )
% 0.35/0.63 => ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_int ) )
% 0.35/0.63 => ( sums_int @ F2 @ ( groups3539618377306564664at_int @ F2 @ N6 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_finite
% 0.35/0.63 thf(fact_6046_sums__finite,axiom,
% 0.35/0.63 ! [N6: set_nat,F2: nat > nat] :
% 0.35/0.63 ( ( finite_finite_nat @ N6 )
% 0.35/0.63 => ( ! [N3: nat] :
% 0.35/0.63 ( ~ ( member_nat @ N3 @ N6 )
% 0.35/0.63 => ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_nat ) )
% 0.35/0.63 => ( sums_nat @ F2 @ ( groups3542108847815614940at_nat @ F2 @ N6 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_finite
% 0.35/0.63 thf(fact_6047_sums__finite,axiom,
% 0.35/0.63 ! [N6: set_nat,F2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ N6 )
% 0.35/0.63 => ( ! [N3: nat] :
% 0.35/0.63 ( ~ ( member_nat @ N3 @ N6 )
% 0.35/0.63 => ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_real ) )
% 0.35/0.63 => ( sums_real @ F2 @ ( groups6591440286371151544t_real @ F2 @ N6 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_finite
% 0.35/0.63 thf(fact_6048_sums__zero__iff__shift,axiom,
% 0.35/0.63 ! [N: nat,F2: nat > complex,S2: complex] :
% 0.35/0.63 ( ! [I3: nat] :
% 0.35/0.63 ( ( ord_less_nat @ I3 @ N )
% 0.35/0.63 => ( ( F2 @ I3 )
% 0.35/0.63 = zero_zero_complex ) )
% 0.35/0.63 => ( ( sums_complex
% 0.35/0.63 @ ^ [I: nat] : ( F2 @ ( plus_plus_nat @ I @ N ) )
% 0.35/0.63 @ S2 )
% 0.35/0.63 = ( sums_complex @ F2 @ S2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_zero_iff_shift
% 0.35/0.63 thf(fact_6049_sums__zero__iff__shift,axiom,
% 0.35/0.63 ! [N: nat,F2: nat > real,S2: real] :
% 0.35/0.63 ( ! [I3: nat] :
% 0.35/0.63 ( ( ord_less_nat @ I3 @ N )
% 0.35/0.63 => ( ( F2 @ I3 )
% 0.35/0.63 = zero_zero_real ) )
% 0.35/0.63 => ( ( sums_real
% 0.35/0.63 @ ^ [I: nat] : ( F2 @ ( plus_plus_nat @ I @ N ) )
% 0.35/0.63 @ S2 )
% 0.35/0.63 = ( sums_real @ F2 @ S2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_zero_iff_shift
% 0.35/0.63 thf(fact_6050_zdvd__mono,axiom,
% 0.35/0.63 ! [K2: int,M2: int,T: int] :
% 0.35/0.63 ( ( K2 != zero_zero_int )
% 0.35/0.63 => ( ( dvd_dvd_int @ M2 @ T )
% 0.35/0.63 = ( dvd_dvd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ T ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zdvd_mono
% 0.35/0.63 thf(fact_6051_zdvd__mult__cancel,axiom,
% 0.35/0.63 ! [K2: int,M2: int,N: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ N ) )
% 0.35/0.63 => ( ( K2 != zero_zero_int )
% 0.35/0.63 => ( dvd_dvd_int @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zdvd_mult_cancel
% 0.35/0.63 thf(fact_6052_zdvd__period,axiom,
% 0.35/0.63 ! [A: int,D: int,X: int,T: int,C2: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ A @ D )
% 0.35/0.63 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 0.35/0.63 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C2 @ D ) ) @ T ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % zdvd_period
% 0.35/0.63 thf(fact_6053_zdvd__reduce,axiom,
% 0.35/0.63 ! [K2: int,N: int,M2: int] :
% 0.35/0.63 ( ( dvd_dvd_int @ K2 @ ( plus_plus_int @ N @ ( times_times_int @ K2 @ M2 ) ) )
% 0.35/0.63 = ( dvd_dvd_int @ K2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % zdvd_reduce
% 0.35/0.63 thf(fact_6054_sum__subtractf__nat,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > nat,F2: complex > nat] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ( groups5693394587270226106ex_nat
% 0.35/0.63 @ ^ [X4: complex] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_subtractf_nat
% 0.35/0.63 thf(fact_6055_sum__subtractf__nat,axiom,
% 0.35/0.63 ! [A4: set_real,G2: real > nat,F2: real > nat] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ( groups1935376822645274424al_nat
% 0.35/0.63 @ ^ [X4: real] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ G2 @ A4 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_subtractf_nat
% 0.35/0.63 thf(fact_6056_sum__subtractf__nat,axiom,
% 0.35/0.63 ! [A4: set_set_nat,G2: set_nat > nat,F2: set_nat > nat] :
% 0.35/0.63 ( ! [X3: set_nat] :
% 0.35/0.63 ( ( member_set_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ( groups8294997508430121362at_nat
% 0.35/0.63 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F2 @ A4 ) @ ( groups8294997508430121362at_nat @ G2 @ A4 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_subtractf_nat
% 0.35/0.63 thf(fact_6057_sum__subtractf__nat,axiom,
% 0.35/0.63 ! [A4: set_int,G2: int > nat,F2: int > nat] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ( groups4541462559716669496nt_nat
% 0.35/0.63 @ ^ [X4: int] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_subtractf_nat
% 0.35/0.63 thf(fact_6058_sum__subtractf__nat,axiom,
% 0.35/0.63 ! [A4: set_nat,G2: nat > nat,F2: nat > nat] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [X4: nat] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_subtractf_nat
% 0.35/0.63 thf(fact_6059_sum__eq__Suc0__iff,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 0.35/0.63 = ( suc @ zero_zero_nat ) )
% 0.35/0.63 = ( ? [X4: int] :
% 0.35/0.63 ( ( member_int @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = ( suc @ zero_zero_nat ) )
% 0.35/0.63 & ! [Y4: int] :
% 0.35/0.63 ( ( member_int @ Y4 @ A4 )
% 0.35/0.63 => ( ( X4 != Y4 )
% 0.35/0.63 => ( ( F2 @ Y4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_eq_Suc0_iff
% 0.35/0.63 thf(fact_6060_sum__eq__Suc0__iff,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 0.35/0.63 = ( suc @ zero_zero_nat ) )
% 0.35/0.63 = ( ? [X4: complex] :
% 0.35/0.63 ( ( member_complex @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = ( suc @ zero_zero_nat ) )
% 0.35/0.63 & ! [Y4: complex] :
% 0.35/0.63 ( ( member_complex @ Y4 @ A4 )
% 0.35/0.63 => ( ( X4 != Y4 )
% 0.35/0.63 => ( ( F2 @ Y4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_eq_Suc0_iff
% 0.35/0.63 thf(fact_6061_sum__eq__Suc0__iff,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 0.35/0.63 = ( suc @ zero_zero_nat ) )
% 0.35/0.63 = ( ? [X4: nat] :
% 0.35/0.63 ( ( member_nat @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = ( suc @ zero_zero_nat ) )
% 0.35/0.63 & ! [Y4: nat] :
% 0.35/0.63 ( ( member_nat @ Y4 @ A4 )
% 0.35/0.63 => ( ( X4 != Y4 )
% 0.35/0.63 => ( ( F2 @ Y4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_eq_Suc0_iff
% 0.35/0.63 thf(fact_6062_sum__SucD,axiom,
% 0.35/0.63 ! [F2: nat > nat,A4: set_nat,N: nat] :
% 0.35/0.63 ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 0.35/0.63 = ( suc @ N ) )
% 0.35/0.63 => ? [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 & ( ord_less_nat @ zero_zero_nat @ ( F2 @ X3 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_SucD
% 0.35/0.63 thf(fact_6063_sum__eq__1__iff,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 0.35/0.63 = one_one_nat )
% 0.35/0.63 = ( ? [X4: int] :
% 0.35/0.63 ( ( member_int @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = one_one_nat )
% 0.35/0.63 & ! [Y4: int] :
% 0.35/0.63 ( ( member_int @ Y4 @ A4 )
% 0.35/0.63 => ( ( X4 != Y4 )
% 0.35/0.63 => ( ( F2 @ Y4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_eq_1_iff
% 0.35/0.63 thf(fact_6064_sum__eq__1__iff,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 0.35/0.63 = one_one_nat )
% 0.35/0.63 = ( ? [X4: complex] :
% 0.35/0.63 ( ( member_complex @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = one_one_nat )
% 0.35/0.63 & ! [Y4: complex] :
% 0.35/0.63 ( ( member_complex @ Y4 @ A4 )
% 0.35/0.63 => ( ( X4 != Y4 )
% 0.35/0.63 => ( ( F2 @ Y4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_eq_1_iff
% 0.35/0.63 thf(fact_6065_sum__eq__1__iff,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 0.35/0.63 = one_one_nat )
% 0.35/0.63 = ( ? [X4: nat] :
% 0.35/0.63 ( ( member_nat @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = one_one_nat )
% 0.35/0.63 & ! [Y4: nat] :
% 0.35/0.63 ( ( member_nat @ Y4 @ A4 )
% 0.35/0.63 => ( ( X4 != Y4 )
% 0.35/0.63 => ( ( F2 @ Y4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_eq_1_iff
% 0.35/0.63 thf(fact_6066_sum__Suc,axiom,
% 0.35/0.63 ! [F2: complex > nat,A4: set_complex] :
% 0.35/0.63 ( ( groups5693394587270226106ex_nat
% 0.35/0.63 @ ^ [X4: complex] : ( suc @ ( F2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( finite_card_complex @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc
% 0.35/0.63 thf(fact_6067_sum__Suc,axiom,
% 0.35/0.63 ! [F2: int > nat,A4: set_int] :
% 0.35/0.63 ( ( groups4541462559716669496nt_nat
% 0.35/0.63 @ ^ [X4: int] : ( suc @ ( F2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( finite_card_int @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc
% 0.35/0.63 thf(fact_6068_sum__Suc,axiom,
% 0.35/0.63 ! [F2: list_nat > nat,A4: set_list_nat] :
% 0.35/0.63 ( ( groups4396056296759096172at_nat
% 0.35/0.63 @ ^ [X4: list_nat] : ( suc @ ( F2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F2 @ A4 ) @ ( finite_card_list_nat @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc
% 0.35/0.63 thf(fact_6069_sum__Suc,axiom,
% 0.35/0.63 ! [F2: set_nat > nat,A4: set_set_nat] :
% 0.35/0.63 ( ( groups8294997508430121362at_nat
% 0.35/0.63 @ ^ [X4: set_nat] : ( suc @ ( F2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ F2 @ A4 ) @ ( finite_card_set_nat @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc
% 0.35/0.63 thf(fact_6070_sum__Suc,axiom,
% 0.35/0.63 ! [F2: nat > nat,A4: set_nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [X4: nat] : ( suc @ ( F2 @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( finite_card_nat @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_Suc
% 0.35/0.63 thf(fact_6071_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_real,T5: set_real,R2: real > real > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_real @ S3 )
% 0.35/0.63 => ( ( finite_finite_real @ T5 )
% 0.35/0.63 => ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_real
% 0.35/0.63 @ ( collect_real
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( ( member_real @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups1935376822645274424al_nat
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( finite_card_real
% 0.35/0.63 @ ( collect_real
% 0.35/0.63 @ ^ [J: real] :
% 0.35/0.63 ( ( member_real @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6072_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_real,T5: set_nat,R2: real > nat > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_real @ S3 )
% 0.35/0.63 => ( ( finite_finite_nat @ T5 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_real
% 0.35/0.63 @ ( collect_real
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( ( member_real @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups1935376822645274424al_nat
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( finite_card_nat
% 0.35/0.63 @ ( collect_nat
% 0.35/0.63 @ ^ [J: nat] :
% 0.35/0.63 ( ( member_nat @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6073_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_real,T5: set_int,R2: real > int > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_real @ S3 )
% 0.35/0.63 => ( ( finite_finite_int @ T5 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_real
% 0.35/0.63 @ ( collect_real
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( ( member_real @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups1935376822645274424al_nat
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( finite_card_int
% 0.35/0.63 @ ( collect_int
% 0.35/0.63 @ ^ [J: int] :
% 0.35/0.63 ( ( member_int @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_int @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6074_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_real,T5: set_complex,R2: real > complex > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_real @ S3 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_real
% 0.35/0.63 @ ( collect_real
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( ( member_real @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups1935376822645274424al_nat
% 0.35/0.63 @ ^ [I: real] :
% 0.35/0.63 ( finite_card_complex
% 0.35/0.63 @ ( collect_complex
% 0.35/0.63 @ ^ [J: complex] :
% 0.35/0.63 ( ( member_complex @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_complex @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6075_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_int,T5: set_real,R2: int > real > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_int @ S3 )
% 0.35/0.63 => ( ( finite_finite_real @ T5 )
% 0.35/0.63 => ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_int
% 0.35/0.63 @ ( collect_int
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( ( member_int @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups4541462559716669496nt_nat
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( finite_card_real
% 0.35/0.63 @ ( collect_real
% 0.35/0.63 @ ^ [J: real] :
% 0.35/0.63 ( ( member_real @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6076_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_int,T5: set_nat,R2: int > nat > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_int @ S3 )
% 0.35/0.63 => ( ( finite_finite_nat @ T5 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_int
% 0.35/0.63 @ ( collect_int
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( ( member_int @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups4541462559716669496nt_nat
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( finite_card_nat
% 0.35/0.63 @ ( collect_nat
% 0.35/0.63 @ ^ [J: nat] :
% 0.35/0.63 ( ( member_nat @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6077_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_int,T5: set_int,R2: int > int > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_int @ S3 )
% 0.35/0.63 => ( ( finite_finite_int @ T5 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_int
% 0.35/0.63 @ ( collect_int
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( ( member_int @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups4541462559716669496nt_nat
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( finite_card_int
% 0.35/0.63 @ ( collect_int
% 0.35/0.63 @ ^ [J: int] :
% 0.35/0.63 ( ( member_int @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_int @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6078_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_int,T5: set_complex,R2: int > complex > $o,K2: nat] :
% 0.35/0.63 ( ( finite_finite_int @ S3 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ T5 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_int
% 0.35/0.63 @ ( collect_int
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( ( member_int @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups4541462559716669496nt_nat
% 0.35/0.63 @ ^ [I: int] :
% 0.35/0.63 ( finite_card_complex
% 0.35/0.63 @ ( collect_complex
% 0.35/0.63 @ ^ [J: complex] :
% 0.35/0.63 ( ( member_complex @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_complex @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6079_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_complex,T5: set_real,R2: complex > real > $o,K2: nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63 => ( ( finite_finite_real @ T5 )
% 0.35/0.63 => ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_complex
% 0.35/0.63 @ ( collect_complex
% 0.35/0.63 @ ^ [I: complex] :
% 0.35/0.63 ( ( member_complex @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups5693394587270226106ex_nat
% 0.35/0.63 @ ^ [I: complex] :
% 0.35/0.63 ( finite_card_real
% 0.35/0.63 @ ( collect_real
% 0.35/0.63 @ ^ [J: real] :
% 0.35/0.63 ( ( member_real @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6080_sum__multicount,axiom,
% 0.35/0.63 ! [S3: set_complex,T5: set_nat,R2: complex > nat > $o,K2: nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63 => ( ( finite_finite_nat @ T5 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ T5 )
% 0.35/0.63 => ( ( finite_card_complex
% 0.35/0.63 @ ( collect_complex
% 0.35/0.63 @ ^ [I: complex] :
% 0.35/0.63 ( ( member_complex @ I @ S3 )
% 0.35/0.63 & ( R2 @ I @ X3 ) ) ) )
% 0.35/0.63 = K2 ) )
% 0.35/0.63 => ( ( groups5693394587270226106ex_nat
% 0.35/0.63 @ ^ [I: complex] :
% 0.35/0.63 ( finite_card_nat
% 0.35/0.63 @ ( collect_nat
% 0.35/0.63 @ ^ [J: nat] :
% 0.35/0.63 ( ( member_nat @ J @ T5 )
% 0.35/0.63 & ( R2 @ I @ J ) ) ) )
% 0.35/0.63 @ S3 )
% 0.35/0.63 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_multicount
% 0.35/0.63 thf(fact_6081_mod__int__pos__iff,axiom,
% 0.35/0.63 ! [K2: int,L: int] :
% 0.35/0.63 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K2 @ L ) )
% 0.35/0.63 = ( ( dvd_dvd_int @ L @ K2 )
% 0.35/0.63 | ( ( L = zero_zero_int )
% 0.35/0.63 & ( ord_less_eq_int @ zero_zero_int @ K2 ) )
% 0.35/0.63 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % mod_int_pos_iff
% 0.35/0.63 thf(fact_6082_sum__count__set,axiom,
% 0.35/0.63 ! [Xs2: list_complex,X8: set_complex] :
% 0.35/0.63 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ X8 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ X8 )
% 0.35/0.63 => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs2 ) @ X8 )
% 0.35/0.63 = ( size_s3451745648224563538omplex @ Xs2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_count_set
% 0.35/0.63 thf(fact_6083_sum__count__set,axiom,
% 0.35/0.63 ! [Xs2: list_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 0.35/0.63 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ X8 )
% 0.35/0.63 => ( ( finite5795047828879050333T_VEBT @ X8 )
% 0.35/0.63 => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs2 ) @ X8 )
% 0.35/0.63 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_count_set
% 0.35/0.63 thf(fact_6084_sum__count__set,axiom,
% 0.35/0.63 ! [Xs2: list_o,X8: set_o] :
% 0.35/0.63 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ X8 )
% 0.35/0.63 => ( ( finite_finite_o @ X8 )
% 0.35/0.63 => ( ( groups8507830703676809646_o_nat @ ( count_list_o @ Xs2 ) @ X8 )
% 0.35/0.63 = ( size_size_list_o @ Xs2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_count_set
% 0.35/0.63 thf(fact_6085_sum__count__set,axiom,
% 0.35/0.63 ! [Xs2: list_int,X8: set_int] :
% 0.35/0.63 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ X8 )
% 0.35/0.63 => ( ( finite_finite_int @ X8 )
% 0.35/0.63 => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs2 ) @ X8 )
% 0.35/0.63 = ( size_size_list_int @ Xs2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_count_set
% 0.35/0.63 thf(fact_6086_sum__count__set,axiom,
% 0.35/0.63 ! [Xs2: list_nat,X8: set_nat] :
% 0.35/0.63 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ X8 )
% 0.35/0.63 => ( ( finite_finite_nat @ X8 )
% 0.35/0.63 => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs2 ) @ X8 )
% 0.35/0.63 = ( size_size_list_nat @ Xs2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_count_set
% 0.35/0.63 thf(fact_6087_sums__le,axiom,
% 0.35/0.63 ! [F2: nat > real,G2: nat > real,S2: real,T: real] :
% 0.35/0.63 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 0.35/0.63 => ( ( sums_real @ F2 @ S2 )
% 0.35/0.63 => ( ( sums_real @ G2 @ T )
% 0.35/0.63 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_le
% 0.35/0.63 thf(fact_6088_sums__le,axiom,
% 0.35/0.63 ! [F2: nat > nat,G2: nat > nat,S2: nat,T: nat] :
% 0.35/0.63 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 0.35/0.63 => ( ( sums_nat @ F2 @ S2 )
% 0.35/0.63 => ( ( sums_nat @ G2 @ T )
% 0.35/0.63 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_le
% 0.35/0.63 thf(fact_6089_sums__le,axiom,
% 0.35/0.63 ! [F2: nat > int,G2: nat > int,S2: int,T: int] :
% 0.35/0.63 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 0.35/0.63 => ( ( sums_int @ F2 @ S2 )
% 0.35/0.63 => ( ( sums_int @ G2 @ T )
% 0.35/0.63 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_le
% 0.35/0.63 thf(fact_6090_sums__0,axiom,
% 0.35/0.63 ! [F2: nat > complex] :
% 0.35/0.63 ( ! [N3: nat] :
% 0.35/0.63 ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_complex )
% 0.35/0.63 => ( sums_complex @ F2 @ zero_zero_complex ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_0
% 0.35/0.63 thf(fact_6091_sums__0,axiom,
% 0.35/0.63 ! [F2: nat > real] :
% 0.35/0.63 ( ! [N3: nat] :
% 0.35/0.63 ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_real )
% 0.35/0.63 => ( sums_real @ F2 @ zero_zero_real ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_0
% 0.35/0.63 thf(fact_6092_sums__0,axiom,
% 0.35/0.63 ! [F2: nat > nat] :
% 0.35/0.63 ( ! [N3: nat] :
% 0.35/0.63 ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_nat )
% 0.35/0.63 => ( sums_nat @ F2 @ zero_zero_nat ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_0
% 0.35/0.63 thf(fact_6093_sums__0,axiom,
% 0.35/0.63 ! [F2: nat > int] :
% 0.35/0.63 ( ! [N3: nat] :
% 0.35/0.63 ( ( F2 @ N3 )
% 0.35/0.63 = zero_zero_int )
% 0.35/0.63 => ( sums_int @ F2 @ zero_zero_int ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_0
% 0.35/0.63 thf(fact_6094_sums__single,axiom,
% 0.35/0.63 ! [I2: nat,F2: nat > complex] :
% 0.35/0.63 ( sums_complex
% 0.35/0.63 @ ^ [R: nat] : ( if_complex @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_complex )
% 0.35/0.63 @ ( F2 @ I2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_single
% 0.35/0.63 thf(fact_6095_sums__single,axiom,
% 0.35/0.63 ! [I2: nat,F2: nat > real] :
% 0.35/0.63 ( sums_real
% 0.35/0.63 @ ^ [R: nat] : ( if_real @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_real )
% 0.35/0.63 @ ( F2 @ I2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_single
% 0.35/0.63 thf(fact_6096_sums__single,axiom,
% 0.35/0.63 ! [I2: nat,F2: nat > nat] :
% 0.35/0.63 ( sums_nat
% 0.35/0.63 @ ^ [R: nat] : ( if_nat @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_nat )
% 0.35/0.63 @ ( F2 @ I2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_single
% 0.35/0.63 thf(fact_6097_sums__single,axiom,
% 0.35/0.63 ! [I2: nat,F2: nat > int] :
% 0.35/0.63 ( sums_int
% 0.35/0.63 @ ^ [R: nat] : ( if_int @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_int )
% 0.35/0.63 @ ( F2 @ I2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_single
% 0.35/0.63 thf(fact_6098_sums__mult2,axiom,
% 0.35/0.63 ! [F2: nat > real,A: real,C2: real] :
% 0.35/0.63 ( ( sums_real @ F2 @ A )
% 0.35/0.63 => ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ C2 )
% 0.35/0.63 @ ( times_times_real @ A @ C2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult2
% 0.35/0.63 thf(fact_6099_sums__mult,axiom,
% 0.35/0.63 ! [F2: nat > real,A: real,C2: real] :
% 0.35/0.63 ( ( sums_real @ F2 @ A )
% 0.35/0.63 => ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 0.35/0.63 @ ( times_times_real @ C2 @ A ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult
% 0.35/0.63 thf(fact_6100_Sum__Icc__int,axiom,
% 0.35/0.63 ! [M2: int,N: int] :
% 0.35/0.63 ( ( ord_less_eq_int @ M2 @ N )
% 0.35/0.63 => ( ( groups4538972089207619220nt_int
% 0.35/0.63 @ ^ [X4: int] : X4
% 0.35/0.63 @ ( set_or1266510415728281911st_int @ M2 @ N ) )
% 0.35/0.63 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Sum_Icc_int
% 0.35/0.63 thf(fact_6101_sums__mult__iff,axiom,
% 0.35/0.63 ! [C2: complex,F2: nat > complex,D: complex] :
% 0.35/0.63 ( ( C2 != zero_zero_complex )
% 0.35/0.63 => ( ( sums_complex
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F2 @ N4 ) )
% 0.35/0.63 @ ( times_times_complex @ C2 @ D ) )
% 0.35/0.63 = ( sums_complex @ F2 @ D ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult_iff
% 0.35/0.63 thf(fact_6102_sums__mult__iff,axiom,
% 0.35/0.63 ! [C2: real,F2: nat > real,D: real] :
% 0.35/0.63 ( ( C2 != zero_zero_real )
% 0.35/0.63 => ( ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 0.35/0.63 @ ( times_times_real @ C2 @ D ) )
% 0.35/0.63 = ( sums_real @ F2 @ D ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult_iff
% 0.35/0.63 thf(fact_6103_sums__mult2__iff,axiom,
% 0.35/0.63 ! [C2: complex,F2: nat > complex,D: complex] :
% 0.35/0.63 ( ( C2 != zero_zero_complex )
% 0.35/0.63 => ( ( sums_complex
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_complex @ ( F2 @ N4 ) @ C2 )
% 0.35/0.63 @ ( times_times_complex @ D @ C2 ) )
% 0.35/0.63 = ( sums_complex @ F2 @ D ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult2_iff
% 0.35/0.63 thf(fact_6104_sums__mult2__iff,axiom,
% 0.35/0.63 ! [C2: real,F2: nat > real,D: real] :
% 0.35/0.63 ( ( C2 != zero_zero_real )
% 0.35/0.63 => ( ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ C2 )
% 0.35/0.63 @ ( times_times_real @ D @ C2 ) )
% 0.35/0.63 = ( sums_real @ F2 @ D ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult2_iff
% 0.35/0.63 thf(fact_6105_sums__mult__D,axiom,
% 0.35/0.63 ! [C2: complex,F2: nat > complex,A: complex] :
% 0.35/0.63 ( ( sums_complex
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F2 @ N4 ) )
% 0.35/0.63 @ A )
% 0.35/0.63 => ( ( C2 != zero_zero_complex )
% 0.35/0.63 => ( sums_complex @ F2 @ ( divide1717551699836669952omplex @ A @ C2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult_D
% 0.35/0.63 thf(fact_6106_sums__mult__D,axiom,
% 0.35/0.63 ! [C2: real,F2: nat > real,A: real] :
% 0.35/0.63 ( ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 0.35/0.63 @ A )
% 0.35/0.63 => ( ( C2 != zero_zero_real )
% 0.35/0.63 => ( sums_real @ F2 @ ( divide_divide_real @ A @ C2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_mult_D
% 0.35/0.63 thf(fact_6107_sums__Suc__imp,axiom,
% 0.35/0.63 ! [F2: nat > complex,S2: complex] :
% 0.35/0.63 ( ( ( F2 @ zero_zero_nat )
% 0.35/0.63 = zero_zero_complex )
% 0.35/0.63 => ( ( sums_complex
% 0.35/0.63 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 0.35/0.63 @ S2 )
% 0.35/0.63 => ( sums_complex @ F2 @ S2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_Suc_imp
% 0.35/0.63 thf(fact_6108_sums__Suc__imp,axiom,
% 0.35/0.63 ! [F2: nat > real,S2: real] :
% 0.35/0.63 ( ( ( F2 @ zero_zero_nat )
% 0.35/0.63 = zero_zero_real )
% 0.35/0.63 => ( ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 0.35/0.63 @ S2 )
% 0.35/0.63 => ( sums_real @ F2 @ S2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_Suc_imp
% 0.35/0.63 thf(fact_6109_sums__Suc__iff,axiom,
% 0.35/0.63 ! [F2: nat > real,S2: real] :
% 0.35/0.63 ( ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 0.35/0.63 @ S2 )
% 0.35/0.63 = ( sums_real @ F2 @ ( plus_plus_real @ S2 @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_Suc_iff
% 0.35/0.63 thf(fact_6110_sums__Suc,axiom,
% 0.35/0.63 ! [F2: nat > real,L: real] :
% 0.35/0.63 ( ( sums_real
% 0.35/0.63 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 0.35/0.63 @ L )
% 0.35/0.63 => ( sums_real @ F2 @ ( plus_plus_real @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_Suc
% 0.35/0.63 thf(fact_6111_sums__Suc,axiom,
% 0.35/0.63 ! [F2: nat > nat,L: nat] :
% 0.35/0.63 ( ( sums_nat
% 0.35/0.63 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 0.35/0.63 @ L )
% 0.35/0.63 => ( sums_nat @ F2 @ ( plus_plus_nat @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_Suc
% 0.35/0.63 thf(fact_6112_sums__Suc,axiom,
% 0.35/0.63 ! [F2: nat > int,L: int] :
% 0.35/0.63 ( ( sums_int
% 0.35/0.63 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 0.35/0.63 @ L )
% 0.35/0.63 => ( sums_int @ F2 @ ( plus_plus_int @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sums_Suc
% 0.35/0.63 thf(fact_6113_pochhammer__times__pochhammer__half,axiom,
% 0.35/0.63 ! [Z3: complex,N: nat] :
% 0.35/0.63 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z3 @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.35/0.63 = ( groups6464643781859351333omplex
% 0.35/0.63 @ ^ [K3: nat] : ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_times_pochhammer_half
% 0.35/0.63 thf(fact_6114_pochhammer__times__pochhammer__half,axiom,
% 0.35/0.63 ! [Z3: rat,N: nat] :
% 0.35/0.63 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.35/0.63 = ( groups73079841787564623at_rat
% 0.35/0.63 @ ^ [K3: nat] : ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_times_pochhammer_half
% 0.35/0.63 thf(fact_6115_pochhammer__times__pochhammer__half,axiom,
% 0.35/0.63 ! [Z3: real,N: nat] :
% 0.35/0.63 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 0.35/0.63 = ( groups129246275422532515t_real
% 0.35/0.63 @ ^ [K3: nat] : ( plus_plus_real @ Z3 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_times_pochhammer_half
% 0.35/0.63 thf(fact_6116_lemma__termdiff2,axiom,
% 0.35/0.63 ! [H: complex,Z3: complex,N: nat] :
% 0.35/0.63 ( ( H != zero_zero_complex )
% 0.35/0.63 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ N ) @ ( power_power_complex @ Z3 @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.63 = ( times_times_complex @ H
% 0.35/0.63 @ ( groups2073611262835488442omplex
% 0.35/0.63 @ ^ [P5: nat] :
% 0.35/0.63 ( groups2073611262835488442omplex
% 0.35/0.63 @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ Q5 ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lemma_termdiff2
% 0.35/0.63 thf(fact_6117_lemma__termdiff2,axiom,
% 0.35/0.63 ! [H: rat,Z3: rat,N: nat] :
% 0.35/0.63 ( ( H != zero_zero_rat )
% 0.35/0.63 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ N ) @ ( power_power_rat @ Z3 @ N ) ) @ H ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.63 = ( times_times_rat @ H
% 0.35/0.63 @ ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [P5: nat] :
% 0.35/0.63 ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ Q5 ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lemma_termdiff2
% 0.35/0.63 thf(fact_6118_lemma__termdiff2,axiom,
% 0.35/0.63 ! [H: real,Z3: real,N: nat] :
% 0.35/0.63 ( ( H != zero_zero_real )
% 0.35/0.63 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ N ) @ ( power_power_real @ Z3 @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.63 = ( times_times_real @ H
% 0.35/0.63 @ ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [P5: nat] :
% 0.35/0.63 ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ Q5 ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lemma_termdiff2
% 0.35/0.63 thf(fact_6119_pochhammer__code,axiom,
% 0.35/0.63 ( comm_s8582702949713902594nteger
% 0.35/0.63 = ( ^ [A5: code_integer,N4: nat] :
% 0.35/0.63 ( if_Code_integer @ ( N4 = zero_zero_nat ) @ one_one_Code_integer
% 0.35/0.63 @ ( set_fo1084959871951514735nteger
% 0.35/0.63 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ O ) ) )
% 0.35/0.63 @ zero_zero_nat
% 0.35/0.63 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.35/0.63 @ one_one_Code_integer ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_code
% 0.35/0.63 thf(fact_6120_pochhammer__code,axiom,
% 0.35/0.63 ( comm_s2602460028002588243omplex
% 0.35/0.63 = ( ^ [A5: complex,N4: nat] :
% 0.35/0.63 ( if_complex @ ( N4 = zero_zero_nat ) @ one_one_complex
% 0.35/0.63 @ ( set_fo1517530859248394432omplex
% 0.35/0.63 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A5 @ ( semiri8010041392384452111omplex @ O ) ) )
% 0.35/0.63 @ zero_zero_nat
% 0.35/0.63 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.35/0.63 @ one_one_complex ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_code
% 0.35/0.63 thf(fact_6121_pochhammer__code,axiom,
% 0.35/0.63 ( comm_s4028243227959126397er_rat
% 0.35/0.63 = ( ^ [A5: rat,N4: nat] :
% 0.35/0.63 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 0.35/0.63 @ ( set_fo1949268297981939178at_rat
% 0.35/0.63 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 0.35/0.63 @ zero_zero_nat
% 0.35/0.63 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.35/0.63 @ one_one_rat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_code
% 0.35/0.63 thf(fact_6122_pochhammer__code,axiom,
% 0.35/0.63 ( comm_s7457072308508201937r_real
% 0.35/0.63 = ( ^ [A5: real,N4: nat] :
% 0.35/0.63 ( if_real @ ( N4 = zero_zero_nat ) @ one_one_real
% 0.35/0.63 @ ( set_fo3111899725591712190t_real
% 0.35/0.63 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ O ) ) )
% 0.35/0.63 @ zero_zero_nat
% 0.35/0.63 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.35/0.63 @ one_one_real ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_code
% 0.35/0.63 thf(fact_6123_pochhammer__code,axiom,
% 0.35/0.63 ( comm_s4660882817536571857er_int
% 0.35/0.63 = ( ^ [A5: int,N4: nat] :
% 0.35/0.63 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 0.35/0.63 @ ( set_fo2581907887559384638at_int
% 0.35/0.63 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 0.35/0.63 @ zero_zero_nat
% 0.35/0.63 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.35/0.63 @ one_one_int ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_code
% 0.35/0.63 thf(fact_6124_pochhammer__code,axiom,
% 0.35/0.63 ( comm_s4663373288045622133er_nat
% 0.35/0.63 = ( ^ [A5: nat,N4: nat] :
% 0.35/0.63 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 0.35/0.63 @ ( set_fo2584398358068434914at_nat
% 0.35/0.63 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 0.35/0.63 @ zero_zero_nat
% 0.35/0.63 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 0.35/0.63 @ one_one_nat ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % pochhammer_code
% 0.35/0.63 thf(fact_6125_of__nat__code,axiom,
% 0.35/0.63 ( semiri4939895301339042750nteger
% 0.35/0.63 = ( ^ [N4: nat] :
% 0.35/0.63 ( semiri4055485073559036834nteger
% 0.35/0.63 @ ^ [I: code_integer] : ( plus_p5714425477246183910nteger @ I @ one_one_Code_integer )
% 0.35/0.63 @ N4
% 0.35/0.63 @ zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % of_nat_code
% 0.35/0.63 thf(fact_6126_of__nat__code,axiom,
% 0.35/0.63 ( semiri8010041392384452111omplex
% 0.35/0.63 = ( ^ [N4: nat] :
% 0.35/0.63 ( semiri2816024913162550771omplex
% 0.35/0.63 @ ^ [I: complex] : ( plus_plus_complex @ I @ one_one_complex )
% 0.35/0.63 @ N4
% 0.35/0.63 @ zero_zero_complex ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % of_nat_code
% 0.35/0.63 thf(fact_6127_of__nat__code,axiom,
% 0.35/0.63 ( semiri681578069525770553at_rat
% 0.35/0.63 = ( ^ [N4: nat] :
% 0.35/0.63 ( semiri7787848453975740701ux_rat
% 0.35/0.63 @ ^ [I: rat] : ( plus_plus_rat @ I @ one_one_rat )
% 0.35/0.63 @ N4
% 0.35/0.63 @ zero_zero_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % of_nat_code
% 0.35/0.63 thf(fact_6128_of__nat__code,axiom,
% 0.35/0.63 ( semiri5074537144036343181t_real
% 0.35/0.63 = ( ^ [N4: nat] :
% 0.35/0.63 ( semiri7260567687927622513x_real
% 0.35/0.63 @ ^ [I: real] : ( plus_plus_real @ I @ one_one_real )
% 0.35/0.63 @ N4
% 0.35/0.63 @ zero_zero_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % of_nat_code
% 0.35/0.63 thf(fact_6129_of__nat__code,axiom,
% 0.35/0.63 ( semiri1314217659103216013at_int
% 0.35/0.63 = ( ^ [N4: nat] :
% 0.35/0.63 ( semiri8420488043553186161ux_int
% 0.35/0.63 @ ^ [I: int] : ( plus_plus_int @ I @ one_one_int )
% 0.35/0.63 @ N4
% 0.35/0.63 @ zero_zero_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % of_nat_code
% 0.35/0.63 thf(fact_6130_of__nat__code,axiom,
% 0.35/0.63 ( semiri1316708129612266289at_nat
% 0.35/0.63 = ( ^ [N4: nat] :
% 0.35/0.63 ( semiri8422978514062236437ux_nat
% 0.35/0.63 @ ^ [I: nat] : ( plus_plus_nat @ I @ one_one_nat )
% 0.35/0.63 @ N4
% 0.35/0.63 @ zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % of_nat_code
% 0.35/0.63 thf(fact_6131_central__binomial__lower__bound,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.63 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % central_binomial_lower_bound
% 0.35/0.63 thf(fact_6132_concat__bit__Suc,axiom,
% 0.35/0.63 ! [N: nat,K2: int,L: int] :
% 0.35/0.63 ( ( bit_concat_bit @ ( suc @ N ) @ K2 @ L )
% 0.35/0.63 = ( plus_plus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % concat_bit_Suc
% 0.35/0.63 thf(fact_6133_dbl__simps_I3_J,axiom,
% 0.35/0.63 ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 0.35/0.63 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(3)
% 0.35/0.63 thf(fact_6134_dbl__simps_I3_J,axiom,
% 0.35/0.63 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 0.35/0.63 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(3)
% 0.35/0.63 thf(fact_6135_dbl__simps_I3_J,axiom,
% 0.35/0.63 ( ( neg_numeral_dbl_real @ one_one_real )
% 0.35/0.63 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(3)
% 0.35/0.63 thf(fact_6136_dbl__simps_I3_J,axiom,
% 0.35/0.63 ( ( neg_numeral_dbl_int @ one_one_int )
% 0.35/0.63 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(3)
% 0.35/0.63 thf(fact_6137_lessThan__eq__iff,axiom,
% 0.35/0.63 ! [X: nat,Y: nat] :
% 0.35/0.63 ( ( ( set_ord_lessThan_nat @ X )
% 0.35/0.63 = ( set_ord_lessThan_nat @ Y ) )
% 0.35/0.63 = ( X = Y ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_eq_iff
% 0.35/0.63 thf(fact_6138_lessThan__iff,axiom,
% 0.35/0.63 ! [I2: set_nat,K2: set_nat] :
% 0.35/0.63 ( ( member_set_nat @ I2 @ ( set_or890127255671739683et_nat @ K2 ) )
% 0.35/0.63 = ( ord_less_set_nat @ I2 @ K2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_iff
% 0.35/0.63 thf(fact_6139_lessThan__iff,axiom,
% 0.35/0.63 ! [I2: real,K2: real] :
% 0.35/0.63 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K2 ) )
% 0.35/0.63 = ( ord_less_real @ I2 @ K2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_iff
% 0.35/0.63 thf(fact_6140_lessThan__iff,axiom,
% 0.35/0.63 ! [I2: rat,K2: rat] :
% 0.35/0.63 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K2 ) )
% 0.35/0.63 = ( ord_less_rat @ I2 @ K2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_iff
% 0.35/0.63 thf(fact_6141_lessThan__iff,axiom,
% 0.35/0.63 ! [I2: num,K2: num] :
% 0.35/0.63 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K2 ) )
% 0.35/0.63 = ( ord_less_num @ I2 @ K2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_iff
% 0.35/0.63 thf(fact_6142_lessThan__iff,axiom,
% 0.35/0.63 ! [I2: int,K2: int] :
% 0.35/0.63 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K2 ) )
% 0.35/0.63 = ( ord_less_int @ I2 @ K2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_iff
% 0.35/0.63 thf(fact_6143_lessThan__iff,axiom,
% 0.35/0.63 ! [I2: nat,K2: nat] :
% 0.35/0.63 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K2 ) )
% 0.35/0.63 = ( ord_less_nat @ I2 @ K2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_iff
% 0.35/0.63 thf(fact_6144_finite__lessThan,axiom,
% 0.35/0.63 ! [K2: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K2 ) ) ).
% 0.35/0.63
% 0.35/0.63 % finite_lessThan
% 0.35/0.63 thf(fact_6145_concat__bit__0,axiom,
% 0.35/0.63 ! [K2: int,L: int] :
% 0.35/0.63 ( ( bit_concat_bit @ zero_zero_nat @ K2 @ L )
% 0.35/0.63 = L ) ).
% 0.35/0.63
% 0.35/0.63 % concat_bit_0
% 0.35/0.63 thf(fact_6146_card__lessThan,axiom,
% 0.35/0.63 ! [U: nat] :
% 0.35/0.63 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 0.35/0.63 = U ) ).
% 0.35/0.63
% 0.35/0.63 % card_lessThan
% 0.35/0.63 thf(fact_6147_dbl__simps_I2_J,axiom,
% 0.35/0.63 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 0.35/0.63 = zero_zero_complex ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(2)
% 0.35/0.63 thf(fact_6148_dbl__simps_I2_J,axiom,
% 0.35/0.63 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 0.35/0.63 = zero_zero_real ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(2)
% 0.35/0.63 thf(fact_6149_dbl__simps_I2_J,axiom,
% 0.35/0.63 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 0.35/0.63 = zero_zero_rat ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(2)
% 0.35/0.63 thf(fact_6150_dbl__simps_I2_J,axiom,
% 0.35/0.63 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 0.35/0.63 = zero_zero_int ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(2)
% 0.35/0.63 thf(fact_6151_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > complex] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( ( groups6464643781859351333omplex @ F2 @ A4 )
% 0.35/0.63 = zero_zero_complex )
% 0.35/0.63 = ( ? [X4: nat] :
% 0.35/0.63 ( ( member_nat @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_complex ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6152_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > complex] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( groups7440179247065528705omplex @ F2 @ A4 )
% 0.35/0.63 = zero_zero_complex )
% 0.35/0.63 = ( ? [X4: int] :
% 0.35/0.63 ( ( member_int @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_complex ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6153_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( ( groups3708469109370488835omplex @ F2 @ A4 )
% 0.35/0.63 = zero_zero_complex )
% 0.35/0.63 = ( ? [X4: complex] :
% 0.35/0.63 ( ( member_complex @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_complex ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6154_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( ( groups129246275422532515t_real @ F2 @ A4 )
% 0.35/0.63 = zero_zero_real )
% 0.35/0.63 = ( ? [X4: nat] :
% 0.35/0.63 ( ( member_nat @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6155_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( groups2316167850115554303t_real @ F2 @ A4 )
% 0.35/0.63 = zero_zero_real )
% 0.35/0.63 = ( ? [X4: int] :
% 0.35/0.63 ( ( member_int @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6156_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( ( groups766887009212190081x_real @ F2 @ A4 )
% 0.35/0.63 = zero_zero_real )
% 0.35/0.63 = ( ? [X4: complex] :
% 0.35/0.63 ( ( member_complex @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6157_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( ( groups73079841787564623at_rat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_rat )
% 0.35/0.63 = ( ? [X4: nat] :
% 0.35/0.63 ( ( member_nat @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6158_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( groups1072433553688619179nt_rat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_rat )
% 0.35/0.63 = ( ? [X4: int] :
% 0.35/0.63 ( ( member_int @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6159_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( ( groups225925009352817453ex_rat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_rat )
% 0.35/0.63 = ( ? [X4: complex] :
% 0.35/0.63 ( ( member_complex @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_rat ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6160_prod__zero__iff,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( groups1707563613775114915nt_nat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_nat )
% 0.35/0.63 = ( ? [X4: int] :
% 0.35/0.63 ( ( member_int @ X4 @ A4 )
% 0.35/0.63 & ( ( F2 @ X4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero_iff
% 0.35/0.63 thf(fact_6161_lessThan__subset__iff,axiom,
% 0.35/0.63 ! [X: rat,Y: rat] :
% 0.35/0.63 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 0.35/0.63 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_subset_iff
% 0.35/0.63 thf(fact_6162_lessThan__subset__iff,axiom,
% 0.35/0.63 ! [X: num,Y: num] :
% 0.35/0.63 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 0.35/0.63 = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_subset_iff
% 0.35/0.63 thf(fact_6163_lessThan__subset__iff,axiom,
% 0.35/0.63 ! [X: int,Y: int] :
% 0.35/0.63 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 0.35/0.63 = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_subset_iff
% 0.35/0.63 thf(fact_6164_lessThan__subset__iff,axiom,
% 0.35/0.63 ! [X: nat,Y: nat] :
% 0.35/0.63 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 0.35/0.63 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_subset_iff
% 0.35/0.63 thf(fact_6165_lessThan__0,axiom,
% 0.35/0.63 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 0.35/0.63 = bot_bot_set_nat ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_0
% 0.35/0.63 thf(fact_6166_dbl__simps_I5_J,axiom,
% 0.35/0.63 ! [K2: num] :
% 0.35/0.63 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K2 ) )
% 0.35/0.63 = ( numera6690914467698888265omplex @ ( bit0 @ K2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(5)
% 0.35/0.63 thf(fact_6167_dbl__simps_I5_J,axiom,
% 0.35/0.63 ! [K2: num] :
% 0.35/0.63 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K2 ) )
% 0.35/0.63 = ( numeral_numeral_real @ ( bit0 @ K2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(5)
% 0.35/0.63 thf(fact_6168_dbl__simps_I5_J,axiom,
% 0.35/0.63 ! [K2: num] :
% 0.35/0.63 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K2 ) )
% 0.35/0.63 = ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_simps(5)
% 0.35/0.63 thf(fact_6169_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > real] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ~ ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6170_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_nat,X: nat,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ~ ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6171_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ~ ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6172_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_complex,X: complex,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ~ ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6173_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > rat] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ~ ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6174_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ~ ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6175_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ~ ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6176_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ~ ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6177_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > nat] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ~ ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6178_prod_Oinsert,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ~ ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert
% 0.35/0.63 thf(fact_6179_sum_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > rat,N: nat] :
% 0.35/0.63 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc
% 0.35/0.63 thf(fact_6180_sum_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc
% 0.35/0.63 thf(fact_6181_sum_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc
% 0.35/0.63 thf(fact_6182_sum_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > real,N: nat] :
% 0.35/0.63 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc
% 0.35/0.63 thf(fact_6183_single__Diff__lessThan,axiom,
% 0.35/0.63 ! [K2: int] :
% 0.35/0.63 ( ( minus_minus_set_int @ ( insert_int @ K2 @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K2 ) )
% 0.35/0.63 = ( insert_int @ K2 @ bot_bot_set_int ) ) ).
% 0.35/0.63
% 0.35/0.63 % single_Diff_lessThan
% 0.35/0.63 thf(fact_6184_single__Diff__lessThan,axiom,
% 0.35/0.63 ! [K2: real] :
% 0.35/0.63 ( ( minus_minus_set_real @ ( insert_real @ K2 @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K2 ) )
% 0.35/0.63 = ( insert_real @ K2 @ bot_bot_set_real ) ) ).
% 0.35/0.63
% 0.35/0.63 % single_Diff_lessThan
% 0.35/0.63 thf(fact_6185_single__Diff__lessThan,axiom,
% 0.35/0.63 ! [K2: nat] :
% 0.35/0.63 ( ( minus_minus_set_nat @ ( insert_nat @ K2 @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K2 ) )
% 0.35/0.63 = ( insert_nat @ K2 @ bot_bot_set_nat ) ) ).
% 0.35/0.63
% 0.35/0.63 % single_Diff_lessThan
% 0.35/0.63 thf(fact_6186_prod_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > real,N: nat] :
% 0.35/0.63 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc
% 0.35/0.63 thf(fact_6187_prod_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > rat,N: nat] :
% 0.35/0.63 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc
% 0.35/0.63 thf(fact_6188_prod_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc
% 0.35/0.63 thf(fact_6189_prod_OlessThan__Suc,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc
% 0.35/0.63 thf(fact_6190_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.63 ! [N: nat,M2: nat,G2: nat > code_integer] :
% 0.35/0.63 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = one_one_Code_integer ) )
% 0.35/0.63 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.cl_ivl_Suc
% 0.35/0.63 thf(fact_6191_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.63 ! [N: nat,M2: nat,G2: nat > complex] :
% 0.35/0.63 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = one_one_complex ) )
% 0.35/0.63 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_complex @ ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.cl_ivl_Suc
% 0.35/0.63 thf(fact_6192_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.63 ! [N: nat,M2: nat,G2: nat > real] :
% 0.35/0.63 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = one_one_real ) )
% 0.35/0.63 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.cl_ivl_Suc
% 0.35/0.63 thf(fact_6193_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.63 ! [N: nat,M2: nat,G2: nat > rat] :
% 0.35/0.63 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = one_one_rat ) )
% 0.35/0.63 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.cl_ivl_Suc
% 0.35/0.63 thf(fact_6194_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.63 ! [N: nat,M2: nat,G2: nat > int] :
% 0.35/0.63 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = one_one_int ) )
% 0.35/0.63 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.cl_ivl_Suc
% 0.35/0.63 thf(fact_6195_prod_Ocl__ivl__Suc,axiom,
% 0.35/0.63 ! [N: nat,M2: nat,G2: nat > nat] :
% 0.35/0.63 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = one_one_nat ) )
% 0.35/0.63 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 0.35/0.63 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.cl_ivl_Suc
% 0.35/0.63 thf(fact_6196_prod_Onat__diff__reindex,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.63 = ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.nat_diff_reindex
% 0.35/0.63 thf(fact_6197_prod_Onat__diff__reindex,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.63 = ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.nat_diff_reindex
% 0.35/0.63 thf(fact_6198_lessThan__non__empty,axiom,
% 0.35/0.63 ! [X: int] :
% 0.35/0.63 ( ( set_ord_lessThan_int @ X )
% 0.35/0.63 != bot_bot_set_int ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_non_empty
% 0.35/0.63 thf(fact_6199_lessThan__non__empty,axiom,
% 0.35/0.63 ! [X: real] :
% 0.35/0.63 ( ( set_or5984915006950818249n_real @ X )
% 0.35/0.63 != bot_bot_set_real ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_non_empty
% 0.35/0.63 thf(fact_6200_infinite__Iio,axiom,
% 0.35/0.63 ! [A: int] :
% 0.35/0.63 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 0.35/0.63
% 0.35/0.63 % infinite_Iio
% 0.35/0.63 thf(fact_6201_prod_Odistrib,axiom,
% 0.35/0.63 ! [G2: nat > int,H: nat > int,A4: set_nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [X4: nat] : ( times_times_int @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A4 ) @ ( groups705719431365010083at_int @ H @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.distrib
% 0.35/0.63 thf(fact_6202_prod_Odistrib,axiom,
% 0.35/0.63 ! [G2: int > int,H: int > int,A4: set_int] :
% 0.35/0.63 ( ( groups1705073143266064639nt_int
% 0.35/0.63 @ ^ [X4: int] : ( times_times_int @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A4 ) @ ( groups1705073143266064639nt_int @ H @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.distrib
% 0.35/0.63 thf(fact_6203_prod_Odistrib,axiom,
% 0.35/0.63 ! [G2: nat > nat,H: nat > nat,A4: set_nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [X4: nat] : ( times_times_nat @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 0.35/0.63 @ A4 )
% 0.35/0.63 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A4 ) @ ( groups708209901874060359at_nat @ H @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.distrib
% 0.35/0.63 thf(fact_6204_lessThan__def,axiom,
% 0.35/0.63 ( set_or890127255671739683et_nat
% 0.35/0.63 = ( ^ [U2: set_nat] :
% 0.35/0.63 ( collect_set_nat
% 0.35/0.63 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_def
% 0.35/0.63 thf(fact_6205_lessThan__def,axiom,
% 0.35/0.63 ( set_or5984915006950818249n_real
% 0.35/0.63 = ( ^ [U2: real] :
% 0.35/0.63 ( collect_real
% 0.35/0.63 @ ^ [X4: real] : ( ord_less_real @ X4 @ U2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_def
% 0.35/0.63 thf(fact_6206_lessThan__def,axiom,
% 0.35/0.63 ( set_ord_lessThan_rat
% 0.35/0.63 = ( ^ [U2: rat] :
% 0.35/0.63 ( collect_rat
% 0.35/0.63 @ ^ [X4: rat] : ( ord_less_rat @ X4 @ U2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_def
% 0.35/0.63 thf(fact_6207_lessThan__def,axiom,
% 0.35/0.63 ( set_ord_lessThan_num
% 0.35/0.63 = ( ^ [U2: num] :
% 0.35/0.63 ( collect_num
% 0.35/0.63 @ ^ [X4: num] : ( ord_less_num @ X4 @ U2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_def
% 0.35/0.63 thf(fact_6208_lessThan__def,axiom,
% 0.35/0.63 ( set_ord_lessThan_int
% 0.35/0.63 = ( ^ [U2: int] :
% 0.35/0.63 ( collect_int
% 0.35/0.63 @ ^ [X4: int] : ( ord_less_int @ X4 @ U2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_def
% 0.35/0.63 thf(fact_6209_lessThan__def,axiom,
% 0.35/0.63 ( set_ord_lessThan_nat
% 0.35/0.63 = ( ^ [U2: nat] :
% 0.35/0.63 ( collect_nat
% 0.35/0.63 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U2 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_def
% 0.35/0.63 thf(fact_6210_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > real,N: nat] :
% 0.35/0.63 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups129246275422532515t_real
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6211_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > rat,N: nat] :
% 0.35/0.63 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups73079841787564623at_rat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6212_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6213_prod_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6214_prod_OatLeast1__atMost__eq,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.63 = ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast1_atMost_eq
% 0.35/0.63 thf(fact_6215_prod_OatLeast1__atMost__eq,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.63 = ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast1_atMost_eq
% 0.35/0.63 thf(fact_6216_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 0.35/0.63 ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6217_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > real,G2: real > real] :
% 0.35/0.63 ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6218_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 0.35/0.63 ( ! [I3: nat] :
% 0.35/0.63 ( ( member_nat @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6219_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > real,G2: int > real] :
% 0.35/0.63 ( ! [I3: int] :
% 0.35/0.63 ( ( member_int @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6220_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 0.35/0.63 ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6221_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > rat,G2: real > rat] :
% 0.35/0.63 ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6222_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 0.35/0.63 ( ! [I3: nat] :
% 0.35/0.63 ( ( member_nat @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6223_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 0.35/0.63 ( ! [I3: int] :
% 0.35/0.63 ( ( member_int @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6224_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 0.35/0.63 ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6225_prod__mono,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > nat,G2: real > nat] :
% 0.35/0.63 ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F2 @ A4 ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono
% 0.35/0.63 thf(fact_6226_prod__nonneg,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > int] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_nonneg
% 0.35/0.63 thf(fact_6227_prod__nonneg,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > int] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_nonneg
% 0.35/0.63 thf(fact_6228_prod__nonneg,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > nat] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_nonneg
% 0.35/0.63 thf(fact_6229_prod__pos,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > int] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_pos
% 0.35/0.63 thf(fact_6230_prod__pos,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > int] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_pos
% 0.35/0.63 thf(fact_6231_prod__pos,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > nat] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_pos
% 0.35/0.63 thf(fact_6232_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > code_integer] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ A4 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups8682486955453173170nteger @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6233_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > code_integer] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ A4 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups6225526099057966256nteger @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6234_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > code_integer] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6235_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > code_integer] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ A4 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6236_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > real] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6237_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > real] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6238_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > real] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6239_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > real] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6240_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > rat] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6241_prod__ge__1,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > rat] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ A4 )
% 0.35/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X3 ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_ge_1
% 0.35/0.63 thf(fact_6242_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > complex] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ? [X5: nat] :
% 0.35/0.63 ( ( member_nat @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_complex ) )
% 0.35/0.63 => ( ( groups6464643781859351333omplex @ F2 @ A4 )
% 0.35/0.63 = zero_zero_complex ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6243_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > complex] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ? [X5: int] :
% 0.35/0.63 ( ( member_int @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_complex ) )
% 0.35/0.63 => ( ( groups7440179247065528705omplex @ F2 @ A4 )
% 0.35/0.63 = zero_zero_complex ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6244_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ? [X5: complex] :
% 0.35/0.63 ( ( member_complex @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_complex ) )
% 0.35/0.63 => ( ( groups3708469109370488835omplex @ F2 @ A4 )
% 0.35/0.63 = zero_zero_complex ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6245_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ? [X5: nat] :
% 0.35/0.63 ( ( member_nat @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_real ) )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ F2 @ A4 )
% 0.35/0.63 = zero_zero_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6246_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ? [X5: int] :
% 0.35/0.63 ( ( member_int @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_real ) )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ F2 @ A4 )
% 0.35/0.63 = zero_zero_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6247_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ? [X5: complex] :
% 0.35/0.63 ( ( member_complex @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_real ) )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ F2 @ A4 )
% 0.35/0.63 = zero_zero_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6248_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ? [X5: nat] :
% 0.35/0.63 ( ( member_nat @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_rat ) )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6249_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ? [X5: int] :
% 0.35/0.63 ( ( member_int @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_rat ) )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6250_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ? [X5: complex] :
% 0.35/0.63 ( ( member_complex @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_rat ) )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6251_prod__zero,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ? [X5: int] :
% 0.35/0.63 ( ( member_int @ X5 @ A4 )
% 0.35/0.63 & ( ( F2 @ X5 )
% 0.35/0.63 = zero_zero_nat ) )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ F2 @ A4 )
% 0.35/0.63 = zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_zero
% 0.35/0.63 thf(fact_6252_prod__atLeastAtMost__code,axiom,
% 0.35/0.63 ! [F2: nat > code_integer,A: nat,B: nat] :
% 0.35/0.63 ( ( groups3455450783089532116nteger @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.63 = ( set_fo1084959871951514735nteger
% 0.35/0.63 @ ^ [A5: nat] : ( times_3573771949741848930nteger @ ( F2 @ A5 ) )
% 0.35/0.63 @ A
% 0.35/0.63 @ B
% 0.35/0.63 @ one_one_Code_integer ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_atLeastAtMost_code
% 0.35/0.63 thf(fact_6253_prod__atLeastAtMost__code,axiom,
% 0.35/0.63 ! [F2: nat > complex,A: nat,B: nat] :
% 0.35/0.63 ( ( groups6464643781859351333omplex @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.63 = ( set_fo1517530859248394432omplex
% 0.35/0.63 @ ^ [A5: nat] : ( times_times_complex @ ( F2 @ A5 ) )
% 0.35/0.63 @ A
% 0.35/0.63 @ B
% 0.35/0.63 @ one_one_complex ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_atLeastAtMost_code
% 0.35/0.63 thf(fact_6254_prod__atLeastAtMost__code,axiom,
% 0.35/0.63 ! [F2: nat > real,A: nat,B: nat] :
% 0.35/0.63 ( ( groups129246275422532515t_real @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.63 = ( set_fo3111899725591712190t_real
% 0.35/0.63 @ ^ [A5: nat] : ( times_times_real @ ( F2 @ A5 ) )
% 0.35/0.63 @ A
% 0.35/0.63 @ B
% 0.35/0.63 @ one_one_real ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_atLeastAtMost_code
% 0.35/0.63 thf(fact_6255_prod__atLeastAtMost__code,axiom,
% 0.35/0.63 ! [F2: nat > rat,A: nat,B: nat] :
% 0.35/0.63 ( ( groups73079841787564623at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.63 = ( set_fo1949268297981939178at_rat
% 0.35/0.63 @ ^ [A5: nat] : ( times_times_rat @ ( F2 @ A5 ) )
% 0.35/0.63 @ A
% 0.35/0.63 @ B
% 0.35/0.63 @ one_one_rat ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_atLeastAtMost_code
% 0.35/0.63 thf(fact_6256_prod__atLeastAtMost__code,axiom,
% 0.35/0.63 ! [F2: nat > int,A: nat,B: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.63 = ( set_fo2581907887559384638at_int
% 0.35/0.63 @ ^ [A5: nat] : ( times_times_int @ ( F2 @ A5 ) )
% 0.35/0.63 @ A
% 0.35/0.63 @ B
% 0.35/0.63 @ one_one_int ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_atLeastAtMost_code
% 0.35/0.63 thf(fact_6257_prod__atLeastAtMost__code,axiom,
% 0.35/0.63 ! [F2: nat > nat,A: nat,B: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.63 = ( set_fo2584398358068434914at_nat
% 0.35/0.63 @ ^ [A5: nat] : ( times_times_nat @ ( F2 @ A5 ) )
% 0.35/0.63 @ A
% 0.35/0.63 @ B
% 0.35/0.63 @ one_one_nat ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_atLeastAtMost_code
% 0.35/0.63 thf(fact_6258_Iio__eq__empty__iff,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( ( set_ord_lessThan_nat @ N )
% 0.35/0.63 = bot_bot_set_nat )
% 0.35/0.63 = ( N = bot_bot_nat ) ) ).
% 0.35/0.63
% 0.35/0.63 % Iio_eq_empty_iff
% 0.35/0.63 thf(fact_6259_lessThan__strict__subset__iff,axiom,
% 0.35/0.63 ! [M2: real,N: real] :
% 0.35/0.63 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M2 ) @ ( set_or5984915006950818249n_real @ N ) )
% 0.35/0.63 = ( ord_less_real @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_strict_subset_iff
% 0.35/0.63 thf(fact_6260_lessThan__strict__subset__iff,axiom,
% 0.35/0.63 ! [M2: rat,N: rat] :
% 0.35/0.63 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M2 ) @ ( set_ord_lessThan_rat @ N ) )
% 0.35/0.63 = ( ord_less_rat @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_strict_subset_iff
% 0.35/0.63 thf(fact_6261_lessThan__strict__subset__iff,axiom,
% 0.35/0.63 ! [M2: num,N: num] :
% 0.35/0.63 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M2 ) @ ( set_ord_lessThan_num @ N ) )
% 0.35/0.63 = ( ord_less_num @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_strict_subset_iff
% 0.35/0.63 thf(fact_6262_lessThan__strict__subset__iff,axiom,
% 0.35/0.63 ! [M2: int,N: int] :
% 0.35/0.63 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M2 ) @ ( set_ord_lessThan_int @ N ) )
% 0.35/0.63 = ( ord_less_int @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_strict_subset_iff
% 0.35/0.63 thf(fact_6263_lessThan__strict__subset__iff,axiom,
% 0.35/0.63 ! [M2: nat,N: nat] :
% 0.35/0.63 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M2 ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.63 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_strict_subset_iff
% 0.35/0.63 thf(fact_6264_lessThan__Suc,axiom,
% 0.35/0.63 ! [K2: nat] :
% 0.35/0.63 ( ( set_ord_lessThan_nat @ ( suc @ K2 ) )
% 0.35/0.63 = ( insert_nat @ K2 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_Suc
% 0.35/0.63 thf(fact_6265_lessThan__empty__iff,axiom,
% 0.35/0.63 ! [N: nat] :
% 0.35/0.63 ( ( ( set_ord_lessThan_nat @ N )
% 0.35/0.63 = bot_bot_set_nat )
% 0.35/0.63 = ( N = zero_zero_nat ) ) ).
% 0.35/0.63
% 0.35/0.63 % lessThan_empty_iff
% 0.35/0.63 thf(fact_6266_dbl__def,axiom,
% 0.35/0.63 ( neg_numeral_dbl_real
% 0.35/0.63 = ( ^ [X4: real] : ( plus_plus_real @ X4 @ X4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_def
% 0.35/0.63 thf(fact_6267_dbl__def,axiom,
% 0.35/0.63 ( neg_numeral_dbl_rat
% 0.35/0.63 = ( ^ [X4: rat] : ( plus_plus_rat @ X4 @ X4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_def
% 0.35/0.63 thf(fact_6268_dbl__def,axiom,
% 0.35/0.63 ( neg_numeral_dbl_int
% 0.35/0.63 = ( ^ [X4: int] : ( plus_plus_int @ X4 @ X4 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % dbl_def
% 0.35/0.63 thf(fact_6269_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.63 ! [G2: nat > int,M2: nat,N: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 0.35/0.63 = ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.shift_bounds_cl_Suc_ivl
% 0.35/0.63 thf(fact_6270_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 0.35/0.63 ! [G2: nat > nat,M2: nat,N: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 0.35/0.63 = ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.shift_bounds_cl_Suc_ivl
% 0.35/0.63 thf(fact_6271_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.63 ! [G2: nat > int,M2: nat,K2: nat,N: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 0.35/0.63 = ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.shift_bounds_cl_nat_ivl
% 0.35/0.63 thf(fact_6272_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 0.35/0.63 ! [G2: nat > nat,M2: nat,K2: nat,N: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 0.35/0.63 = ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.shift_bounds_cl_nat_ivl
% 0.35/0.63 thf(fact_6273_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > code_integer] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6274_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > code_integer] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6275_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > code_integer] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6276_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > code_integer] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6277_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > real] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6278_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > real] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6279_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > real] :
% 0.35/0.63 ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6280_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > real] :
% 0.35/0.63 ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 0.35/0.63 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6281_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > rat] :
% 0.35/0.63 ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ one_one_rat ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ one_one_rat ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6282_prod__le__1,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > rat] :
% 0.35/0.63 ( ! [X3: real] :
% 0.35/0.63 ( ( member_real @ X3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) )
% 0.35/0.63 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ one_one_rat ) ) )
% 0.35/0.63 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ one_one_rat ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_le_1
% 0.35/0.63 thf(fact_6283_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: code_integer > code_integer > $o,S3: set_nat,H: nat > code_integer,G2: nat > code_integer] :
% 0.35/0.63 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 0.35/0.63 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite_finite_nat @ S3 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups3455450783089532116nteger @ H @ S3 ) @ ( groups3455450783089532116nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6284_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: code_integer > code_integer > $o,S3: set_int,H: int > code_integer,G2: int > code_integer] :
% 0.35/0.63 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 0.35/0.63 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite_finite_int @ S3 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups3827104343326376752nteger @ H @ S3 ) @ ( groups3827104343326376752nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6285_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: code_integer > code_integer > $o,S3: set_complex,H: complex > code_integer,G2: complex > code_integer] :
% 0.35/0.63 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 0.35/0.63 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups8682486955453173170nteger @ H @ S3 ) @ ( groups8682486955453173170nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6286_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: complex > complex > $o,S3: set_nat,H: nat > complex,G2: nat > complex] :
% 0.35/0.63 ( ( R2 @ one_one_complex @ one_one_complex )
% 0.35/0.63 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite_finite_nat @ S3 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups6464643781859351333omplex @ H @ S3 ) @ ( groups6464643781859351333omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6287_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: complex > complex > $o,S3: set_int,H: int > complex,G2: int > complex] :
% 0.35/0.63 ( ( R2 @ one_one_complex @ one_one_complex )
% 0.35/0.63 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite_finite_int @ S3 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups7440179247065528705omplex @ H @ S3 ) @ ( groups7440179247065528705omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6288_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: complex > complex > $o,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 0.35/0.63 ( ( R2 @ one_one_complex @ one_one_complex )
% 0.35/0.63 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups3708469109370488835omplex @ H @ S3 ) @ ( groups3708469109370488835omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6289_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: real > real > $o,S3: set_nat,H: nat > real,G2: nat > real] :
% 0.35/0.63 ( ( R2 @ one_one_real @ one_one_real )
% 0.35/0.63 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite_finite_nat @ S3 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups129246275422532515t_real @ H @ S3 ) @ ( groups129246275422532515t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6290_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: real > real > $o,S3: set_int,H: int > real,G2: int > real] :
% 0.35/0.63 ( ( R2 @ one_one_real @ one_one_real )
% 0.35/0.63 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite_finite_int @ S3 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups2316167850115554303t_real @ H @ S3 ) @ ( groups2316167850115554303t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6291_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: real > real > $o,S3: set_complex,H: complex > real,G2: complex > real] :
% 0.35/0.63 ( ( R2 @ one_one_real @ one_one_real )
% 0.35/0.63 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups766887009212190081x_real @ H @ S3 ) @ ( groups766887009212190081x_real @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6292_prod_Orelated,axiom,
% 0.35/0.63 ! [R2: rat > rat > $o,S3: set_nat,H: nat > rat,G2: nat > rat] :
% 0.35/0.63 ( ( R2 @ one_one_rat @ one_one_rat )
% 0.35/0.63 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 0.35/0.63 ( ( ( R2 @ X15 @ X23 )
% 0.35/0.63 & ( R2 @ Y15 @ Y23 ) )
% 0.35/0.63 => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 0.35/0.63 => ( ( finite_finite_nat @ S3 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ S3 )
% 0.35/0.63 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 0.35/0.63 => ( R2 @ ( groups73079841787564623at_rat @ H @ S3 ) @ ( groups73079841787564623at_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.related
% 0.35/0.63 thf(fact_6293_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > real] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( groups1681761925125756287l_real @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6294_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_nat,X: nat,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( groups129246275422532515t_real @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6295_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( groups2316167850115554303t_real @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6296_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_complex,X: complex,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( groups766887009212190081x_real @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6297_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > rat] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( groups4061424788464935467al_rat @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6298_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( groups73079841787564623at_rat @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6299_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6300_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( groups225925009352817453ex_rat @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6301_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > nat] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( groups4696554848551431203al_nat @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6302_prod_Oinsert__if,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) )
% 0.35/0.63 & ( ~ ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_if
% 0.35/0.63 thf(fact_6303_ivl__disj__int__one_I4_J,axiom,
% 0.35/0.63 ! [L: nat,U: nat] :
% 0.35/0.63 ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.35/0.63 = bot_bot_set_nat ) ).
% 0.35/0.63
% 0.35/0.63 % ivl_disj_int_one(4)
% 0.35/0.63 thf(fact_6304_ivl__disj__int__one_I4_J,axiom,
% 0.35/0.63 ! [L: int,U: int] :
% 0.35/0.63 ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.35/0.63 = bot_bot_set_int ) ).
% 0.35/0.63
% 0.35/0.63 % ivl_disj_int_one(4)
% 0.35/0.63 thf(fact_6305_ivl__disj__int__one_I4_J,axiom,
% 0.35/0.63 ! [L: real,U: real] :
% 0.35/0.63 ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ L ) @ ( set_or1222579329274155063t_real @ L @ U ) )
% 0.35/0.63 = bot_bot_set_real ) ).
% 0.35/0.63
% 0.35/0.63 % ivl_disj_int_one(4)
% 0.35/0.63 thf(fact_6306_prod_OatLeastAtMost__rev,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat,M2: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 0.35/0.63 = ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeastAtMost_rev
% 0.35/0.63 thf(fact_6307_prod_OatLeastAtMost__rev,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat,M2: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 0.35/0.63 = ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeastAtMost_rev
% 0.35/0.63 thf(fact_6308_sum_Onat__diff__reindex,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.63 = ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.nat_diff_reindex
% 0.35/0.63 thf(fact_6309_sum_Onat__diff__reindex,axiom,
% 0.35/0.63 ! [G2: nat > real,N: nat] :
% 0.35/0.63 ( ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.63 = ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.nat_diff_reindex
% 0.35/0.63 thf(fact_6310_sum__diff__distrib,axiom,
% 0.35/0.63 ! [Q: nat > nat,P2: nat > nat,N: nat] :
% 0.35/0.63 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P2 @ X3 ) )
% 0.35/0.63 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P2 @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 0.35/0.63 = ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [X4: nat] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q @ X4 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_diff_distrib
% 0.35/0.63 thf(fact_6311_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_real,I2: real,F2: real > code_integer] :
% 0.35/0.63 ( ( finite_finite_real @ I5 )
% 0.35/0.63 => ( ( member_real @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ I5 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups6225526099057966256nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6312_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_nat,I2: nat,F2: nat > code_integer] :
% 0.35/0.63 ( ( finite_finite_nat @ I5 )
% 0.35/0.63 => ( ( member_nat @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: nat] :
% 0.35/0.63 ( ( member_nat @ I3 @ I5 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6313_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_int,I2: int,F2: int > code_integer] :
% 0.35/0.63 ( ( finite_finite_int @ I5 )
% 0.35/0.63 => ( ( member_int @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: int] :
% 0.35/0.63 ( ( member_int @ I3 @ I5 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6314_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_complex,I2: complex,F2: complex > code_integer] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.63 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ I5 )
% 0.35/0.63 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups8682486955453173170nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6315_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_real,I2: real,F2: real > real] :
% 0.35/0.63 ( ( finite_finite_real @ I5 )
% 0.35/0.63 => ( ( member_real @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ I5 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6316_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_nat,I2: nat,F2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ I5 )
% 0.35/0.63 => ( ( member_nat @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: nat] :
% 0.35/0.63 ( ( member_nat @ I3 @ I5 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6317_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_int,I2: int,F2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ I5 )
% 0.35/0.63 => ( ( member_int @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: int] :
% 0.35/0.63 ( ( member_int @ I3 @ I5 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6318_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_complex,I2: complex,F2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ I5 )
% 0.35/0.63 => ( ( member_complex @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ I5 )
% 0.35/0.63 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6319_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_real,I2: real,F2: real > rat] :
% 0.35/0.63 ( ( finite_finite_real @ I5 )
% 0.35/0.63 => ( ( member_real @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ I5 )
% 0.35/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6320_less__1__prod2,axiom,
% 0.35/0.63 ! [I5: set_nat,I2: nat,F2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ I5 )
% 0.35/0.63 => ( ( member_nat @ I2 @ I5 )
% 0.35/0.63 => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) )
% 0.35/0.63 => ( ! [I3: nat] :
% 0.35/0.63 ( ( member_nat @ I3 @ I5 )
% 0.35/0.63 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I3 ) ) )
% 0.35/0.63 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % less_1_prod2
% 0.35/0.63 thf(fact_6321_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_int,A4: set_int,G2: int > real] :
% 0.35/0.63 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6322_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_complex,A4: set_complex,G2: complex > real] :
% 0.35/0.63 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6323_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_int,A4: set_int,G2: int > rat] :
% 0.35/0.63 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6324_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_complex,A4: set_complex,G2: complex > rat] :
% 0.35/0.63 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6325_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_int,A4: set_int,G2: int > nat] :
% 0.35/0.63 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6326_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_complex,A4: set_complex,G2: complex > nat] :
% 0.35/0.63 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6327_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_complex,A4: set_complex,G2: complex > int] :
% 0.35/0.63 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups858564598930262913ex_int @ G2 @ A4 )
% 0.35/0.63 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6328_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_nat,A4: set_nat,G2: nat > real] :
% 0.35/0.63 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6329_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_nat,A4: set_nat,G2: nat > rat] :
% 0.35/0.63 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6330_prod_Osubset__diff,axiom,
% 0.35/0.63 ! [B5: set_nat,A4: set_nat,G2: nat > int] :
% 0.35/0.63 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ A4 )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.subset_diff
% 0.35/0.63 thf(fact_6331_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6332_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6333_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6334_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6335_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6336_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6337_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6338_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6339_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ A4 ) @ ( groups858564598930262913ex_int @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6340_prod_Ounion__inter,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > int] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A4 ) @ ( groups705719431365010083at_int @ G2 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter
% 0.35/0.63 thf(fact_6341_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_int,G2: int > real,B5: set_int] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6342_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > real,B5: set_complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6343_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_nat,G2: nat > real,B5: set_nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6344_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_int,G2: int > rat,B5: set_int] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6345_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > rat,B5: set_complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6346_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_nat,G2: nat > rat,B5: set_nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6347_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_int,G2: int > nat,B5: set_int] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6348_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > nat,B5: set_complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6349_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > int,B5: set_complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups858564598930262913ex_int @ G2 @ A4 )
% 0.35/0.63 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6350_prod_OInt__Diff,axiom,
% 0.35/0.63 ! [A4: set_nat,G2: nat > int,B5: set_nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ A4 )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Int_Diff
% 0.35/0.63 thf(fact_6351_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.63 ! [G2: nat > real,N: nat] :
% 0.35/0.63 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast0_atMost_Suc
% 0.35/0.63 thf(fact_6352_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.63 ! [G2: nat > rat,N: nat] :
% 0.35/0.63 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast0_atMost_Suc
% 0.35/0.63 thf(fact_6353_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat] :
% 0.35/0.63 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast0_atMost_Suc
% 0.35/0.63 thf(fact_6354_prod_OatLeast0__atMost__Suc,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast0_atMost_Suc
% 0.35/0.63 thf(fact_6355_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ M2 ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast_Suc_atMost
% 0.35/0.63 thf(fact_6356_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > rat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ M2 ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast_Suc_atMost
% 0.35/0.63 thf(fact_6357_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( times_times_int @ ( G2 @ M2 ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast_Suc_atMost
% 0.35/0.63 thf(fact_6358_prod_OatLeast__Suc__atMost,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ M2 ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.atLeast_Suc_atMost
% 0.35/0.63 thf(fact_6359_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.nat_ivl_Suc'
% 0.35/0.63 thf(fact_6360_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > rat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.nat_ivl_Suc'
% 0.35/0.63 thf(fact_6361_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( G2 @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.nat_ivl_Suc'
% 0.35/0.63 thf(fact_6362_prod_Onat__ivl__Suc_H,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 0.35/0.63 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.nat_ivl_Suc'
% 0.35/0.63 thf(fact_6363_Iio__Int__singleton,axiom,
% 0.35/0.63 ! [X: real,K2: real] :
% 0.35/0.63 ( ( ( ord_less_real @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.35/0.63 = ( insert_real @ X @ bot_bot_set_real ) ) )
% 0.35/0.63 & ( ~ ( ord_less_real @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 0.35/0.63 = bot_bot_set_real ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Iio_Int_singleton
% 0.35/0.63 thf(fact_6364_Iio__Int__singleton,axiom,
% 0.35/0.63 ! [X: rat,K2: rat] :
% 0.35/0.63 ( ( ( ord_less_rat @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 0.35/0.63 = ( insert_rat @ X @ bot_bot_set_rat ) ) )
% 0.35/0.63 & ( ~ ( ord_less_rat @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 0.35/0.63 = bot_bot_set_rat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Iio_Int_singleton
% 0.35/0.63 thf(fact_6365_Iio__Int__singleton,axiom,
% 0.35/0.63 ! [X: num,K2: num] :
% 0.35/0.63 ( ( ( ord_less_num @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 0.35/0.63 = ( insert_num @ X @ bot_bot_set_num ) ) )
% 0.35/0.63 & ( ~ ( ord_less_num @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 0.35/0.63 = bot_bot_set_num ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Iio_Int_singleton
% 0.35/0.63 thf(fact_6366_Iio__Int__singleton,axiom,
% 0.35/0.63 ! [X: int,K2: int] :
% 0.35/0.63 ( ( ( ord_less_int @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.35/0.63 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 0.35/0.63 & ( ~ ( ord_less_int @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 0.35/0.63 = bot_bot_set_int ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Iio_Int_singleton
% 0.35/0.63 thf(fact_6367_Iio__Int__singleton,axiom,
% 0.35/0.63 ! [X: nat,K2: nat] :
% 0.35/0.63 ( ( ( ord_less_nat @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.35/0.63 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 0.35/0.63 & ( ~ ( ord_less_nat @ X @ K2 )
% 0.35/0.63 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 0.35/0.63 = bot_bot_set_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % Iio_Int_singleton
% 0.35/0.63 thf(fact_6368_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > real] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ M2 )
% 0.35/0.63 @ ( groups129246275422532515t_real
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Suc_reindex_ivl
% 0.35/0.63 thf(fact_6369_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > rat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ M2 )
% 0.35/0.63 @ ( groups73079841787564623at_rat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Suc_reindex_ivl
% 0.35/0.63 thf(fact_6370_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > int] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_int @ ( G2 @ M2 )
% 0.35/0.63 @ ( groups705719431365010083at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Suc_reindex_ivl
% 0.35/0.63 thf(fact_6371_prod_OSuc__reindex__ivl,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.63 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ M2 )
% 0.35/0.63 @ ( groups708209901874060359at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.Suc_reindex_ivl
% 0.35/0.63 thf(fact_6372_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > rat,N: nat] :
% 0.35/0.63 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6373_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > int,N: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6374_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6375_sum_OlessThan__Suc__shift,axiom,
% 0.35/0.63 ! [G2: nat > real,N: nat] :
% 0.35/0.63 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.63 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 0.35/0.63 @ ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.lessThan_Suc_shift
% 0.35/0.63 thf(fact_6376_sum__lessThan__telescope_H,axiom,
% 0.35/0.63 ! [F2: nat > rat,M2: nat] :
% 0.35/0.63 ( ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [N4: nat] : ( minus_minus_rat @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.63 = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_lessThan_telescope'
% 0.35/0.63 thf(fact_6377_sum__lessThan__telescope_H,axiom,
% 0.35/0.63 ! [F2: nat > int,M2: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [N4: nat] : ( minus_minus_int @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.63 = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_lessThan_telescope'
% 0.35/0.63 thf(fact_6378_sum__lessThan__telescope_H,axiom,
% 0.35/0.63 ! [F2: nat > real,M2: nat] :
% 0.35/0.63 ( ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.63 = ( minus_minus_real @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_lessThan_telescope'
% 0.35/0.63 thf(fact_6379_sum__lessThan__telescope,axiom,
% 0.35/0.63 ! [F2: nat > rat,M2: nat] :
% 0.35/0.63 ( ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [N4: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.63 = ( minus_minus_rat @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_lessThan_telescope
% 0.35/0.63 thf(fact_6380_sum__lessThan__telescope,axiom,
% 0.35/0.63 ! [F2: nat > int,M2: nat] :
% 0.35/0.63 ( ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [N4: nat] : ( minus_minus_int @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.63 = ( minus_minus_int @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_lessThan_telescope
% 0.35/0.63 thf(fact_6381_sum__lessThan__telescope,axiom,
% 0.35/0.63 ! [F2: nat > real,M2: nat] :
% 0.35/0.63 ( ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.63 = ( minus_minus_real @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum_lessThan_telescope
% 0.35/0.63 thf(fact_6382_sumr__diff__mult__const2,axiom,
% 0.35/0.63 ! [F2: nat > rat,N: nat,R3: rat] :
% 0.35/0.63 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R3 ) )
% 0.35/0.63 = ( groups2906978787729119204at_rat
% 0.35/0.63 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ I ) @ R3 )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sumr_diff_mult_const2
% 0.35/0.63 thf(fact_6383_sumr__diff__mult__const2,axiom,
% 0.35/0.63 ! [F2: nat > int,N: nat,R3: int] :
% 0.35/0.63 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R3 ) )
% 0.35/0.63 = ( groups3539618377306564664at_int
% 0.35/0.63 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ I ) @ R3 )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sumr_diff_mult_const2
% 0.35/0.63 thf(fact_6384_sumr__diff__mult__const2,axiom,
% 0.35/0.63 ! [F2: nat > real,N: nat,R3: real] :
% 0.35/0.63 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R3 ) )
% 0.35/0.63 = ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ I ) @ R3 )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sumr_diff_mult_const2
% 0.35/0.63 thf(fact_6385_sum_OatLeast1__atMost__eq,axiom,
% 0.35/0.63 ! [G2: nat > nat,N: nat] :
% 0.35/0.63 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.63 = ( groups3542108847815614940at_nat
% 0.35/0.63 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.atLeast1_atMost_eq
% 0.35/0.63 thf(fact_6386_sum_OatLeast1__atMost__eq,axiom,
% 0.35/0.63 ! [G2: nat > real,N: nat] :
% 0.35/0.63 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.63 = ( groups6591440286371151544t_real
% 0.35/0.63 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 0.35/0.63 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % sum.atLeast1_atMost_eq
% 0.35/0.63 thf(fact_6387_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_complex )
% 0.35/0.63 => ( ord_less_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6388_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ! [I3: nat] :
% 0.35/0.63 ( ( member_nat @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_nat )
% 0.35/0.63 => ( ord_less_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6389_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > real,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ! [I3: int] :
% 0.35/0.63 ( ( member_int @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_int )
% 0.35/0.63 => ( ord_less_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6390_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > real,G2: real > real] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_real )
% 0.35/0.63 => ( ord_less_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6391_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_complex )
% 0.35/0.63 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6392_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ! [I3: nat] :
% 0.35/0.63 ( ( member_nat @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_nat )
% 0.35/0.63 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6393_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ! [I3: int] :
% 0.35/0.63 ( ( member_int @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_int )
% 0.35/0.63 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6394_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_real,F2: real > rat,G2: real > rat] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ! [I3: real] :
% 0.35/0.63 ( ( member_real @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_real )
% 0.35/0.63 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6395_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ! [I3: complex] :
% 0.35/0.63 ( ( member_complex @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_complex )
% 0.35/0.63 => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6396_prod__mono__strict,axiom,
% 0.35/0.63 ! [A4: set_int,F2: int > nat,G2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ! [I3: int] :
% 0.35/0.63 ( ( member_int @ I3 @ A4 )
% 0.35/0.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 0.35/0.63 & ( ord_less_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 0.35/0.63 => ( ( A4 != bot_bot_set_int )
% 0.35/0.63 => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod_mono_strict
% 0.35/0.63 thf(fact_6397_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_complex,X: complex,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6398_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6399_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > real] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups1681761925125756287l_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6400_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_nat,X: nat,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6401_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6402_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6403_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_real,X: real,G2: real > rat] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( member_real @ X @ A4 )
% 0.35/0.63 => ( ( groups4061424788464935467al_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6404_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( member_nat @ X @ A4 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6405_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_complex,X: complex,G2: complex > nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( member_complex @ X @ A4 )
% 0.35/0.63 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6406_prod_Oremove,axiom,
% 0.35/0.63 ! [A4: set_int,X: int,G2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( member_int @ X @ A4 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.remove
% 0.35/0.63 thf(fact_6407_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > real,X: complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6408_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_int,G2: int > real,X: int] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6409_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_real,G2: real > real,X: real] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6410_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_nat,G2: nat > real,X: nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6411_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > rat,X: complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6412_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_int,G2: int > rat,X: int] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6413_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_real,G2: real > rat,X: real] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6414_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_nat,G2: nat > rat,X: nat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 0.35/0.63 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6415_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_complex,G2: complex > nat,X: complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( groups861055069439313189ex_nat @ G2 @ ( insert_complex @ X @ A4 ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6416_prod_Oinsert__remove,axiom,
% 0.35/0.63 ! [A4: set_int,G2: int > nat,X: int] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 0.35/0.63 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.insert_remove
% 0.35/0.63 thf(fact_6417_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > code_integer] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_Code_integer ) )
% 0.35/0.63 => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A4 ) @ ( groups3827104343326376752nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6418_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > code_integer] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_Code_integer ) )
% 0.35/0.63 => ( ( groups8682486955453173170nteger @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_3573771949741848930nteger @ ( groups8682486955453173170nteger @ G2 @ A4 ) @ ( groups8682486955453173170nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6419_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > complex] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_complex ) )
% 0.35/0.63 => ( ( groups7440179247065528705omplex @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_complex @ ( groups7440179247065528705omplex @ G2 @ A4 ) @ ( groups7440179247065528705omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6420_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > complex] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_complex ) )
% 0.35/0.63 => ( ( groups3708469109370488835omplex @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_complex @ ( groups3708469109370488835omplex @ G2 @ A4 ) @ ( groups3708469109370488835omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6421_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > code_integer] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_Code_integer ) )
% 0.35/0.63 => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A4 ) @ ( groups3455450783089532116nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6422_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > complex] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_complex ) )
% 0.35/0.63 => ( ( groups6464643781859351333omplex @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_complex @ ( groups6464643781859351333omplex @ G2 @ A4 ) @ ( groups6464643781859351333omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6423_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_real ) )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6424_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ! [X3: complex] :
% 0.35/0.63 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_real ) )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6425_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ! [X3: nat] :
% 0.35/0.63 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_real ) )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6426_prod_Ounion__inter__neutral,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ! [X3: int] :
% 0.35/0.63 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.63 => ( ( G2 @ X3 )
% 0.35/0.63 = one_one_rat ) )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_inter_neutral
% 0.35/0.63 thf(fact_6427_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_complex )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6428_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_nat )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6429_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_int )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6430_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_real,B5: set_real,G2: real > real] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( finite_finite_real @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_real @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_real )
% 0.35/0.63 => ( ( groups1681761925125756287l_real @ G2 @ ( sup_sup_set_real @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( groups1681761925125756287l_real @ G2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6431_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_complex )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6432_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_nat )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6433_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_int )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6434_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_real,B5: set_real,G2: real > rat] :
% 0.35/0.63 ( ( finite_finite_real @ A4 )
% 0.35/0.63 => ( ( finite_finite_real @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_real @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_real )
% 0.35/0.63 => ( ( groups4061424788464935467al_rat @ G2 @ ( sup_sup_set_real @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( groups4061424788464935467al_rat @ G2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6435_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_complex )
% 0.35/0.63 => ( ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6436_prod_Ounion__disjoint,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 0.35/0.63 = bot_bot_set_int )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_disjoint
% 0.35/0.63 thf(fact_6437_binomial__maximum_H,axiom,
% 0.35/0.63 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K2 ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.35/0.63
% 0.35/0.63 % binomial_maximum'
% 0.35/0.63 thf(fact_6438_binomial__mono,axiom,
% 0.35/0.63 ! [K2: nat,K6: nat,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ K2 @ K6 )
% 0.35/0.63 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.35/0.63 => ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % binomial_mono
% 0.35/0.63 thf(fact_6439_binomial__antimono,axiom,
% 0.35/0.63 ! [K2: nat,K6: nat,N: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ K2 @ K6 )
% 0.35/0.63 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K2 )
% 0.35/0.63 => ( ( ord_less_eq_nat @ K6 @ N )
% 0.35/0.63 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K2 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % binomial_antimono
% 0.35/0.63 thf(fact_6440_binomial__maximum,axiom,
% 0.35/0.63 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % binomial_maximum
% 0.35/0.63 thf(fact_6441_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > real] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6442_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6443_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_real @ ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6444_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6445_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6446_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6447_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 0.35/0.63 ( ( finite_finite_int @ A4 )
% 0.35/0.63 => ( ( finite_finite_int @ B5 )
% 0.35/0.63 => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_nat @ ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6448_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_nat @ ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6449_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 0.35/0.63 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.63 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.63 => ( ( groups858564598930262913ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_int @ ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6450_prod_Ounion__diff2,axiom,
% 0.35/0.63 ! [A4: set_nat,B5: set_nat,G2: nat > int] :
% 0.35/0.63 ( ( finite_finite_nat @ A4 )
% 0.35/0.63 => ( ( finite_finite_nat @ B5 )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.63 = ( times_times_int @ ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.union_diff2
% 0.35/0.63 thf(fact_6451_prod_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > real,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.ub_add_nat
% 0.35/0.63 thf(fact_6452_prod_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > rat,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.ub_add_nat
% 0.35/0.63 thf(fact_6453_prod_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > int,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.ub_add_nat
% 0.35/0.63 thf(fact_6454_prod_Oub__add__nat,axiom,
% 0.35/0.63 ! [M2: nat,N: nat,G2: nat > nat,P: nat] :
% 0.35/0.63 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 0.35/0.63 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 0.35/0.63 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % prod.ub_add_nat
% 0.35/0.63 thf(fact_6455_fold__atLeastAtMost__nat_Osimps,axiom,
% 0.35/0.63 ( set_fo2584398358068434914at_nat
% 0.35/0.63 = ( ^ [F4: nat > nat > nat,A5: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F4 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B4 @ ( F4 @ A5 @ Acc2 ) ) ) ) ) ).
% 0.35/0.63
% 0.35/0.63 % fold_atLeastAtMost_nat.simps
% 0.35/0.63 thf(fact_6456_fold__atLeastAtMost__nat_Oelims,axiom,
% 0.35/0.63 ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y: nat] :
% 0.35/0.63 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 0.35/0.64 = Y )
% 0.35/0.64 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 0.35/0.64 => ( Y = Xc ) )
% 0.35/0.64 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 0.35/0.64 => ( Y
% 0.35/0.64 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % fold_atLeastAtMost_nat.elims
% 0.35/0.64 thf(fact_6457_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_complex,A: complex,B: complex > real,C2: complex > real] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.64 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups766887009212190081x_real
% 0.35/0.64 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups766887009212190081x_real
% 0.35/0.64 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6458_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_int,A: int,B: int > real,C2: int > real] :
% 0.35/0.64 ( ( finite_finite_int @ S3 )
% 0.35/0.64 => ( ( ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups2316167850115554303t_real
% 0.35/0.64 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups2316167850115554303t_real
% 0.35/0.64 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6459_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_real,A: real,B: real > real,C2: real > real] :
% 0.35/0.64 ( ( finite_finite_real @ S3 )
% 0.35/0.64 => ( ( ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups1681761925125756287l_real
% 0.35/0.64 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups1681761925125756287l_real
% 0.35/0.64 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6460_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_nat,A: nat,B: nat > real,C2: nat > real] :
% 0.35/0.64 ( ( finite_finite_nat @ S3 )
% 0.35/0.64 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups129246275422532515t_real
% 0.35/0.64 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups129246275422532515t_real
% 0.35/0.64 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6461_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_complex,A: complex,B: complex > rat,C2: complex > rat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.64 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups225925009352817453ex_rat
% 0.35/0.64 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_rat @ ( B @ A ) @ ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups225925009352817453ex_rat
% 0.35/0.64 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6462_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_int,A: int,B: int > rat,C2: int > rat] :
% 0.35/0.64 ( ( finite_finite_int @ S3 )
% 0.35/0.64 => ( ( ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups1072433553688619179nt_rat
% 0.35/0.64 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups1072433553688619179nt_rat
% 0.35/0.64 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6463_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_real,A: real,B: real > rat,C2: real > rat] :
% 0.35/0.64 ( ( finite_finite_real @ S3 )
% 0.35/0.64 => ( ( ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups4061424788464935467al_rat
% 0.35/0.64 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_rat @ ( B @ A ) @ ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups4061424788464935467al_rat
% 0.35/0.64 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6464_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_nat,A: nat,B: nat > rat,C2: nat > rat] :
% 0.35/0.64 ( ( finite_finite_nat @ S3 )
% 0.35/0.64 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups73079841787564623at_rat
% 0.35/0.64 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups73079841787564623at_rat
% 0.35/0.64 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6465_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_complex,A: complex,B: complex > nat,C2: complex > nat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.64 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups861055069439313189ex_nat
% 0.35/0.64 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_nat @ ( B @ A ) @ ( groups861055069439313189ex_nat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups861055069439313189ex_nat
% 0.35/0.64 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups861055069439313189ex_nat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6466_prod_Odelta__remove,axiom,
% 0.35/0.64 ! [S3: set_int,A: int,B: int > nat,C2: int > nat] :
% 0.35/0.64 ( ( finite_finite_int @ S3 )
% 0.35/0.64 => ( ( ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups1707563613775114915nt_nat
% 0.35/0.64 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_nat @ ( B @ A ) @ ( groups1707563613775114915nt_nat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups1707563613775114915nt_nat
% 0.35/0.64 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( groups1707563613775114915nt_nat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.delta_remove
% 0.35/0.64 thf(fact_6467_power__diff__1__eq,axiom,
% 0.35/0.64 ! [X: code_integer,N: nat] :
% 0.35/0.64 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N ) @ one_one_Code_integer )
% 0.35/0.64 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_1_eq
% 0.35/0.64 thf(fact_6468_power__diff__1__eq,axiom,
% 0.35/0.64 ! [X: complex,N: nat] :
% 0.35/0.64 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 0.35/0.64 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_1_eq
% 0.35/0.64 thf(fact_6469_power__diff__1__eq,axiom,
% 0.35/0.64 ! [X: rat,N: nat] :
% 0.35/0.64 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 0.35/0.64 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_1_eq
% 0.35/0.64 thf(fact_6470_power__diff__1__eq,axiom,
% 0.35/0.64 ! [X: int,N: nat] :
% 0.35/0.64 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 0.35/0.64 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_1_eq
% 0.35/0.64 thf(fact_6471_power__diff__1__eq,axiom,
% 0.35/0.64 ! [X: real,N: nat] :
% 0.35/0.64 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 0.35/0.64 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_1_eq
% 0.35/0.64 thf(fact_6472_one__diff__power__eq,axiom,
% 0.35/0.64 ! [X: code_integer,N: nat] :
% 0.35/0.64 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.35/0.64 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq
% 0.35/0.64 thf(fact_6473_one__diff__power__eq,axiom,
% 0.35/0.64 ! [X: complex,N: nat] :
% 0.35/0.64 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 0.35/0.64 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq
% 0.35/0.64 thf(fact_6474_one__diff__power__eq,axiom,
% 0.35/0.64 ! [X: rat,N: nat] :
% 0.35/0.64 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.35/0.64 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq
% 0.35/0.64 thf(fact_6475_one__diff__power__eq,axiom,
% 0.35/0.64 ! [X: int,N: nat] :
% 0.35/0.64 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.35/0.64 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq
% 0.35/0.64 thf(fact_6476_one__diff__power__eq,axiom,
% 0.35/0.64 ! [X: real,N: nat] :
% 0.35/0.64 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 0.35/0.64 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq
% 0.35/0.64 thf(fact_6477_geometric__sum,axiom,
% 0.35/0.64 ! [X: complex,N: nat] :
% 0.35/0.64 ( ( X != one_one_complex )
% 0.35/0.64 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % geometric_sum
% 0.35/0.64 thf(fact_6478_geometric__sum,axiom,
% 0.35/0.64 ! [X: rat,N: nat] :
% 0.35/0.64 ( ( X != one_one_rat )
% 0.35/0.64 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % geometric_sum
% 0.35/0.64 thf(fact_6479_geometric__sum,axiom,
% 0.35/0.64 ! [X: real,N: nat] :
% 0.35/0.64 ( ( X != one_one_real )
% 0.35/0.64 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % geometric_sum
% 0.35/0.64 thf(fact_6480_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_real,A4: set_real,F2: real > code_integer] :
% 0.35/0.64 ( ( finite_finite_real @ B5 )
% 0.35/0.64 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: real] :
% 0.35/0.64 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: real] :
% 0.35/0.64 ( ( member_real @ A3 @ A4 )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ ( groups6225526099057966256nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6481_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_int,A4: set_int,F2: int > code_integer] :
% 0.35/0.64 ( ( finite_finite_int @ B5 )
% 0.35/0.64 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: int] :
% 0.35/0.64 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: int] :
% 0.35/0.64 ( ( member_int @ A3 @ A4 )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ ( groups3827104343326376752nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6482_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_complex,A4: set_complex,F2: complex > code_integer] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.64 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: complex] :
% 0.35/0.64 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: complex] :
% 0.35/0.64 ( ( member_complex @ A3 @ A4 )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ ( groups8682486955453173170nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6483_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_real,A4: set_real,F2: real > real] :
% 0.35/0.64 ( ( finite_finite_real @ B5 )
% 0.35/0.64 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: real] :
% 0.35/0.64 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: real] :
% 0.35/0.64 ( ( member_real @ A3 @ A4 )
% 0.35/0.64 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6484_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_int,A4: set_int,F2: int > real] :
% 0.35/0.64 ( ( finite_finite_int @ B5 )
% 0.35/0.64 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: int] :
% 0.35/0.64 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: int] :
% 0.35/0.64 ( ( member_int @ A3 @ A4 )
% 0.35/0.64 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6485_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_complex,A4: set_complex,F2: complex > real] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.64 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: complex] :
% 0.35/0.64 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: complex] :
% 0.35/0.64 ( ( member_complex @ A3 @ A4 )
% 0.35/0.64 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6486_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_real,A4: set_real,F2: real > rat] :
% 0.35/0.64 ( ( finite_finite_real @ B5 )
% 0.35/0.64 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: real] :
% 0.35/0.64 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: real] :
% 0.35/0.64 ( ( member_real @ A3 @ A4 )
% 0.35/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6487_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_int,A4: set_int,F2: int > rat] :
% 0.35/0.64 ( ( finite_finite_int @ B5 )
% 0.35/0.64 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: int] :
% 0.35/0.64 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: int] :
% 0.35/0.64 ( ( member_int @ A3 @ A4 )
% 0.35/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6488_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_complex,A4: set_complex,F2: complex > rat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.64 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: complex] :
% 0.35/0.64 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: complex] :
% 0.35/0.64 ( ( member_complex @ A3 @ A4 )
% 0.35/0.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6489_prod__mono2,axiom,
% 0.35/0.64 ! [B5: set_real,A4: set_real,F2: real > int] :
% 0.35/0.64 ( ( finite_finite_real @ B5 )
% 0.35/0.64 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 0.35/0.64 => ( ! [B3: real] :
% 0.35/0.64 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 0.35/0.64 => ( ord_less_eq_int @ one_one_int @ ( F2 @ B3 ) ) )
% 0.35/0.64 => ( ! [A3: real] :
% 0.35/0.64 ( ( member_real @ A3 @ A4 )
% 0.35/0.64 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A3 ) ) )
% 0.35/0.64 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F2 @ A4 ) @ ( groups4694064378042380927al_int @ F2 @ B5 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_mono2
% 0.35/0.64 thf(fact_6490_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > code_integer,N: code_integer,K2: nat] :
% 0.35/0.64 ( ! [I3: real] :
% 0.35/0.64 ( ( member_real @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6491_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_nat,F2: nat > code_integer,N: code_integer,K2: nat] :
% 0.35/0.64 ( ! [I3: nat] :
% 0.35/0.64 ( ( member_nat @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6492_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > code_integer,N: code_integer,K2: nat] :
% 0.35/0.64 ( ! [I3: complex] :
% 0.35/0.64 ( ( member_complex @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6493_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > code_integer,N: code_integer,K2: nat] :
% 0.35/0.64 ( ! [I3: int] :
% 0.35/0.64 ( ( member_int @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 0.35/0.64 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6494_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > real,N: real,K2: nat] :
% 0.35/0.64 ( ! [I3: real] :
% 0.35/0.64 ( ( member_real @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_less_eq_real @ one_one_real @ N )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6495_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_nat,F2: nat > real,N: real,K2: nat] :
% 0.35/0.64 ( ! [I3: nat] :
% 0.35/0.64 ( ( member_nat @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_less_eq_real @ one_one_real @ N )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6496_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > real,N: real,K2: nat] :
% 0.35/0.64 ( ! [I3: complex] :
% 0.35/0.64 ( ( member_complex @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_less_eq_real @ one_one_real @ N )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6497_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > real,N: real,K2: nat] :
% 0.35/0.64 ( ! [I3: int] :
% 0.35/0.64 ( ( member_int @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_less_eq_real @ one_one_real @ N )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6498_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > rat,N: rat,K2: nat] :
% 0.35/0.64 ( ! [I3: real] :
% 0.35/0.64 ( ( member_real @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 0.35/0.64 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( power_power_rat @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6499_prod__le__power,axiom,
% 0.35/0.64 ! [A4: set_nat,F2: nat > rat,N: rat,K2: nat] :
% 0.35/0.64 ( ! [I3: nat] :
% 0.35/0.64 ( ( member_nat @ I3 @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 0.35/0.64 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ N ) ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 0.35/0.64 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 0.35/0.64 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( power_power_rat @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_le_power
% 0.35/0.64 thf(fact_6500_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_int,B5: set_int,F2: int > complex] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( finite_finite_int @ B5 )
% 0.35/0.64 => ( ! [X3: int] :
% 0.35/0.64 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_complex ) )
% 0.35/0.64 => ( ( groups7440179247065528705omplex @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups7440179247065528705omplex @ F2 @ A4 ) @ ( groups7440179247065528705omplex @ F2 @ B5 ) ) @ ( groups7440179247065528705omplex @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6501_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_complex,B5: set_complex,F2: complex > complex] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.64 => ( ! [X3: complex] :
% 0.35/0.64 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_complex ) )
% 0.35/0.64 => ( ( groups3708469109370488835omplex @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups3708469109370488835omplex @ F2 @ A4 ) @ ( groups3708469109370488835omplex @ F2 @ B5 ) ) @ ( groups3708469109370488835omplex @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6502_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_nat,B5: set_nat,F2: nat > complex] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( finite_finite_nat @ B5 )
% 0.35/0.64 => ( ! [X3: nat] :
% 0.35/0.64 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_complex ) )
% 0.35/0.64 => ( ( groups6464643781859351333omplex @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups6464643781859351333omplex @ F2 @ A4 ) @ ( groups6464643781859351333omplex @ F2 @ B5 ) ) @ ( groups6464643781859351333omplex @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6503_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_int,B5: set_int,F2: int > real] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( finite_finite_int @ B5 )
% 0.35/0.64 => ( ! [X3: int] :
% 0.35/0.64 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_real ) )
% 0.35/0.64 => ( ( groups2316167850115554303t_real @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.64 = ( divide_divide_real @ ( times_times_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ F2 @ B5 ) ) @ ( groups2316167850115554303t_real @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6504_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_complex,B5: set_complex,F2: complex > real] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.64 => ( ! [X3: complex] :
% 0.35/0.64 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_real ) )
% 0.35/0.64 => ( ( groups766887009212190081x_real @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.64 = ( divide_divide_real @ ( times_times_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ F2 @ B5 ) ) @ ( groups766887009212190081x_real @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6505_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_nat,B5: set_nat,F2: nat > real] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( finite_finite_nat @ B5 )
% 0.35/0.64 => ( ! [X3: nat] :
% 0.35/0.64 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_real ) )
% 0.35/0.64 => ( ( groups129246275422532515t_real @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.64 = ( divide_divide_real @ ( times_times_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ F2 @ B5 ) ) @ ( groups129246275422532515t_real @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6506_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_int,B5: set_int,F2: int > rat] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( finite_finite_int @ B5 )
% 0.35/0.64 => ( ! [X3: int] :
% 0.35/0.64 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_rat ) )
% 0.35/0.64 => ( ( groups1072433553688619179nt_rat @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 0.35/0.64 = ( divide_divide_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ F2 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6507_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_complex,B5: set_complex,F2: complex > rat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( finite3207457112153483333omplex @ B5 )
% 0.35/0.64 => ( ! [X3: complex] :
% 0.35/0.64 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_rat ) )
% 0.35/0.64 => ( ( groups225925009352817453ex_rat @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 0.35/0.64 = ( divide_divide_rat @ ( times_times_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ F2 @ B5 ) ) @ ( groups225925009352817453ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6508_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_nat,B5: set_nat,F2: nat > rat] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( finite_finite_nat @ B5 )
% 0.35/0.64 => ( ! [X3: nat] :
% 0.35/0.64 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_rat ) )
% 0.35/0.64 => ( ( groups73079841787564623at_rat @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 0.35/0.64 = ( divide_divide_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ F2 @ B5 ) ) @ ( groups73079841787564623at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6509_prod__Un,axiom,
% 0.35/0.64 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > complex] :
% 0.35/0.64 ( ( finite6177210948735845034at_nat @ A4 )
% 0.35/0.64 => ( ( finite6177210948735845034at_nat @ B5 )
% 0.35/0.64 => ( ! [X3: product_prod_nat_nat] :
% 0.35/0.64 ( ( member8440522571783428010at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 0.35/0.64 => ( ( F2 @ X3 )
% 0.35/0.64 != zero_zero_complex ) )
% 0.35/0.64 => ( ( groups8110221916422527690omplex @ F2 @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups8110221916422527690omplex @ F2 @ A4 ) @ ( groups8110221916422527690omplex @ F2 @ B5 ) ) @ ( groups8110221916422527690omplex @ F2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_Un
% 0.35/0.64 thf(fact_6510_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > complex,A: complex] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_complex )
% 0.35/0.64 => ( ( ( member_complex @ A @ A4 )
% 0.35/0.64 => ( ( groups3708469109370488835omplex @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ A4 )
% 0.35/0.64 => ( ( groups3708469109370488835omplex @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64 = ( groups3708469109370488835omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6511_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > complex,A: int] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_complex )
% 0.35/0.64 => ( ( ( member_int @ A @ A4 )
% 0.35/0.64 => ( ( groups7440179247065528705omplex @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ A4 )
% 0.35/0.64 => ( ( groups7440179247065528705omplex @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64 = ( groups7440179247065528705omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6512_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > complex,A: real] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_complex )
% 0.35/0.64 => ( ( ( member_real @ A @ A4 )
% 0.35/0.64 => ( ( groups713298508707869441omplex @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_real @ A @ A4 )
% 0.35/0.64 => ( ( groups713298508707869441omplex @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64 = ( groups713298508707869441omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6513_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_nat,F2: nat > complex,A: nat] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_complex )
% 0.35/0.64 => ( ( ( member_nat @ A @ A4 )
% 0.35/0.64 => ( ( groups6464643781859351333omplex @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_nat @ A @ A4 )
% 0.35/0.64 => ( ( groups6464643781859351333omplex @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64 = ( groups6464643781859351333omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6514_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > real,A: complex] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_real )
% 0.35/0.64 => ( ( ( member_complex @ A @ A4 )
% 0.35/0.64 => ( ( groups766887009212190081x_real @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64 = ( divide_divide_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ A4 )
% 0.35/0.64 => ( ( groups766887009212190081x_real @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64 = ( groups766887009212190081x_real @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6515_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > real,A: int] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_real )
% 0.35/0.64 => ( ( ( member_int @ A @ A4 )
% 0.35/0.64 => ( ( groups2316167850115554303t_real @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64 = ( divide_divide_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ A4 )
% 0.35/0.64 => ( ( groups2316167850115554303t_real @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64 = ( groups2316167850115554303t_real @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6516_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > real,A: real] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_real )
% 0.35/0.64 => ( ( ( member_real @ A @ A4 )
% 0.35/0.64 => ( ( groups1681761925125756287l_real @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64 = ( divide_divide_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_real @ A @ A4 )
% 0.35/0.64 => ( ( groups1681761925125756287l_real @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 0.35/0.64 = ( groups1681761925125756287l_real @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6517_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_nat,F2: nat > real,A: nat] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_real )
% 0.35/0.64 => ( ( ( member_nat @ A @ A4 )
% 0.35/0.64 => ( ( groups129246275422532515t_real @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64 = ( divide_divide_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_nat @ A @ A4 )
% 0.35/0.64 => ( ( groups129246275422532515t_real @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 0.35/0.64 = ( groups129246275422532515t_real @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6518_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > rat,A: complex] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_rat )
% 0.35/0.64 => ( ( ( member_complex @ A @ A4 )
% 0.35/0.64 => ( ( groups225925009352817453ex_rat @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64 = ( divide_divide_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ A4 )
% 0.35/0.64 => ( ( groups225925009352817453ex_rat @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 0.35/0.64 = ( groups225925009352817453ex_rat @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6519_prod__diff1,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > rat,A: int] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( ( F2 @ A )
% 0.35/0.64 != zero_zero_rat )
% 0.35/0.64 => ( ( ( member_int @ A @ A4 )
% 0.35/0.64 => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64 = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ A4 )
% 0.35/0.64 => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 0.35/0.64 = ( groups1072433553688619179nt_rat @ F2 @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_diff1
% 0.35/0.64 thf(fact_6520_binomial__less__binomial__Suc,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ K2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.64 => ( ord_less_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_less_binomial_Suc
% 0.35/0.64 thf(fact_6521_binomial__strict__antimono,axiom,
% 0.35/0.64 ! [K2: nat,K6: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ K2 @ K6 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K6 @ N )
% 0.35/0.64 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_strict_antimono
% 0.35/0.64 thf(fact_6522_binomial__strict__mono,axiom,
% 0.35/0.64 ! [K2: nat,K6: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ K2 @ K6 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 0.35/0.64 => ( ord_less_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_strict_mono
% 0.35/0.64 thf(fact_6523_central__binomial__odd,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.64 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.64 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % central_binomial_odd
% 0.35/0.64 thf(fact_6524_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_real,A: real,B: real > complex,C2: complex] :
% 0.35/0.64 ( ( finite_finite_real @ S3 )
% 0.35/0.64 => ( ( ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups713298508707869441omplex
% 0.35/0.64 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups713298508707869441omplex
% 0.35/0.64 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_complex @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6525_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_nat,A: nat,B: nat > complex,C2: complex] :
% 0.35/0.64 ( ( finite_finite_nat @ S3 )
% 0.35/0.64 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups6464643781859351333omplex
% 0.35/0.64 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups6464643781859351333omplex
% 0.35/0.64 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_complex @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6526_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_int,A: int,B: int > complex,C2: complex] :
% 0.35/0.64 ( ( finite_finite_int @ S3 )
% 0.35/0.64 => ( ( ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups7440179247065528705omplex
% 0.35/0.64 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_int @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups7440179247065528705omplex
% 0.35/0.64 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_complex @ C2 @ ( finite_card_int @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6527_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_complex,A: complex,B: complex > complex,C2: complex] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.64 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups3708469109370488835omplex
% 0.35/0.64 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_complex @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups3708469109370488835omplex
% 0.35/0.64 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_complex @ C2 @ ( finite_card_complex @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6528_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_real,A: real,B: real > real,C2: real] :
% 0.35/0.64 ( ( finite_finite_real @ S3 )
% 0.35/0.64 => ( ( ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups1681761925125756287l_real
% 0.35/0.64 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups1681761925125756287l_real
% 0.35/0.64 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_real @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6529_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_nat,A: nat,B: nat > real,C2: real] :
% 0.35/0.64 ( ( finite_finite_nat @ S3 )
% 0.35/0.64 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups129246275422532515t_real
% 0.35/0.64 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups129246275422532515t_real
% 0.35/0.64 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_real @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6530_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_int,A: int,B: int > real,C2: real] :
% 0.35/0.64 ( ( finite_finite_int @ S3 )
% 0.35/0.64 => ( ( ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups2316167850115554303t_real
% 0.35/0.64 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_int @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_int @ A @ S3 )
% 0.35/0.64 => ( ( groups2316167850115554303t_real
% 0.35/0.64 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_real @ C2 @ ( finite_card_int @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6531_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_complex,A: complex,B: complex > real,C2: real] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ S3 )
% 0.35/0.64 => ( ( ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups766887009212190081x_real
% 0.35/0.64 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_complex @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_complex @ A @ S3 )
% 0.35/0.64 => ( ( groups766887009212190081x_real
% 0.35/0.64 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_real @ C2 @ ( finite_card_complex @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6532_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_real,A: real,B: real > rat,C2: rat] :
% 0.35/0.64 ( ( finite_finite_real @ S3 )
% 0.35/0.64 => ( ( ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups4061424788464935467al_rat
% 0.35/0.64 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_real @ A @ S3 )
% 0.35/0.64 => ( ( groups4061424788464935467al_rat
% 0.35/0.64 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_rat @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6533_prod__gen__delta,axiom,
% 0.35/0.64 ! [S3: set_nat,A: nat,B: nat > rat,C2: rat] :
% 0.35/0.64 ( ( finite_finite_nat @ S3 )
% 0.35/0.64 => ( ( ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups73079841787564623at_rat
% 0.35/0.64 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 0.35/0.64 & ( ~ ( member_nat @ A @ S3 )
% 0.35/0.64 => ( ( groups73079841787564623at_rat
% 0.35/0.64 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 0.35/0.64 @ S3 )
% 0.35/0.64 = ( power_power_rat @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_gen_delta
% 0.35/0.64 thf(fact_6534_pochhammer__Suc__prod,axiom,
% 0.35/0.64 ! [A: rat,N: nat] :
% 0.35/0.64 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups73079841787564623at_rat
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod
% 0.35/0.64 thf(fact_6535_pochhammer__Suc__prod,axiom,
% 0.35/0.64 ! [A: real,N: nat] :
% 0.35/0.64 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups129246275422532515t_real
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod
% 0.35/0.64 thf(fact_6536_pochhammer__Suc__prod,axiom,
% 0.35/0.64 ! [A: int,N: nat] :
% 0.35/0.64 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups705719431365010083at_int
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod
% 0.35/0.64 thf(fact_6537_pochhammer__Suc__prod,axiom,
% 0.35/0.64 ! [A: nat,N: nat] :
% 0.35/0.64 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod
% 0.35/0.64 thf(fact_6538_sum__gp__strict,axiom,
% 0.35/0.64 ! [X: complex,N: nat] :
% 0.35/0.64 ( ( ( X = one_one_complex )
% 0.35/0.64 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( semiri8010041392384452111omplex @ N ) ) )
% 0.35/0.64 & ( ( X != one_one_complex )
% 0.35/0.64 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_gp_strict
% 0.35/0.64 thf(fact_6539_sum__gp__strict,axiom,
% 0.35/0.64 ! [X: rat,N: nat] :
% 0.35/0.64 ( ( ( X = one_one_rat )
% 0.35/0.64 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( semiri681578069525770553at_rat @ N ) ) )
% 0.35/0.64 & ( ( X != one_one_rat )
% 0.35/0.64 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_gp_strict
% 0.35/0.64 thf(fact_6540_sum__gp__strict,axiom,
% 0.35/0.64 ! [X: real,N: nat] :
% 0.35/0.64 ( ( ( X = one_one_real )
% 0.35/0.64 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.64 & ( ( X != one_one_real )
% 0.35/0.64 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_gp_strict
% 0.35/0.64 thf(fact_6541_lemma__termdiff1,axiom,
% 0.35/0.64 ! [Z3: complex,H: complex,M2: nat] :
% 0.35/0.64 ( ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_complex @ Z3 @ P5 ) ) @ ( power_power_complex @ Z3 @ M2 ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.64 = ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z3 @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % lemma_termdiff1
% 0.35/0.64 thf(fact_6542_lemma__termdiff1,axiom,
% 0.35/0.64 ! [Z3: rat,H: rat,M2: nat] :
% 0.35/0.64 ( ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_rat @ Z3 @ P5 ) ) @ ( power_power_rat @ Z3 @ M2 ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.64 = ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z3 @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % lemma_termdiff1
% 0.35/0.64 thf(fact_6543_lemma__termdiff1,axiom,
% 0.35/0.64 ! [Z3: int,H: int,M2: nat] :
% 0.35/0.64 ( ( groups3539618377306564664at_int
% 0.35/0.64 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_int @ Z3 @ P5 ) ) @ ( power_power_int @ Z3 @ M2 ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.64 = ( groups3539618377306564664at_int
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z3 @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_int @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % lemma_termdiff1
% 0.35/0.64 thf(fact_6544_lemma__termdiff1,axiom,
% 0.35/0.64 ! [Z3: real,H: real,M2: nat] :
% 0.35/0.64 ( ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_real @ Z3 @ P5 ) ) @ ( power_power_real @ Z3 @ M2 ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) )
% 0.35/0.64 = ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z3 @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % lemma_termdiff1
% 0.35/0.64 thf(fact_6545_diff__power__eq__sum,axiom,
% 0.35/0.64 ! [X: complex,N: nat,Y: complex] :
% 0.35/0.64 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.35/0.64 @ ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % diff_power_eq_sum
% 0.35/0.64 thf(fact_6546_diff__power__eq__sum,axiom,
% 0.35/0.64 ! [X: rat,N: nat,Y: rat] :
% 0.35/0.64 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.35/0.64 @ ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % diff_power_eq_sum
% 0.35/0.64 thf(fact_6547_diff__power__eq__sum,axiom,
% 0.35/0.64 ! [X: int,N: nat,Y: int] :
% 0.35/0.64 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.35/0.64 @ ( groups3539618377306564664at_int
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % diff_power_eq_sum
% 0.35/0.64 thf(fact_6548_diff__power__eq__sum,axiom,
% 0.35/0.64 ! [X: real,N: nat,Y: real] :
% 0.35/0.64 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.35/0.64 @ ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % diff_power_eq_sum
% 0.35/0.64 thf(fact_6549_power__diff__sumr2,axiom,
% 0.35/0.64 ! [X: complex,N: nat,Y: complex] :
% 0.35/0.64 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 0.35/0.64 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.35/0.64 @ ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [I: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_complex @ X @ I ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_sumr2
% 0.35/0.64 thf(fact_6550_power__diff__sumr2,axiom,
% 0.35/0.64 ! [X: rat,N: nat,Y: rat] :
% 0.35/0.64 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 0.35/0.64 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.35/0.64 @ ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_rat @ X @ I ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_sumr2
% 0.35/0.64 thf(fact_6551_power__diff__sumr2,axiom,
% 0.35/0.64 ! [X: int,N: nat,Y: int] :
% 0.35/0.64 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 0.35/0.64 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.35/0.64 @ ( groups3539618377306564664at_int
% 0.35/0.64 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_int @ X @ I ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_sumr2
% 0.35/0.64 thf(fact_6552_power__diff__sumr2,axiom,
% 0.35/0.64 ! [X: real,N: nat,Y: real] :
% 0.35/0.64 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 0.35/0.64 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.35/0.64 @ ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_real @ X @ I ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % power_diff_sumr2
% 0.35/0.64 thf(fact_6553_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.64 ! [N: nat,F2: nat > rat,K5: rat,K2: nat] :
% 0.35/0.64 ( ! [P7: nat] :
% 0.35/0.64 ( ( ord_less_nat @ P7 @ N )
% 0.35/0.64 => ( ord_less_eq_rat @ ( F2 @ P7 ) @ K5 ) )
% 0.35/0.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 0.35/0.64 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % real_sum_nat_ivl_bounded2
% 0.35/0.64 thf(fact_6554_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.64 ! [N: nat,F2: nat > int,K5: int,K2: nat] :
% 0.35/0.64 ( ! [P7: nat] :
% 0.35/0.64 ( ( ord_less_nat @ P7 @ N )
% 0.35/0.64 => ( ord_less_eq_int @ ( F2 @ P7 ) @ K5 ) )
% 0.35/0.64 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 0.35/0.64 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % real_sum_nat_ivl_bounded2
% 0.35/0.64 thf(fact_6555_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.64 ! [N: nat,F2: nat > nat,K5: nat,K2: nat] :
% 0.35/0.64 ( ! [P7: nat] :
% 0.35/0.64 ( ( ord_less_nat @ P7 @ N )
% 0.35/0.64 => ( ord_less_eq_nat @ ( F2 @ P7 ) @ K5 ) )
% 0.35/0.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 0.35/0.64 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % real_sum_nat_ivl_bounded2
% 0.35/0.64 thf(fact_6556_real__sum__nat__ivl__bounded2,axiom,
% 0.35/0.64 ! [N: nat,F2: nat > real,K5: real,K2: nat] :
% 0.35/0.64 ( ! [P7: nat] :
% 0.35/0.64 ( ( ord_less_nat @ P7 @ N )
% 0.35/0.64 => ( ord_less_eq_real @ ( F2 @ P7 ) @ K5 ) )
% 0.35/0.64 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 0.35/0.64 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % real_sum_nat_ivl_bounded2
% 0.35/0.64 thf(fact_6557_prod_Oin__pairs,axiom,
% 0.35/0.64 ! [G2: nat > real,M2: nat,N: nat] :
% 0.35/0.64 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64 = ( groups129246275422532515t_real
% 0.35/0.64 @ ^ [I: nat] : ( times_times_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.in_pairs
% 0.35/0.64 thf(fact_6558_prod_Oin__pairs,axiom,
% 0.35/0.64 ! [G2: nat > rat,M2: nat,N: nat] :
% 0.35/0.64 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64 = ( groups73079841787564623at_rat
% 0.35/0.64 @ ^ [I: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.in_pairs
% 0.35/0.64 thf(fact_6559_prod_Oin__pairs,axiom,
% 0.35/0.64 ! [G2: nat > int,M2: nat,N: nat] :
% 0.35/0.64 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64 = ( groups705719431365010083at_int
% 0.35/0.64 @ ^ [I: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.in_pairs
% 0.35/0.64 thf(fact_6560_prod_Oin__pairs,axiom,
% 0.35/0.64 ! [G2: nat > nat,M2: nat,N: nat] :
% 0.35/0.64 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [I: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.in_pairs
% 0.35/0.64 thf(fact_6561_sum__atLeastAtMost__code,axiom,
% 0.35/0.64 ! [F2: nat > complex,A: nat,B: nat] :
% 0.35/0.64 ( ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.64 = ( set_fo1517530859248394432omplex
% 0.35/0.64 @ ^ [A5: nat] : ( plus_plus_complex @ ( F2 @ A5 ) )
% 0.35/0.64 @ A
% 0.35/0.64 @ B
% 0.35/0.64 @ zero_zero_complex ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_atLeastAtMost_code
% 0.35/0.64 thf(fact_6562_sum__atLeastAtMost__code,axiom,
% 0.35/0.64 ! [F2: nat > rat,A: nat,B: nat] :
% 0.35/0.64 ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.64 = ( set_fo1949268297981939178at_rat
% 0.35/0.64 @ ^ [A5: nat] : ( plus_plus_rat @ ( F2 @ A5 ) )
% 0.35/0.64 @ A
% 0.35/0.64 @ B
% 0.35/0.64 @ zero_zero_rat ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_atLeastAtMost_code
% 0.35/0.64 thf(fact_6563_sum__atLeastAtMost__code,axiom,
% 0.35/0.64 ! [F2: nat > int,A: nat,B: nat] :
% 0.35/0.64 ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.64 = ( set_fo2581907887559384638at_int
% 0.35/0.64 @ ^ [A5: nat] : ( plus_plus_int @ ( F2 @ A5 ) )
% 0.35/0.64 @ A
% 0.35/0.64 @ B
% 0.35/0.64 @ zero_zero_int ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_atLeastAtMost_code
% 0.35/0.64 thf(fact_6564_sum__atLeastAtMost__code,axiom,
% 0.35/0.64 ! [F2: nat > nat,A: nat,B: nat] :
% 0.35/0.64 ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.64 = ( set_fo2584398358068434914at_nat
% 0.35/0.64 @ ^ [A5: nat] : ( plus_plus_nat @ ( F2 @ A5 ) )
% 0.35/0.64 @ A
% 0.35/0.64 @ B
% 0.35/0.64 @ zero_zero_nat ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_atLeastAtMost_code
% 0.35/0.64 thf(fact_6565_sum__atLeastAtMost__code,axiom,
% 0.35/0.64 ! [F2: nat > real,A: nat,B: nat] :
% 0.35/0.64 ( ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.64 = ( set_fo3111899725591712190t_real
% 0.35/0.64 @ ^ [A5: nat] : ( plus_plus_real @ ( F2 @ A5 ) )
% 0.35/0.64 @ A
% 0.35/0.64 @ B
% 0.35/0.64 @ zero_zero_real ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_atLeastAtMost_code
% 0.35/0.64 thf(fact_6566_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.64 ! [A: rat,N: nat] :
% 0.35/0.64 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups73079841787564623at_rat
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod_rev
% 0.35/0.64 thf(fact_6567_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.64 ! [A: real,N: nat] :
% 0.35/0.64 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups129246275422532515t_real
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod_rev
% 0.35/0.64 thf(fact_6568_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.64 ! [A: int,N: nat] :
% 0.35/0.64 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups705719431365010083at_int
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod_rev
% 0.35/0.64 thf(fact_6569_pochhammer__Suc__prod__rev,axiom,
% 0.35/0.64 ! [A: nat,N: nat] :
% 0.35/0.64 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % pochhammer_Suc_prod_rev
% 0.35/0.64 thf(fact_6570_one__diff__power__eq_H,axiom,
% 0.35/0.64 ! [X: code_integer,N: nat] :
% 0.35/0.64 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 0.35/0.64 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 0.35/0.64 @ ( groups7501900531339628137nteger
% 0.35/0.64 @ ^ [I: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq'
% 0.35/0.64 thf(fact_6571_one__diff__power__eq_H,axiom,
% 0.35/0.64 ! [X: complex,N: nat] :
% 0.35/0.64 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 0.35/0.64 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 0.35/0.64 @ ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [I: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq'
% 0.35/0.64 thf(fact_6572_one__diff__power__eq_H,axiom,
% 0.35/0.64 ! [X: rat,N: nat] :
% 0.35/0.64 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 0.35/0.64 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 0.35/0.64 @ ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [I: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq'
% 0.35/0.64 thf(fact_6573_one__diff__power__eq_H,axiom,
% 0.35/0.64 ! [X: int,N: nat] :
% 0.35/0.64 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 0.35/0.64 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 0.35/0.64 @ ( groups3539618377306564664at_int
% 0.35/0.64 @ ^ [I: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq'
% 0.35/0.64 thf(fact_6574_one__diff__power__eq_H,axiom,
% 0.35/0.64 ! [X: real,N: nat] :
% 0.35/0.64 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 0.35/0.64 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 0.35/0.64 @ ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [I: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_diff_power_eq'
% 0.35/0.64 thf(fact_6575_sum__split__even__odd,axiom,
% 0.35/0.64 ! [F2: nat > real,G2: nat > real,N: nat] :
% 0.35/0.64 ( ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [I: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( F2 @ I ) @ ( G2 @ I ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.64 = ( plus_plus_real
% 0.35/0.64 @ ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [I: nat] : ( F2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.64 @ ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ one_one_nat ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_split_even_odd
% 0.35/0.64 thf(fact_6576_zero__less__binomial__iff,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K2 ) )
% 0.35/0.64 = ( ord_less_eq_nat @ K2 @ N ) ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_binomial_iff
% 0.35/0.64 thf(fact_6577_choose__two,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_two
% 0.35/0.64 thf(fact_6578_binomial__n__0,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( binomial @ N @ zero_zero_nat )
% 0.35/0.64 = one_one_nat ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_n_0
% 0.35/0.64 thf(fact_6579_binomial__Suc__Suc,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( binomial @ ( suc @ N ) @ ( suc @ K2 ) )
% 0.35/0.64 = ( plus_plus_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_Suc_Suc
% 0.35/0.64 thf(fact_6580_binomial__eq__0__iff,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( ( binomial @ N @ K2 )
% 0.35/0.64 = zero_zero_nat )
% 0.35/0.64 = ( ord_less_nat @ N @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_eq_0_iff
% 0.35/0.64 thf(fact_6581_binomial__1,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.64 = N ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_1
% 0.35/0.64 thf(fact_6582_binomial__0__Suc,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( binomial @ zero_zero_nat @ ( suc @ K2 ) )
% 0.35/0.64 = zero_zero_nat ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_0_Suc
% 0.35/0.64 thf(fact_6583_binomial__Suc__n,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( binomial @ ( suc @ N ) @ N )
% 0.35/0.64 = ( suc @ N ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_Suc_n
% 0.35/0.64 thf(fact_6584_prod__pos__nat__iff,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > nat] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F2 @ A4 ) )
% 0.35/0.64 = ( ! [X4: int] :
% 0.35/0.64 ( ( member_int @ X4 @ A4 )
% 0.35/0.64 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_pos_nat_iff
% 0.35/0.64 thf(fact_6585_prod__pos__nat__iff,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > nat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) )
% 0.35/0.64 = ( ! [X4: complex] :
% 0.35/0.64 ( ( member_complex @ X4 @ A4 )
% 0.35/0.64 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_pos_nat_iff
% 0.35/0.64 thf(fact_6586_prod__pos__nat__iff,axiom,
% 0.35/0.64 ! [A4: set_nat,F2: nat > nat] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) )
% 0.35/0.64 = ( ! [X4: nat] :
% 0.35/0.64 ( ( member_nat @ X4 @ A4 )
% 0.35/0.64 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_pos_nat_iff
% 0.35/0.64 thf(fact_6587_prod__int__eq,axiom,
% 0.35/0.64 ! [I2: nat,J2: nat] :
% 0.35/0.64 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 0.35/0.64 = ( groups1705073143266064639nt_int
% 0.35/0.64 @ ^ [X4: int] : X4
% 0.35/0.64 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_int_eq
% 0.35/0.64 thf(fact_6588_prod__int__plus__eq,axiom,
% 0.35/0.64 ! [I2: nat,J2: nat] :
% 0.35/0.64 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J2 ) ) )
% 0.35/0.64 = ( groups1705073143266064639nt_int
% 0.35/0.64 @ ^ [X4: int] : X4
% 0.35/0.64 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod_int_plus_eq
% 0.35/0.64 thf(fact_6589_binomial__eq__0,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ N @ K2 )
% 0.35/0.64 => ( ( binomial @ N @ K2 )
% 0.35/0.64 = zero_zero_nat ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_eq_0
% 0.35/0.64 thf(fact_6590_Suc__times__binomial,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( times_times_nat @ ( suc @ K2 ) @ ( binomial @ ( suc @ N ) @ ( suc @ K2 ) ) )
% 0.35/0.64 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Suc_times_binomial
% 0.35/0.64 thf(fact_6591_Suc__times__binomial__eq,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) )
% 0.35/0.64 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K2 ) ) @ ( suc @ K2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Suc_times_binomial_eq
% 0.35/0.64 thf(fact_6592_binomial__symmetric,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.64 => ( ( binomial @ N @ K2 )
% 0.35/0.64 = ( binomial @ N @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_symmetric
% 0.35/0.64 thf(fact_6593_choose__mult__lemma,axiom,
% 0.35/0.64 ! [M2: nat,R3: nat,K2: nat] :
% 0.35/0.64 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R3 ) @ K2 ) @ ( plus_plus_nat @ M2 @ K2 ) ) @ ( binomial @ ( plus_plus_nat @ M2 @ K2 ) @ K2 ) )
% 0.35/0.64 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R3 ) @ K2 ) @ K2 ) @ ( binomial @ ( plus_plus_nat @ M2 @ R3 ) @ M2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_mult_lemma
% 0.35/0.64 thf(fact_6594_binomial__le__pow,axiom,
% 0.35/0.64 ! [R3: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_eq_nat @ R3 @ N )
% 0.35/0.64 => ( ord_less_eq_nat @ ( binomial @ N @ R3 ) @ ( power_power_nat @ N @ R3 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_le_pow
% 0.35/0.64 thf(fact_6595_zero__less__binomial,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.64 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_binomial
% 0.35/0.64 thf(fact_6596_Suc__times__binomial__add,axiom,
% 0.35/0.64 ! [A: nat,B: nat] :
% 0.35/0.64 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 0.35/0.64 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Suc_times_binomial_add
% 0.35/0.64 thf(fact_6597_binomial__Suc__Suc__eq__times,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( binomial @ ( suc @ N ) @ ( suc @ K2 ) )
% 0.35/0.64 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) ) @ ( suc @ K2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_Suc_Suc_eq_times
% 0.35/0.64 thf(fact_6598_choose__mult,axiom,
% 0.35/0.64 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.64 => ( ( times_times_nat @ ( binomial @ N @ M2 ) @ ( binomial @ M2 @ K2 ) )
% 0.35/0.64 = ( times_times_nat @ ( binomial @ N @ K2 ) @ ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_mult
% 0.35/0.64 thf(fact_6599_binomial__absorb__comp,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( times_times_nat @ ( minus_minus_nat @ N @ K2 ) @ ( binomial @ N @ K2 ) )
% 0.35/0.64 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_absorb_comp
% 0.35/0.64 thf(fact_6600_binomial__absorption,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( times_times_nat @ ( suc @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) )
% 0.35/0.64 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_absorption
% 0.35/0.64 thf(fact_6601_sum__bounds__lt__plus1,axiom,
% 0.35/0.64 ! [F2: nat > nat,Mm: nat] :
% 0.35/0.64 ( ( groups3542108847815614940at_nat
% 0.35/0.64 @ ^ [K3: nat] : ( F2 @ ( suc @ K3 ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ Mm ) )
% 0.35/0.64 = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_bounds_lt_plus1
% 0.35/0.64 thf(fact_6602_sum__bounds__lt__plus1,axiom,
% 0.35/0.64 ! [F2: nat > real,Mm: nat] :
% 0.35/0.64 ( ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [K3: nat] : ( F2 @ ( suc @ K3 ) )
% 0.35/0.64 @ ( set_ord_lessThan_nat @ Mm ) )
% 0.35/0.64 = ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_bounds_lt_plus1
% 0.35/0.64 thf(fact_6603_binomial__ge__n__over__k__pow__k,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.64 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_ge_n_over_k_pow_k
% 0.35/0.64 thf(fact_6604_binomial__ge__n__over__k__pow__k,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.64 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_ge_n_over_k_pow_k
% 0.35/0.64 thf(fact_6605_binomial__le__pow2,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_le_pow2
% 0.35/0.64 thf(fact_6606_choose__reduce__nat,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.64 => ( ( binomial @ N @ K2 )
% 0.35/0.64 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_reduce_nat
% 0.35/0.64 thf(fact_6607_times__binomial__minus1__eq,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.64 => ( ( times_times_nat @ K2 @ ( binomial @ N @ K2 ) )
% 0.35/0.64 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % times_binomial_minus1_eq
% 0.35/0.64 thf(fact_6608_binomial__addition__formula,axiom,
% 0.35/0.64 ! [N: nat,K2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( binomial @ N @ ( suc @ K2 ) )
% 0.35/0.64 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K2 ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % binomial_addition_formula
% 0.35/0.64 thf(fact_6609_choose__odd__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [I: nat] :
% 0.35/0.64 ( if_rat
% 0.35/0.64 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 0.35/0.64 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) )
% 0.35/0.64 @ zero_zero_rat )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_odd_sum
% 0.35/0.64 thf(fact_6610_choose__odd__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [I: nat] :
% 0.35/0.64 ( if_complex
% 0.35/0.64 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 0.35/0.64 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) )
% 0.35/0.64 @ zero_zero_complex )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_odd_sum
% 0.35/0.64 thf(fact_6611_choose__odd__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups3539618377306564664at_int
% 0.35/0.64 @ ^ [I: nat] :
% 0.35/0.64 ( if_int
% 0.35/0.64 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 0.35/0.64 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) )
% 0.35/0.64 @ zero_zero_int )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_odd_sum
% 0.35/0.64 thf(fact_6612_choose__odd__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [I: nat] :
% 0.35/0.64 ( if_real
% 0.35/0.64 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 0.35/0.64 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) )
% 0.35/0.64 @ zero_zero_real )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_odd_sum
% 0.35/0.64 thf(fact_6613_choose__even__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [I: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) @ zero_zero_rat )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_even_sum
% 0.35/0.64 thf(fact_6614_choose__even__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [I: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) @ zero_zero_complex )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_even_sum
% 0.35/0.64 thf(fact_6615_choose__even__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups3539618377306564664at_int
% 0.35/0.64 @ ^ [I: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) @ zero_zero_int )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_even_sum
% 0.35/0.64 thf(fact_6616_choose__even__sum,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.64 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.35/0.64 @ ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [I: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) @ zero_zero_real )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.64 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % choose_even_sum
% 0.35/0.64 thf(fact_6617_card__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_list_nat,K2: nat] :
% 0.35/0.64 ( ( finite8100373058378681591st_nat @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_list_nat @ A4 ) )
% 0.35/0.64 => ( ( finite7325466520557071688st_nat
% 0.35/0.64 @ ( collec5989764272469232197st_nat
% 0.35/0.64 @ ^ [Xs: list_list_nat] :
% 0.35/0.64 ( ( ( size_s3023201423986296836st_nat @ Xs )
% 0.35/0.64 = K2 )
% 0.35/0.64 & ( distinct_list_nat @ Xs )
% 0.35/0.64 & ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [X4: nat] : X4
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6618_card__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_set_nat,K2: nat] :
% 0.35/0.64 ( ( finite1152437895449049373et_nat @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_set_nat @ A4 ) )
% 0.35/0.64 => ( ( finite5631907774883551598et_nat
% 0.35/0.64 @ ( collect_list_set_nat
% 0.35/0.64 @ ^ [Xs: list_set_nat] :
% 0.35/0.64 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 0.35/0.64 = K2 )
% 0.35/0.64 & ( distinct_set_nat @ Xs )
% 0.35/0.64 & ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [X4: nat] : X4
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6619_card__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,K2: nat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_complex @ A4 ) )
% 0.35/0.64 => ( ( finite5120063068150530198omplex
% 0.35/0.64 @ ( collect_list_complex
% 0.35/0.64 @ ^ [Xs: list_complex] :
% 0.35/0.64 ( ( ( size_s3451745648224563538omplex @ Xs )
% 0.35/0.64 = K2 )
% 0.35/0.64 & ( distinct_complex @ Xs )
% 0.35/0.64 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [X4: nat] : X4
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6620_card__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_VEBT_VEBT,K2: nat] :
% 0.35/0.64 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K2 @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 0.35/0.64 => ( ( finite5915292604075114978T_VEBT
% 0.35/0.64 @ ( collec5608196760682091941T_VEBT
% 0.35/0.64 @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.64 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.35/0.64 = K2 )
% 0.35/0.64 & ( distinct_VEBT_VEBT @ Xs )
% 0.35/0.64 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [X4: nat] : X4
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6621_card__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_o,K2: nat] :
% 0.35/0.64 ( ( finite_finite_o @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_o @ A4 ) )
% 0.35/0.64 => ( ( finite_card_list_o
% 0.35/0.64 @ ( collect_list_o
% 0.35/0.64 @ ^ [Xs: list_o] :
% 0.35/0.64 ( ( ( size_size_list_o @ Xs )
% 0.35/0.64 = K2 )
% 0.35/0.64 & ( distinct_o @ Xs )
% 0.35/0.64 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [X4: nat] : X4
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_o @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_o @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6622_card__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_int,K2: nat] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_int @ A4 ) )
% 0.35/0.64 => ( ( finite_card_list_int
% 0.35/0.64 @ ( collect_list_int
% 0.35/0.64 @ ^ [Xs: list_int] :
% 0.35/0.64 ( ( ( size_size_list_int @ Xs )
% 0.35/0.64 = K2 )
% 0.35/0.64 & ( distinct_int @ Xs )
% 0.35/0.64 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [X4: nat] : X4
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6623_card__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_nat,K2: nat] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_nat @ A4 ) )
% 0.35/0.64 => ( ( finite_card_list_nat
% 0.35/0.64 @ ( collect_list_nat
% 0.35/0.64 @ ^ [Xs: list_nat] :
% 0.35/0.64 ( ( ( size_size_list_nat @ Xs )
% 0.35/0.64 = K2 )
% 0.35/0.64 & ( distinct_nat @ Xs )
% 0.35/0.64 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.64 = ( groups708209901874060359at_nat
% 0.35/0.64 @ ^ [X4: nat] : X4
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6624_gchoose__row__sum__weighted,axiom,
% 0.35/0.64 ! [R3: complex,M2: nat] :
% 0.35/0.64 ( ( groups2073611262835488442omplex
% 0.35/0.64 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R3 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 0.35/0.64 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M2 ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R3 @ ( suc @ M2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % gchoose_row_sum_weighted
% 0.35/0.64 thf(fact_6625_gchoose__row__sum__weighted,axiom,
% 0.35/0.64 ! [R3: rat,M2: nat] :
% 0.35/0.64 ( ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 0.35/0.64 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M2 ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % gchoose_row_sum_weighted
% 0.35/0.64 thf(fact_6626_gchoose__row__sum__weighted,axiom,
% 0.35/0.64 ! [R3: real,M2: nat] :
% 0.35/0.64 ( ( groups6591440286371151544t_real
% 0.35/0.64 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R3 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 0.35/0.64 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 0.35/0.64 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R3 @ ( suc @ M2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % gchoose_row_sum_weighted
% 0.35/0.64 thf(fact_6627_vebt__buildup_Opelims,axiom,
% 0.35/0.64 ! [X: nat,Y: vEBT_VEBT] :
% 0.35/0.64 ( ( ( vEBT_vebt_buildup @ X )
% 0.35/0.64 = Y )
% 0.35/0.64 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 0.35/0.64 => ( ( ( X = zero_zero_nat )
% 0.35/0.64 => ( ( Y
% 0.35/0.64 = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.64 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 0.35/0.64 => ( ( ( X
% 0.35/0.64 = ( suc @ zero_zero_nat ) )
% 0.35/0.64 => ( ( Y
% 0.35/0.64 = ( vEBT_Leaf @ $false @ $false ) )
% 0.35/0.64 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 0.35/0.64 => ~ ! [Va: nat] :
% 0.35/0.64 ( ( X
% 0.35/0.64 = ( suc @ ( suc @ Va ) ) )
% 0.35/0.64 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.64 => ( Y
% 0.35/0.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.64 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 0.35/0.64 => ( Y
% 0.35/0.64 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.35/0.64 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % vebt_buildup.pelims
% 0.35/0.64 thf(fact_6628_flip__bit__0,axiom,
% 0.35/0.64 ! [A: nat] :
% 0.35/0.64 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 0.35/0.64 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % flip_bit_0
% 0.35/0.64 thf(fact_6629_flip__bit__0,axiom,
% 0.35/0.64 ! [A: int] :
% 0.35/0.64 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 0.35/0.64 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % flip_bit_0
% 0.35/0.64 thf(fact_6630_flip__bit__0,axiom,
% 0.35/0.64 ! [A: code_integer] :
% 0.35/0.64 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 0.35/0.64 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % flip_bit_0
% 0.35/0.64 thf(fact_6631_atMost__eq__iff,axiom,
% 0.35/0.64 ! [X: nat,Y: nat] :
% 0.35/0.64 ( ( ( set_ord_atMost_nat @ X )
% 0.35/0.64 = ( set_ord_atMost_nat @ Y ) )
% 0.35/0.64 = ( X = Y ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_eq_iff
% 0.35/0.64 thf(fact_6632_atMost__iff,axiom,
% 0.35/0.64 ! [I2: real,K2: real] :
% 0.35/0.64 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K2 ) )
% 0.35/0.64 = ( ord_less_eq_real @ I2 @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_iff
% 0.35/0.64 thf(fact_6633_atMost__iff,axiom,
% 0.35/0.64 ! [I2: set_nat,K2: set_nat] :
% 0.35/0.64 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K2 ) )
% 0.35/0.64 = ( ord_less_eq_set_nat @ I2 @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_iff
% 0.35/0.64 thf(fact_6634_atMost__iff,axiom,
% 0.35/0.64 ! [I2: rat,K2: rat] :
% 0.35/0.64 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K2 ) )
% 0.35/0.64 = ( ord_less_eq_rat @ I2 @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_iff
% 0.35/0.64 thf(fact_6635_atMost__iff,axiom,
% 0.35/0.64 ! [I2: num,K2: num] :
% 0.35/0.64 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K2 ) )
% 0.35/0.64 = ( ord_less_eq_num @ I2 @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_iff
% 0.35/0.64 thf(fact_6636_atMost__iff,axiom,
% 0.35/0.64 ! [I2: int,K2: int] :
% 0.35/0.64 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K2 ) )
% 0.35/0.64 = ( ord_less_eq_int @ I2 @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_iff
% 0.35/0.64 thf(fact_6637_atMost__iff,axiom,
% 0.35/0.64 ! [I2: nat,K2: nat] :
% 0.35/0.64 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K2 ) )
% 0.35/0.64 = ( ord_less_eq_nat @ I2 @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_iff
% 0.35/0.64 thf(fact_6638_of__bool__less__eq__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.35/0.64 = ( P2
% 0.35/0.64 => Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_iff
% 0.35/0.64 thf(fact_6639_of__bool__less__eq__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.35/0.64 = ( P2
% 0.35/0.64 => Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_iff
% 0.35/0.64 thf(fact_6640_of__bool__less__eq__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.35/0.64 = ( P2
% 0.35/0.64 => Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_iff
% 0.35/0.64 thf(fact_6641_of__bool__less__eq__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.35/0.64 = ( P2
% 0.35/0.64 => Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_iff
% 0.35/0.64 thf(fact_6642_of__bool__eq_I1_J,axiom,
% 0.35/0.64 ( ( zero_n1201886186963655149omplex @ $false )
% 0.35/0.64 = zero_zero_complex ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(1)
% 0.35/0.64 thf(fact_6643_of__bool__eq_I1_J,axiom,
% 0.35/0.64 ( ( zero_n3304061248610475627l_real @ $false )
% 0.35/0.64 = zero_zero_real ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(1)
% 0.35/0.64 thf(fact_6644_of__bool__eq_I1_J,axiom,
% 0.35/0.64 ( ( zero_n2052037380579107095ol_rat @ $false )
% 0.35/0.64 = zero_zero_rat ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(1)
% 0.35/0.64 thf(fact_6645_of__bool__eq_I1_J,axiom,
% 0.35/0.64 ( ( zero_n2687167440665602831ol_nat @ $false )
% 0.35/0.64 = zero_zero_nat ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(1)
% 0.35/0.64 thf(fact_6646_of__bool__eq_I1_J,axiom,
% 0.35/0.64 ( ( zero_n2684676970156552555ol_int @ $false )
% 0.35/0.64 = zero_zero_int ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(1)
% 0.35/0.64 thf(fact_6647_of__bool__eq_I1_J,axiom,
% 0.35/0.64 ( ( zero_n356916108424825756nteger @ $false )
% 0.35/0.64 = zero_z3403309356797280102nteger ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(1)
% 0.35/0.64 thf(fact_6648_of__bool__eq__0__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n1201886186963655149omplex @ P2 )
% 0.35/0.64 = zero_zero_complex )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_0_iff
% 0.35/0.64 thf(fact_6649_of__bool__eq__0__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n3304061248610475627l_real @ P2 )
% 0.35/0.64 = zero_zero_real )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_0_iff
% 0.35/0.64 thf(fact_6650_of__bool__eq__0__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n2052037380579107095ol_rat @ P2 )
% 0.35/0.64 = zero_zero_rat )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_0_iff
% 0.35/0.64 thf(fact_6651_of__bool__eq__0__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 0.35/0.64 = zero_zero_nat )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_0_iff
% 0.35/0.64 thf(fact_6652_of__bool__eq__0__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 0.35/0.64 = zero_zero_int )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_0_iff
% 0.35/0.64 thf(fact_6653_of__bool__eq__0__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n356916108424825756nteger @ P2 )
% 0.35/0.64 = zero_z3403309356797280102nteger )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_0_iff
% 0.35/0.64 thf(fact_6654_of__bool__less__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P2 ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 0.35/0.64 = ( ~ P2
% 0.35/0.64 & Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_iff
% 0.35/0.64 thf(fact_6655_of__bool__less__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 0.35/0.64 = ( ~ P2
% 0.35/0.64 & Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_iff
% 0.35/0.64 thf(fact_6656_of__bool__less__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 0.35/0.64 = ( ~ P2
% 0.35/0.64 & Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_iff
% 0.35/0.64 thf(fact_6657_of__bool__less__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 0.35/0.64 = ( ~ P2
% 0.35/0.64 & Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_iff
% 0.35/0.64 thf(fact_6658_of__bool__less__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) )
% 0.35/0.64 = ( ~ P2
% 0.35/0.64 & Q ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_iff
% 0.35/0.64 thf(fact_6659_of__bool__eq__1__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n1201886186963655149omplex @ P2 )
% 0.35/0.64 = one_one_complex )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_1_iff
% 0.35/0.64 thf(fact_6660_of__bool__eq__1__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n3304061248610475627l_real @ P2 )
% 0.35/0.64 = one_one_real )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_1_iff
% 0.35/0.64 thf(fact_6661_of__bool__eq__1__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 0.35/0.64 = one_one_nat )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_1_iff
% 0.35/0.64 thf(fact_6662_of__bool__eq__1__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 0.35/0.64 = one_one_int )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_1_iff
% 0.35/0.64 thf(fact_6663_of__bool__eq__1__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ( zero_n356916108424825756nteger @ P2 )
% 0.35/0.64 = one_one_Code_integer )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_1_iff
% 0.35/0.64 thf(fact_6664_of__bool__eq_I2_J,axiom,
% 0.35/0.64 ( ( zero_n1201886186963655149omplex @ $true )
% 0.35/0.64 = one_one_complex ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(2)
% 0.35/0.64 thf(fact_6665_of__bool__eq_I2_J,axiom,
% 0.35/0.64 ( ( zero_n3304061248610475627l_real @ $true )
% 0.35/0.64 = one_one_real ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(2)
% 0.35/0.64 thf(fact_6666_of__bool__eq_I2_J,axiom,
% 0.35/0.64 ( ( zero_n2687167440665602831ol_nat @ $true )
% 0.35/0.64 = one_one_nat ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(2)
% 0.35/0.64 thf(fact_6667_of__bool__eq_I2_J,axiom,
% 0.35/0.64 ( ( zero_n2684676970156552555ol_int @ $true )
% 0.35/0.64 = one_one_int ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(2)
% 0.35/0.64 thf(fact_6668_of__bool__eq_I2_J,axiom,
% 0.35/0.64 ( ( zero_n356916108424825756nteger @ $true )
% 0.35/0.64 = one_one_Code_integer ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq(2)
% 0.35/0.64 thf(fact_6669_of__nat__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 0.35/0.64 = ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_nat_of_bool
% 0.35/0.64 thf(fact_6670_of__nat__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 0.35/0.64 = ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_nat_of_bool
% 0.35/0.64 thf(fact_6671_of__nat__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 0.35/0.64 = ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_nat_of_bool
% 0.35/0.64 thf(fact_6672_of__nat__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 0.35/0.64 = ( zero_n356916108424825756nteger @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_nat_of_bool
% 0.35/0.64 thf(fact_6673_of__bool__or__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n2687167440665602831ol_nat
% 0.35/0.64 @ ( P2
% 0.35/0.64 | Q ) )
% 0.35/0.64 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_or_iff
% 0.35/0.64 thf(fact_6674_of__bool__or__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n2684676970156552555ol_int
% 0.35/0.64 @ ( P2
% 0.35/0.64 | Q ) )
% 0.35/0.64 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_or_iff
% 0.35/0.64 thf(fact_6675_of__bool__or__iff,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n356916108424825756nteger
% 0.35/0.64 @ ( P2
% 0.35/0.64 | Q ) )
% 0.35/0.64 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_or_iff
% 0.35/0.64 thf(fact_6676_finite__atMost,axiom,
% 0.35/0.64 ! [K2: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % finite_atMost
% 0.35/0.64 thf(fact_6677_zero__less__of__bool__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P2 ) )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_of_bool_iff
% 0.35/0.64 thf(fact_6678_zero__less__of__bool__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_of_bool_iff
% 0.35/0.64 thf(fact_6679_zero__less__of__bool__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_of_bool_iff
% 0.35/0.64 thf(fact_6680_zero__less__of__bool__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_of_bool_iff
% 0.35/0.64 thf(fact_6681_zero__less__of__bool__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) )
% 0.35/0.64 = P2 ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_of_bool_iff
% 0.35/0.64 thf(fact_6682_atMost__subset__iff,axiom,
% 0.35/0.64 ! [X: set_nat,Y: set_nat] :
% 0.35/0.64 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 0.35/0.64 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_subset_iff
% 0.35/0.64 thf(fact_6683_atMost__subset__iff,axiom,
% 0.35/0.64 ! [X: rat,Y: rat] :
% 0.35/0.64 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 0.35/0.64 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_subset_iff
% 0.35/0.64 thf(fact_6684_atMost__subset__iff,axiom,
% 0.35/0.64 ! [X: num,Y: num] :
% 0.35/0.64 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 0.35/0.64 = ( ord_less_eq_num @ X @ Y ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_subset_iff
% 0.35/0.64 thf(fact_6685_atMost__subset__iff,axiom,
% 0.35/0.64 ! [X: int,Y: int] :
% 0.35/0.64 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 0.35/0.64 = ( ord_less_eq_int @ X @ Y ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_subset_iff
% 0.35/0.64 thf(fact_6686_atMost__subset__iff,axiom,
% 0.35/0.64 ! [X: nat,Y: nat] :
% 0.35/0.64 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 0.35/0.64 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_subset_iff
% 0.35/0.64 thf(fact_6687_of__bool__less__one__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P2 ) @ one_one_real )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_one_iff
% 0.35/0.64 thf(fact_6688_of__bool__less__one__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_one_iff
% 0.35/0.64 thf(fact_6689_of__bool__less__one__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_one_iff
% 0.35/0.64 thf(fact_6690_of__bool__less__one__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_one_iff
% 0.35/0.64 thf(fact_6691_of__bool__less__one__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer )
% 0.35/0.64 = ( ~ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_one_iff
% 0.35/0.64 thf(fact_6692_of__bool__not__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( zero_n1201886186963655149omplex @ ~ P2 )
% 0.35/0.64 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_not_iff
% 0.35/0.64 thf(fact_6693_of__bool__not__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( zero_n3304061248610475627l_real @ ~ P2 )
% 0.35/0.64 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_not_iff
% 0.35/0.64 thf(fact_6694_of__bool__not__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( zero_n2052037380579107095ol_rat @ ~ P2 )
% 0.35/0.64 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_not_iff
% 0.35/0.64 thf(fact_6695_of__bool__not__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( zero_n2684676970156552555ol_int @ ~ P2 )
% 0.35/0.64 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_not_iff
% 0.35/0.64 thf(fact_6696_of__bool__not__iff,axiom,
% 0.35/0.64 ! [P2: $o] :
% 0.35/0.64 ( ( zero_n356916108424825756nteger @ ~ P2 )
% 0.35/0.64 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_not_iff
% 0.35/0.64 thf(fact_6697_Suc__0__mod__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.64 = ( zero_n2687167440665602831ol_nat
% 0.35/0.64 @ ( N
% 0.35/0.64 != ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Suc_0_mod_eq
% 0.35/0.64 thf(fact_6698_gbinomial__0_I2_J,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K2 ) )
% 0.35/0.64 = zero_zero_complex ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(2)
% 0.35/0.64 thf(fact_6699_gbinomial__0_I2_J,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K2 ) )
% 0.35/0.64 = zero_zero_real ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(2)
% 0.35/0.64 thf(fact_6700_gbinomial__0_I2_J,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K2 ) )
% 0.35/0.64 = zero_zero_rat ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(2)
% 0.35/0.64 thf(fact_6701_gbinomial__0_I2_J,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K2 ) )
% 0.35/0.64 = zero_zero_nat ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(2)
% 0.35/0.64 thf(fact_6702_gbinomial__0_I2_J,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K2 ) )
% 0.35/0.64 = zero_zero_int ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(2)
% 0.35/0.64 thf(fact_6703_gbinomial__0_I1_J,axiom,
% 0.35/0.64 ! [A: code_integer] :
% 0.35/0.64 ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 0.35/0.64 = one_one_Code_integer ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(1)
% 0.35/0.64 thf(fact_6704_gbinomial__0_I1_J,axiom,
% 0.35/0.64 ! [A: complex] :
% 0.35/0.64 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 0.35/0.64 = one_one_complex ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(1)
% 0.35/0.64 thf(fact_6705_gbinomial__0_I1_J,axiom,
% 0.35/0.64 ! [A: real] :
% 0.35/0.64 ( ( gbinomial_real @ A @ zero_zero_nat )
% 0.35/0.64 = one_one_real ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(1)
% 0.35/0.64 thf(fact_6706_gbinomial__0_I1_J,axiom,
% 0.35/0.64 ! [A: nat] :
% 0.35/0.64 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 0.35/0.64 = one_one_nat ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(1)
% 0.35/0.64 thf(fact_6707_gbinomial__0_I1_J,axiom,
% 0.35/0.64 ! [A: int] :
% 0.35/0.64 ( ( gbinomial_int @ A @ zero_zero_nat )
% 0.35/0.64 = one_one_int ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_0(1)
% 0.35/0.64 thf(fact_6708_card__atMost,axiom,
% 0.35/0.64 ! [U: nat] :
% 0.35/0.64 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 0.35/0.64 = ( suc @ U ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_atMost
% 0.35/0.64 thf(fact_6709_Icc__subset__Iic__iff,axiom,
% 0.35/0.64 ! [L: set_nat,H: set_nat,H3: set_nat] :
% 0.35/0.64 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 0.35/0.64 = ( ~ ( ord_less_eq_set_nat @ L @ H )
% 0.35/0.64 | ( ord_less_eq_set_nat @ H @ H3 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Icc_subset_Iic_iff
% 0.35/0.64 thf(fact_6710_Icc__subset__Iic__iff,axiom,
% 0.35/0.64 ! [L: rat,H: rat,H3: rat] :
% 0.35/0.64 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H3 ) )
% 0.35/0.64 = ( ~ ( ord_less_eq_rat @ L @ H )
% 0.35/0.64 | ( ord_less_eq_rat @ H @ H3 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Icc_subset_Iic_iff
% 0.35/0.64 thf(fact_6711_Icc__subset__Iic__iff,axiom,
% 0.35/0.64 ! [L: num,H: num,H3: num] :
% 0.35/0.64 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H3 ) )
% 0.35/0.64 = ( ~ ( ord_less_eq_num @ L @ H )
% 0.35/0.64 | ( ord_less_eq_num @ H @ H3 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Icc_subset_Iic_iff
% 0.35/0.64 thf(fact_6712_Icc__subset__Iic__iff,axiom,
% 0.35/0.64 ! [L: nat,H: nat,H3: nat] :
% 0.35/0.64 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H3 ) )
% 0.35/0.64 = ( ~ ( ord_less_eq_nat @ L @ H )
% 0.35/0.64 | ( ord_less_eq_nat @ H @ H3 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Icc_subset_Iic_iff
% 0.35/0.64 thf(fact_6713_Icc__subset__Iic__iff,axiom,
% 0.35/0.64 ! [L: int,H: int,H3: int] :
% 0.35/0.64 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H3 ) )
% 0.35/0.64 = ( ~ ( ord_less_eq_int @ L @ H )
% 0.35/0.64 | ( ord_less_eq_int @ H @ H3 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Icc_subset_Iic_iff
% 0.35/0.64 thf(fact_6714_Icc__subset__Iic__iff,axiom,
% 0.35/0.64 ! [L: real,H: real,H3: real] :
% 0.35/0.64 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H ) @ ( set_ord_atMost_real @ H3 ) )
% 0.35/0.64 = ( ~ ( ord_less_eq_real @ L @ H )
% 0.35/0.64 | ( ord_less_eq_real @ H @ H3 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % Icc_subset_Iic_iff
% 0.35/0.64 thf(fact_6715_sum_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > rat,N: nat] :
% 0.35/0.64 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum.atMost_Suc
% 0.35/0.64 thf(fact_6716_sum_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > int,N: nat] :
% 0.35/0.64 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum.atMost_Suc
% 0.35/0.64 thf(fact_6717_sum_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > nat,N: nat] :
% 0.35/0.64 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum.atMost_Suc
% 0.35/0.64 thf(fact_6718_sum_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > real,N: nat] :
% 0.35/0.64 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum.atMost_Suc
% 0.35/0.64 thf(fact_6719_prod_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > real,N: nat] :
% 0.35/0.64 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.atMost_Suc
% 0.35/0.64 thf(fact_6720_prod_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > rat,N: nat] :
% 0.35/0.64 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.atMost_Suc
% 0.35/0.64 thf(fact_6721_prod_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > int,N: nat] :
% 0.35/0.64 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.atMost_Suc
% 0.35/0.64 thf(fact_6722_prod_OatMost__Suc,axiom,
% 0.35/0.64 ! [G2: nat > nat,N: nat] :
% 0.35/0.64 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.64 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % prod.atMost_Suc
% 0.35/0.64 thf(fact_6723_atMost__0,axiom,
% 0.35/0.64 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 0.35/0.64 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_0
% 0.35/0.64 thf(fact_6724_distinct__swap,axiom,
% 0.35/0.64 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.64 => ( ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) @ J2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 0.35/0.64 = ( distinct_VEBT_VEBT @ Xs2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_swap
% 0.35/0.64 thf(fact_6725_distinct__swap,axiom,
% 0.35/0.64 ! [I2: nat,Xs2: list_o,J2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.64 => ( ( distinct_o @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J2 ) ) @ J2 @ ( nth_o @ Xs2 @ I2 ) ) )
% 0.35/0.64 = ( distinct_o @ Xs2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_swap
% 0.35/0.64 thf(fact_6726_distinct__swap,axiom,
% 0.35/0.64 ! [I2: nat,Xs2: list_nat,J2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.64 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J2 ) ) @ J2 @ ( nth_nat @ Xs2 @ I2 ) ) )
% 0.35/0.64 = ( distinct_nat @ Xs2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_swap
% 0.35/0.64 thf(fact_6727_distinct__swap,axiom,
% 0.35/0.64 ! [I2: nat,Xs2: list_int,J2: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.64 => ( ( distinct_int @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J2 ) ) @ J2 @ ( nth_int @ Xs2 @ I2 ) ) )
% 0.35/0.64 = ( distinct_int @ Xs2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_swap
% 0.35/0.64 thf(fact_6728_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > real,P2: real > $o] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( groups8097168146408367636l_real
% 0.35/0.64 @ ^ [X4: real] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups8097168146408367636l_real @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6729_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > real,P2: int > $o] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( groups8778361861064173332t_real
% 0.35/0.64 @ ^ [X4: int] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups8778361861064173332t_real @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6730_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > real,P2: complex > $o] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( groups5808333547571424918x_real
% 0.35/0.64 @ ^ [X4: complex] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups5808333547571424918x_real @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6731_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > rat,P2: real > $o] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( groups1300246762558778688al_rat
% 0.35/0.64 @ ^ [X4: real] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups1300246762558778688al_rat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6732_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > rat,P2: int > $o] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( groups3906332499630173760nt_rat
% 0.35/0.64 @ ^ [X4: int] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6733_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > rat,P2: complex > $o] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( groups5058264527183730370ex_rat
% 0.35/0.64 @ ^ [X4: complex] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups5058264527183730370ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6734_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_nat,F2: nat > rat,P2: nat > $o] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [X4: nat] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6735_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_real,F2: real > nat,P2: real > $o] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( groups1935376822645274424al_nat
% 0.35/0.64 @ ^ [X4: real] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups1935376822645274424al_nat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6736_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_int,F2: int > nat,P2: int > $o] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( groups4541462559716669496nt_nat
% 0.35/0.64 @ ^ [X4: int] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6737_sum__mult__of__bool__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,F2: complex > nat,P2: complex > $o] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( groups5693394587270226106ex_nat
% 0.35/0.64 @ ^ [X4: complex] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups5693394587270226106ex_nat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_mult_of_bool_eq
% 0.35/0.64 thf(fact_6738_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_real,P2: real > $o,F2: real > real] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( groups8097168146408367636l_real
% 0.35/0.64 @ ^ [X4: real] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups8097168146408367636l_real @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6739_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_int,P2: int > $o,F2: int > real] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( groups8778361861064173332t_real
% 0.35/0.64 @ ^ [X4: int] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups8778361861064173332t_real @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6740_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,P2: complex > $o,F2: complex > real] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( groups5808333547571424918x_real
% 0.35/0.64 @ ^ [X4: complex] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups5808333547571424918x_real @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6741_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_real,P2: real > $o,F2: real > rat] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( groups1300246762558778688al_rat
% 0.35/0.64 @ ^ [X4: real] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups1300246762558778688al_rat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6742_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_int,P2: int > $o,F2: int > rat] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( groups3906332499630173760nt_rat
% 0.35/0.64 @ ^ [X4: int] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6743_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,P2: complex > $o,F2: complex > rat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( groups5058264527183730370ex_rat
% 0.35/0.64 @ ^ [X4: complex] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups5058264527183730370ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6744_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_nat,P2: nat > $o,F2: nat > rat] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( ( groups2906978787729119204at_rat
% 0.35/0.64 @ ^ [X4: nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6745_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_real,P2: real > $o,F2: real > nat] :
% 0.35/0.64 ( ( finite_finite_real @ A4 )
% 0.35/0.64 => ( ( groups1935376822645274424al_nat
% 0.35/0.64 @ ^ [X4: real] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups1935376822645274424al_nat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6746_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_int,P2: int > $o,F2: int > nat] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( ( groups4541462559716669496nt_nat
% 0.35/0.64 @ ^ [X4: int] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6747_sum__of__bool__mult__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,P2: complex > $o,F2: complex > nat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( ( groups5693394587270226106ex_nat
% 0.35/0.64 @ ^ [X4: complex] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 0.35/0.64 @ A4 )
% 0.35/0.64 = ( groups5693394587270226106ex_nat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_of_bool_mult_eq
% 0.35/0.64 thf(fact_6748_of__bool__half__eq__0,axiom,
% 0.35/0.64 ! [B: $o] :
% 0.35/0.64 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.64 = zero_zero_nat ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_half_eq_0
% 0.35/0.64 thf(fact_6749_of__bool__half__eq__0,axiom,
% 0.35/0.64 ! [B: $o] :
% 0.35/0.64 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.64 = zero_zero_int ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_half_eq_0
% 0.35/0.64 thf(fact_6750_of__bool__half__eq__0,axiom,
% 0.35/0.64 ! [B: $o] :
% 0.35/0.64 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.64 = zero_z3403309356797280102nteger ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_half_eq_0
% 0.35/0.64 thf(fact_6751_finite__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_complex,N: nat] :
% 0.35/0.64 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.64 => ( finite8712137658972009173omplex
% 0.35/0.64 @ ( collect_list_complex
% 0.35/0.64 @ ^ [Xs: list_complex] :
% 0.35/0.64 ( ( ( size_s3451745648224563538omplex @ Xs )
% 0.35/0.64 = N )
% 0.35/0.64 & ( distinct_complex @ Xs )
% 0.35/0.64 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % finite_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6752_finite__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.35/0.64 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.35/0.64 => ( finite3004134309566078307T_VEBT
% 0.35/0.64 @ ( collec5608196760682091941T_VEBT
% 0.35/0.64 @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.64 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.35/0.64 = N )
% 0.35/0.64 & ( distinct_VEBT_VEBT @ Xs )
% 0.35/0.64 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % finite_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6753_finite__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_o,N: nat] :
% 0.35/0.64 ( ( finite_finite_o @ A4 )
% 0.35/0.64 => ( finite_finite_list_o
% 0.35/0.64 @ ( collect_list_o
% 0.35/0.64 @ ^ [Xs: list_o] :
% 0.35/0.64 ( ( ( size_size_list_o @ Xs )
% 0.35/0.64 = N )
% 0.35/0.64 & ( distinct_o @ Xs )
% 0.35/0.64 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % finite_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6754_finite__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_int,N: nat] :
% 0.35/0.64 ( ( finite_finite_int @ A4 )
% 0.35/0.64 => ( finite3922522038869484883st_int
% 0.35/0.64 @ ( collect_list_int
% 0.35/0.64 @ ^ [Xs: list_int] :
% 0.35/0.64 ( ( ( size_size_list_int @ Xs )
% 0.35/0.64 = N )
% 0.35/0.64 & ( distinct_int @ Xs )
% 0.35/0.64 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % finite_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6755_finite__lists__distinct__length__eq,axiom,
% 0.35/0.64 ! [A4: set_nat,N: nat] :
% 0.35/0.64 ( ( finite_finite_nat @ A4 )
% 0.35/0.64 => ( finite8100373058378681591st_nat
% 0.35/0.64 @ ( collect_list_nat
% 0.35/0.64 @ ^ [Xs: list_nat] :
% 0.35/0.64 ( ( ( size_size_list_nat @ Xs )
% 0.35/0.64 = N )
% 0.35/0.64 & ( distinct_nat @ Xs )
% 0.35/0.64 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % finite_lists_distinct_length_eq
% 0.35/0.64 thf(fact_6756_one__div__2__pow__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_div_2_pow_eq
% 0.35/0.64 thf(fact_6757_one__div__2__pow__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_div_2_pow_eq
% 0.35/0.64 thf(fact_6758_one__div__2__pow__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_div_2_pow_eq
% 0.35/0.64 thf(fact_6759_bits__1__div__exp,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % bits_1_div_exp
% 0.35/0.64 thf(fact_6760_bits__1__div__exp,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % bits_1_div_exp
% 0.35/0.64 thf(fact_6761_bits__1__div__exp,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % bits_1_div_exp
% 0.35/0.64 thf(fact_6762_one__mod__2__pow__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_mod_2_pow_eq
% 0.35/0.64 thf(fact_6763_one__mod__2__pow__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_mod_2_pow_eq
% 0.35/0.64 thf(fact_6764_one__mod__2__pow__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_mod_2_pow_eq
% 0.35/0.64 thf(fact_6765_one__mod__2__pow__eq,axiom,
% 0.35/0.64 ! [N: nat] :
% 0.35/0.64 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.64 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % one_mod_2_pow_eq
% 0.35/0.64 thf(fact_6766_of__bool__eq__iff,axiom,
% 0.35/0.64 ! [P: $o,Q2: $o] :
% 0.35/0.64 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 0.35/0.64 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 0.35/0.64 = ( P = Q2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_iff
% 0.35/0.64 thf(fact_6767_of__bool__eq__iff,axiom,
% 0.35/0.64 ! [P: $o,Q2: $o] :
% 0.35/0.64 ( ( ( zero_n2684676970156552555ol_int @ P )
% 0.35/0.64 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 0.35/0.64 = ( P = Q2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_iff
% 0.35/0.64 thf(fact_6768_of__bool__eq__iff,axiom,
% 0.35/0.64 ! [P: $o,Q2: $o] :
% 0.35/0.64 ( ( ( zero_n356916108424825756nteger @ P )
% 0.35/0.64 = ( zero_n356916108424825756nteger @ Q2 ) )
% 0.35/0.64 = ( P = Q2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_eq_iff
% 0.35/0.64 thf(fact_6769_of__bool__conj,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n3304061248610475627l_real
% 0.35/0.64 @ ( P2
% 0.35/0.64 & Q ) )
% 0.35/0.64 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P2 ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_conj
% 0.35/0.64 thf(fact_6770_of__bool__conj,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n2052037380579107095ol_rat
% 0.35/0.64 @ ( P2
% 0.35/0.64 & Q ) )
% 0.35/0.64 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_conj
% 0.35/0.64 thf(fact_6771_of__bool__conj,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n2687167440665602831ol_nat
% 0.35/0.64 @ ( P2
% 0.35/0.64 & Q ) )
% 0.35/0.64 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_conj
% 0.35/0.64 thf(fact_6772_of__bool__conj,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n2684676970156552555ol_int
% 0.35/0.64 @ ( P2
% 0.35/0.64 & Q ) )
% 0.35/0.64 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_conj
% 0.35/0.64 thf(fact_6773_of__bool__conj,axiom,
% 0.35/0.64 ! [P2: $o,Q: $o] :
% 0.35/0.64 ( ( zero_n356916108424825756nteger
% 0.35/0.64 @ ( P2
% 0.35/0.64 & Q ) )
% 0.35/0.64 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_conj
% 0.35/0.64 thf(fact_6774_not__empty__eq__Iic__eq__empty,axiom,
% 0.35/0.64 ! [H: int] :
% 0.35/0.64 ( bot_bot_set_int
% 0.35/0.64 != ( set_ord_atMost_int @ H ) ) ).
% 0.35/0.64
% 0.35/0.64 % not_empty_eq_Iic_eq_empty
% 0.35/0.64 thf(fact_6775_not__empty__eq__Iic__eq__empty,axiom,
% 0.35/0.64 ! [H: real] :
% 0.35/0.64 ( bot_bot_set_real
% 0.35/0.64 != ( set_ord_atMost_real @ H ) ) ).
% 0.35/0.64
% 0.35/0.64 % not_empty_eq_Iic_eq_empty
% 0.35/0.64 thf(fact_6776_not__empty__eq__Iic__eq__empty,axiom,
% 0.35/0.64 ! [H: nat] :
% 0.35/0.64 ( bot_bot_set_nat
% 0.35/0.64 != ( set_ord_atMost_nat @ H ) ) ).
% 0.35/0.64
% 0.35/0.64 % not_empty_eq_Iic_eq_empty
% 0.35/0.64 thf(fact_6777_infinite__Iic,axiom,
% 0.35/0.64 ! [A: int] :
% 0.35/0.64 ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 0.35/0.64
% 0.35/0.64 % infinite_Iic
% 0.35/0.64 thf(fact_6778_not__Iic__eq__Icc,axiom,
% 0.35/0.64 ! [H3: int,L: int,H: int] :
% 0.35/0.64 ( ( set_ord_atMost_int @ H3 )
% 0.35/0.64 != ( set_or1266510415728281911st_int @ L @ H ) ) ).
% 0.35/0.64
% 0.35/0.64 % not_Iic_eq_Icc
% 0.35/0.64 thf(fact_6779_not__Iic__eq__Icc,axiom,
% 0.35/0.64 ! [H3: real,L: real,H: real] :
% 0.35/0.64 ( ( set_ord_atMost_real @ H3 )
% 0.35/0.64 != ( set_or1222579329274155063t_real @ L @ H ) ) ).
% 0.35/0.64
% 0.35/0.64 % not_Iic_eq_Icc
% 0.35/0.64 thf(fact_6780_atMost__def,axiom,
% 0.35/0.64 ( set_ord_atMost_real
% 0.35/0.64 = ( ^ [U2: real] :
% 0.35/0.64 ( collect_real
% 0.35/0.64 @ ^ [X4: real] : ( ord_less_eq_real @ X4 @ U2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_def
% 0.35/0.64 thf(fact_6781_atMost__def,axiom,
% 0.35/0.64 ( set_or4236626031148496127et_nat
% 0.35/0.64 = ( ^ [U2: set_nat] :
% 0.35/0.64 ( collect_set_nat
% 0.35/0.64 @ ^ [X4: set_nat] : ( ord_less_eq_set_nat @ X4 @ U2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_def
% 0.35/0.64 thf(fact_6782_atMost__def,axiom,
% 0.35/0.64 ( set_ord_atMost_rat
% 0.35/0.64 = ( ^ [U2: rat] :
% 0.35/0.64 ( collect_rat
% 0.35/0.64 @ ^ [X4: rat] : ( ord_less_eq_rat @ X4 @ U2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_def
% 0.35/0.64 thf(fact_6783_atMost__def,axiom,
% 0.35/0.64 ( set_ord_atMost_num
% 0.35/0.64 = ( ^ [U2: num] :
% 0.35/0.64 ( collect_num
% 0.35/0.64 @ ^ [X4: num] : ( ord_less_eq_num @ X4 @ U2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_def
% 0.35/0.64 thf(fact_6784_atMost__def,axiom,
% 0.35/0.64 ( set_ord_atMost_int
% 0.35/0.64 = ( ^ [U2: int] :
% 0.35/0.64 ( collect_int
% 0.35/0.64 @ ^ [X4: int] : ( ord_less_eq_int @ X4 @ U2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_def
% 0.35/0.64 thf(fact_6785_atMost__def,axiom,
% 0.35/0.64 ( set_ord_atMost_nat
% 0.35/0.64 = ( ^ [U2: nat] :
% 0.35/0.64 ( collect_nat
% 0.35/0.64 @ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_def
% 0.35/0.64 thf(fact_6786_zero__less__eq__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_eq_of_bool
% 0.35/0.64 thf(fact_6787_zero__less__eq__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_eq_of_bool
% 0.35/0.64 thf(fact_6788_zero__less__eq__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_eq_of_bool
% 0.35/0.64 thf(fact_6789_zero__less__eq__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_eq_of_bool
% 0.35/0.64 thf(fact_6790_zero__less__eq__of__bool,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % zero_less_eq_of_bool
% 0.35/0.64 thf(fact_6791_of__bool__less__eq__one,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P2 ) @ one_one_real ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_one
% 0.35/0.64 thf(fact_6792_of__bool__less__eq__one,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_one
% 0.35/0.64 thf(fact_6793_of__bool__less__eq__one,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_one
% 0.35/0.64 thf(fact_6794_of__bool__less__eq__one,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_one
% 0.35/0.64 thf(fact_6795_of__bool__less__eq__one,axiom,
% 0.35/0.64 ! [P2: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_less_eq_one
% 0.35/0.64 thf(fact_6796_of__bool__def,axiom,
% 0.35/0.64 ( zero_n1201886186963655149omplex
% 0.35/0.64 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_def
% 0.35/0.64 thf(fact_6797_of__bool__def,axiom,
% 0.35/0.64 ( zero_n3304061248610475627l_real
% 0.35/0.64 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_def
% 0.35/0.64 thf(fact_6798_of__bool__def,axiom,
% 0.35/0.64 ( zero_n2052037380579107095ol_rat
% 0.35/0.64 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_def
% 0.35/0.64 thf(fact_6799_of__bool__def,axiom,
% 0.35/0.64 ( zero_n2687167440665602831ol_nat
% 0.35/0.64 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_def
% 0.35/0.64 thf(fact_6800_of__bool__def,axiom,
% 0.35/0.64 ( zero_n2684676970156552555ol_int
% 0.35/0.64 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_def
% 0.35/0.64 thf(fact_6801_of__bool__def,axiom,
% 0.35/0.64 ( zero_n356916108424825756nteger
% 0.35/0.64 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % of_bool_def
% 0.35/0.64 thf(fact_6802_split__of__bool,axiom,
% 0.35/0.64 ! [P2: complex > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n1201886186963655149omplex @ P ) )
% 0.35/0.64 = ( ( P
% 0.35/0.64 => ( P2 @ one_one_complex ) )
% 0.35/0.64 & ( ~ P
% 0.35/0.64 => ( P2 @ zero_zero_complex ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool
% 0.35/0.64 thf(fact_6803_split__of__bool,axiom,
% 0.35/0.64 ! [P2: real > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n3304061248610475627l_real @ P ) )
% 0.35/0.64 = ( ( P
% 0.35/0.64 => ( P2 @ one_one_real ) )
% 0.35/0.64 & ( ~ P
% 0.35/0.64 => ( P2 @ zero_zero_real ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool
% 0.35/0.64 thf(fact_6804_split__of__bool,axiom,
% 0.35/0.64 ! [P2: rat > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.35/0.64 = ( ( P
% 0.35/0.64 => ( P2 @ one_one_rat ) )
% 0.35/0.64 & ( ~ P
% 0.35/0.64 => ( P2 @ zero_zero_rat ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool
% 0.35/0.64 thf(fact_6805_split__of__bool,axiom,
% 0.35/0.64 ! [P2: nat > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.64 = ( ( P
% 0.35/0.64 => ( P2 @ one_one_nat ) )
% 0.35/0.64 & ( ~ P
% 0.35/0.64 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool
% 0.35/0.64 thf(fact_6806_split__of__bool,axiom,
% 0.35/0.64 ! [P2: int > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.35/0.64 = ( ( P
% 0.35/0.64 => ( P2 @ one_one_int ) )
% 0.35/0.64 & ( ~ P
% 0.35/0.64 => ( P2 @ zero_zero_int ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool
% 0.35/0.64 thf(fact_6807_split__of__bool,axiom,
% 0.35/0.64 ! [P2: code_integer > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n356916108424825756nteger @ P ) )
% 0.35/0.64 = ( ( P
% 0.35/0.64 => ( P2 @ one_one_Code_integer ) )
% 0.35/0.64 & ( ~ P
% 0.35/0.64 => ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool
% 0.35/0.64 thf(fact_6808_split__of__bool__asm,axiom,
% 0.35/0.64 ! [P2: complex > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n1201886186963655149omplex @ P ) )
% 0.35/0.64 = ( ~ ( ( P
% 0.35/0.64 & ~ ( P2 @ one_one_complex ) )
% 0.35/0.64 | ( ~ P
% 0.35/0.64 & ~ ( P2 @ zero_zero_complex ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool_asm
% 0.35/0.64 thf(fact_6809_split__of__bool__asm,axiom,
% 0.35/0.64 ! [P2: real > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n3304061248610475627l_real @ P ) )
% 0.35/0.64 = ( ~ ( ( P
% 0.35/0.64 & ~ ( P2 @ one_one_real ) )
% 0.35/0.64 | ( ~ P
% 0.35/0.64 & ~ ( P2 @ zero_zero_real ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool_asm
% 0.35/0.64 thf(fact_6810_split__of__bool__asm,axiom,
% 0.35/0.64 ! [P2: rat > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P ) )
% 0.35/0.64 = ( ~ ( ( P
% 0.35/0.64 & ~ ( P2 @ one_one_rat ) )
% 0.35/0.64 | ( ~ P
% 0.35/0.64 & ~ ( P2 @ zero_zero_rat ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool_asm
% 0.35/0.64 thf(fact_6811_split__of__bool__asm,axiom,
% 0.35/0.64 ! [P2: nat > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P ) )
% 0.35/0.64 = ( ~ ( ( P
% 0.35/0.64 & ~ ( P2 @ one_one_nat ) )
% 0.35/0.64 | ( ~ P
% 0.35/0.64 & ~ ( P2 @ zero_zero_nat ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool_asm
% 0.35/0.64 thf(fact_6812_split__of__bool__asm,axiom,
% 0.35/0.64 ! [P2: int > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 0.35/0.64 = ( ~ ( ( P
% 0.35/0.64 & ~ ( P2 @ one_one_int ) )
% 0.35/0.64 | ( ~ P
% 0.35/0.64 & ~ ( P2 @ zero_zero_int ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool_asm
% 0.35/0.64 thf(fact_6813_split__of__bool__asm,axiom,
% 0.35/0.64 ! [P2: code_integer > $o,P: $o] :
% 0.35/0.64 ( ( P2 @ ( zero_n356916108424825756nteger @ P ) )
% 0.35/0.64 = ( ~ ( ( P
% 0.35/0.64 & ~ ( P2 @ one_one_Code_integer ) )
% 0.35/0.64 | ( ~ P
% 0.35/0.64 & ~ ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % split_of_bool_asm
% 0.35/0.64 thf(fact_6814_atMost__atLeast0,axiom,
% 0.35/0.64 ( set_ord_atMost_nat
% 0.35/0.64 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_atLeast0
% 0.35/0.64 thf(fact_6815_lessThan__Suc__atMost,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( set_ord_lessThan_nat @ ( suc @ K2 ) )
% 0.35/0.64 = ( set_ord_atMost_nat @ K2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % lessThan_Suc_atMost
% 0.35/0.64 thf(fact_6816_atMost__Suc,axiom,
% 0.35/0.64 ! [K2: nat] :
% 0.35/0.64 ( ( set_ord_atMost_nat @ ( suc @ K2 ) )
% 0.35/0.64 = ( insert_nat @ ( suc @ K2 ) @ ( set_ord_atMost_nat @ K2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % atMost_Suc
% 0.35/0.64 thf(fact_6817_not__Iic__le__Icc,axiom,
% 0.35/0.64 ! [H: int,L3: int,H3: int] :
% 0.35/0.64 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 0.35/0.64
% 0.35/0.64 % not_Iic_le_Icc
% 0.35/0.64 thf(fact_6818_not__Iic__le__Icc,axiom,
% 0.35/0.64 ! [H: real,L3: real,H3: real] :
% 0.35/0.64 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 0.35/0.64
% 0.35/0.64 % not_Iic_le_Icc
% 0.35/0.64 thf(fact_6819_nth__eq__iff__index__eq,axiom,
% 0.35/0.64 ! [Xs2: list_VEBT_VEBT,I2: nat,J2: nat] :
% 0.35/0.64 ( ( distinct_VEBT_VEBT @ Xs2 )
% 0.35/0.64 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.64 => ( ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 0.35/0.64 = ( nth_VEBT_VEBT @ Xs2 @ J2 ) )
% 0.35/0.64 = ( I2 = J2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % nth_eq_iff_index_eq
% 0.35/0.64 thf(fact_6820_nth__eq__iff__index__eq,axiom,
% 0.35/0.64 ! [Xs2: list_o,I2: nat,J2: nat] :
% 0.35/0.64 ( ( distinct_o @ Xs2 )
% 0.35/0.64 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.64 => ( ( ( nth_o @ Xs2 @ I2 )
% 0.35/0.64 = ( nth_o @ Xs2 @ J2 ) )
% 0.35/0.64 = ( I2 = J2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % nth_eq_iff_index_eq
% 0.35/0.64 thf(fact_6821_nth__eq__iff__index__eq,axiom,
% 0.35/0.64 ! [Xs2: list_nat,I2: nat,J2: nat] :
% 0.35/0.64 ( ( distinct_nat @ Xs2 )
% 0.35/0.64 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.64 => ( ( ( nth_nat @ Xs2 @ I2 )
% 0.35/0.64 = ( nth_nat @ Xs2 @ J2 ) )
% 0.35/0.64 = ( I2 = J2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % nth_eq_iff_index_eq
% 0.35/0.64 thf(fact_6822_nth__eq__iff__index__eq,axiom,
% 0.35/0.64 ! [Xs2: list_int,I2: nat,J2: nat] :
% 0.35/0.64 ( ( distinct_int @ Xs2 )
% 0.35/0.64 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.64 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.64 => ( ( ( nth_int @ Xs2 @ I2 )
% 0.35/0.64 = ( nth_int @ Xs2 @ J2 ) )
% 0.35/0.64 = ( I2 = J2 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % nth_eq_iff_index_eq
% 0.35/0.64 thf(fact_6823_distinct__conv__nth,axiom,
% 0.35/0.64 ( distinct_VEBT_VEBT
% 0.35/0.64 = ( ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.64 ! [I: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.35/0.64 => ! [J: nat] :
% 0.35/0.64 ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 0.35/0.64 => ( ( I != J )
% 0.35/0.64 => ( ( nth_VEBT_VEBT @ Xs @ I )
% 0.35/0.64 != ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_conv_nth
% 0.35/0.64 thf(fact_6824_distinct__conv__nth,axiom,
% 0.35/0.64 ( distinct_o
% 0.35/0.64 = ( ^ [Xs: list_o] :
% 0.35/0.64 ! [I: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 0.35/0.64 => ! [J: nat] :
% 0.35/0.64 ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 0.35/0.64 => ( ( I != J )
% 0.35/0.64 => ( ( nth_o @ Xs @ I )
% 0.35/0.64 != ( nth_o @ Xs @ J ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_conv_nth
% 0.35/0.64 thf(fact_6825_distinct__conv__nth,axiom,
% 0.35/0.64 ( distinct_nat
% 0.35/0.64 = ( ^ [Xs: list_nat] :
% 0.35/0.64 ! [I: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 0.35/0.64 => ! [J: nat] :
% 0.35/0.64 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 0.35/0.64 => ( ( I != J )
% 0.35/0.64 => ( ( nth_nat @ Xs @ I )
% 0.35/0.64 != ( nth_nat @ Xs @ J ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_conv_nth
% 0.35/0.64 thf(fact_6826_distinct__conv__nth,axiom,
% 0.35/0.64 ( distinct_int
% 0.35/0.64 = ( ^ [Xs: list_int] :
% 0.35/0.64 ! [I: nat] :
% 0.35/0.64 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 0.35/0.64 => ! [J: nat] :
% 0.35/0.64 ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 0.35/0.64 => ( ( I != J )
% 0.35/0.64 => ( ( nth_int @ Xs @ I )
% 0.35/0.64 != ( nth_int @ Xs @ J ) ) ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_conv_nth
% 0.35/0.64 thf(fact_6827_card__distinct,axiom,
% 0.35/0.64 ! [Xs2: list_complex] :
% 0.35/0.64 ( ( ( finite_card_complex @ ( set_complex2 @ Xs2 ) )
% 0.35/0.64 = ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.35/0.64 => ( distinct_complex @ Xs2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_distinct
% 0.35/0.64 thf(fact_6828_card__distinct,axiom,
% 0.35/0.64 ! [Xs2: list_list_nat] :
% 0.35/0.64 ( ( ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) )
% 0.35/0.64 = ( size_s3023201423986296836st_nat @ Xs2 ) )
% 0.35/0.64 => ( distinct_list_nat @ Xs2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_distinct
% 0.35/0.64 thf(fact_6829_card__distinct,axiom,
% 0.35/0.64 ! [Xs2: list_set_nat] :
% 0.35/0.64 ( ( ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) )
% 0.35/0.64 = ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.35/0.64 => ( distinct_set_nat @ Xs2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_distinct
% 0.35/0.64 thf(fact_6830_card__distinct,axiom,
% 0.35/0.64 ! [Xs2: list_VEBT_VEBT] :
% 0.35/0.64 ( ( ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.64 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.64 => ( distinct_VEBT_VEBT @ Xs2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_distinct
% 0.35/0.64 thf(fact_6831_card__distinct,axiom,
% 0.35/0.64 ! [Xs2: list_o] :
% 0.35/0.64 ( ( ( finite_card_o @ ( set_o2 @ Xs2 ) )
% 0.35/0.64 = ( size_size_list_o @ Xs2 ) )
% 0.35/0.64 => ( distinct_o @ Xs2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_distinct
% 0.35/0.64 thf(fact_6832_card__distinct,axiom,
% 0.35/0.64 ! [Xs2: list_nat] :
% 0.35/0.64 ( ( ( finite_card_nat @ ( set_nat2 @ Xs2 ) )
% 0.35/0.64 = ( size_size_list_nat @ Xs2 ) )
% 0.35/0.64 => ( distinct_nat @ Xs2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_distinct
% 0.35/0.64 thf(fact_6833_card__distinct,axiom,
% 0.35/0.64 ! [Xs2: list_int] :
% 0.35/0.64 ( ( ( finite_card_int @ ( set_int2 @ Xs2 ) )
% 0.35/0.64 = ( size_size_list_int @ Xs2 ) )
% 0.35/0.64 => ( distinct_int @ Xs2 ) ) ).
% 0.35/0.64
% 0.35/0.64 % card_distinct
% 0.35/0.64 thf(fact_6834_distinct__card,axiom,
% 0.35/0.64 ! [Xs2: list_complex] :
% 0.35/0.64 ( ( distinct_complex @ Xs2 )
% 0.35/0.64 => ( ( finite_card_complex @ ( set_complex2 @ Xs2 ) )
% 0.35/0.64 = ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_card
% 0.35/0.64 thf(fact_6835_distinct__card,axiom,
% 0.35/0.64 ! [Xs2: list_list_nat] :
% 0.35/0.64 ( ( distinct_list_nat @ Xs2 )
% 0.35/0.64 => ( ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) )
% 0.35/0.64 = ( size_s3023201423986296836st_nat @ Xs2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_card
% 0.35/0.64 thf(fact_6836_distinct__card,axiom,
% 0.35/0.64 ! [Xs2: list_set_nat] :
% 0.35/0.64 ( ( distinct_set_nat @ Xs2 )
% 0.35/0.64 => ( ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) )
% 0.35/0.64 = ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_card
% 0.35/0.64 thf(fact_6837_distinct__card,axiom,
% 0.35/0.64 ! [Xs2: list_VEBT_VEBT] :
% 0.35/0.64 ( ( distinct_VEBT_VEBT @ Xs2 )
% 0.35/0.64 => ( ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.64 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_card
% 0.35/0.64 thf(fact_6838_distinct__card,axiom,
% 0.35/0.64 ! [Xs2: list_o] :
% 0.35/0.64 ( ( distinct_o @ Xs2 )
% 0.35/0.64 => ( ( finite_card_o @ ( set_o2 @ Xs2 ) )
% 0.35/0.64 = ( size_size_list_o @ Xs2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_card
% 0.35/0.64 thf(fact_6839_distinct__card,axiom,
% 0.35/0.64 ! [Xs2: list_nat] :
% 0.35/0.64 ( ( distinct_nat @ Xs2 )
% 0.35/0.64 => ( ( finite_card_nat @ ( set_nat2 @ Xs2 ) )
% 0.35/0.64 = ( size_size_list_nat @ Xs2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_card
% 0.35/0.64 thf(fact_6840_distinct__card,axiom,
% 0.35/0.64 ! [Xs2: list_int] :
% 0.35/0.64 ( ( distinct_int @ Xs2 )
% 0.35/0.64 => ( ( finite_card_int @ ( set_int2 @ Xs2 ) )
% 0.35/0.64 = ( size_size_list_int @ Xs2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_card
% 0.35/0.64 thf(fact_6841_gbinomial__Suc__Suc,axiom,
% 0.35/0.64 ! [A: complex,K2: nat] :
% 0.35/0.64 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 0.35/0.64 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K2 ) @ ( gbinomial_complex @ A @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_Suc_Suc
% 0.35/0.64 thf(fact_6842_gbinomial__Suc__Suc,axiom,
% 0.35/0.64 ! [A: real,K2: nat] :
% 0.35/0.64 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 0.35/0.64 = ( plus_plus_real @ ( gbinomial_real @ A @ K2 ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_Suc_Suc
% 0.35/0.64 thf(fact_6843_gbinomial__Suc__Suc,axiom,
% 0.35/0.64 ! [A: rat,K2: nat] :
% 0.35/0.64 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 0.35/0.64 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_Suc_Suc
% 0.35/0.64 thf(fact_6844_gbinomial__of__nat__symmetric,axiom,
% 0.35/0.64 ! [K2: nat,N: nat] :
% 0.35/0.64 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.64 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K2 )
% 0.35/0.64 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % gbinomial_of_nat_symmetric
% 0.35/0.64 thf(fact_6845_Iic__subset__Iio__iff,axiom,
% 0.35/0.64 ! [A: real,B: real] :
% 0.35/0.64 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 0.35/0.64 = ( ord_less_real @ A @ B ) ) ).
% 0.35/0.64
% 0.35/0.64 % Iic_subset_Iio_iff
% 0.35/0.64 thf(fact_6846_Iic__subset__Iio__iff,axiom,
% 0.35/0.64 ! [A: rat,B: rat] :
% 0.35/0.64 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 0.35/0.64 = ( ord_less_rat @ A @ B ) ) ).
% 0.35/0.64
% 0.35/0.64 % Iic_subset_Iio_iff
% 0.35/0.64 thf(fact_6847_Iic__subset__Iio__iff,axiom,
% 0.35/0.64 ! [A: num,B: num] :
% 0.35/0.64 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 0.35/0.64 = ( ord_less_num @ A @ B ) ) ).
% 0.35/0.64
% 0.35/0.64 % Iic_subset_Iio_iff
% 0.35/0.64 thf(fact_6848_Iic__subset__Iio__iff,axiom,
% 0.35/0.64 ! [A: int,B: int] :
% 0.35/0.64 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 0.35/0.64 = ( ord_less_int @ A @ B ) ) ).
% 0.35/0.64
% 0.35/0.64 % Iic_subset_Iio_iff
% 0.35/0.64 thf(fact_6849_Iic__subset__Iio__iff,axiom,
% 0.35/0.64 ! [A: nat,B: nat] :
% 0.35/0.64 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 0.35/0.64 = ( ord_less_nat @ A @ B ) ) ).
% 0.35/0.64
% 0.35/0.64 % Iic_subset_Iio_iff
% 0.35/0.64 thf(fact_6850_sum__choose__upper,axiom,
% 0.35/0.64 ! [M2: nat,N: nat] :
% 0.35/0.64 ( ( groups3542108847815614940at_nat
% 0.35/0.64 @ ^ [K3: nat] : ( binomial @ K3 @ M2 )
% 0.35/0.64 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.64 = ( binomial @ ( suc @ N ) @ ( suc @ M2 ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % sum_choose_upper
% 0.35/0.64 thf(fact_6851_distinct__Ex1,axiom,
% 0.35/0.64 ! [Xs2: list_complex,X: complex] :
% 0.35/0.64 ( ( distinct_complex @ Xs2 )
% 0.35/0.64 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 0.35/0.64 => ? [X3: nat] :
% 0.35/0.64 ( ( ord_less_nat @ X3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.35/0.64 & ( ( nth_complex @ Xs2 @ X3 )
% 0.35/0.64 = X )
% 0.35/0.64 & ! [Y6: nat] :
% 0.35/0.64 ( ( ( ord_less_nat @ Y6 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 0.35/0.64 & ( ( nth_complex @ Xs2 @ Y6 )
% 0.35/0.64 = X ) )
% 0.35/0.64 => ( Y6 = X3 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_Ex1
% 0.35/0.64 thf(fact_6852_distinct__Ex1,axiom,
% 0.35/0.64 ! [Xs2: list_real,X: real] :
% 0.35/0.64 ( ( distinct_real @ Xs2 )
% 0.35/0.64 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 0.35/0.64 => ? [X3: nat] :
% 0.35/0.64 ( ( ord_less_nat @ X3 @ ( size_size_list_real @ Xs2 ) )
% 0.35/0.64 & ( ( nth_real @ Xs2 @ X3 )
% 0.35/0.64 = X )
% 0.35/0.64 & ! [Y6: nat] :
% 0.35/0.64 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_real @ Xs2 ) )
% 0.35/0.64 & ( ( nth_real @ Xs2 @ Y6 )
% 0.35/0.64 = X ) )
% 0.35/0.64 => ( Y6 = X3 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_Ex1
% 0.35/0.64 thf(fact_6853_distinct__Ex1,axiom,
% 0.35/0.64 ! [Xs2: list_set_nat,X: set_nat] :
% 0.35/0.64 ( ( distinct_set_nat @ Xs2 )
% 0.35/0.64 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 0.35/0.64 => ? [X3: nat] :
% 0.35/0.64 ( ( ord_less_nat @ X3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.35/0.64 & ( ( nth_set_nat @ Xs2 @ X3 )
% 0.35/0.64 = X )
% 0.35/0.64 & ! [Y6: nat] :
% 0.35/0.64 ( ( ( ord_less_nat @ Y6 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 0.35/0.64 & ( ( nth_set_nat @ Xs2 @ Y6 )
% 0.35/0.64 = X ) )
% 0.35/0.64 => ( Y6 = X3 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_Ex1
% 0.35/0.64 thf(fact_6854_distinct__Ex1,axiom,
% 0.35/0.64 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 0.35/0.64 ( ( distinct_VEBT_VEBT @ Xs2 )
% 0.35/0.64 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 0.35/0.64 => ? [X3: nat] :
% 0.35/0.64 ( ( ord_less_nat @ X3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.64 & ( ( nth_VEBT_VEBT @ Xs2 @ X3 )
% 0.35/0.64 = X )
% 0.35/0.64 & ! [Y6: nat] :
% 0.35/0.64 ( ( ( ord_less_nat @ Y6 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.64 & ( ( nth_VEBT_VEBT @ Xs2 @ Y6 )
% 0.35/0.64 = X ) )
% 0.35/0.64 => ( Y6 = X3 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_Ex1
% 0.35/0.64 thf(fact_6855_distinct__Ex1,axiom,
% 0.35/0.64 ! [Xs2: list_o,X: $o] :
% 0.35/0.64 ( ( distinct_o @ Xs2 )
% 0.35/0.64 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 0.35/0.64 => ? [X3: nat] :
% 0.35/0.64 ( ( ord_less_nat @ X3 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.64 & ( ( nth_o @ Xs2 @ X3 )
% 0.35/0.64 = X )
% 0.35/0.64 & ! [Y6: nat] :
% 0.35/0.64 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.64 & ( ( nth_o @ Xs2 @ Y6 )
% 0.35/0.64 = X ) )
% 0.35/0.64 => ( Y6 = X3 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_Ex1
% 0.35/0.64 thf(fact_6856_distinct__Ex1,axiom,
% 0.35/0.64 ! [Xs2: list_nat,X: nat] :
% 0.35/0.64 ( ( distinct_nat @ Xs2 )
% 0.35/0.64 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 0.35/0.64 => ? [X3: nat] :
% 0.35/0.64 ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.64 & ( ( nth_nat @ Xs2 @ X3 )
% 0.35/0.64 = X )
% 0.35/0.64 & ! [Y6: nat] :
% 0.35/0.64 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.64 & ( ( nth_nat @ Xs2 @ Y6 )
% 0.35/0.64 = X ) )
% 0.35/0.64 => ( Y6 = X3 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_Ex1
% 0.35/0.64 thf(fact_6857_distinct__Ex1,axiom,
% 0.35/0.64 ! [Xs2: list_int,X: int] :
% 0.35/0.64 ( ( distinct_int @ Xs2 )
% 0.35/0.64 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 0.35/0.64 => ? [X3: nat] :
% 0.35/0.64 ( ( ord_less_nat @ X3 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.64 & ( ( nth_int @ Xs2 @ X3 )
% 0.35/0.64 = X )
% 0.35/0.64 & ! [Y6: nat] :
% 0.35/0.64 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.64 & ( ( nth_int @ Xs2 @ Y6 )
% 0.35/0.64 = X ) )
% 0.35/0.64 => ( Y6 = X3 ) ) ) ) ) ).
% 0.35/0.64
% 0.35/0.64 % distinct_Ex1
% 0.35/0.64 thf(fact_6858_gbinomial__partial__sum__poly__xpos,axiom,
% 0.35/0.65 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_partial_sum_poly_xpos
% 0.35/0.65 thf(fact_6859_gbinomial__partial__sum__poly__xpos,axiom,
% 0.35/0.65 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_partial_sum_poly_xpos
% 0.35/0.65 thf(fact_6860_gbinomial__partial__sum__poly__xpos,axiom,
% 0.35/0.65 ! [M2: nat,A: real,X: real,Y: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_partial_sum_poly_xpos
% 0.35/0.65 thf(fact_6861_gbinomial__addition__formula,axiom,
% 0.35/0.65 ! [A: complex,K2: nat] :
% 0.35/0.65 ( ( gbinomial_complex @ A @ ( suc @ K2 ) )
% 0.35/0.65 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_addition_formula
% 0.35/0.65 thf(fact_6862_gbinomial__addition__formula,axiom,
% 0.35/0.65 ! [A: real,K2: nat] :
% 0.35/0.65 ( ( gbinomial_real @ A @ ( suc @ K2 ) )
% 0.35/0.65 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K2 ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_addition_formula
% 0.35/0.65 thf(fact_6863_gbinomial__addition__formula,axiom,
% 0.35/0.65 ! [A: rat,K2: nat] :
% 0.35/0.65 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 0.35/0.65 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_addition_formula
% 0.35/0.65 thf(fact_6864_gbinomial__absorb__comp,axiom,
% 0.35/0.65 ! [A: complex,K2: nat] :
% 0.35/0.65 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( gbinomial_complex @ A @ K2 ) )
% 0.35/0.65 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorb_comp
% 0.35/0.65 thf(fact_6865_gbinomial__absorb__comp,axiom,
% 0.35/0.65 ! [A: rat,K2: nat] :
% 0.35/0.65 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( gbinomial_rat @ A @ K2 ) )
% 0.35/0.65 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorb_comp
% 0.35/0.65 thf(fact_6866_gbinomial__absorb__comp,axiom,
% 0.35/0.65 ! [A: real,K2: nat] :
% 0.35/0.65 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( gbinomial_real @ A @ K2 ) )
% 0.35/0.65 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorb_comp
% 0.35/0.65 thf(fact_6867_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.35/0.65 ! [K2: nat,A: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K2 ) @ A )
% 0.35/0.65 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_ge_n_over_k_pow_k
% 0.35/0.65 thf(fact_6868_gbinomial__ge__n__over__k__pow__k,axiom,
% 0.35/0.65 ! [K2: nat,A: rat] :
% 0.35/0.65 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A )
% 0.35/0.65 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_ge_n_over_k_pow_k
% 0.35/0.65 thf(fact_6869_gbinomial__mult__1_H,axiom,
% 0.35/0.65 ! [A: rat,K2: nat] :
% 0.35/0.65 ( ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ A )
% 0.35/0.65 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_mult_1'
% 0.35/0.65 thf(fact_6870_gbinomial__mult__1_H,axiom,
% 0.35/0.65 ! [A: real,K2: nat] :
% 0.35/0.65 ( ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ A )
% 0.35/0.65 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_mult_1'
% 0.35/0.65 thf(fact_6871_gbinomial__mult__1,axiom,
% 0.35/0.65 ! [A: rat,K2: nat] :
% 0.35/0.65 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K2 ) )
% 0.35/0.65 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_mult_1
% 0.35/0.65 thf(fact_6872_gbinomial__mult__1,axiom,
% 0.35/0.65 ! [A: real,K2: nat] :
% 0.35/0.65 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K2 ) )
% 0.35/0.65 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_mult_1
% 0.35/0.65 thf(fact_6873_sum_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > rat,N: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_Suc_shift
% 0.35/0.65 thf(fact_6874_sum_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > int,N: nat] :
% 0.35/0.65 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_Suc_shift
% 0.35/0.65 thf(fact_6875_sum_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > nat,N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_Suc_shift
% 0.35/0.65 thf(fact_6876_sum_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > real,N: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_Suc_shift
% 0.35/0.65 thf(fact_6877_sum__telescope,axiom,
% 0.35/0.65 ! [F2: nat > rat,I2: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ I2 ) )
% 0.35/0.65 = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_telescope
% 0.35/0.65 thf(fact_6878_sum__telescope,axiom,
% 0.35/0.65 ! [F2: nat > int,I2: nat] :
% 0.35/0.65 ( ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ I2 ) )
% 0.35/0.65 = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_telescope
% 0.35/0.65 thf(fact_6879_sum__telescope,axiom,
% 0.35/0.65 ! [F2: nat > real,I2: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ I2 ) )
% 0.35/0.65 = ( minus_minus_real @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_telescope
% 0.35/0.65 thf(fact_6880_polyfun__eq__coeffs,axiom,
% 0.35/0.65 ! [C2: nat > complex,N: nat,D: nat > complex] :
% 0.35/0.65 ( ( ! [X4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( D @ I ) @ ( power_power_complex @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) )
% 0.35/0.65 = ( ! [I: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ I @ N )
% 0.35/0.65 => ( ( C2 @ I )
% 0.35/0.65 = ( D @ I ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_eq_coeffs
% 0.35/0.65 thf(fact_6881_polyfun__eq__coeffs,axiom,
% 0.35/0.65 ! [C2: nat > real,N: nat,D: nat > real] :
% 0.35/0.65 ( ( ! [X4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( D @ I ) @ ( power_power_real @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) )
% 0.35/0.65 = ( ! [I: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ I @ N )
% 0.35/0.65 => ( ( C2 @ I )
% 0.35/0.65 = ( D @ I ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_eq_coeffs
% 0.35/0.65 thf(fact_6882_prod_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > real,N: nat] :
% 0.35/0.65 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups129246275422532515t_real
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_Suc_shift
% 0.35/0.65 thf(fact_6883_prod_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > rat,N: nat] :
% 0.35/0.65 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups73079841787564623at_rat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_Suc_shift
% 0.35/0.65 thf(fact_6884_prod_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > int,N: nat] :
% 0.35/0.65 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_Suc_shift
% 0.35/0.65 thf(fact_6885_prod_OatMost__Suc__shift,axiom,
% 0.35/0.65 ! [G2: nat > nat,N: nat] :
% 0.35/0.65 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 0.35/0.65 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_Suc_shift
% 0.35/0.65 thf(fact_6886_sum_Onested__swap_H,axiom,
% 0.35/0.65 ! [A: nat > nat > nat,N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [I: nat] : ( groups3542108847815614940at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [I: nat] : ( A @ I @ J )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.nested_swap'
% 0.35/0.65 thf(fact_6887_sum_Onested__swap_H,axiom,
% 0.35/0.65 ! [A: nat > nat > real,N: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( groups6591440286371151544t_real @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( A @ I @ J )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.nested_swap'
% 0.35/0.65 thf(fact_6888_ivl__disj__un__one_I4_J,axiom,
% 0.35/0.65 ! [L: rat,U: rat] :
% 0.35/0.65 ( ( ord_less_eq_rat @ L @ U )
% 0.35/0.65 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 0.35/0.65 = ( set_ord_atMost_rat @ U ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_one(4)
% 0.35/0.65 thf(fact_6889_ivl__disj__un__one_I4_J,axiom,
% 0.35/0.65 ! [L: num,U: num] :
% 0.35/0.65 ( ( ord_less_eq_num @ L @ U )
% 0.35/0.65 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or7049704709247886629st_num @ L @ U ) )
% 0.35/0.65 = ( set_ord_atMost_num @ U ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_one(4)
% 0.35/0.65 thf(fact_6890_ivl__disj__un__one_I4_J,axiom,
% 0.35/0.65 ! [L: nat,U: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ L @ U )
% 0.35/0.65 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 0.35/0.65 = ( set_ord_atMost_nat @ U ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_one(4)
% 0.35/0.65 thf(fact_6891_ivl__disj__un__one_I4_J,axiom,
% 0.35/0.65 ! [L: int,U: int] :
% 0.35/0.65 ( ( ord_less_eq_int @ L @ U )
% 0.35/0.65 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.35/0.65 = ( set_ord_atMost_int @ U ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_one(4)
% 0.35/0.65 thf(fact_6892_ivl__disj__un__one_I4_J,axiom,
% 0.35/0.65 ! [L: real,U: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ L @ U )
% 0.35/0.65 => ( ( sup_sup_set_real @ ( set_or5984915006950818249n_real @ L ) @ ( set_or1222579329274155063t_real @ L @ U ) )
% 0.35/0.65 = ( set_ord_atMost_real @ U ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_one(4)
% 0.35/0.65 thf(fact_6893_ivl__disj__un__singleton_I2_J,axiom,
% 0.35/0.65 ! [U: int] :
% 0.35/0.65 ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 0.35/0.65 = ( set_ord_atMost_int @ U ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_singleton(2)
% 0.35/0.65 thf(fact_6894_ivl__disj__un__singleton_I2_J,axiom,
% 0.35/0.65 ! [U: real] :
% 0.35/0.65 ( ( sup_sup_set_real @ ( set_or5984915006950818249n_real @ U ) @ ( insert_real @ U @ bot_bot_set_real ) )
% 0.35/0.65 = ( set_ord_atMost_real @ U ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_singleton(2)
% 0.35/0.65 thf(fact_6895_ivl__disj__un__singleton_I2_J,axiom,
% 0.35/0.65 ! [U: nat] :
% 0.35/0.65 ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 0.35/0.65 = ( set_ord_atMost_nat @ U ) ) ).
% 0.35/0.65
% 0.35/0.65 % ivl_disj_un_singleton(2)
% 0.35/0.65 thf(fact_6896_prod_Onested__swap_H,axiom,
% 0.35/0.65 ! [A: nat > nat > int,N: nat] :
% 0.35/0.65 ( ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [I: nat] : ( groups705719431365010083at_int @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [I: nat] : ( A @ I @ J )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.nested_swap'
% 0.35/0.65 thf(fact_6897_prod_Onested__swap_H,axiom,
% 0.35/0.65 ! [A: nat > nat > nat,N: nat] :
% 0.35/0.65 ( ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [I: nat] : ( groups708209901874060359at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [I: nat] : ( A @ I @ J )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.nested_swap'
% 0.35/0.65 thf(fact_6898_sum__choose__lower,axiom,
% 0.35/0.65 ! [R3: nat,N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K3 ) @ K3 )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N ) ) @ N ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_choose_lower
% 0.35/0.65 thf(fact_6899_Suc__times__gbinomial,axiom,
% 0.35/0.65 ! [K2: nat,A: complex] :
% 0.35/0.65 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) ) )
% 0.35/0.65 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % Suc_times_gbinomial
% 0.35/0.65 thf(fact_6900_Suc__times__gbinomial,axiom,
% 0.35/0.65 ! [K2: nat,A: rat] :
% 0.35/0.65 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) )
% 0.35/0.65 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % Suc_times_gbinomial
% 0.35/0.65 thf(fact_6901_Suc__times__gbinomial,axiom,
% 0.35/0.65 ! [K2: nat,A: real] :
% 0.35/0.65 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) ) )
% 0.35/0.65 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % Suc_times_gbinomial
% 0.35/0.65 thf(fact_6902_gbinomial__absorption,axiom,
% 0.35/0.65 ! [K2: nat,A: complex] :
% 0.35/0.65 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) @ ( gbinomial_complex @ A @ ( suc @ K2 ) ) )
% 0.35/0.65 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorption
% 0.35/0.65 thf(fact_6903_gbinomial__absorption,axiom,
% 0.35/0.65 ! [K2: nat,A: rat] :
% 0.35/0.65 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) )
% 0.35/0.65 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorption
% 0.35/0.65 thf(fact_6904_gbinomial__absorption,axiom,
% 0.35/0.65 ! [K2: nat,A: real] :
% 0.35/0.65 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) )
% 0.35/0.65 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorption
% 0.35/0.65 thf(fact_6905_gbinomial__trinomial__revision,axiom,
% 0.35/0.65 ! [K2: nat,M2: nat,A: rat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.35/0.65 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M2 ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M2 ) @ K2 ) )
% 0.35/0.65 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_trinomial_revision
% 0.35/0.65 thf(fact_6906_gbinomial__trinomial__revision,axiom,
% 0.35/0.65 ! [K2: nat,M2: nat,A: real] :
% 0.35/0.65 ( ( ord_less_eq_nat @ K2 @ M2 )
% 0.35/0.65 => ( ( times_times_real @ ( gbinomial_real @ A @ M2 ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M2 ) @ K2 ) )
% 0.35/0.65 = ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_trinomial_revision
% 0.35/0.65 thf(fact_6907_zero__polynom__imp__zero__coeffs,axiom,
% 0.35/0.65 ! [C2: nat > complex,N: nat,K2: nat] :
% 0.35/0.65 ( ! [W: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ W @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( ( C2 @ K2 )
% 0.35/0.65 = zero_zero_complex ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % zero_polynom_imp_zero_coeffs
% 0.35/0.65 thf(fact_6908_zero__polynom__imp__zero__coeffs,axiom,
% 0.35/0.65 ! [C2: nat > real,N: nat,K2: nat] :
% 0.35/0.65 ( ! [W: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ W @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( ( C2 @ K2 )
% 0.35/0.65 = zero_zero_real ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % zero_polynom_imp_zero_coeffs
% 0.35/0.65 thf(fact_6909_polyfun__eq__0,axiom,
% 0.35/0.65 ! [C2: nat > complex,N: nat] :
% 0.35/0.65 ( ( ! [X4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex ) )
% 0.35/0.65 = ( ! [I: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ I @ N )
% 0.35/0.65 => ( ( C2 @ I )
% 0.35/0.65 = zero_zero_complex ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_eq_0
% 0.35/0.65 thf(fact_6910_polyfun__eq__0,axiom,
% 0.35/0.65 ! [C2: nat > real,N: nat] :
% 0.35/0.65 ( ( ! [X4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real ) )
% 0.35/0.65 = ( ! [I: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ I @ N )
% 0.35/0.65 => ( ( C2 @ I )
% 0.35/0.65 = zero_zero_real ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_eq_0
% 0.35/0.65 thf(fact_6911_sum_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > rat,N: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_shift
% 0.35/0.65 thf(fact_6912_sum_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > int,N: nat] :
% 0.35/0.65 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_shift
% 0.35/0.65 thf(fact_6913_sum_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > nat,N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_shift
% 0.35/0.65 thf(fact_6914_sum_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > real,N: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.atMost_shift
% 0.35/0.65 thf(fact_6915_sum__up__index__split,axiom,
% 0.35/0.65 ! [F2: nat > rat,M2: nat,N: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.65 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_up_index_split
% 0.35/0.65 thf(fact_6916_sum__up__index__split,axiom,
% 0.35/0.65 ! [F2: nat > int,M2: nat,N: nat] :
% 0.35/0.65 ( ( groups3539618377306564664at_int @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.65 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_up_index_split
% 0.35/0.65 thf(fact_6917_sum__up__index__split,axiom,
% 0.35/0.65 ! [F2: nat > nat,M2: nat,N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.65 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_up_index_split
% 0.35/0.65 thf(fact_6918_sum__up__index__split,axiom,
% 0.35/0.65 ! [F2: nat > real,M2: nat,N: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 0.35/0.65 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_up_index_split
% 0.35/0.65 thf(fact_6919_prod_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > real,N: nat] :
% 0.35/0.65 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups129246275422532515t_real
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_shift
% 0.35/0.65 thf(fact_6920_prod_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > rat,N: nat] :
% 0.35/0.65 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups73079841787564623at_rat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_shift
% 0.35/0.65 thf(fact_6921_prod_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > int,N: nat] :
% 0.35/0.65 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_shift
% 0.35/0.65 thf(fact_6922_prod_OatMost__shift,axiom,
% 0.35/0.65 ! [G2: nat > nat,N: nat] :
% 0.35/0.65 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 0.35/0.65 @ ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.atMost_shift
% 0.35/0.65 thf(fact_6923_gbinomial__r__part__sum,axiom,
% 0.35/0.65 ! [M2: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_r_part_sum
% 0.35/0.65 thf(fact_6924_gbinomial__r__part__sum,axiom,
% 0.35/0.65 ! [M2: nat] :
% 0.35/0.65 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_r_part_sum
% 0.35/0.65 thf(fact_6925_gbinomial__r__part__sum,axiom,
% 0.35/0.65 ! [M2: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_r_part_sum
% 0.35/0.65 thf(fact_6926_sum__choose__diagonal,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.65 => ( ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M2 @ K3 ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( binomial @ ( suc @ N ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_choose_diagonal
% 0.35/0.65 thf(fact_6927_vandermonde,axiom,
% 0.35/0.65 ! [M2: nat,N: nat,R3: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M2 @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R3 @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ R3 ) )
% 0.35/0.65 = ( binomial @ ( plus_plus_nat @ M2 @ N ) @ R3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % vandermonde
% 0.35/0.65 thf(fact_6928_bits__induct,axiom,
% 0.35/0.65 ! [P2: nat > $o,A: nat] :
% 0.35/0.65 ( ! [A3: nat] :
% 0.35/0.65 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65 = A3 )
% 0.35/0.65 => ( P2 @ A3 ) )
% 0.35/0.65 => ( ! [A3: nat,B3: $o] :
% 0.35/0.65 ( ( P2 @ A3 )
% 0.35/0.65 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65 = A3 )
% 0.35/0.65 => ( P2 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 0.35/0.65 => ( P2 @ A ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % bits_induct
% 0.35/0.65 thf(fact_6929_bits__induct,axiom,
% 0.35/0.65 ! [P2: int > $o,A: int] :
% 0.35/0.65 ( ! [A3: int] :
% 0.35/0.65 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.65 = A3 )
% 0.35/0.65 => ( P2 @ A3 ) )
% 0.35/0.65 => ( ! [A3: int,B3: $o] :
% 0.35/0.65 ( ( P2 @ A3 )
% 0.35/0.65 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.65 = A3 )
% 0.35/0.65 => ( P2 @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 0.35/0.65 => ( P2 @ A ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % bits_induct
% 0.35/0.65 thf(fact_6930_bits__induct,axiom,
% 0.35/0.65 ! [P2: code_integer > $o,A: code_integer] :
% 0.35/0.65 ( ! [A3: code_integer] :
% 0.35/0.65 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.65 = A3 )
% 0.35/0.65 => ( P2 @ A3 ) )
% 0.35/0.65 => ( ! [A3: code_integer,B3: $o] :
% 0.35/0.65 ( ( P2 @ A3 )
% 0.35/0.65 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 0.35/0.65 = A3 )
% 0.35/0.65 => ( P2 @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 0.35/0.65 => ( P2 @ A ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % bits_induct
% 0.35/0.65 thf(fact_6931_gbinomial__partial__row__sum,axiom,
% 0.35/0.65 ! [A: complex,M2: nat] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_partial_row_sum
% 0.35/0.65 thf(fact_6932_gbinomial__partial__row__sum,axiom,
% 0.35/0.65 ! [A: rat,M2: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_partial_row_sum
% 0.35/0.65 thf(fact_6933_gbinomial__partial__row__sum,axiom,
% 0.35/0.65 ! [A: real,M2: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_partial_row_sum
% 0.35/0.65 thf(fact_6934_gbinomial__factors,axiom,
% 0.35/0.65 ! [A: complex,K2: nat] :
% 0.35/0.65 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 0.35/0.65 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) ) @ ( gbinomial_complex @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_factors
% 0.35/0.65 thf(fact_6935_gbinomial__factors,axiom,
% 0.35/0.65 ! [A: rat,K2: nat] :
% 0.35/0.65 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 0.35/0.65 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_factors
% 0.35/0.65 thf(fact_6936_gbinomial__factors,axiom,
% 0.35/0.65 ! [A: real,K2: nat] :
% 0.35/0.65 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 0.35/0.65 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_factors
% 0.35/0.65 thf(fact_6937_gbinomial__rec,axiom,
% 0.35/0.65 ! [A: complex,K2: nat] :
% 0.35/0.65 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 0.35/0.65 = ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_rec
% 0.35/0.65 thf(fact_6938_gbinomial__rec,axiom,
% 0.35/0.65 ! [A: rat,K2: nat] :
% 0.35/0.65 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 0.35/0.65 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_rec
% 0.35/0.65 thf(fact_6939_gbinomial__rec,axiom,
% 0.35/0.65 ! [A: real,K2: nat] :
% 0.35/0.65 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 0.35/0.65 = ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_rec
% 0.35/0.65 thf(fact_6940_sum__gp__basic,axiom,
% 0.35/0.65 ! [X: code_integer,N: nat] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp_basic
% 0.35/0.65 thf(fact_6941_sum__gp__basic,axiom,
% 0.35/0.65 ! [X: complex,N: nat] :
% 0.35/0.65 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp_basic
% 0.35/0.65 thf(fact_6942_sum__gp__basic,axiom,
% 0.35/0.65 ! [X: rat,N: nat] :
% 0.35/0.65 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp_basic
% 0.35/0.65 thf(fact_6943_sum__gp__basic,axiom,
% 0.35/0.65 ! [X: int,N: nat] :
% 0.35/0.65 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp_basic
% 0.35/0.65 thf(fact_6944_sum__gp__basic,axiom,
% 0.35/0.65 ! [X: real,N: nat] :
% 0.35/0.65 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp_basic
% 0.35/0.65 thf(fact_6945_polyfun__finite__roots,axiom,
% 0.35/0.65 ! [C2: nat > complex,N: nat] :
% 0.35/0.65 ( ( finite3207457112153483333omplex
% 0.35/0.65 @ ( collect_complex
% 0.35/0.65 @ ^ [X4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex ) ) )
% 0.35/0.65 = ( ? [I: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ I @ N )
% 0.35/0.65 & ( ( C2 @ I )
% 0.35/0.65 != zero_zero_complex ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_finite_roots
% 0.35/0.65 thf(fact_6946_polyfun__finite__roots,axiom,
% 0.35/0.65 ! [C2: nat > real,N: nat] :
% 0.35/0.65 ( ( finite_finite_real
% 0.35/0.65 @ ( collect_real
% 0.35/0.65 @ ^ [X4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real ) ) )
% 0.35/0.65 = ( ? [I: nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ I @ N )
% 0.35/0.65 & ( ( C2 @ I )
% 0.35/0.65 != zero_zero_real ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_finite_roots
% 0.35/0.65 thf(fact_6947_polyfun__roots__finite,axiom,
% 0.35/0.65 ! [C2: nat > complex,K2: nat,N: nat] :
% 0.35/0.65 ( ( ( C2 @ K2 )
% 0.35/0.65 != zero_zero_complex )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( finite3207457112153483333omplex
% 0.35/0.65 @ ( collect_complex
% 0.35/0.65 @ ^ [Z4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_roots_finite
% 0.35/0.65 thf(fact_6948_polyfun__roots__finite,axiom,
% 0.35/0.65 ! [C2: nat > real,K2: nat,N: nat] :
% 0.35/0.65 ( ( ( C2 @ K2 )
% 0.35/0.65 != zero_zero_real )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( finite_finite_real
% 0.35/0.65 @ ( collect_real
% 0.35/0.65 @ ^ [Z4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_roots_finite
% 0.35/0.65 thf(fact_6949_polyfun__roots__card,axiom,
% 0.35/0.65 ! [C2: nat > complex,K2: nat,N: nat] :
% 0.35/0.65 ( ( ( C2 @ K2 )
% 0.35/0.65 != zero_zero_complex )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( ord_less_eq_nat
% 0.35/0.65 @ ( finite_card_complex
% 0.35/0.65 @ ( collect_complex
% 0.35/0.65 @ ^ [Z4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex ) ) )
% 0.35/0.65 @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_roots_card
% 0.35/0.65 thf(fact_6950_polyfun__roots__card,axiom,
% 0.35/0.65 ! [C2: nat > real,K2: nat,N: nat] :
% 0.35/0.65 ( ( ( C2 @ K2 )
% 0.35/0.65 != zero_zero_real )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( ord_less_eq_nat
% 0.35/0.65 @ ( finite_card_real
% 0.35/0.65 @ ( collect_real
% 0.35/0.65 @ ^ [Z4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real ) ) )
% 0.35/0.65 @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_roots_card
% 0.35/0.65 thf(fact_6951_polyfun__linear__factor__root,axiom,
% 0.35/0.65 ! [C2: nat > complex,A: complex,N: nat] :
% 0.35/0.65 ( ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex )
% 0.35/0.65 => ~ ! [B3: nat > complex] :
% 0.35/0.65 ~ ! [Z5: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( B3 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor_root
% 0.35/0.65 thf(fact_6952_polyfun__linear__factor__root,axiom,
% 0.35/0.65 ! [C2: nat > rat,A: rat,N: nat] :
% 0.35/0.65 ( ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_rat )
% 0.35/0.65 => ~ ! [B3: nat > rat] :
% 0.35/0.65 ~ ! [Z5: rat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( B3 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor_root
% 0.35/0.65 thf(fact_6953_polyfun__linear__factor__root,axiom,
% 0.35/0.65 ! [C2: nat > int,A: int,N: nat] :
% 0.35/0.65 ( ( ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_int )
% 0.35/0.65 => ~ ! [B3: nat > int] :
% 0.35/0.65 ~ ! [Z5: int] :
% 0.35/0.65 ( ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( B3 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor_root
% 0.35/0.65 thf(fact_6954_polyfun__linear__factor__root,axiom,
% 0.35/0.65 ! [C2: nat > real,A: real,N: nat] :
% 0.35/0.65 ( ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real )
% 0.35/0.65 => ~ ! [B3: nat > real] :
% 0.35/0.65 ~ ! [Z5: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( B3 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor_root
% 0.35/0.65 thf(fact_6955_polyfun__linear__factor,axiom,
% 0.35/0.65 ! [C2: nat > complex,N: nat,A: complex] :
% 0.35/0.65 ? [B3: nat > complex] :
% 0.35/0.65 ! [Z5: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_complex
% 0.35/0.65 @ ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( B3 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor
% 0.35/0.65 thf(fact_6956_polyfun__linear__factor,axiom,
% 0.35/0.65 ! [C2: nat > rat,N: nat,A: rat] :
% 0.35/0.65 ? [B3: nat > rat] :
% 0.35/0.65 ! [Z5: rat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_rat
% 0.35/0.65 @ ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( B3 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor
% 0.35/0.65 thf(fact_6957_polyfun__linear__factor,axiom,
% 0.35/0.65 ! [C2: nat > int,N: nat,A: int] :
% 0.35/0.65 ? [B3: nat > int] :
% 0.35/0.65 ! [Z5: int] :
% 0.35/0.65 ( ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_int
% 0.35/0.65 @ ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( B3 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor
% 0.35/0.65 thf(fact_6958_polyfun__linear__factor,axiom,
% 0.35/0.65 ! [C2: nat > real,N: nat,A: real] :
% 0.35/0.65 ? [B3: nat > real] :
% 0.35/0.65 ! [Z5: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( plus_plus_real
% 0.35/0.65 @ ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( B3 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ A @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_linear_factor
% 0.35/0.65 thf(fact_6959_sum__power__shift,axiom,
% 0.35/0.65 ! [M2: nat,N: nat,X: complex] :
% 0.35/0.65 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.65 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.65 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_power_shift
% 0.35/0.65 thf(fact_6960_sum__power__shift,axiom,
% 0.35/0.65 ! [M2: nat,N: nat,X: rat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.65 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.65 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_power_shift
% 0.35/0.65 thf(fact_6961_sum__power__shift,axiom,
% 0.35/0.65 ! [M2: nat,N: nat,X: int] :
% 0.35/0.65 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.65 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.65 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_power_shift
% 0.35/0.65 thf(fact_6962_sum__power__shift,axiom,
% 0.35/0.65 ! [M2: nat,N: nat,X: real] :
% 0.35/0.65 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.65 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 0.35/0.65 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_power_shift
% 0.35/0.65 thf(fact_6963_binomial,axiom,
% 0.35/0.65 ! [A: nat,B: nat,N: nat] :
% 0.35/0.65 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.35/0.65 = ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % binomial
% 0.35/0.65 thf(fact_6964_atLeast1__atMost__eq__remove0,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.65 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % atLeast1_atMost_eq_remove0
% 0.35/0.65 thf(fact_6965_exp__mod__exp,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M2 @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % exp_mod_exp
% 0.35/0.65 thf(fact_6966_exp__mod__exp,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % exp_mod_exp
% 0.35/0.65 thf(fact_6967_exp__mod__exp,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % exp_mod_exp
% 0.35/0.65 thf(fact_6968_exp__mod__exp,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M2 @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % exp_mod_exp
% 0.35/0.65 thf(fact_6969_gbinomial__reduce__nat,axiom,
% 0.35/0.65 ! [K2: nat,A: complex] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.65 => ( ( gbinomial_complex @ A @ K2 )
% 0.35/0.65 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_reduce_nat
% 0.35/0.65 thf(fact_6970_gbinomial__reduce__nat,axiom,
% 0.35/0.65 ! [K2: nat,A: real] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.65 => ( ( gbinomial_real @ A @ K2 )
% 0.35/0.65 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_reduce_nat
% 0.35/0.65 thf(fact_6971_gbinomial__reduce__nat,axiom,
% 0.35/0.65 ! [K2: nat,A: rat] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.65 => ( ( gbinomial_rat @ A @ K2 )
% 0.35/0.65 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_reduce_nat
% 0.35/0.65 thf(fact_6972_sum_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > rat,N: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.in_pairs_0
% 0.35/0.65 thf(fact_6973_sum_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > int,N: nat] :
% 0.35/0.65 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.in_pairs_0
% 0.35/0.65 thf(fact_6974_sum_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > nat,N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [I: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.in_pairs_0
% 0.35/0.65 thf(fact_6975_sum_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > real,N: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( plus_plus_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.in_pairs_0
% 0.35/0.65 thf(fact_6976_polyfun__rootbound,axiom,
% 0.35/0.65 ! [C2: nat > complex,K2: nat,N: nat] :
% 0.35/0.65 ( ( ( C2 @ K2 )
% 0.35/0.65 != zero_zero_complex )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( ( finite3207457112153483333omplex
% 0.35/0.65 @ ( collect_complex
% 0.35/0.65 @ ^ [Z4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex ) ) )
% 0.35/0.65 & ( ord_less_eq_nat
% 0.35/0.65 @ ( finite_card_complex
% 0.35/0.65 @ ( collect_complex
% 0.35/0.65 @ ^ [Z4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex ) ) )
% 0.35/0.65 @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_rootbound
% 0.35/0.65 thf(fact_6977_polyfun__rootbound,axiom,
% 0.35/0.65 ! [C2: nat > real,K2: nat,N: nat] :
% 0.35/0.65 ( ( ( C2 @ K2 )
% 0.35/0.65 != zero_zero_real )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.65 => ( ( finite_finite_real
% 0.35/0.65 @ ( collect_real
% 0.35/0.65 @ ^ [Z4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real ) ) )
% 0.35/0.65 & ( ord_less_eq_nat
% 0.35/0.65 @ ( finite_card_real
% 0.35/0.65 @ ( collect_real
% 0.35/0.65 @ ^ [Z4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real ) ) )
% 0.35/0.65 @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_rootbound
% 0.35/0.65 thf(fact_6978_polynomial__product,axiom,
% 0.35/0.65 ! [M2: nat,A: nat > complex,N: nat,B: nat > complex,X: complex] :
% 0.35/0.65 ( ! [I3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ M2 @ I3 )
% 0.35/0.65 => ( ( A @ I3 )
% 0.35/0.65 = zero_zero_complex ) )
% 0.35/0.65 => ( ! [J3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ N @ J3 )
% 0.35/0.65 => ( ( B @ J3 )
% 0.35/0.65 = zero_zero_complex ) )
% 0.35/0.65 => ( ( times_times_complex
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [J: nat] : ( times_times_complex @ ( B @ J ) @ ( power_power_complex @ X @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [R: nat] :
% 0.35/0.65 ( times_times_complex
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ R ) )
% 0.35/0.65 @ ( power_power_complex @ X @ R ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polynomial_product
% 0.35/0.65 thf(fact_6979_polynomial__product,axiom,
% 0.35/0.65 ! [M2: nat,A: nat > rat,N: nat,B: nat > rat,X: rat] :
% 0.35/0.65 ( ! [I3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ M2 @ I3 )
% 0.35/0.65 => ( ( A @ I3 )
% 0.35/0.65 = zero_zero_rat ) )
% 0.35/0.65 => ( ! [J3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ N @ J3 )
% 0.35/0.65 => ( ( B @ J3 )
% 0.35/0.65 = zero_zero_rat ) )
% 0.35/0.65 => ( ( times_times_rat
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [J: nat] : ( times_times_rat @ ( B @ J ) @ ( power_power_rat @ X @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [R: nat] :
% 0.35/0.65 ( times_times_rat
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ R ) )
% 0.35/0.65 @ ( power_power_rat @ X @ R ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polynomial_product
% 0.35/0.65 thf(fact_6980_polynomial__product,axiom,
% 0.35/0.65 ! [M2: nat,A: nat > int,N: nat,B: nat > int,X: int] :
% 0.35/0.65 ( ! [I3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ M2 @ I3 )
% 0.35/0.65 => ( ( A @ I3 )
% 0.35/0.65 = zero_zero_int ) )
% 0.35/0.65 => ( ! [J3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ N @ J3 )
% 0.35/0.65 => ( ( B @ J3 )
% 0.35/0.65 = zero_zero_int ) )
% 0.35/0.65 => ( ( times_times_int
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [J: nat] : ( times_times_int @ ( B @ J ) @ ( power_power_int @ X @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [R: nat] :
% 0.35/0.65 ( times_times_int
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ R ) )
% 0.35/0.65 @ ( power_power_int @ X @ R ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polynomial_product
% 0.35/0.65 thf(fact_6981_polynomial__product,axiom,
% 0.35/0.65 ! [M2: nat,A: nat > real,N: nat,B: nat > real,X: real] :
% 0.35/0.65 ( ! [I3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ M2 @ I3 )
% 0.35/0.65 => ( ( A @ I3 )
% 0.35/0.65 = zero_zero_real ) )
% 0.35/0.65 => ( ! [J3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ N @ J3 )
% 0.35/0.65 => ( ( B @ J3 )
% 0.35/0.65 = zero_zero_real ) )
% 0.35/0.65 => ( ( times_times_real
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [J: nat] : ( times_times_real @ ( B @ J ) @ ( power_power_real @ X @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [R: nat] :
% 0.35/0.65 ( times_times_real
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ R ) )
% 0.35/0.65 @ ( power_power_real @ X @ R ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polynomial_product
% 0.35/0.65 thf(fact_6982_prod_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > real,N: nat] :
% 0.35/0.65 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups129246275422532515t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.in_pairs_0
% 0.35/0.65 thf(fact_6983_prod_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > rat,N: nat] :
% 0.35/0.65 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups73079841787564623at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.in_pairs_0
% 0.35/0.65 thf(fact_6984_prod_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > int,N: nat] :
% 0.35/0.65 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.in_pairs_0
% 0.35/0.65 thf(fact_6985_prod_Oin__pairs__0,axiom,
% 0.35/0.65 ! [G2: nat > nat,N: nat] :
% 0.35/0.65 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.in_pairs_0
% 0.35/0.65 thf(fact_6986_polyfun__eq__const,axiom,
% 0.35/0.65 ! [C2: nat > complex,N: nat,K2: complex] :
% 0.35/0.65 ( ( ! [X4: complex] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = K2 ) )
% 0.35/0.65 = ( ( ( C2 @ zero_zero_nat )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ! [X4: nat] :
% 0.35/0.65 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 0.35/0.65 => ( ( C2 @ X4 )
% 0.35/0.65 = zero_zero_complex ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_eq_const
% 0.35/0.65 thf(fact_6987_polyfun__eq__const,axiom,
% 0.35/0.65 ! [C2: nat > real,N: nat,K2: real] :
% 0.35/0.65 ( ( ! [X4: real] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = K2 ) )
% 0.35/0.65 = ( ( ( C2 @ zero_zero_nat )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ! [X4: nat] :
% 0.35/0.65 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 0.35/0.65 => ( ( C2 @ X4 )
% 0.35/0.65 = zero_zero_real ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_eq_const
% 0.35/0.65 thf(fact_6988_binomial__ring,axiom,
% 0.35/0.65 ! [A: complex,B: complex,N: nat] :
% 0.35/0.65 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 0.35/0.65 = ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % binomial_ring
% 0.35/0.65 thf(fact_6989_binomial__ring,axiom,
% 0.35/0.65 ! [A: rat,B: rat,N: nat] :
% 0.35/0.65 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 0.35/0.65 = ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % binomial_ring
% 0.35/0.65 thf(fact_6990_binomial__ring,axiom,
% 0.35/0.65 ! [A: int,B: int,N: nat] :
% 0.35/0.65 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 0.35/0.65 = ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % binomial_ring
% 0.35/0.65 thf(fact_6991_binomial__ring,axiom,
% 0.35/0.65 ! [A: nat,B: nat,N: nat] :
% 0.35/0.65 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 0.35/0.65 = ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % binomial_ring
% 0.35/0.65 thf(fact_6992_binomial__ring,axiom,
% 0.35/0.65 ! [A: real,B: real,N: nat] :
% 0.35/0.65 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % binomial_ring
% 0.35/0.65 thf(fact_6993_pochhammer__binomial__sum,axiom,
% 0.35/0.65 ! [A: rat,B: rat,N: nat] :
% 0.35/0.65 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 0.35/0.65 = ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % pochhammer_binomial_sum
% 0.35/0.65 thf(fact_6994_pochhammer__binomial__sum,axiom,
% 0.35/0.65 ! [A: int,B: int,N: nat] :
% 0.35/0.65 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 0.35/0.65 = ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % pochhammer_binomial_sum
% 0.35/0.65 thf(fact_6995_pochhammer__binomial__sum,axiom,
% 0.35/0.65 ! [A: real,B: real,N: nat] :
% 0.35/0.65 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % pochhammer_binomial_sum
% 0.35/0.65 thf(fact_6996_polynomial__product__nat,axiom,
% 0.35/0.65 ! [M2: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 0.35/0.65 ( ! [I3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ M2 @ I3 )
% 0.35/0.65 => ( ( A @ I3 )
% 0.35/0.65 = zero_zero_nat ) )
% 0.35/0.65 => ( ! [J3: nat] :
% 0.35/0.65 ( ( ord_less_nat @ N @ J3 )
% 0.35/0.65 => ( ( B @ J3 )
% 0.35/0.65 = zero_zero_nat ) )
% 0.35/0.65 => ( ( times_times_nat
% 0.35/0.65 @ ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_nat @ ( A @ I ) @ ( power_power_nat @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 @ ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [J: nat] : ( times_times_nat @ ( B @ J ) @ ( power_power_nat @ X @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [R: nat] :
% 0.35/0.65 ( times_times_nat
% 0.35/0.65 @ ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ R ) )
% 0.35/0.65 @ ( power_power_nat @ X @ R ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polynomial_product_nat
% 0.35/0.65 thf(fact_6997_choose__square__sum,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 0.35/0.65
% 0.35/0.65 % choose_square_sum
% 0.35/0.65 thf(fact_6998_set__update__distinct,axiom,
% 0.35/0.65 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 0.35/0.65 ( ( distinct_VEBT_VEBT @ Xs2 )
% 0.35/0.65 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 0.35/0.65 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) )
% 0.35/0.65 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_update_distinct
% 0.35/0.65 thf(fact_6999_set__update__distinct,axiom,
% 0.35/0.65 ! [Xs2: list_o,N: nat,X: $o] :
% 0.35/0.65 ( ( distinct_o @ Xs2 )
% 0.35/0.65 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 0.35/0.65 => ( ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) )
% 0.35/0.65 = ( insert_o @ X @ ( minus_minus_set_o @ ( set_o2 @ Xs2 ) @ ( insert_o @ ( nth_o @ Xs2 @ N ) @ bot_bot_set_o ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_update_distinct
% 0.35/0.65 thf(fact_7000_set__update__distinct,axiom,
% 0.35/0.65 ! [Xs2: list_int,N: nat,X: int] :
% 0.35/0.65 ( ( distinct_int @ Xs2 )
% 0.35/0.65 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 0.35/0.65 => ( ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) )
% 0.35/0.65 = ( insert_int @ X @ ( minus_minus_set_int @ ( set_int2 @ Xs2 ) @ ( insert_int @ ( nth_int @ Xs2 @ N ) @ bot_bot_set_int ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_update_distinct
% 0.35/0.65 thf(fact_7001_set__update__distinct,axiom,
% 0.35/0.65 ! [Xs2: list_real,N: nat,X: real] :
% 0.35/0.65 ( ( distinct_real @ Xs2 )
% 0.35/0.65 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 0.35/0.65 => ( ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) )
% 0.35/0.65 = ( insert_real @ X @ ( minus_minus_set_real @ ( set_real2 @ Xs2 ) @ ( insert_real @ ( nth_real @ Xs2 @ N ) @ bot_bot_set_real ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_update_distinct
% 0.35/0.65 thf(fact_7002_set__update__distinct,axiom,
% 0.35/0.65 ! [Xs2: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 0.35/0.65 ( ( distin6923225563576452346at_nat @ Xs2 )
% 0.35/0.65 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 0.35/0.65 => ( ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X ) )
% 0.35/0.65 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ ( insert8211810215607154385at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_update_distinct
% 0.35/0.65 thf(fact_7003_set__update__distinct,axiom,
% 0.35/0.65 ! [Xs2: list_nat,N: nat,X: nat] :
% 0.35/0.65 ( ( distinct_nat @ Xs2 )
% 0.35/0.65 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 0.35/0.65 => ( ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) )
% 0.35/0.65 = ( insert_nat @ X @ ( minus_minus_set_nat @ ( set_nat2 @ Xs2 ) @ ( insert_nat @ ( nth_nat @ Xs2 @ N ) @ bot_bot_set_nat ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_update_distinct
% 0.35/0.65 thf(fact_7004_sum_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > complex,H: nat > complex] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_complex @ ( J = K2 ) @ zero_zero_complex @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.zero_middle
% 0.35/0.65 thf(fact_7005_sum_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > rat,H: nat > rat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_rat @ ( J = K2 ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.zero_middle
% 0.35/0.65 thf(fact_7006_sum_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > int,H: nat > int] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_int @ ( J = K2 ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.zero_middle
% 0.35/0.65 thf(fact_7007_sum_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > nat,H: nat > nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_nat @ ( J = K2 ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.zero_middle
% 0.35/0.65 thf(fact_7008_sum_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > real,H: nat > real] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_real @ ( J = K2 ) @ zero_zero_real @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum.zero_middle
% 0.35/0.65 thf(fact_7009_prod_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > code_integer,H: nat > code_integer] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups3455450783089532116nteger
% 0.35/0.65 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_Code_integer @ ( J = K2 ) @ one_one_Code_integer @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups3455450783089532116nteger
% 0.35/0.65 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.zero_middle
% 0.35/0.65 thf(fact_7010_prod_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > complex,H: nat > complex] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups6464643781859351333omplex
% 0.35/0.65 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_complex @ ( J = K2 ) @ one_one_complex @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups6464643781859351333omplex
% 0.35/0.65 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.zero_middle
% 0.35/0.65 thf(fact_7011_prod_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > real,H: nat > real] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups129246275422532515t_real
% 0.35/0.65 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_real @ ( J = K2 ) @ one_one_real @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups129246275422532515t_real
% 0.35/0.65 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.zero_middle
% 0.35/0.65 thf(fact_7012_prod_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > int,H: nat > int] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_int @ ( J = K2 ) @ one_one_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups705719431365010083at_int
% 0.35/0.65 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.zero_middle
% 0.35/0.65 thf(fact_7013_prod_Ozero__middle,axiom,
% 0.35/0.65 ! [P: nat,K2: nat,G2: nat > nat,H: nat > nat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 0.35/0.65 => ( ( ord_less_eq_nat @ K2 @ P )
% 0.35/0.65 => ( ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_nat @ ( J = K2 ) @ one_one_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ P ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % prod.zero_middle
% 0.35/0.65 thf(fact_7014_gbinomial__sum__up__index,axiom,
% 0.35/0.65 ! [K2: nat,N: nat] :
% 0.35/0.65 ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [J: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J ) @ K2 )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.65 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_sum_up_index
% 0.35/0.65 thf(fact_7015_gbinomial__sum__up__index,axiom,
% 0.35/0.65 ! [K2: nat,N: nat] :
% 0.35/0.65 ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [J: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J ) @ K2 )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.65 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_sum_up_index
% 0.35/0.65 thf(fact_7016_gbinomial__sum__up__index,axiom,
% 0.35/0.65 ! [K2: nat,N: nat] :
% 0.35/0.65 ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [J: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J ) @ K2 )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 0.35/0.65 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_sum_up_index
% 0.35/0.65 thf(fact_7017_exp__div__exp__eq,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65 = ( times_times_nat
% 0.35/0.65 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.65 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 0.35/0.65 != zero_zero_nat )
% 0.35/0.65 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 0.35/0.65 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % exp_div_exp_eq
% 0.35/0.65 thf(fact_7018_exp__div__exp__eq,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65 = ( times_times_int
% 0.35/0.65 @ ( zero_n2684676970156552555ol_int
% 0.35/0.65 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 0.35/0.65 != zero_zero_int )
% 0.35/0.65 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 0.35/0.65 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % exp_div_exp_eq
% 0.35/0.65 thf(fact_7019_exp__div__exp__eq,axiom,
% 0.35/0.65 ! [M2: nat,N: nat] :
% 0.35/0.65 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.65 = ( times_3573771949741848930nteger
% 0.35/0.65 @ ( zero_n356916108424825756nteger
% 0.35/0.65 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 )
% 0.35/0.65 != zero_z3403309356797280102nteger )
% 0.35/0.65 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 0.35/0.65 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % exp_div_exp_eq
% 0.35/0.65 thf(fact_7020_gbinomial__absorption_H,axiom,
% 0.35/0.65 ! [K2: nat,A: complex] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.65 => ( ( gbinomial_complex @ A @ K2 )
% 0.35/0.65 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorption'
% 0.35/0.65 thf(fact_7021_gbinomial__absorption_H,axiom,
% 0.35/0.65 ! [K2: nat,A: rat] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.65 => ( ( gbinomial_rat @ A @ K2 )
% 0.35/0.65 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorption'
% 0.35/0.65 thf(fact_7022_gbinomial__absorption_H,axiom,
% 0.35/0.65 ! [K2: nat,A: real] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.65 => ( ( gbinomial_real @ A @ K2 )
% 0.35/0.65 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_absorption'
% 0.35/0.65 thf(fact_7023_sum__gp0,axiom,
% 0.35/0.65 ! [X: complex,N: nat] :
% 0.35/0.65 ( ( ( X = one_one_complex )
% 0.35/0.65 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 0.35/0.65 & ( ( X != one_one_complex )
% 0.35/0.65 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp0
% 0.35/0.65 thf(fact_7024_sum__gp0,axiom,
% 0.35/0.65 ! [X: rat,N: nat] :
% 0.35/0.65 ( ( ( X = one_one_rat )
% 0.35/0.65 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 0.35/0.65 & ( ( X != one_one_rat )
% 0.35/0.65 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp0
% 0.35/0.65 thf(fact_7025_sum__gp0,axiom,
% 0.35/0.65 ! [X: real,N: nat] :
% 0.35/0.65 ( ( ( X = one_one_real )
% 0.35/0.65 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 0.35/0.65 & ( ( X != one_one_real )
% 0.35/0.65 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % sum_gp0
% 0.35/0.65 thf(fact_7026_polyfun__diff__alt,axiom,
% 0.35/0.65 ! [N: nat,A: nat > complex,X: complex,Y: complex] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_complex
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K3 ) ) @ ( power_power_complex @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff_alt
% 0.35/0.65 thf(fact_7027_polyfun__diff__alt,axiom,
% 0.35/0.65 ! [N: nat,A: nat > rat,X: rat,Y: rat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_rat
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K3 ) ) @ ( power_power_rat @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff_alt
% 0.35/0.65 thf(fact_7028_polyfun__diff__alt,axiom,
% 0.35/0.65 ! [N: nat,A: nat > int,X: int,Y: int] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_int
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K3 ) ) @ ( power_power_int @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff_alt
% 0.35/0.65 thf(fact_7029_polyfun__diff__alt,axiom,
% 0.35/0.65 ! [N: nat,A: nat > real,X: real,Y: real] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_real
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K3 ) ) @ ( power_power_real @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff_alt
% 0.35/0.65 thf(fact_7030_binomial__r__part__sum,axiom,
% 0.35/0.65 ! [M2: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.65 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % binomial_r_part_sum
% 0.35/0.65 thf(fact_7031_choose__linear__sum,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( groups3542108847815614940at_nat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_nat @ I @ ( binomial @ N @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % choose_linear_sum
% 0.35/0.65 thf(fact_7032_card__lists__length__le,axiom,
% 0.35/0.65 ! [A4: set_list_nat,N: nat] :
% 0.35/0.65 ( ( finite8100373058378681591st_nat @ A4 )
% 0.35/0.65 => ( ( finite7325466520557071688st_nat
% 0.35/0.65 @ ( collec5989764272469232197st_nat
% 0.35/0.65 @ ^ [Xs: list_list_nat] :
% 0.35/0.65 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 )
% 0.35/0.65 & ( ord_less_eq_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_list_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_length_le
% 0.35/0.65 thf(fact_7033_card__lists__length__le,axiom,
% 0.35/0.65 ! [A4: set_set_nat,N: nat] :
% 0.35/0.65 ( ( finite1152437895449049373et_nat @ A4 )
% 0.35/0.65 => ( ( finite5631907774883551598et_nat
% 0.35/0.65 @ ( collect_list_set_nat
% 0.35/0.65 @ ^ [Xs: list_set_nat] :
% 0.35/0.65 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 0.35/0.65 & ( ord_less_eq_nat @ ( size_s3254054031482475050et_nat @ Xs ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_set_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_length_le
% 0.35/0.65 thf(fact_7034_card__lists__length__le,axiom,
% 0.35/0.65 ! [A4: set_complex,N: nat] :
% 0.35/0.65 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.65 => ( ( finite5120063068150530198omplex
% 0.35/0.65 @ ( collect_list_complex
% 0.35/0.65 @ ^ [Xs: list_complex] :
% 0.35/0.65 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 0.35/0.65 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_complex @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_length_le
% 0.35/0.65 thf(fact_7035_card__lists__length__le,axiom,
% 0.35/0.65 ! [A4: set_VEBT_VEBT,N: nat] :
% 0.35/0.65 ( ( finite5795047828879050333T_VEBT @ A4 )
% 0.35/0.65 => ( ( finite5915292604075114978T_VEBT
% 0.35/0.65 @ ( collec5608196760682091941T_VEBT
% 0.35/0.65 @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.65 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 0.35/0.65 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_length_le
% 0.35/0.65 thf(fact_7036_card__lists__length__le,axiom,
% 0.35/0.65 ! [A4: set_o,N: nat] :
% 0.35/0.65 ( ( finite_finite_o @ A4 )
% 0.35/0.65 => ( ( finite_card_list_o
% 0.35/0.65 @ ( collect_list_o
% 0.35/0.65 @ ^ [Xs: list_o] :
% 0.35/0.65 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 0.35/0.65 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_o @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_length_le
% 0.35/0.65 thf(fact_7037_card__lists__length__le,axiom,
% 0.35/0.65 ! [A4: set_int,N: nat] :
% 0.35/0.65 ( ( finite_finite_int @ A4 )
% 0.35/0.65 => ( ( finite_card_list_int
% 0.35/0.65 @ ( collect_list_int
% 0.35/0.65 @ ^ [Xs: list_int] :
% 0.35/0.65 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 0.35/0.65 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_int @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_length_le
% 0.35/0.65 thf(fact_7038_card__lists__length__le,axiom,
% 0.35/0.65 ! [A4: set_nat,N: nat] :
% 0.35/0.65 ( ( finite_finite_nat @ A4 )
% 0.35/0.65 => ( ( finite_card_list_nat
% 0.35/0.65 @ ( collect_list_nat
% 0.35/0.65 @ ^ [Xs: list_nat] :
% 0.35/0.65 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 0.35/0.65 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) )
% 0.35/0.65 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_length_le
% 0.35/0.65 thf(fact_7039_polyfun__extremal__lemma,axiom,
% 0.35/0.65 ! [E: real,C2: nat > complex,N: nat] :
% 0.35/0.65 ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.65 => ? [M8: real] :
% 0.35/0.65 ! [Z5: complex] :
% 0.35/0.65 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z5 ) )
% 0.35/0.65 => ( ord_less_eq_real
% 0.35/0.65 @ ( real_V1022390504157884413omplex
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_extremal_lemma
% 0.35/0.65 thf(fact_7040_polyfun__extremal__lemma,axiom,
% 0.35/0.65 ! [E: real,C2: nat > real,N: nat] :
% 0.35/0.65 ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.65 => ? [M8: real] :
% 0.35/0.65 ! [Z5: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z5 ) )
% 0.35/0.65 => ( ord_less_eq_real
% 0.35/0.65 @ ( real_V7735802525324610683m_real
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_extremal_lemma
% 0.35/0.65 thf(fact_7041_polyfun__diff,axiom,
% 0.35/0.65 ! [N: nat,A: nat > complex,X: complex,Y: complex] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_complex
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( times_times_complex
% 0.35/0.65 @ ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( power_power_complex @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff
% 0.35/0.65 thf(fact_7042_polyfun__diff,axiom,
% 0.35/0.65 ! [N: nat,A: nat > rat,X: rat,Y: rat] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_rat
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( times_times_rat
% 0.35/0.65 @ ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( power_power_rat @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff
% 0.35/0.65 thf(fact_7043_polyfun__diff,axiom,
% 0.35/0.65 ! [N: nat,A: nat > int,X: int,Y: int] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_int
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( times_times_int
% 0.35/0.65 @ ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( power_power_int @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff
% 0.35/0.65 thf(fact_7044_polyfun__diff,axiom,
% 0.35/0.65 ! [N: nat,A: nat > real,X: real,Y: real] :
% 0.35/0.65 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.65 => ( ( minus_minus_real
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ I ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) ) )
% 0.35/0.65 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [J: nat] :
% 0.35/0.65 ( times_times_real
% 0.35/0.65 @ ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 0.35/0.65 @ ( power_power_real @ X @ J ) )
% 0.35/0.65 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % polyfun_diff
% 0.35/0.65 thf(fact_7045_card__lists__distinct__length__eq_H,axiom,
% 0.35/0.65 ! [K2: nat,A4: set_complex] :
% 0.35/0.65 ( ( ord_less_nat @ K2 @ ( finite_card_complex @ A4 ) )
% 0.35/0.65 => ( ( finite5120063068150530198omplex
% 0.35/0.65 @ ( collect_list_complex
% 0.35/0.65 @ ^ [Xs: list_complex] :
% 0.35/0.65 ( ( ( size_s3451745648224563538omplex @ Xs )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ( distinct_complex @ Xs )
% 0.35/0.65 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [X4: nat] : X4
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_distinct_length_eq'
% 0.35/0.65 thf(fact_7046_card__lists__distinct__length__eq_H,axiom,
% 0.35/0.65 ! [K2: nat,A4: set_list_nat] :
% 0.35/0.65 ( ( ord_less_nat @ K2 @ ( finite_card_list_nat @ A4 ) )
% 0.35/0.65 => ( ( finite7325466520557071688st_nat
% 0.35/0.65 @ ( collec5989764272469232197st_nat
% 0.35/0.65 @ ^ [Xs: list_list_nat] :
% 0.35/0.65 ( ( ( size_s3023201423986296836st_nat @ Xs )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ( distinct_list_nat @ Xs )
% 0.35/0.65 & ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [X4: nat] : X4
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_distinct_length_eq'
% 0.35/0.65 thf(fact_7047_card__lists__distinct__length__eq_H,axiom,
% 0.35/0.65 ! [K2: nat,A4: set_set_nat] :
% 0.35/0.65 ( ( ord_less_nat @ K2 @ ( finite_card_set_nat @ A4 ) )
% 0.35/0.65 => ( ( finite5631907774883551598et_nat
% 0.35/0.65 @ ( collect_list_set_nat
% 0.35/0.65 @ ^ [Xs: list_set_nat] :
% 0.35/0.65 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ( distinct_set_nat @ Xs )
% 0.35/0.65 & ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [X4: nat] : X4
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_distinct_length_eq'
% 0.35/0.65 thf(fact_7048_card__lists__distinct__length__eq_H,axiom,
% 0.35/0.65 ! [K2: nat,A4: set_VEBT_VEBT] :
% 0.35/0.65 ( ( ord_less_nat @ K2 @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 0.35/0.65 => ( ( finite5915292604075114978T_VEBT
% 0.35/0.65 @ ( collec5608196760682091941T_VEBT
% 0.35/0.65 @ ^ [Xs: list_VEBT_VEBT] :
% 0.35/0.65 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ( distinct_VEBT_VEBT @ Xs )
% 0.35/0.65 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [X4: nat] : X4
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_distinct_length_eq'
% 0.35/0.65 thf(fact_7049_card__lists__distinct__length__eq_H,axiom,
% 0.35/0.65 ! [K2: nat,A4: set_o] :
% 0.35/0.65 ( ( ord_less_nat @ K2 @ ( finite_card_o @ A4 ) )
% 0.35/0.65 => ( ( finite_card_list_o
% 0.35/0.65 @ ( collect_list_o
% 0.35/0.65 @ ^ [Xs: list_o] :
% 0.35/0.65 ( ( ( size_size_list_o @ Xs )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ( distinct_o @ Xs )
% 0.35/0.65 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [X4: nat] : X4
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_o @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_o @ A4 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_distinct_length_eq'
% 0.35/0.65 thf(fact_7050_card__lists__distinct__length__eq_H,axiom,
% 0.35/0.65 ! [K2: nat,A4: set_int] :
% 0.35/0.65 ( ( ord_less_nat @ K2 @ ( finite_card_int @ A4 ) )
% 0.35/0.65 => ( ( finite_card_list_int
% 0.35/0.65 @ ( collect_list_int
% 0.35/0.65 @ ^ [Xs: list_int] :
% 0.35/0.65 ( ( ( size_size_list_int @ Xs )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ( distinct_int @ Xs )
% 0.35/0.65 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [X4: nat] : X4
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_distinct_length_eq'
% 0.35/0.65 thf(fact_7051_card__lists__distinct__length__eq_H,axiom,
% 0.35/0.65 ! [K2: nat,A4: set_nat] :
% 0.35/0.65 ( ( ord_less_nat @ K2 @ ( finite_card_nat @ A4 ) )
% 0.35/0.65 => ( ( finite_card_list_nat
% 0.35/0.65 @ ( collect_list_nat
% 0.35/0.65 @ ^ [Xs: list_nat] :
% 0.35/0.65 ( ( ( size_size_list_nat @ Xs )
% 0.35/0.65 = K2 )
% 0.35/0.65 & ( distinct_nat @ Xs )
% 0.35/0.65 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) )
% 0.35/0.65 = ( groups708209901874060359at_nat
% 0.35/0.65 @ ^ [X4: nat] : X4
% 0.35/0.65 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % card_lists_distinct_length_eq'
% 0.35/0.65 thf(fact_7052_Divides_Oadjust__div__eq,axiom,
% 0.35/0.65 ! [Q2: int,R3: int] :
% 0.35/0.65 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.65 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % Divides.adjust_div_eq
% 0.35/0.65 thf(fact_7053_list__decode_Opinduct,axiom,
% 0.35/0.65 ! [A0: nat,P2: nat > $o] :
% 0.35/0.65 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 0.35/0.65 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.35/0.65 => ( P2 @ zero_zero_nat ) )
% 0.35/0.65 => ( ! [N3: nat] :
% 0.35/0.65 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 0.35/0.65 => ( ! [X5: nat,Y6: nat] :
% 0.35/0.65 ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 0.35/0.65 = ( nat_prod_decode @ N3 ) )
% 0.35/0.65 => ( P2 @ Y6 ) )
% 0.35/0.65 => ( P2 @ ( suc @ N3 ) ) ) )
% 0.35/0.65 => ( P2 @ A0 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % list_decode.pinduct
% 0.35/0.65 thf(fact_7054_gbinomial__code,axiom,
% 0.35/0.65 ( gbinomial_complex
% 0.35/0.65 = ( ^ [A5: complex,K3: nat] :
% 0.35/0.65 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 0.35/0.65 @ ( divide1717551699836669952omplex
% 0.35/0.65 @ ( set_fo1517530859248394432omplex
% 0.35/0.65 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A5 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 0.35/0.65 @ zero_zero_nat
% 0.35/0.65 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 0.35/0.65 @ one_one_complex )
% 0.35/0.65 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_code
% 0.35/0.65 thf(fact_7055_gbinomial__code,axiom,
% 0.35/0.65 ( gbinomial_rat
% 0.35/0.65 = ( ^ [A5: rat,K3: nat] :
% 0.35/0.65 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 0.35/0.65 @ ( divide_divide_rat
% 0.35/0.65 @ ( set_fo1949268297981939178at_rat
% 0.35/0.65 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 0.35/0.65 @ zero_zero_nat
% 0.35/0.65 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 0.35/0.65 @ one_one_rat )
% 0.35/0.65 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_code
% 0.35/0.65 thf(fact_7056_gbinomial__code,axiom,
% 0.35/0.65 ( gbinomial_real
% 0.35/0.65 = ( ^ [A5: real,K3: nat] :
% 0.35/0.65 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 0.35/0.65 @ ( divide_divide_real
% 0.35/0.65 @ ( set_fo3111899725591712190t_real
% 0.35/0.65 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A5 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 0.35/0.65 @ zero_zero_nat
% 0.35/0.65 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 0.35/0.65 @ one_one_real )
% 0.35/0.65 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % gbinomial_code
% 0.35/0.65 thf(fact_7057_choose__alternating__sum,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65 => ( ( groups2073611262835488442omplex
% 0.35/0.65 @ ^ [I: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_complex ) ) ).
% 0.35/0.65
% 0.35/0.65 % choose_alternating_sum
% 0.35/0.65 thf(fact_7058_choose__alternating__sum,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65 => ( ( groups7501900531339628137nteger
% 0.35/0.65 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % choose_alternating_sum
% 0.35/0.65 thf(fact_7059_choose__alternating__sum,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65 => ( ( groups2906978787729119204at_rat
% 0.35/0.65 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % choose_alternating_sum
% 0.35/0.65 thf(fact_7060_choose__alternating__sum,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65 => ( ( groups3539618377306564664at_int
% 0.35/0.65 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % choose_alternating_sum
% 0.35/0.65 thf(fact_7061_choose__alternating__sum,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.65 => ( ( groups6591440286371151544t_real
% 0.35/0.65 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) )
% 0.35/0.65 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.65 = zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % choose_alternating_sum
% 0.35/0.65 thf(fact_7062_signed__take__bit__Suc,axiom,
% 0.35/0.65 ! [N: nat,A: int] :
% 0.35/0.65 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 0.35/0.65 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % signed_take_bit_Suc
% 0.35/0.65 thf(fact_7063_set__decode__0,axiom,
% 0.35/0.65 ! [X: nat] :
% 0.35/0.65 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 0.35/0.65 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_decode_0
% 0.35/0.65 thf(fact_7064_add_Oinverse__inverse,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_inverse
% 0.35/0.65 thf(fact_7065_add_Oinverse__inverse,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_inverse
% 0.35/0.65 thf(fact_7066_add_Oinverse__inverse,axiom,
% 0.35/0.65 ! [A: complex] :
% 0.35/0.65 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_inverse
% 0.35/0.65 thf(fact_7067_add_Oinverse__inverse,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_inverse
% 0.35/0.65 thf(fact_7068_add_Oinverse__inverse,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_inverse
% 0.35/0.65 thf(fact_7069_neg__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( ( uminus_uminus_int @ A )
% 0.35/0.65 = ( uminus_uminus_int @ B ) )
% 0.35/0.65 = ( A = B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_iff_equal
% 0.35/0.65 thf(fact_7070_neg__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( ( uminus_uminus_real @ A )
% 0.35/0.65 = ( uminus_uminus_real @ B ) )
% 0.35/0.65 = ( A = B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_iff_equal
% 0.35/0.65 thf(fact_7071_neg__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.65 = ( A = B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_iff_equal
% 0.35/0.65 thf(fact_7072_neg__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.65 = ( A = B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_iff_equal
% 0.35/0.65 thf(fact_7073_neg__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( ( uminus_uminus_rat @ A )
% 0.35/0.65 = ( uminus_uminus_rat @ B ) )
% 0.35/0.65 = ( A = B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_iff_equal
% 0.35/0.65 thf(fact_7074_of__nat__id,axiom,
% 0.35/0.65 ( semiri1316708129612266289at_nat
% 0.35/0.65 = ( ^ [N4: nat] : N4 ) ) ).
% 0.35/0.65
% 0.35/0.65 % of_nat_id
% 0.35/0.65 thf(fact_7075_compl__le__compl__iff,axiom,
% 0.35/0.65 ! [X: set_nat,Y: set_nat] :
% 0.35/0.65 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 0.35/0.65 = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 0.35/0.65
% 0.35/0.65 % compl_le_compl_iff
% 0.35/0.65 thf(fact_7076_neg__le__iff__le,axiom,
% 0.35/0.65 ! [B: real,A: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( ord_less_eq_real @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_iff_le
% 0.35/0.65 thf(fact_7077_neg__le__iff__le,axiom,
% 0.35/0.65 ! [B: code_integer,A: code_integer] :
% 0.35/0.65 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_iff_le
% 0.35/0.65 thf(fact_7078_neg__le__iff__le,axiom,
% 0.35/0.65 ! [B: rat,A: rat] :
% 0.35/0.65 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( ord_less_eq_rat @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_iff_le
% 0.35/0.65 thf(fact_7079_neg__le__iff__le,axiom,
% 0.35/0.65 ! [B: int,A: int] :
% 0.35/0.65 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( ord_less_eq_int @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_iff_le
% 0.35/0.65 thf(fact_7080_neg__equal__zero,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ( uminus_uminus_int @ A )
% 0.35/0.65 = A )
% 0.35/0.65 = ( A = zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_zero
% 0.35/0.65 thf(fact_7081_neg__equal__zero,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ( uminus_uminus_real @ A )
% 0.35/0.65 = A )
% 0.35/0.65 = ( A = zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_zero
% 0.35/0.65 thf(fact_7082_neg__equal__zero,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.65 = A )
% 0.35/0.65 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_zero
% 0.35/0.65 thf(fact_7083_neg__equal__zero,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ( uminus_uminus_rat @ A )
% 0.35/0.65 = A )
% 0.35/0.65 = ( A = zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_zero
% 0.35/0.65 thf(fact_7084_equal__neg__zero,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( A
% 0.35/0.65 = ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( A = zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % equal_neg_zero
% 0.35/0.65 thf(fact_7085_equal__neg__zero,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( A
% 0.35/0.65 = ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( A = zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % equal_neg_zero
% 0.35/0.65 thf(fact_7086_equal__neg__zero,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( A
% 0.35/0.65 = ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % equal_neg_zero
% 0.35/0.65 thf(fact_7087_equal__neg__zero,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( A
% 0.35/0.65 = ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( A = zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % equal_neg_zero
% 0.35/0.65 thf(fact_7088_neg__equal__0__iff__equal,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ( uminus_uminus_int @ A )
% 0.35/0.65 = zero_zero_int )
% 0.35/0.65 = ( A = zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_0_iff_equal
% 0.35/0.65 thf(fact_7089_neg__equal__0__iff__equal,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ( uminus_uminus_real @ A )
% 0.35/0.65 = zero_zero_real )
% 0.35/0.65 = ( A = zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_0_iff_equal
% 0.35/0.65 thf(fact_7090_neg__equal__0__iff__equal,axiom,
% 0.35/0.65 ! [A: complex] :
% 0.35/0.65 ( ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.65 = zero_zero_complex )
% 0.35/0.65 = ( A = zero_zero_complex ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_0_iff_equal
% 0.35/0.65 thf(fact_7091_neg__equal__0__iff__equal,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.65 = zero_z3403309356797280102nteger )
% 0.35/0.65 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_0_iff_equal
% 0.35/0.65 thf(fact_7092_neg__equal__0__iff__equal,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ( uminus_uminus_rat @ A )
% 0.35/0.65 = zero_zero_rat )
% 0.35/0.65 = ( A = zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_equal_0_iff_equal
% 0.35/0.65 thf(fact_7093_neg__0__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( zero_zero_int
% 0.35/0.65 = ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( zero_zero_int = A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_equal_iff_equal
% 0.35/0.65 thf(fact_7094_neg__0__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( zero_zero_real
% 0.35/0.65 = ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( zero_zero_real = A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_equal_iff_equal
% 0.35/0.65 thf(fact_7095_neg__0__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: complex] :
% 0.35/0.65 ( ( zero_zero_complex
% 0.35/0.65 = ( uminus1482373934393186551omplex @ A ) )
% 0.35/0.65 = ( zero_zero_complex = A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_equal_iff_equal
% 0.35/0.65 thf(fact_7096_neg__0__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( zero_z3403309356797280102nteger
% 0.35/0.65 = ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( zero_z3403309356797280102nteger = A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_equal_iff_equal
% 0.35/0.65 thf(fact_7097_neg__0__equal__iff__equal,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( zero_zero_rat
% 0.35/0.65 = ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( zero_zero_rat = A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_equal_iff_equal
% 0.35/0.65 thf(fact_7098_add_Oinverse__neutral,axiom,
% 0.35/0.65 ( ( uminus_uminus_int @ zero_zero_int )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_neutral
% 0.35/0.65 thf(fact_7099_add_Oinverse__neutral,axiom,
% 0.35/0.65 ( ( uminus_uminus_real @ zero_zero_real )
% 0.35/0.65 = zero_zero_real ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_neutral
% 0.35/0.65 thf(fact_7100_add_Oinverse__neutral,axiom,
% 0.35/0.65 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 0.35/0.65 = zero_zero_complex ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_neutral
% 0.35/0.65 thf(fact_7101_add_Oinverse__neutral,axiom,
% 0.35/0.65 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_neutral
% 0.35/0.65 thf(fact_7102_add_Oinverse__neutral,axiom,
% 0.35/0.65 ( ( uminus_uminus_rat @ zero_zero_rat )
% 0.35/0.65 = zero_zero_rat ) ).
% 0.35/0.65
% 0.35/0.65 % add.inverse_neutral
% 0.35/0.65 thf(fact_7103_neg__less__iff__less,axiom,
% 0.35/0.65 ! [B: int,A: int] :
% 0.35/0.65 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( ord_less_int @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_iff_less
% 0.35/0.65 thf(fact_7104_neg__less__iff__less,axiom,
% 0.35/0.65 ! [B: real,A: real] :
% 0.35/0.65 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( ord_less_real @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_iff_less
% 0.35/0.65 thf(fact_7105_neg__less__iff__less,axiom,
% 0.35/0.65 ! [B: code_integer,A: code_integer] :
% 0.35/0.65 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_iff_less
% 0.35/0.65 thf(fact_7106_neg__less__iff__less,axiom,
% 0.35/0.65 ! [B: rat,A: rat] :
% 0.35/0.65 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( ord_less_rat @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_iff_less
% 0.35/0.65 thf(fact_7107_neg__numeral__eq__iff,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 0.35/0.65 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.65 = ( M2 = N ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_numeral_eq_iff
% 0.35/0.65 thf(fact_7108_neg__numeral__eq__iff,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 0.35/0.65 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.65 = ( M2 = N ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_numeral_eq_iff
% 0.35/0.65 thf(fact_7109_neg__numeral__eq__iff,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.65 = ( M2 = N ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_numeral_eq_iff
% 0.35/0.65 thf(fact_7110_neg__numeral__eq__iff,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.65 = ( M2 = N ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_numeral_eq_iff
% 0.35/0.65 thf(fact_7111_neg__numeral__eq__iff,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 0.35/0.65 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.65 = ( M2 = N ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_numeral_eq_iff
% 0.35/0.65 thf(fact_7112_mult__minus__right,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.65 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_right
% 0.35/0.65 thf(fact_7113_mult__minus__right,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.65 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_right
% 0.35/0.65 thf(fact_7114_mult__minus__right,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_right
% 0.35/0.65 thf(fact_7115_mult__minus__right,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_right
% 0.35/0.65 thf(fact_7116_mult__minus__right,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.65 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_right
% 0.35/0.65 thf(fact_7117_minus__mult__minus,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 0.35/0.65 = ( times_times_int @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_mult_minus
% 0.35/0.65 thf(fact_7118_minus__mult__minus,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.35/0.65 = ( times_times_real @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_mult_minus
% 0.35/0.65 thf(fact_7119_minus__mult__minus,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.65 = ( times_times_complex @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_mult_minus
% 0.35/0.65 thf(fact_7120_minus__mult__minus,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.65 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_mult_minus
% 0.35/0.65 thf(fact_7121_minus__mult__minus,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.35/0.65 = ( times_times_rat @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_mult_minus
% 0.35/0.65 thf(fact_7122_mult__minus__left,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.65 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_left
% 0.35/0.65 thf(fact_7123_mult__minus__left,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.65 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_left
% 0.35/0.65 thf(fact_7124_mult__minus__left,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_left
% 0.35/0.65 thf(fact_7125_mult__minus__left,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_left
% 0.35/0.65 thf(fact_7126_mult__minus__left,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.65 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus_left
% 0.35/0.65 thf(fact_7127_add__minus__cancel,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % add_minus_cancel
% 0.35/0.65 thf(fact_7128_add__minus__cancel,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % add_minus_cancel
% 0.35/0.65 thf(fact_7129_add__minus__cancel,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % add_minus_cancel
% 0.35/0.65 thf(fact_7130_add__minus__cancel,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % add_minus_cancel
% 0.35/0.65 thf(fact_7131_add__minus__cancel,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % add_minus_cancel
% 0.35/0.65 thf(fact_7132_minus__add__cancel,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_cancel
% 0.35/0.65 thf(fact_7133_minus__add__cancel,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_cancel
% 0.35/0.65 thf(fact_7134_minus__add__cancel,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_cancel
% 0.35/0.65 thf(fact_7135_minus__add__cancel,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_cancel
% 0.35/0.65 thf(fact_7136_minus__add__cancel,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.65 = B ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_cancel
% 0.35/0.65 thf(fact_7137_minus__add__distrib,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.35/0.65 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_distrib
% 0.35/0.65 thf(fact_7138_minus__add__distrib,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.35/0.65 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_distrib
% 0.35/0.65 thf(fact_7139_minus__add__distrib,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.65 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_distrib
% 0.35/0.65 thf(fact_7140_minus__add__distrib,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.65 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_distrib
% 0.35/0.65 thf(fact_7141_minus__add__distrib,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.65 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_add_distrib
% 0.35/0.65 thf(fact_7142_minus__diff__eq,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 0.35/0.65 = ( minus_minus_int @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_diff_eq
% 0.35/0.65 thf(fact_7143_minus__diff__eq,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 0.35/0.65 = ( minus_minus_real @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_diff_eq
% 0.35/0.65 thf(fact_7144_minus__diff__eq,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 0.35/0.65 = ( minus_minus_complex @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_diff_eq
% 0.35/0.65 thf(fact_7145_minus__diff__eq,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.35/0.65 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_diff_eq
% 0.35/0.65 thf(fact_7146_minus__diff__eq,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 0.35/0.65 = ( minus_minus_rat @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_diff_eq
% 0.35/0.65 thf(fact_7147_dvd__minus__iff,axiom,
% 0.35/0.65 ! [X: int,Y: int] :
% 0.35/0.65 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 0.35/0.65 = ( dvd_dvd_int @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % dvd_minus_iff
% 0.35/0.65 thf(fact_7148_dvd__minus__iff,axiom,
% 0.35/0.65 ! [X: real,Y: real] :
% 0.35/0.65 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 0.35/0.65 = ( dvd_dvd_real @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % dvd_minus_iff
% 0.35/0.65 thf(fact_7149_dvd__minus__iff,axiom,
% 0.35/0.65 ! [X: complex,Y: complex] :
% 0.35/0.65 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 0.35/0.65 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % dvd_minus_iff
% 0.35/0.65 thf(fact_7150_dvd__minus__iff,axiom,
% 0.35/0.65 ! [X: code_integer,Y: code_integer] :
% 0.35/0.65 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 0.35/0.65 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % dvd_minus_iff
% 0.35/0.65 thf(fact_7151_dvd__minus__iff,axiom,
% 0.35/0.65 ! [X: rat,Y: rat] :
% 0.35/0.65 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 0.35/0.65 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % dvd_minus_iff
% 0.35/0.65 thf(fact_7152_minus__dvd__iff,axiom,
% 0.35/0.65 ! [X: int,Y: int] :
% 0.35/0.65 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 0.35/0.65 = ( dvd_dvd_int @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_dvd_iff
% 0.35/0.65 thf(fact_7153_minus__dvd__iff,axiom,
% 0.35/0.65 ! [X: real,Y: real] :
% 0.35/0.65 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 0.35/0.65 = ( dvd_dvd_real @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_dvd_iff
% 0.35/0.65 thf(fact_7154_minus__dvd__iff,axiom,
% 0.35/0.65 ! [X: complex,Y: complex] :
% 0.35/0.65 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 0.35/0.65 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_dvd_iff
% 0.35/0.65 thf(fact_7155_minus__dvd__iff,axiom,
% 0.35/0.65 ! [X: code_integer,Y: code_integer] :
% 0.35/0.65 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 0.35/0.65 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_dvd_iff
% 0.35/0.65 thf(fact_7156_minus__dvd__iff,axiom,
% 0.35/0.65 ! [X: rat,Y: rat] :
% 0.35/0.65 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 0.35/0.65 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 0.35/0.65
% 0.35/0.65 % minus_dvd_iff
% 0.35/0.65 thf(fact_7157_negative__eq__positive,axiom,
% 0.35/0.65 ! [N: nat,M2: nat] :
% 0.35/0.65 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.65 = ( semiri1314217659103216013at_int @ M2 ) )
% 0.35/0.65 = ( ( N = zero_zero_nat )
% 0.35/0.65 & ( M2 = zero_zero_nat ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % negative_eq_positive
% 0.35/0.65 thf(fact_7158_signed__take__bit__of__0,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % signed_take_bit_of_0
% 0.35/0.65 thf(fact_7159_set__decode__inverse,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 0.35/0.65 = N ) ).
% 0.35/0.65
% 0.35/0.65 % set_decode_inverse
% 0.35/0.65 thf(fact_7160_neg__less__eq__nonneg,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.65 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_eq_nonneg
% 0.35/0.65 thf(fact_7161_neg__less__eq__nonneg,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.65 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_eq_nonneg
% 0.35/0.65 thf(fact_7162_neg__less__eq__nonneg,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.65 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_eq_nonneg
% 0.35/0.65 thf(fact_7163_neg__less__eq__nonneg,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.65 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_eq_nonneg
% 0.35/0.65 thf(fact_7164_less__eq__neg__nonpos,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_eq_neg_nonpos
% 0.35/0.65 thf(fact_7165_less__eq__neg__nonpos,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_eq_neg_nonpos
% 0.35/0.65 thf(fact_7166_less__eq__neg__nonpos,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_eq_neg_nonpos
% 0.35/0.65 thf(fact_7167_less__eq__neg__nonpos,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_eq_neg_nonpos
% 0.35/0.65 thf(fact_7168_neg__le__0__iff__le,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.35/0.65 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_0_iff_le
% 0.35/0.65 thf(fact_7169_neg__le__0__iff__le,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.35/0.65 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_0_iff_le
% 0.35/0.65 thf(fact_7170_neg__le__0__iff__le,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.35/0.65 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_0_iff_le
% 0.35/0.65 thf(fact_7171_neg__le__0__iff__le,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.35/0.65 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_le_0_iff_le
% 0.35/0.65 thf(fact_7172_neg__0__le__iff__le,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_le_iff_le
% 0.35/0.65 thf(fact_7173_neg__0__le__iff__le,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_le_iff_le
% 0.35/0.65 thf(fact_7174_neg__0__le__iff__le,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_le_iff_le
% 0.35/0.65 thf(fact_7175_neg__0__le__iff__le,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_le_iff_le
% 0.35/0.65 thf(fact_7176_less__neg__neg,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_neg_neg
% 0.35/0.65 thf(fact_7177_less__neg__neg,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_neg_neg
% 0.35/0.65 thf(fact_7178_less__neg__neg,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_neg_neg
% 0.35/0.65 thf(fact_7179_less__neg__neg,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % less_neg_neg
% 0.35/0.65 thf(fact_7180_neg__less__pos,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.65 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_pos
% 0.35/0.65 thf(fact_7181_neg__less__pos,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.65 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_pos
% 0.35/0.65 thf(fact_7182_neg__less__pos,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.65 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_pos
% 0.35/0.65 thf(fact_7183_neg__less__pos,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.65 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_pos
% 0.35/0.65 thf(fact_7184_neg__0__less__iff__less,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_less_iff_less
% 0.35/0.65 thf(fact_7185_neg__0__less__iff__less,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_less_iff_less
% 0.35/0.65 thf(fact_7186_neg__0__less__iff__less,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_less_iff_less
% 0.35/0.65 thf(fact_7187_neg__0__less__iff__less,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_0_less_iff_less
% 0.35/0.65 thf(fact_7188_neg__less__0__iff__less,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 0.35/0.65 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_0_iff_less
% 0.35/0.65 thf(fact_7189_neg__less__0__iff__less,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 0.35/0.65 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_0_iff_less
% 0.35/0.65 thf(fact_7190_neg__less__0__iff__less,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 0.35/0.65 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_0_iff_less
% 0.35/0.65 thf(fact_7191_neg__less__0__iff__less,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 0.35/0.65 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_less_0_iff_less
% 0.35/0.65 thf(fact_7192_add_Oright__inverse,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % add.right_inverse
% 0.35/0.65 thf(fact_7193_add_Oright__inverse,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 0.35/0.65 = zero_zero_real ) ).
% 0.35/0.65
% 0.35/0.65 % add.right_inverse
% 0.35/0.65 thf(fact_7194_add_Oright__inverse,axiom,
% 0.35/0.65 ! [A: complex] :
% 0.35/0.65 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 0.35/0.65 = zero_zero_complex ) ).
% 0.35/0.65
% 0.35/0.65 % add.right_inverse
% 0.35/0.65 thf(fact_7195_add_Oright__inverse,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ).
% 0.35/0.65
% 0.35/0.65 % add.right_inverse
% 0.35/0.65 thf(fact_7196_add_Oright__inverse,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 0.35/0.65 = zero_zero_rat ) ).
% 0.35/0.65
% 0.35/0.65 % add.right_inverse
% 0.35/0.65 thf(fact_7197_ab__left__minus,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % ab_left_minus
% 0.35/0.65 thf(fact_7198_ab__left__minus,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.65 = zero_zero_real ) ).
% 0.35/0.65
% 0.35/0.65 % ab_left_minus
% 0.35/0.65 thf(fact_7199_ab__left__minus,axiom,
% 0.35/0.65 ! [A: complex] :
% 0.35/0.65 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.35/0.65 = zero_zero_complex ) ).
% 0.35/0.65
% 0.35/0.65 % ab_left_minus
% 0.35/0.65 thf(fact_7200_ab__left__minus,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ).
% 0.35/0.65
% 0.35/0.65 % ab_left_minus
% 0.35/0.65 thf(fact_7201_ab__left__minus,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.65 = zero_zero_rat ) ).
% 0.35/0.65
% 0.35/0.65 % ab_left_minus
% 0.35/0.65 thf(fact_7202_verit__minus__simplify_I3_J,axiom,
% 0.35/0.65 ! [B: int] :
% 0.35/0.65 ( ( minus_minus_int @ zero_zero_int @ B )
% 0.35/0.65 = ( uminus_uminus_int @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % verit_minus_simplify(3)
% 0.35/0.65 thf(fact_7203_verit__minus__simplify_I3_J,axiom,
% 0.35/0.65 ! [B: real] :
% 0.35/0.65 ( ( minus_minus_real @ zero_zero_real @ B )
% 0.35/0.65 = ( uminus_uminus_real @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % verit_minus_simplify(3)
% 0.35/0.65 thf(fact_7204_verit__minus__simplify_I3_J,axiom,
% 0.35/0.65 ! [B: complex] :
% 0.35/0.65 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % verit_minus_simplify(3)
% 0.35/0.65 thf(fact_7205_verit__minus__simplify_I3_J,axiom,
% 0.35/0.65 ! [B: code_integer] :
% 0.35/0.65 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % verit_minus_simplify(3)
% 0.35/0.65 thf(fact_7206_verit__minus__simplify_I3_J,axiom,
% 0.35/0.65 ! [B: rat] :
% 0.35/0.65 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 0.35/0.65 = ( uminus_uminus_rat @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % verit_minus_simplify(3)
% 0.35/0.65 thf(fact_7207_diff__0,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( minus_minus_int @ zero_zero_int @ A )
% 0.35/0.65 = ( uminus_uminus_int @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_0
% 0.35/0.65 thf(fact_7208_diff__0,axiom,
% 0.35/0.65 ! [A: real] :
% 0.35/0.65 ( ( minus_minus_real @ zero_zero_real @ A )
% 0.35/0.65 = ( uminus_uminus_real @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_0
% 0.35/0.65 thf(fact_7209_diff__0,axiom,
% 0.35/0.65 ! [A: complex] :
% 0.35/0.65 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_0
% 0.35/0.65 thf(fact_7210_diff__0,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_0
% 0.35/0.65 thf(fact_7211_diff__0,axiom,
% 0.35/0.65 ! [A: rat] :
% 0.35/0.65 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 0.35/0.65 = ( uminus_uminus_rat @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_0
% 0.35/0.65 thf(fact_7212_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.65 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_simps(3)
% 0.35/0.65 thf(fact_7213_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.65 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_simps(3)
% 0.35/0.65 thf(fact_7214_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_simps(3)
% 0.35/0.65 thf(fact_7215_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_simps(3)
% 0.35/0.65 thf(fact_7216_add__neg__numeral__simps_I3_J,axiom,
% 0.35/0.65 ! [M2: num,N: num] :
% 0.35/0.65 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.65 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_simps(3)
% 0.35/0.65 thf(fact_7217_mult__minus1__right,axiom,
% 0.35/0.65 ! [Z3: int] :
% 0.35/0.65 ( ( times_times_int @ Z3 @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.65 = ( uminus_uminus_int @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1_right
% 0.35/0.65 thf(fact_7218_mult__minus1__right,axiom,
% 0.35/0.65 ! [Z3: real] :
% 0.35/0.65 ( ( times_times_real @ Z3 @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.65 = ( uminus_uminus_real @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1_right
% 0.35/0.65 thf(fact_7219_mult__minus1__right,axiom,
% 0.35/0.65 ! [Z3: complex] :
% 0.35/0.65 ( ( times_times_complex @ Z3 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1_right
% 0.35/0.65 thf(fact_7220_mult__minus1__right,axiom,
% 0.35/0.65 ! [Z3: code_integer] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ Z3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1_right
% 0.35/0.65 thf(fact_7221_mult__minus1__right,axiom,
% 0.35/0.65 ! [Z3: rat] :
% 0.35/0.65 ( ( times_times_rat @ Z3 @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.65 = ( uminus_uminus_rat @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1_right
% 0.35/0.65 thf(fact_7222_mult__minus1,axiom,
% 0.35/0.65 ! [Z3: int] :
% 0.35/0.65 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z3 )
% 0.35/0.65 = ( uminus_uminus_int @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1
% 0.35/0.65 thf(fact_7223_mult__minus1,axiom,
% 0.35/0.65 ! [Z3: real] :
% 0.35/0.65 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z3 )
% 0.35/0.65 = ( uminus_uminus_real @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1
% 0.35/0.65 thf(fact_7224_mult__minus1,axiom,
% 0.35/0.65 ! [Z3: complex] :
% 0.35/0.65 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z3 )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1
% 0.35/0.65 thf(fact_7225_mult__minus1,axiom,
% 0.35/0.65 ! [Z3: code_integer] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z3 )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1
% 0.35/0.65 thf(fact_7226_mult__minus1,axiom,
% 0.35/0.65 ! [Z3: rat] :
% 0.35/0.65 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z3 )
% 0.35/0.65 = ( uminus_uminus_rat @ Z3 ) ) ).
% 0.35/0.65
% 0.35/0.65 % mult_minus1
% 0.35/0.65 thf(fact_7227_diff__minus__eq__add,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.65 = ( plus_plus_int @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_minus_eq_add
% 0.35/0.65 thf(fact_7228_diff__minus__eq__add,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.65 = ( plus_plus_real @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_minus_eq_add
% 0.35/0.65 thf(fact_7229_diff__minus__eq__add,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.65 = ( plus_plus_complex @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_minus_eq_add
% 0.35/0.65 thf(fact_7230_diff__minus__eq__add,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.65 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_minus_eq_add
% 0.35/0.65 thf(fact_7231_diff__minus__eq__add,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.65 = ( plus_plus_rat @ A @ B ) ) ).
% 0.35/0.65
% 0.35/0.65 % diff_minus_eq_add
% 0.35/0.65 thf(fact_7232_uminus__add__conv__diff,axiom,
% 0.35/0.65 ! [A: int,B: int] :
% 0.35/0.65 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.65 = ( minus_minus_int @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % uminus_add_conv_diff
% 0.35/0.65 thf(fact_7233_uminus__add__conv__diff,axiom,
% 0.35/0.65 ! [A: real,B: real] :
% 0.35/0.65 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.65 = ( minus_minus_real @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % uminus_add_conv_diff
% 0.35/0.65 thf(fact_7234_uminus__add__conv__diff,axiom,
% 0.35/0.65 ! [A: complex,B: complex] :
% 0.35/0.65 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.65 = ( minus_minus_complex @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % uminus_add_conv_diff
% 0.35/0.65 thf(fact_7235_uminus__add__conv__diff,axiom,
% 0.35/0.65 ! [A: code_integer,B: code_integer] :
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.65 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % uminus_add_conv_diff
% 0.35/0.65 thf(fact_7236_uminus__add__conv__diff,axiom,
% 0.35/0.65 ! [A: rat,B: rat] :
% 0.35/0.65 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.65 = ( minus_minus_rat @ B @ A ) ) ).
% 0.35/0.65
% 0.35/0.65 % uminus_add_conv_diff
% 0.35/0.65 thf(fact_7237_fact__0,axiom,
% 0.35/0.65 ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 0.35/0.65 = one_one_Code_integer ) ).
% 0.35/0.65
% 0.35/0.65 % fact_0
% 0.35/0.65 thf(fact_7238_fact__0,axiom,
% 0.35/0.65 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 0.35/0.65 = one_one_complex ) ).
% 0.35/0.65
% 0.35/0.65 % fact_0
% 0.35/0.65 thf(fact_7239_fact__0,axiom,
% 0.35/0.65 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 0.35/0.65 = one_one_int ) ).
% 0.35/0.65
% 0.35/0.65 % fact_0
% 0.35/0.65 thf(fact_7240_fact__0,axiom,
% 0.35/0.65 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 0.35/0.65 = one_one_nat ) ).
% 0.35/0.65
% 0.35/0.65 % fact_0
% 0.35/0.65 thf(fact_7241_fact__0,axiom,
% 0.35/0.65 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 0.35/0.65 = one_one_real ) ).
% 0.35/0.65
% 0.35/0.65 % fact_0
% 0.35/0.65 thf(fact_7242_negative__zless,axiom,
% 0.35/0.65 ! [N: nat,M2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 0.35/0.65
% 0.35/0.65 % negative_zless
% 0.35/0.65 thf(fact_7243_signed__take__bit__Suc__1,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ one_one_Code_integer )
% 0.35/0.65 = one_one_Code_integer ) ).
% 0.35/0.65
% 0.35/0.65 % signed_take_bit_Suc_1
% 0.35/0.65 thf(fact_7244_signed__take__bit__Suc__1,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 0.35/0.65 = one_one_int ) ).
% 0.35/0.65
% 0.35/0.65 % signed_take_bit_Suc_1
% 0.35/0.65 thf(fact_7245_dbl__simps_I1_J,axiom,
% 0.35/0.65 ! [K2: num] :
% 0.35/0.65 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 0.35/0.65 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_simps(1)
% 0.35/0.65 thf(fact_7246_dbl__simps_I1_J,axiom,
% 0.35/0.65 ! [K2: num] :
% 0.35/0.65 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 0.35/0.65 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_simps(1)
% 0.35/0.65 thf(fact_7247_dbl__simps_I1_J,axiom,
% 0.35/0.65 ! [K2: num] :
% 0.35/0.65 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_simps(1)
% 0.35/0.65 thf(fact_7248_dbl__simps_I1_J,axiom,
% 0.35/0.65 ! [K2: num] :
% 0.35/0.65 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_simps(1)
% 0.35/0.65 thf(fact_7249_dbl__simps_I1_J,axiom,
% 0.35/0.65 ! [K2: num] :
% 0.35/0.65 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 0.35/0.65 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_simps(1)
% 0.35/0.65 thf(fact_7250_dbl__inc__simps_I4_J,axiom,
% 0.35/0.65 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.65 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_inc_simps(4)
% 0.35/0.65 thf(fact_7251_dbl__inc__simps_I4_J,axiom,
% 0.35/0.65 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.65 = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_inc_simps(4)
% 0.35/0.65 thf(fact_7252_dbl__inc__simps_I4_J,axiom,
% 0.35/0.65 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_inc_simps(4)
% 0.35/0.65 thf(fact_7253_dbl__inc__simps_I4_J,axiom,
% 0.35/0.65 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_inc_simps(4)
% 0.35/0.65 thf(fact_7254_dbl__inc__simps_I4_J,axiom,
% 0.35/0.65 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.65 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.65
% 0.35/0.65 % dbl_inc_simps(4)
% 0.35/0.65 thf(fact_7255_set__decode__zero,axiom,
% 0.35/0.65 ( ( nat_set_decode @ zero_zero_nat )
% 0.35/0.65 = bot_bot_set_nat ) ).
% 0.35/0.65
% 0.35/0.65 % set_decode_zero
% 0.35/0.65 thf(fact_7256_set__encode__inverse,axiom,
% 0.35/0.65 ! [A4: set_nat] :
% 0.35/0.65 ( ( finite_finite_nat @ A4 )
% 0.35/0.65 => ( ( nat_set_decode @ ( nat_set_encode @ A4 ) )
% 0.35/0.65 = A4 ) ) ).
% 0.35/0.65
% 0.35/0.65 % set_encode_inverse
% 0.35/0.65 thf(fact_7257_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.65 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(7)
% 0.35/0.65 thf(fact_7258_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.65 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.65 = zero_zero_real ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(7)
% 0.35/0.65 thf(fact_7259_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.65 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.65 = zero_zero_complex ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(7)
% 0.35/0.65 thf(fact_7260_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(7)
% 0.35/0.65 thf(fact_7261_add__neg__numeral__special_I7_J,axiom,
% 0.35/0.65 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.65 = zero_zero_rat ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(7)
% 0.35/0.65 thf(fact_7262_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.65 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(8)
% 0.35/0.65 thf(fact_7263_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.65 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.35/0.65 = zero_zero_real ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(8)
% 0.35/0.65 thf(fact_7264_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.65 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.35/0.65 = zero_zero_complex ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(8)
% 0.35/0.65 thf(fact_7265_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.65 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(8)
% 0.35/0.65 thf(fact_7266_add__neg__numeral__special_I8_J,axiom,
% 0.35/0.65 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.35/0.65 = zero_zero_rat ) ).
% 0.35/0.65
% 0.35/0.65 % add_neg_numeral_special(8)
% 0.35/0.65 thf(fact_7267_diff__numeral__special_I12_J,axiom,
% 0.35/0.65 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % diff_numeral_special(12)
% 0.35/0.65 thf(fact_7268_diff__numeral__special_I12_J,axiom,
% 0.35/0.65 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.65 = zero_zero_real ) ).
% 0.35/0.65
% 0.35/0.65 % diff_numeral_special(12)
% 0.35/0.65 thf(fact_7269_diff__numeral__special_I12_J,axiom,
% 0.35/0.65 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.65 = zero_zero_complex ) ).
% 0.35/0.65
% 0.35/0.65 % diff_numeral_special(12)
% 0.35/0.65 thf(fact_7270_diff__numeral__special_I12_J,axiom,
% 0.35/0.65 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ).
% 0.35/0.65
% 0.35/0.65 % diff_numeral_special(12)
% 0.35/0.65 thf(fact_7271_diff__numeral__special_I12_J,axiom,
% 0.35/0.65 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.65 = zero_zero_rat ) ).
% 0.35/0.65
% 0.35/0.65 % diff_numeral_special(12)
% 0.35/0.65 thf(fact_7272_neg__one__eq__numeral__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_int @ one_one_int )
% 0.35/0.65 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_one_eq_numeral_iff
% 0.35/0.65 thf(fact_7273_neg__one__eq__numeral__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_real @ one_one_real )
% 0.35/0.65 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_one_eq_numeral_iff
% 0.35/0.65 thf(fact_7274_neg__one__eq__numeral__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_one_eq_numeral_iff
% 0.35/0.65 thf(fact_7275_neg__one__eq__numeral__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_one_eq_numeral_iff
% 0.35/0.65 thf(fact_7276_neg__one__eq__numeral__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_rat @ one_one_rat )
% 0.35/0.65 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % neg_one_eq_numeral_iff
% 0.35/0.65 thf(fact_7277_numeral__eq__neg__one__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 0.35/0.65 = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % numeral_eq_neg_one_iff
% 0.35/0.65 thf(fact_7278_numeral__eq__neg__one__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 0.35/0.65 = ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % numeral_eq_neg_one_iff
% 0.35/0.65 thf(fact_7279_numeral__eq__neg__one__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 0.35/0.65 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % numeral_eq_neg_one_iff
% 0.35/0.65 thf(fact_7280_numeral__eq__neg__one__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % numeral_eq_neg_one_iff
% 0.35/0.65 thf(fact_7281_numeral__eq__neg__one__iff,axiom,
% 0.35/0.65 ! [N: num] :
% 0.35/0.65 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 0.35/0.65 = ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.65 = ( N = one ) ) ).
% 0.35/0.65
% 0.35/0.65 % numeral_eq_neg_one_iff
% 0.35/0.65 thf(fact_7282_left__minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat,A: int] :
% 0.35/0.65 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % left_minus_one_mult_self
% 0.35/0.65 thf(fact_7283_left__minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat,A: real] :
% 0.35/0.65 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % left_minus_one_mult_self
% 0.35/0.65 thf(fact_7284_left__minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat,A: complex] :
% 0.35/0.65 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % left_minus_one_mult_self
% 0.35/0.65 thf(fact_7285_left__minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat,A: code_integer] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % left_minus_one_mult_self
% 0.35/0.65 thf(fact_7286_left__minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat,A: rat] :
% 0.35/0.65 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 0.35/0.65 = A ) ).
% 0.35/0.65
% 0.35/0.65 % left_minus_one_mult_self
% 0.35/0.65 thf(fact_7287_minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 0.35/0.65 = one_one_int ) ).
% 0.35/0.65
% 0.35/0.65 % minus_one_mult_self
% 0.35/0.65 thf(fact_7288_minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 0.35/0.65 = one_one_real ) ).
% 0.35/0.65
% 0.35/0.65 % minus_one_mult_self
% 0.35/0.65 thf(fact_7289_minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 0.35/0.65 = one_one_complex ) ).
% 0.35/0.65
% 0.35/0.65 % minus_one_mult_self
% 0.35/0.65 thf(fact_7290_minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 0.35/0.65 = one_one_Code_integer ) ).
% 0.35/0.65
% 0.35/0.65 % minus_one_mult_self
% 0.35/0.65 thf(fact_7291_minus__one__mult__self,axiom,
% 0.35/0.65 ! [N: nat] :
% 0.35/0.65 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 0.35/0.65 = one_one_rat ) ).
% 0.35/0.65
% 0.35/0.65 % minus_one_mult_self
% 0.35/0.65 thf(fact_7292_mod__minus1__right,axiom,
% 0.35/0.65 ! [A: int] :
% 0.35/0.65 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.65 = zero_zero_int ) ).
% 0.35/0.65
% 0.35/0.65 % mod_minus1_right
% 0.35/0.65 thf(fact_7293_mod__minus1__right,axiom,
% 0.35/0.65 ! [A: code_integer] :
% 0.35/0.65 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.65 = zero_z3403309356797280102nteger ) ).
% 0.35/0.65
% 0.35/0.65 % mod_minus1_right
% 0.35/0.65 thf(fact_7294_max__number__of_I2_J,axiom,
% 0.35/0.65 ! [U: num,V2: num] :
% 0.35/0.65 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.65 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.65 = ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) ) )
% 0.35/0.65 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.65 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.65 = ( numeral_numeral_real @ U ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % max_number_of(2)
% 0.35/0.65 thf(fact_7295_max__number__of_I2_J,axiom,
% 0.35/0.65 ! [U: num,V2: num] :
% 0.35/0.65 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.65 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.65 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) ) )
% 0.35/0.65 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.65 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.65 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 0.35/0.65
% 0.35/0.65 % max_number_of(2)
% 0.35/0.65 thf(fact_7296_max__number__of_I2_J,axiom,
% 0.35/0.65 ! [U: num,V2: num] :
% 0.35/0.65 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(2)
% 0.35/0.66 thf(fact_7297_max__number__of_I2_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 = ( numeral_numeral_int @ U ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(2)
% 0.35/0.66 thf(fact_7298_max__number__of_I3_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.66 = ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(3)
% 0.35/0.66 thf(fact_7299_max__number__of_I3_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 0.35/0.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 0.35/0.66 = ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.66 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 0.35/0.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(3)
% 0.35/0.66 thf(fact_7300_max__number__of_I3_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.66 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.66 = ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.66 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(3)
% 0.35/0.66 thf(fact_7301_max__number__of_I3_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.66 = ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(3)
% 0.35/0.66 thf(fact_7302_max__number__of_I4_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(4)
% 0.35/0.66 thf(fact_7303_max__number__of_I4_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) ) )
% 0.35/0.66 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(4)
% 0.35/0.66 thf(fact_7304_max__number__of_I4_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(4)
% 0.35/0.66 thf(fact_7305_max__number__of_I4_J,axiom,
% 0.35/0.66 ! [U: num,V2: num] :
% 0.35/0.66 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) ) )
% 0.35/0.66 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % max_number_of(4)
% 0.35/0.66 thf(fact_7306_fact__Suc__0,axiom,
% 0.35/0.66 ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 0.35/0.66 = one_one_Code_integer ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc_0
% 0.35/0.66 thf(fact_7307_fact__Suc__0,axiom,
% 0.35/0.66 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 0.35/0.66 = one_one_complex ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc_0
% 0.35/0.66 thf(fact_7308_fact__Suc__0,axiom,
% 0.35/0.66 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 0.35/0.66 = one_one_int ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc_0
% 0.35/0.66 thf(fact_7309_fact__Suc__0,axiom,
% 0.35/0.66 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 0.35/0.66 = one_one_nat ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc_0
% 0.35/0.66 thf(fact_7310_fact__Suc__0,axiom,
% 0.35/0.66 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 0.35/0.66 = one_one_real ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc_0
% 0.35/0.66 thf(fact_7311_fact__Suc,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 0.35/0.66 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc
% 0.35/0.66 thf(fact_7312_fact__Suc,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 0.35/0.66 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc
% 0.35/0.66 thf(fact_7313_fact__Suc,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 0.35/0.66 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc
% 0.35/0.66 thf(fact_7314_fact__Suc,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 0.35/0.66 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_Suc
% 0.35/0.66 thf(fact_7315_diff__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(3)
% 0.35/0.66 thf(fact_7316_diff__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(3)
% 0.35/0.66 thf(fact_7317_diff__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(3)
% 0.35/0.66 thf(fact_7318_diff__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(3)
% 0.35/0.66 thf(fact_7319_diff__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(3)
% 0.35/0.66 thf(fact_7320_diff__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(2)
% 0.35/0.66 thf(fact_7321_diff__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(2)
% 0.35/0.66 thf(fact_7322_diff__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.66 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(2)
% 0.35/0.66 thf(fact_7323_diff__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.66 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(2)
% 0.35/0.66 thf(fact_7324_diff__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_simps(2)
% 0.35/0.66 thf(fact_7325_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(3)
% 0.35/0.66 thf(fact_7326_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(3)
% 0.35/0.66 thf(fact_7327_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(3)
% 0.35/0.66 thf(fact_7328_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(3)
% 0.35/0.66 thf(fact_7329_mult__neg__numeral__simps_I3_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(3)
% 0.35/0.66 thf(fact_7330_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(2)
% 0.35/0.66 thf(fact_7331_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(2)
% 0.35/0.66 thf(fact_7332_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(2)
% 0.35/0.66 thf(fact_7333_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(2)
% 0.35/0.66 thf(fact_7334_mult__neg__numeral__simps_I2_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(2)
% 0.35/0.66 thf(fact_7335_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(1)
% 0.35/0.66 thf(fact_7336_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(1)
% 0.35/0.66 thf(fact_7337_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.66 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(1)
% 0.35/0.66 thf(fact_7338_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.66 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(1)
% 0.35/0.66 thf(fact_7339_mult__neg__numeral__simps_I1_J,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_neg_numeral_simps(1)
% 0.35/0.66 thf(fact_7340_semiring__norm_I172_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: int] :
% 0.35/0.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(172)
% 0.35/0.66 thf(fact_7341_semiring__norm_I172_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: real] :
% 0.35/0.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(172)
% 0.35/0.66 thf(fact_7342_semiring__norm_I172_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: complex] :
% 0.35/0.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(172)
% 0.35/0.66 thf(fact_7343_semiring__norm_I172_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: code_integer] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(172)
% 0.35/0.66 thf(fact_7344_semiring__norm_I172_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: rat] :
% 0.35/0.66 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(172)
% 0.35/0.66 thf(fact_7345_semiring__norm_I171_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: int] :
% 0.35/0.66 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(171)
% 0.35/0.66 thf(fact_7346_semiring__norm_I171_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: real] :
% 0.35/0.66 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(171)
% 0.35/0.66 thf(fact_7347_semiring__norm_I171_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: complex] :
% 0.35/0.66 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(171)
% 0.35/0.66 thf(fact_7348_semiring__norm_I171_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: code_integer] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(171)
% 0.35/0.66 thf(fact_7349_semiring__norm_I171_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: rat] :
% 0.35/0.66 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 0.35/0.66 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(171)
% 0.35/0.66 thf(fact_7350_semiring__norm_I170_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: int] :
% 0.35/0.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Y ) )
% 0.35/0.66 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(170)
% 0.35/0.66 thf(fact_7351_semiring__norm_I170_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: real] :
% 0.35/0.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Y ) )
% 0.35/0.66 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(170)
% 0.35/0.66 thf(fact_7352_semiring__norm_I170_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: complex] :
% 0.35/0.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Y ) )
% 0.35/0.66 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(170)
% 0.35/0.66 thf(fact_7353_semiring__norm_I170_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: code_integer] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Y ) )
% 0.35/0.66 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(170)
% 0.35/0.66 thf(fact_7354_semiring__norm_I170_J,axiom,
% 0.35/0.66 ! [V2: num,W2: num,Y: rat] :
% 0.35/0.66 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Y ) )
% 0.35/0.66 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % semiring_norm(170)
% 0.35/0.66 thf(fact_7355_neg__numeral__le__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.66 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_iff
% 0.35/0.66 thf(fact_7356_neg__numeral__le__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.66 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_iff
% 0.35/0.66 thf(fact_7357_neg__numeral__le__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.66 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_iff
% 0.35/0.66 thf(fact_7358_neg__numeral__le__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.66 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_iff
% 0.35/0.66 thf(fact_7359_neg__numeral__less__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.66 = ( ord_less_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_iff
% 0.35/0.66 thf(fact_7360_neg__numeral__less__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.66 = ( ord_less_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_iff
% 0.35/0.66 thf(fact_7361_neg__numeral__less__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.66 = ( ord_less_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_iff
% 0.35/0.66 thf(fact_7362_neg__numeral__less__iff,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.66 = ( ord_less_num @ N @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_iff
% 0.35/0.66 thf(fact_7363_dbl__dec__simps_I2_J,axiom,
% 0.35/0.66 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 0.35/0.66 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(2)
% 0.35/0.66 thf(fact_7364_dbl__dec__simps_I2_J,axiom,
% 0.35/0.66 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 0.35/0.66 = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(2)
% 0.35/0.66 thf(fact_7365_dbl__dec__simps_I2_J,axiom,
% 0.35/0.66 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(2)
% 0.35/0.66 thf(fact_7366_dbl__dec__simps_I2_J,axiom,
% 0.35/0.66 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(2)
% 0.35/0.66 thf(fact_7367_dbl__dec__simps_I2_J,axiom,
% 0.35/0.66 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 0.35/0.66 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(2)
% 0.35/0.66 thf(fact_7368_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_le_neg_numeral_iff
% 0.35/0.66 thf(fact_7369_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_le_neg_numeral_iff
% 0.35/0.66 thf(fact_7370_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_le_neg_numeral_iff
% 0.35/0.66 thf(fact_7371_not__neg__one__le__neg__numeral__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_le_neg_numeral_iff
% 0.35/0.66 thf(fact_7372_divide__le__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [B: real,W2: num,A: real] :
% 0.35/0.66 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 0.35/0.66 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_le_eq_numeral1(2)
% 0.35/0.66 thf(fact_7373_divide__le__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [B: rat,W2: num,A: rat] :
% 0.35/0.66 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 0.35/0.66 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_le_eq_numeral1(2)
% 0.35/0.66 thf(fact_7374_le__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [A: real,B: real,W2: num] :
% 0.35/0.66 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.35/0.66 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_divide_eq_numeral1(2)
% 0.35/0.66 thf(fact_7375_le__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [A: rat,B: rat,W2: num] :
% 0.35/0.66 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.35/0.66 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_divide_eq_numeral1(2)
% 0.35/0.66 thf(fact_7376_divide__eq__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [B: real,W2: num,A: real] :
% 0.35/0.66 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.66 = A )
% 0.35/0.66 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.66 != zero_zero_real )
% 0.35/0.66 => ( B
% 0.35/0.66 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 0.35/0.66 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.66 = zero_zero_real )
% 0.35/0.66 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_eq_numeral1(2)
% 0.35/0.66 thf(fact_7377_divide__eq__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [B: complex,W2: num,A: complex] :
% 0.35/0.66 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.35/0.66 = A )
% 0.35/0.66 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.66 != zero_zero_complex )
% 0.35/0.66 => ( B
% 0.35/0.66 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 0.35/0.66 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.66 = zero_zero_complex )
% 0.35/0.66 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_eq_numeral1(2)
% 0.35/0.66 thf(fact_7378_divide__eq__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [B: rat,W2: num,A: rat] :
% 0.35/0.66 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.66 = A )
% 0.35/0.66 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.66 != zero_zero_rat )
% 0.35/0.66 => ( B
% 0.35/0.66 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 0.35/0.66 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.66 = zero_zero_rat )
% 0.35/0.66 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_eq_numeral1(2)
% 0.35/0.66 thf(fact_7379_eq__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [A: real,B: real,W2: num] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.35/0.66 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.66 != zero_zero_real )
% 0.35/0.66 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.66 = zero_zero_real )
% 0.35/0.66 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_divide_eq_numeral1(2)
% 0.35/0.66 thf(fact_7380_eq__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [A: complex,B: complex,W2: num] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 0.35/0.66 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.66 != zero_zero_complex )
% 0.35/0.66 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.66 = zero_zero_complex )
% 0.35/0.66 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_divide_eq_numeral1(2)
% 0.35/0.66 thf(fact_7381_eq__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [A: rat,B: rat,W2: num] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.35/0.66 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.66 != zero_zero_rat )
% 0.35/0.66 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.66 = zero_zero_rat )
% 0.35/0.66 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_divide_eq_numeral1(2)
% 0.35/0.66 thf(fact_7382_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_neg_one_iff
% 0.35/0.66 thf(fact_7383_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_neg_one_iff
% 0.35/0.66 thf(fact_7384_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_neg_one_iff
% 0.35/0.66 thf(fact_7385_neg__numeral__less__neg__one__iff,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.66 = ( M2 != one ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_neg_one_iff
% 0.35/0.66 thf(fact_7386_less__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [A: real,B: real,W2: num] :
% 0.35/0.66 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 0.35/0.66 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_divide_eq_numeral1(2)
% 0.35/0.66 thf(fact_7387_less__divide__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [A: rat,B: rat,W2: num] :
% 0.35/0.66 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 0.35/0.66 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_divide_eq_numeral1(2)
% 0.35/0.66 thf(fact_7388_divide__less__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [B: real,W2: num,A: real] :
% 0.35/0.66 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 0.35/0.66 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_less_eq_numeral1(2)
% 0.35/0.66 thf(fact_7389_divide__less__eq__numeral1_I2_J,axiom,
% 0.35/0.66 ! [B: rat,W2: num,A: rat] :
% 0.35/0.66 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 0.35/0.66 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_less_eq_numeral1(2)
% 0.35/0.66 thf(fact_7390_dbl__dec__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(1)
% 0.35/0.66 thf(fact_7391_dbl__dec__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(1)
% 0.35/0.66 thf(fact_7392_dbl__dec__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(1)
% 0.35/0.66 thf(fact_7393_dbl__dec__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(1)
% 0.35/0.66 thf(fact_7394_dbl__dec__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_dec_simps(1)
% 0.35/0.66 thf(fact_7395_dbl__inc__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_inc_simps(1)
% 0.35/0.66 thf(fact_7396_dbl__inc__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_inc_simps(1)
% 0.35/0.66 thf(fact_7397_dbl__inc__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_inc_simps(1)
% 0.35/0.66 thf(fact_7398_dbl__inc__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_inc_simps(1)
% 0.35/0.66 thf(fact_7399_dbl__inc__simps_I1_J,axiom,
% 0.35/0.66 ! [K2: num] :
% 0.35/0.66 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_inc_simps(1)
% 0.35/0.66 thf(fact_7400_signed__take__bit__Suc__minus__bit0,axiom,
% 0.35/0.66 ! [N: nat,K2: num] :
% 0.35/0.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 0.35/0.66 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % signed_take_bit_Suc_minus_bit0
% 0.35/0.66 thf(fact_7401_signed__take__bit__Suc__bit0,axiom,
% 0.35/0.66 ! [N: nat,K2: num] :
% 0.35/0.66 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) )
% 0.35/0.66 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % signed_take_bit_Suc_bit0
% 0.35/0.66 thf(fact_7402_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.66 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_neg_numeral_special(9)
% 0.35/0.66 thf(fact_7403_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.66 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_neg_numeral_special(9)
% 0.35/0.66 thf(fact_7404_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_neg_numeral_special(9)
% 0.35/0.66 thf(fact_7405_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_neg_numeral_special(9)
% 0.35/0.66 thf(fact_7406_add__neg__numeral__special_I9_J,axiom,
% 0.35/0.66 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_neg_numeral_special(9)
% 0.35/0.66 thf(fact_7407_diff__numeral__special_I11_J,axiom,
% 0.35/0.66 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.66 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(11)
% 0.35/0.66 thf(fact_7408_diff__numeral__special_I11_J,axiom,
% 0.35/0.66 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(11)
% 0.35/0.66 thf(fact_7409_diff__numeral__special_I11_J,axiom,
% 0.35/0.66 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.66 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(11)
% 0.35/0.66 thf(fact_7410_diff__numeral__special_I11_J,axiom,
% 0.35/0.66 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.66 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(11)
% 0.35/0.66 thf(fact_7411_diff__numeral__special_I11_J,axiom,
% 0.35/0.66 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.66 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(11)
% 0.35/0.66 thf(fact_7412_diff__numeral__special_I10_J,axiom,
% 0.35/0.66 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(10)
% 0.35/0.66 thf(fact_7413_diff__numeral__special_I10_J,axiom,
% 0.35/0.66 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(10)
% 0.35/0.66 thf(fact_7414_diff__numeral__special_I10_J,axiom,
% 0.35/0.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(10)
% 0.35/0.66 thf(fact_7415_diff__numeral__special_I10_J,axiom,
% 0.35/0.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(10)
% 0.35/0.66 thf(fact_7416_diff__numeral__special_I10_J,axiom,
% 0.35/0.66 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(10)
% 0.35/0.66 thf(fact_7417_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.66 ! [A: int,N: nat] :
% 0.35/0.66 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % Power.ring_1_class.power_minus_even
% 0.35/0.66 thf(fact_7418_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.66 ! [A: real,N: nat] :
% 0.35/0.66 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % Power.ring_1_class.power_minus_even
% 0.35/0.66 thf(fact_7419_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.66 ! [A: complex,N: nat] :
% 0.35/0.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % Power.ring_1_class.power_minus_even
% 0.35/0.66 thf(fact_7420_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.66 ! [A: code_integer,N: nat] :
% 0.35/0.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % Power.ring_1_class.power_minus_even
% 0.35/0.66 thf(fact_7421_Power_Oring__1__class_Opower__minus__even,axiom,
% 0.35/0.66 ! [A: rat,N: nat] :
% 0.35/0.66 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % Power.ring_1_class.power_minus_even
% 0.35/0.66 thf(fact_7422_diff__numeral__special_I4_J,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(4)
% 0.35/0.66 thf(fact_7423_diff__numeral__special_I4_J,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(4)
% 0.35/0.66 thf(fact_7424_diff__numeral__special_I4_J,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ one_one_complex )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(4)
% 0.35/0.66 thf(fact_7425_diff__numeral__special_I4_J,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(4)
% 0.35/0.66 thf(fact_7426_diff__numeral__special_I4_J,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(4)
% 0.35/0.66 thf(fact_7427_diff__numeral__special_I3_J,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(3)
% 0.35/0.66 thf(fact_7428_diff__numeral__special_I3_J,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(3)
% 0.35/0.66 thf(fact_7429_diff__numeral__special_I3_J,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 0.35/0.66 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(3)
% 0.35/0.66 thf(fact_7430_diff__numeral__special_I3_J,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.66 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(3)
% 0.35/0.66 thf(fact_7431_diff__numeral__special_I3_J,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.66 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_numeral_special(3)
% 0.35/0.66 thf(fact_7432_set__decode__Suc,axiom,
% 0.35/0.66 ! [N: nat,X: nat] :
% 0.35/0.66 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 0.35/0.66 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % set_decode_Suc
% 0.35/0.66 thf(fact_7433_dbl__simps_I4_J,axiom,
% 0.35/0.66 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_simps(4)
% 0.35/0.66 thf(fact_7434_dbl__simps_I4_J,axiom,
% 0.35/0.66 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_simps(4)
% 0.35/0.66 thf(fact_7435_dbl__simps_I4_J,axiom,
% 0.35/0.66 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_simps(4)
% 0.35/0.66 thf(fact_7436_dbl__simps_I4_J,axiom,
% 0.35/0.66 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_simps(4)
% 0.35/0.66 thf(fact_7437_dbl__simps_I4_J,axiom,
% 0.35/0.66 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dbl_simps(4)
% 0.35/0.66 thf(fact_7438_power__minus1__even,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = one_one_int ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus1_even
% 0.35/0.66 thf(fact_7439_power__minus1__even,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = one_one_real ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus1_even
% 0.35/0.66 thf(fact_7440_power__minus1__even,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = one_one_complex ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus1_even
% 0.35/0.66 thf(fact_7441_power__minus1__even,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = one_one_Code_integer ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus1_even
% 0.35/0.66 thf(fact_7442_power__minus1__even,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.66 = one_one_rat ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus1_even
% 0.35/0.66 thf(fact_7443_signed__take__bit__0,axiom,
% 0.35/0.66 ! [A: code_integer] :
% 0.35/0.66 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % signed_take_bit_0
% 0.35/0.66 thf(fact_7444_signed__take__bit__0,axiom,
% 0.35/0.66 ! [A: int] :
% 0.35/0.66 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 0.35/0.66 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % signed_take_bit_0
% 0.35/0.66 thf(fact_7445_equation__minus__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_int @ B ) )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % equation_minus_iff
% 0.35/0.66 thf(fact_7446_equation__minus__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_real @ B ) )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % equation_minus_iff
% 0.35/0.66 thf(fact_7447_equation__minus__iff,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % equation_minus_iff
% 0.35/0.66 thf(fact_7448_equation__minus__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % equation_minus_iff
% 0.35/0.66 thf(fact_7449_equation__minus__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_rat @ B ) )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % equation_minus_iff
% 0.35/0.66 thf(fact_7450_minus__equation__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ( uminus_uminus_int @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( uminus_uminus_int @ B )
% 0.35/0.66 = A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_equation_iff
% 0.35/0.66 thf(fact_7451_minus__equation__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ( uminus_uminus_real @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( uminus_uminus_real @ B )
% 0.35/0.66 = A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_equation_iff
% 0.35/0.66 thf(fact_7452_minus__equation__iff,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( uminus1482373934393186551omplex @ B )
% 0.35/0.66 = A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_equation_iff
% 0.35/0.66 thf(fact_7453_minus__equation__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( uminus1351360451143612070nteger @ B )
% 0.35/0.66 = A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_equation_iff
% 0.35/0.66 thf(fact_7454_minus__equation__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ( uminus_uminus_rat @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( uminus_uminus_rat @ B )
% 0.35/0.66 = A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_equation_iff
% 0.35/0.66 thf(fact_7455_fact__mono__nat,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mono_nat
% 0.35/0.66 thf(fact_7456_fact__ge__self,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_self
% 0.35/0.66 thf(fact_7457_fact__nonzero,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri5044797733671781792omplex @ N )
% 0.35/0.66 != zero_zero_complex ) ).
% 0.35/0.66
% 0.35/0.66 % fact_nonzero
% 0.35/0.66 thf(fact_7458_fact__nonzero,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri773545260158071498ct_rat @ N )
% 0.35/0.66 != zero_zero_rat ) ).
% 0.35/0.66
% 0.35/0.66 % fact_nonzero
% 0.35/0.66 thf(fact_7459_fact__nonzero,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri1406184849735516958ct_int @ N )
% 0.35/0.66 != zero_zero_int ) ).
% 0.35/0.66
% 0.35/0.66 % fact_nonzero
% 0.35/0.66 thf(fact_7460_fact__nonzero,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri1408675320244567234ct_nat @ N )
% 0.35/0.66 != zero_zero_nat ) ).
% 0.35/0.66
% 0.35/0.66 % fact_nonzero
% 0.35/0.66 thf(fact_7461_fact__nonzero,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( semiri2265585572941072030t_real @ N )
% 0.35/0.66 != zero_zero_real ) ).
% 0.35/0.66
% 0.35/0.66 % fact_nonzero
% 0.35/0.66 thf(fact_7462_compl__le__swap2,axiom,
% 0.35/0.66 ! [Y: set_nat,X: set_nat] :
% 0.35/0.66 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 0.35/0.66 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 0.35/0.66
% 0.35/0.66 % compl_le_swap2
% 0.35/0.66 thf(fact_7463_compl__le__swap1,axiom,
% 0.35/0.66 ! [Y: set_nat,X: set_nat] :
% 0.35/0.66 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 0.35/0.66 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % compl_le_swap1
% 0.35/0.66 thf(fact_7464_compl__mono,axiom,
% 0.35/0.66 ! [X: set_nat,Y: set_nat] :
% 0.35/0.66 ( ( ord_less_eq_set_nat @ X @ Y )
% 0.35/0.66 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % compl_mono
% 0.35/0.66 thf(fact_7465_le__imp__neg__le,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ord_less_eq_real @ A @ B )
% 0.35/0.66 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_imp_neg_le
% 0.35/0.66 thf(fact_7466_le__imp__neg__le,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.35/0.66 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_imp_neg_le
% 0.35/0.66 thf(fact_7467_le__imp__neg__le,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.66 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_imp_neg_le
% 0.35/0.66 thf(fact_7468_le__imp__neg__le,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ord_less_eq_int @ A @ B )
% 0.35/0.66 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_imp_neg_le
% 0.35/0.66 thf(fact_7469_minus__le__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.66 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_le_iff
% 0.35/0.66 thf(fact_7470_minus__le__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.66 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_le_iff
% 0.35/0.66 thf(fact_7471_minus__le__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.66 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_le_iff
% 0.35/0.66 thf(fact_7472_minus__le__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.66 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_le_iff
% 0.35/0.66 thf(fact_7473_le__minus__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.66 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_iff
% 0.35/0.66 thf(fact_7474_le__minus__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.66 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_iff
% 0.35/0.66 thf(fact_7475_le__minus__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.66 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_iff
% 0.35/0.66 thf(fact_7476_le__minus__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.66 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_iff
% 0.35/0.66 thf(fact_7477_less__minus__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.66 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_iff
% 0.35/0.66 thf(fact_7478_less__minus__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.66 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_iff
% 0.35/0.66 thf(fact_7479_less__minus__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.66 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_iff
% 0.35/0.66 thf(fact_7480_less__minus__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.66 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_iff
% 0.35/0.66 thf(fact_7481_minus__less__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.66 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_less_iff
% 0.35/0.66 thf(fact_7482_minus__less__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.66 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_less_iff
% 0.35/0.66 thf(fact_7483_minus__less__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.66 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_less_iff
% 0.35/0.66 thf(fact_7484_minus__less__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.66 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_less_iff
% 0.35/0.66 thf(fact_7485_neg__numeral__neq__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 0.35/0.66 != ( numeral_numeral_int @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_neq_numeral
% 0.35/0.66 thf(fact_7486_neg__numeral__neq__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 0.35/0.66 != ( numeral_numeral_real @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_neq_numeral
% 0.35/0.66 thf(fact_7487_neg__numeral__neq__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 0.35/0.66 != ( numera6690914467698888265omplex @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_neq_numeral
% 0.35/0.66 thf(fact_7488_neg__numeral__neq__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 0.35/0.66 != ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_neq_numeral
% 0.35/0.66 thf(fact_7489_neg__numeral__neq__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 0.35/0.66 != ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_neq_numeral
% 0.35/0.66 thf(fact_7490_numeral__neq__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( numeral_numeral_int @ M2 )
% 0.35/0.66 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_numeral
% 0.35/0.66 thf(fact_7491_numeral__neq__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( numeral_numeral_real @ M2 )
% 0.35/0.66 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_numeral
% 0.35/0.66 thf(fact_7492_numeral__neq__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( numera6690914467698888265omplex @ M2 )
% 0.35/0.66 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_numeral
% 0.35/0.66 thf(fact_7493_numeral__neq__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( numera6620942414471956472nteger @ M2 )
% 0.35/0.66 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_numeral
% 0.35/0.66 thf(fact_7494_numeral__neq__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ( ( numeral_numeral_rat @ M2 )
% 0.35/0.66 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_numeral
% 0.35/0.66 thf(fact_7495_minus__mult__commute,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.66 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_mult_commute
% 0.35/0.66 thf(fact_7496_minus__mult__commute,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.66 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_mult_commute
% 0.35/0.66 thf(fact_7497_minus__mult__commute,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.66 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_mult_commute
% 0.35/0.66 thf(fact_7498_minus__mult__commute,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.66 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_mult_commute
% 0.35/0.66 thf(fact_7499_minus__mult__commute,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.66 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_mult_commute
% 0.35/0.66 thf(fact_7500_square__eq__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ( times_times_int @ A @ A )
% 0.35/0.66 = ( times_times_int @ B @ B ) )
% 0.35/0.66 = ( ( A = B )
% 0.35/0.66 | ( A
% 0.35/0.66 = ( uminus_uminus_int @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_iff
% 0.35/0.66 thf(fact_7501_square__eq__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ( times_times_real @ A @ A )
% 0.35/0.66 = ( times_times_real @ B @ B ) )
% 0.35/0.66 = ( ( A = B )
% 0.35/0.66 | ( A
% 0.35/0.66 = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_iff
% 0.35/0.66 thf(fact_7502_square__eq__iff,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( ( times_times_complex @ A @ A )
% 0.35/0.66 = ( times_times_complex @ B @ B ) )
% 0.35/0.66 = ( ( A = B )
% 0.35/0.66 | ( A
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_iff
% 0.35/0.66 thf(fact_7503_square__eq__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ( times_3573771949741848930nteger @ A @ A )
% 0.35/0.66 = ( times_3573771949741848930nteger @ B @ B ) )
% 0.35/0.66 = ( ( A = B )
% 0.35/0.66 | ( A
% 0.35/0.66 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_iff
% 0.35/0.66 thf(fact_7504_square__eq__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ( times_times_rat @ A @ A )
% 0.35/0.66 = ( times_times_rat @ B @ B ) )
% 0.35/0.66 = ( ( A = B )
% 0.35/0.66 | ( A
% 0.35/0.66 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_iff
% 0.35/0.66 thf(fact_7505_is__num__normalize_I8_J,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.35/0.66 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % is_num_normalize(8)
% 0.35/0.66 thf(fact_7506_is__num__normalize_I8_J,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.35/0.66 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % is_num_normalize(8)
% 0.35/0.66 thf(fact_7507_is__num__normalize_I8_J,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % is_num_normalize(8)
% 0.35/0.66 thf(fact_7508_is__num__normalize_I8_J,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % is_num_normalize(8)
% 0.35/0.66 thf(fact_7509_is__num__normalize_I8_J,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.66 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % is_num_normalize(8)
% 0.35/0.66 thf(fact_7510_group__cancel_Oneg1,axiom,
% 0.35/0.66 ! [A4: int,K2: int,A: int] :
% 0.35/0.66 ( ( A4
% 0.35/0.66 = ( plus_plus_int @ K2 @ A ) )
% 0.35/0.66 => ( ( uminus_uminus_int @ A4 )
% 0.35/0.66 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.neg1
% 0.35/0.66 thf(fact_7511_group__cancel_Oneg1,axiom,
% 0.35/0.66 ! [A4: real,K2: real,A: real] :
% 0.35/0.66 ( ( A4
% 0.35/0.66 = ( plus_plus_real @ K2 @ A ) )
% 0.35/0.66 => ( ( uminus_uminus_real @ A4 )
% 0.35/0.66 = ( plus_plus_real @ ( uminus_uminus_real @ K2 ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.neg1
% 0.35/0.66 thf(fact_7512_group__cancel_Oneg1,axiom,
% 0.35/0.66 ! [A4: complex,K2: complex,A: complex] :
% 0.35/0.66 ( ( A4
% 0.35/0.66 = ( plus_plus_complex @ K2 @ A ) )
% 0.35/0.66 => ( ( uminus1482373934393186551omplex @ A4 )
% 0.35/0.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K2 ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.neg1
% 0.35/0.66 thf(fact_7513_group__cancel_Oneg1,axiom,
% 0.35/0.66 ! [A4: code_integer,K2: code_integer,A: code_integer] :
% 0.35/0.66 ( ( A4
% 0.35/0.66 = ( plus_p5714425477246183910nteger @ K2 @ A ) )
% 0.35/0.66 => ( ( uminus1351360451143612070nteger @ A4 )
% 0.35/0.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.neg1
% 0.35/0.66 thf(fact_7514_group__cancel_Oneg1,axiom,
% 0.35/0.66 ! [A4: rat,K2: rat,A: rat] :
% 0.35/0.66 ( ( A4
% 0.35/0.66 = ( plus_plus_rat @ K2 @ A ) )
% 0.35/0.66 => ( ( uminus_uminus_rat @ A4 )
% 0.35/0.66 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.neg1
% 0.35/0.66 thf(fact_7515_add_Oinverse__distrib__swap,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 0.35/0.66 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_distrib_swap
% 0.35/0.66 thf(fact_7516_add_Oinverse__distrib__swap,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 0.35/0.66 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_distrib_swap
% 0.35/0.66 thf(fact_7517_add_Oinverse__distrib__swap,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 0.35/0.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_distrib_swap
% 0.35/0.66 thf(fact_7518_add_Oinverse__distrib__swap,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 0.35/0.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_distrib_swap
% 0.35/0.66 thf(fact_7519_add_Oinverse__distrib__swap,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 0.35/0.66 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_distrib_swap
% 0.35/0.66 thf(fact_7520_one__neq__neg__one,axiom,
% 0.35/0.66 ( one_one_int
% 0.35/0.66 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_one
% 0.35/0.66 thf(fact_7521_one__neq__neg__one,axiom,
% 0.35/0.66 ( one_one_real
% 0.35/0.66 != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_one
% 0.35/0.66 thf(fact_7522_one__neq__neg__one,axiom,
% 0.35/0.66 ( one_one_complex
% 0.35/0.66 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_one
% 0.35/0.66 thf(fact_7523_one__neq__neg__one,axiom,
% 0.35/0.66 ( one_one_Code_integer
% 0.35/0.66 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_one
% 0.35/0.66 thf(fact_7524_one__neq__neg__one,axiom,
% 0.35/0.66 ( one_one_rat
% 0.35/0.66 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_one
% 0.35/0.66 thf(fact_7525_minus__diff__commute,axiom,
% 0.35/0.66 ! [B: int,A: int] :
% 0.35/0.66 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 0.35/0.66 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_diff_commute
% 0.35/0.66 thf(fact_7526_minus__diff__commute,axiom,
% 0.35/0.66 ! [B: real,A: real] :
% 0.35/0.66 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 0.35/0.66 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_diff_commute
% 0.35/0.66 thf(fact_7527_minus__diff__commute,axiom,
% 0.35/0.66 ! [B: complex,A: complex] :
% 0.35/0.66 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 0.35/0.66 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_diff_commute
% 0.35/0.66 thf(fact_7528_minus__diff__commute,axiom,
% 0.35/0.66 ! [B: code_integer,A: code_integer] :
% 0.35/0.66 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 0.35/0.66 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_diff_commute
% 0.35/0.66 thf(fact_7529_minus__diff__commute,axiom,
% 0.35/0.66 ! [B: rat,A: rat] :
% 0.35/0.66 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 0.35/0.66 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_diff_commute
% 0.35/0.66 thf(fact_7530_signed__take__bit__mult,axiom,
% 0.35/0.66 ! [N: nat,K2: int,L: int] :
% 0.35/0.66 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K2 ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 0.35/0.66 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K2 @ L ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % signed_take_bit_mult
% 0.35/0.66 thf(fact_7531_fact__less__mono__nat,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.66 => ( ( ord_less_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_less_mono_nat
% 0.35/0.66 thf(fact_7532_fact__ge__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_zero
% 0.35/0.66 thf(fact_7533_fact__ge__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_zero
% 0.35/0.66 thf(fact_7534_fact__ge__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_zero
% 0.35/0.66 thf(fact_7535_fact__ge__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_zero
% 0.35/0.66 thf(fact_7536_fact__not__neg,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 0.35/0.66
% 0.35/0.66 % fact_not_neg
% 0.35/0.66 thf(fact_7537_fact__not__neg,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 0.35/0.66
% 0.35/0.66 % fact_not_neg
% 0.35/0.66 thf(fact_7538_fact__not__neg,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 0.35/0.66
% 0.35/0.66 % fact_not_neg
% 0.35/0.66 thf(fact_7539_fact__not__neg,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 0.35/0.66
% 0.35/0.66 % fact_not_neg
% 0.35/0.66 thf(fact_7540_fact__gt__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_gt_zero
% 0.35/0.66 thf(fact_7541_fact__gt__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_gt_zero
% 0.35/0.66 thf(fact_7542_fact__gt__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_gt_zero
% 0.35/0.66 thf(fact_7543_fact__gt__zero,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_gt_zero
% 0.35/0.66 thf(fact_7544_finite__set__decode,axiom,
% 0.35/0.66 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % finite_set_decode
% 0.35/0.66 thf(fact_7545_fact__ge__1,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_1
% 0.35/0.66 thf(fact_7546_fact__ge__1,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_1
% 0.35/0.66 thf(fact_7547_fact__ge__1,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_1
% 0.35/0.66 thf(fact_7548_fact__ge__1,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_1
% 0.35/0.66 thf(fact_7549_fact__ge__1,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_1
% 0.35/0.66 thf(fact_7550_neg__numeral__le__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_numeral
% 0.35/0.66 thf(fact_7551_neg__numeral__le__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_numeral
% 0.35/0.66 thf(fact_7552_neg__numeral__le__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_numeral
% 0.35/0.66 thf(fact_7553_neg__numeral__le__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_numeral
% 0.35/0.66 thf(fact_7554_not__numeral__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_numeral
% 0.35/0.66 thf(fact_7555_not__numeral__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_numeral
% 0.35/0.66 thf(fact_7556_not__numeral__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_numeral
% 0.35/0.66 thf(fact_7557_not__numeral__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_numeral
% 0.35/0.66 thf(fact_7558_zero__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( zero_zero_int
% 0.35/0.66 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_numeral
% 0.35/0.66 thf(fact_7559_zero__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( zero_zero_real
% 0.35/0.66 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_numeral
% 0.35/0.66 thf(fact_7560_zero__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( zero_zero_complex
% 0.35/0.66 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_numeral
% 0.35/0.66 thf(fact_7561_zero__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( zero_z3403309356797280102nteger
% 0.35/0.66 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_numeral
% 0.35/0.66 thf(fact_7562_zero__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( zero_zero_rat
% 0.35/0.66 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_numeral
% 0.35/0.66 thf(fact_7563_not__numeral__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_numeral
% 0.35/0.66 thf(fact_7564_not__numeral__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_numeral
% 0.35/0.66 thf(fact_7565_not__numeral__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_numeral
% 0.35/0.66 thf(fact_7566_not__numeral__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] :
% 0.35/0.66 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_numeral
% 0.35/0.66 thf(fact_7567_neg__numeral__less__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_numeral
% 0.35/0.66 thf(fact_7568_neg__numeral__less__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_numeral
% 0.35/0.66 thf(fact_7569_neg__numeral__less__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_numeral
% 0.35/0.66 thf(fact_7570_neg__numeral__less__numeral,axiom,
% 0.35/0.66 ! [M2: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_numeral
% 0.35/0.66 thf(fact_7571_le__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(4)
% 0.35/0.66 thf(fact_7572_le__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(4)
% 0.35/0.66 thf(fact_7573_le__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(4)
% 0.35/0.66 thf(fact_7574_le__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(4)
% 0.35/0.66 thf(fact_7575_le__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(2)
% 0.35/0.66 thf(fact_7576_le__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(2)
% 0.35/0.66 thf(fact_7577_le__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(2)
% 0.35/0.66 thf(fact_7578_le__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(2)
% 0.35/0.66 thf(fact_7579_add__eq__0__iff,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ( plus_plus_int @ A @ B )
% 0.35/0.66 = zero_zero_int )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_eq_0_iff
% 0.35/0.66 thf(fact_7580_add__eq__0__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ( plus_plus_real @ A @ B )
% 0.35/0.66 = zero_zero_real )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_eq_0_iff
% 0.35/0.66 thf(fact_7581_add__eq__0__iff,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( ( plus_plus_complex @ A @ B )
% 0.35/0.66 = zero_zero_complex )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_eq_0_iff
% 0.35/0.66 thf(fact_7582_add__eq__0__iff,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.66 = zero_z3403309356797280102nteger )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_eq_0_iff
% 0.35/0.66 thf(fact_7583_add__eq__0__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ( plus_plus_rat @ A @ B )
% 0.35/0.66 = zero_zero_rat )
% 0.35/0.66 = ( B
% 0.35/0.66 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_eq_0_iff
% 0.35/0.66 thf(fact_7584_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.66 ! [A: int] :
% 0.35/0.66 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 0.35/0.66 = zero_zero_int ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_left_minus
% 0.35/0.66 thf(fact_7585_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.66 ! [A: real] :
% 0.35/0.66 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 0.35/0.66 = zero_zero_real ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_left_minus
% 0.35/0.66 thf(fact_7586_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.66 ! [A: complex] :
% 0.35/0.66 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 0.35/0.66 = zero_zero_complex ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_left_minus
% 0.35/0.66 thf(fact_7587_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.66 ! [A: code_integer] :
% 0.35/0.66 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 0.35/0.66 = zero_z3403309356797280102nteger ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_left_minus
% 0.35/0.66 thf(fact_7588_ab__group__add__class_Oab__left__minus,axiom,
% 0.35/0.66 ! [A: rat] :
% 0.35/0.66 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 0.35/0.66 = zero_zero_rat ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_left_minus
% 0.35/0.66 thf(fact_7589_add_Oinverse__unique,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ( plus_plus_int @ A @ B )
% 0.35/0.66 = zero_zero_int )
% 0.35/0.66 => ( ( uminus_uminus_int @ A )
% 0.35/0.66 = B ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_unique
% 0.35/0.66 thf(fact_7590_add_Oinverse__unique,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ( plus_plus_real @ A @ B )
% 0.35/0.66 = zero_zero_real )
% 0.35/0.66 => ( ( uminus_uminus_real @ A )
% 0.35/0.66 = B ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_unique
% 0.35/0.66 thf(fact_7591_add_Oinverse__unique,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( ( plus_plus_complex @ A @ B )
% 0.35/0.66 = zero_zero_complex )
% 0.35/0.66 => ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.66 = B ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_unique
% 0.35/0.66 thf(fact_7592_add_Oinverse__unique,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.66 = zero_z3403309356797280102nteger )
% 0.35/0.66 => ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.66 = B ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_unique
% 0.35/0.66 thf(fact_7593_add_Oinverse__unique,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ( plus_plus_rat @ A @ B )
% 0.35/0.66 = zero_zero_rat )
% 0.35/0.66 => ( ( uminus_uminus_rat @ A )
% 0.35/0.66 = B ) ) ).
% 0.35/0.66
% 0.35/0.66 % add.inverse_unique
% 0.35/0.66 thf(fact_7594_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_int @ B ) )
% 0.35/0.66 = ( ( plus_plus_int @ A @ B )
% 0.35/0.66 = zero_zero_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_neg_iff_add_eq_0
% 0.35/0.66 thf(fact_7595_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_real @ B ) )
% 0.35/0.66 = ( ( plus_plus_real @ A @ B )
% 0.35/0.66 = zero_zero_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_neg_iff_add_eq_0
% 0.35/0.66 thf(fact_7596_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.66 = ( ( plus_plus_complex @ A @ B )
% 0.35/0.66 = zero_zero_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_neg_iff_add_eq_0
% 0.35/0.66 thf(fact_7597_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.66 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.66 = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_neg_iff_add_eq_0
% 0.35/0.66 thf(fact_7598_eq__neg__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_rat @ B ) )
% 0.35/0.66 = ( ( plus_plus_rat @ A @ B )
% 0.35/0.66 = zero_zero_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_neg_iff_add_eq_0
% 0.35/0.66 thf(fact_7599_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ( uminus_uminus_int @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( plus_plus_int @ A @ B )
% 0.35/0.66 = zero_zero_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_eq_iff_add_eq_0
% 0.35/0.66 thf(fact_7600_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ( uminus_uminus_real @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( plus_plus_real @ A @ B )
% 0.35/0.66 = zero_zero_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_eq_iff_add_eq_0
% 0.35/0.66 thf(fact_7601_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( plus_plus_complex @ A @ B )
% 0.35/0.66 = zero_zero_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_eq_iff_add_eq_0
% 0.35/0.66 thf(fact_7602_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: code_integer,B: code_integer] :
% 0.35/0.66 ( ( ( uminus1351360451143612070nteger @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 0.35/0.66 = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_eq_iff_add_eq_0
% 0.35/0.66 thf(fact_7603_neg__eq__iff__add__eq__0,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ( uminus_uminus_rat @ A )
% 0.35/0.66 = B )
% 0.35/0.66 = ( ( plus_plus_rat @ A @ B )
% 0.35/0.66 = zero_zero_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_eq_iff_add_eq_0
% 0.35/0.66 thf(fact_7604_zero__neq__neg__one,axiom,
% 0.35/0.66 ( zero_zero_int
% 0.35/0.66 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_one
% 0.35/0.66 thf(fact_7605_zero__neq__neg__one,axiom,
% 0.35/0.66 ( zero_zero_real
% 0.35/0.66 != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_one
% 0.35/0.66 thf(fact_7606_zero__neq__neg__one,axiom,
% 0.35/0.66 ( zero_zero_complex
% 0.35/0.66 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_one
% 0.35/0.66 thf(fact_7607_zero__neq__neg__one,axiom,
% 0.35/0.66 ( zero_z3403309356797280102nteger
% 0.35/0.66 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_one
% 0.35/0.66 thf(fact_7608_zero__neq__neg__one,axiom,
% 0.35/0.66 ( zero_zero_rat
% 0.35/0.66 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % zero_neq_neg_one
% 0.35/0.66 thf(fact_7609_less__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(4)
% 0.35/0.66 thf(fact_7610_less__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(4)
% 0.35/0.66 thf(fact_7611_less__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(4)
% 0.35/0.66 thf(fact_7612_less__minus__one__simps_I4_J,axiom,
% 0.35/0.66 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(4)
% 0.35/0.66 thf(fact_7613_less__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(2)
% 0.35/0.66 thf(fact_7614_less__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(2)
% 0.35/0.66 thf(fact_7615_less__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(2)
% 0.35/0.66 thf(fact_7616_less__minus__one__simps_I2_J,axiom,
% 0.35/0.66 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(2)
% 0.35/0.66 thf(fact_7617_numeral__times__minus__swap,axiom,
% 0.35/0.66 ! [W2: num,X: int] :
% 0.35/0.66 ( ( times_times_int @ ( numeral_numeral_int @ W2 ) @ ( uminus_uminus_int @ X ) )
% 0.35/0.66 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_times_minus_swap
% 0.35/0.66 thf(fact_7618_numeral__times__minus__swap,axiom,
% 0.35/0.66 ! [W2: num,X: real] :
% 0.35/0.66 ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( uminus_uminus_real @ X ) )
% 0.35/0.66 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_times_minus_swap
% 0.35/0.66 thf(fact_7619_numeral__times__minus__swap,axiom,
% 0.35/0.66 ! [W2: num,X: complex] :
% 0.35/0.66 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ ( uminus1482373934393186551omplex @ X ) )
% 0.35/0.66 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_times_minus_swap
% 0.35/0.66 thf(fact_7620_numeral__times__minus__swap,axiom,
% 0.35/0.66 ! [W2: num,X: code_integer] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ ( uminus1351360451143612070nteger @ X ) )
% 0.35/0.66 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_times_minus_swap
% 0.35/0.66 thf(fact_7621_numeral__times__minus__swap,axiom,
% 0.35/0.66 ! [W2: num,X: rat] :
% 0.35/0.66 ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ ( uminus_uminus_rat @ X ) )
% 0.35/0.66 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_times_minus_swap
% 0.35/0.66 thf(fact_7622_nonzero__minus__divide__divide,axiom,
% 0.35/0.66 ! [B: real,A: real] :
% 0.35/0.66 ( ( B != zero_zero_real )
% 0.35/0.66 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 0.35/0.66 = ( divide_divide_real @ A @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_minus_divide_divide
% 0.35/0.66 thf(fact_7623_nonzero__minus__divide__divide,axiom,
% 0.35/0.66 ! [B: complex,A: complex] :
% 0.35/0.66 ( ( B != zero_zero_complex )
% 0.35/0.66 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.66 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_minus_divide_divide
% 0.35/0.66 thf(fact_7624_nonzero__minus__divide__divide,axiom,
% 0.35/0.66 ! [B: rat,A: rat] :
% 0.35/0.66 ( ( B != zero_zero_rat )
% 0.35/0.66 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 0.35/0.66 = ( divide_divide_rat @ A @ B ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_minus_divide_divide
% 0.35/0.66 thf(fact_7625_nonzero__minus__divide__right,axiom,
% 0.35/0.66 ! [B: real,A: real] :
% 0.35/0.66 ( ( B != zero_zero_real )
% 0.35/0.66 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.66 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_minus_divide_right
% 0.35/0.66 thf(fact_7626_nonzero__minus__divide__right,axiom,
% 0.35/0.66 ! [B: complex,A: complex] :
% 0.35/0.66 ( ( B != zero_zero_complex )
% 0.35/0.66 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.66 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_minus_divide_right
% 0.35/0.66 thf(fact_7627_nonzero__minus__divide__right,axiom,
% 0.35/0.66 ! [B: rat,A: rat] :
% 0.35/0.66 ( ( B != zero_zero_rat )
% 0.35/0.66 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.66 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_minus_divide_right
% 0.35/0.66 thf(fact_7628_one__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( one_one_int
% 0.35/0.66 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_numeral
% 0.35/0.66 thf(fact_7629_one__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( one_one_real
% 0.35/0.66 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_numeral
% 0.35/0.66 thf(fact_7630_one__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( one_one_complex
% 0.35/0.66 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_numeral
% 0.35/0.66 thf(fact_7631_one__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( one_one_Code_integer
% 0.35/0.66 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_numeral
% 0.35/0.66 thf(fact_7632_one__neq__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( one_one_rat
% 0.35/0.66 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % one_neq_neg_numeral
% 0.35/0.66 thf(fact_7633_numeral__neq__neg__one,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( numeral_numeral_int @ N )
% 0.35/0.66 != ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_one
% 0.35/0.66 thf(fact_7634_numeral__neq__neg__one,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( numeral_numeral_real @ N )
% 0.35/0.66 != ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_one
% 0.35/0.66 thf(fact_7635_numeral__neq__neg__one,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( numera6690914467698888265omplex @ N )
% 0.35/0.66 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_one
% 0.35/0.66 thf(fact_7636_numeral__neq__neg__one,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( numera6620942414471956472nteger @ N )
% 0.35/0.66 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_one
% 0.35/0.66 thf(fact_7637_numeral__neq__neg__one,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ( ( numeral_numeral_rat @ N )
% 0.35/0.66 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % numeral_neq_neg_one
% 0.35/0.66 thf(fact_7638_square__eq__1__iff,axiom,
% 0.35/0.66 ! [X: int] :
% 0.35/0.66 ( ( ( times_times_int @ X @ X )
% 0.35/0.66 = one_one_int )
% 0.35/0.66 = ( ( X = one_one_int )
% 0.35/0.66 | ( X
% 0.35/0.66 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_1_iff
% 0.35/0.66 thf(fact_7639_square__eq__1__iff,axiom,
% 0.35/0.66 ! [X: real] :
% 0.35/0.66 ( ( ( times_times_real @ X @ X )
% 0.35/0.66 = one_one_real )
% 0.35/0.66 = ( ( X = one_one_real )
% 0.35/0.66 | ( X
% 0.35/0.66 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_1_iff
% 0.35/0.66 thf(fact_7640_square__eq__1__iff,axiom,
% 0.35/0.66 ! [X: complex] :
% 0.35/0.66 ( ( ( times_times_complex @ X @ X )
% 0.35/0.66 = one_one_complex )
% 0.35/0.66 = ( ( X = one_one_complex )
% 0.35/0.66 | ( X
% 0.35/0.66 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_1_iff
% 0.35/0.66 thf(fact_7641_square__eq__1__iff,axiom,
% 0.35/0.66 ! [X: code_integer] :
% 0.35/0.66 ( ( ( times_3573771949741848930nteger @ X @ X )
% 0.35/0.66 = one_one_Code_integer )
% 0.35/0.66 = ( ( X = one_one_Code_integer )
% 0.35/0.66 | ( X
% 0.35/0.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_1_iff
% 0.35/0.66 thf(fact_7642_square__eq__1__iff,axiom,
% 0.35/0.66 ! [X: rat] :
% 0.35/0.66 ( ( ( times_times_rat @ X @ X )
% 0.35/0.66 = one_one_rat )
% 0.35/0.66 = ( ( X = one_one_rat )
% 0.35/0.66 | ( X
% 0.35/0.66 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % square_eq_1_iff
% 0.35/0.66 thf(fact_7643_fact__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mono
% 0.35/0.66 thf(fact_7644_fact__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mono
% 0.35/0.66 thf(fact_7645_fact__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mono
% 0.35/0.66 thf(fact_7646_fact__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mono
% 0.35/0.66 thf(fact_7647_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_int
% 0.35/0.66 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.66 thf(fact_7648_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_real
% 0.35/0.66 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.66 thf(fact_7649_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_complex
% 0.35/0.66 = ( ^ [A5: complex,B4: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.66 thf(fact_7650_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_8373710615458151222nteger
% 0.35/0.66 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.66 thf(fact_7651_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_rat
% 0.35/0.66 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % ab_group_add_class.ab_diff_conv_add_uminus
% 0.35/0.66 thf(fact_7652_diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_int
% 0.35/0.66 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_conv_add_uminus
% 0.35/0.66 thf(fact_7653_diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_real
% 0.35/0.66 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_conv_add_uminus
% 0.35/0.66 thf(fact_7654_diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_complex
% 0.35/0.66 = ( ^ [A5: complex,B4: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_conv_add_uminus
% 0.35/0.66 thf(fact_7655_diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_8373710615458151222nteger
% 0.35/0.66 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_conv_add_uminus
% 0.35/0.66 thf(fact_7656_diff__conv__add__uminus,axiom,
% 0.35/0.66 ( minus_minus_rat
% 0.35/0.66 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % diff_conv_add_uminus
% 0.35/0.66 thf(fact_7657_group__cancel_Osub2,axiom,
% 0.35/0.66 ! [B5: int,K2: int,B: int,A: int] :
% 0.35/0.66 ( ( B5
% 0.35/0.66 = ( plus_plus_int @ K2 @ B ) )
% 0.35/0.66 => ( ( minus_minus_int @ A @ B5 )
% 0.35/0.66 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.sub2
% 0.35/0.66 thf(fact_7658_group__cancel_Osub2,axiom,
% 0.35/0.66 ! [B5: real,K2: real,B: real,A: real] :
% 0.35/0.66 ( ( B5
% 0.35/0.66 = ( plus_plus_real @ K2 @ B ) )
% 0.35/0.66 => ( ( minus_minus_real @ A @ B5 )
% 0.35/0.66 = ( plus_plus_real @ ( uminus_uminus_real @ K2 ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.sub2
% 0.35/0.66 thf(fact_7659_group__cancel_Osub2,axiom,
% 0.35/0.66 ! [B5: complex,K2: complex,B: complex,A: complex] :
% 0.35/0.66 ( ( B5
% 0.35/0.66 = ( plus_plus_complex @ K2 @ B ) )
% 0.35/0.66 => ( ( minus_minus_complex @ A @ B5 )
% 0.35/0.66 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K2 ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.sub2
% 0.35/0.66 thf(fact_7660_group__cancel_Osub2,axiom,
% 0.35/0.66 ! [B5: code_integer,K2: code_integer,B: code_integer,A: code_integer] :
% 0.35/0.66 ( ( B5
% 0.35/0.66 = ( plus_p5714425477246183910nteger @ K2 @ B ) )
% 0.35/0.66 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 0.35/0.66 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.sub2
% 0.35/0.66 thf(fact_7661_group__cancel_Osub2,axiom,
% 0.35/0.66 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 0.35/0.66 ( ( B5
% 0.35/0.66 = ( plus_plus_rat @ K2 @ B ) )
% 0.35/0.66 => ( ( minus_minus_rat @ A @ B5 )
% 0.35/0.66 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % group_cancel.sub2
% 0.35/0.66 thf(fact_7662_dvd__neg__div,axiom,
% 0.35/0.66 ! [B: int,A: int] :
% 0.35/0.66 ( ( dvd_dvd_int @ B @ A )
% 0.35/0.66 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.66 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_neg_div
% 0.35/0.66 thf(fact_7663_dvd__neg__div,axiom,
% 0.35/0.66 ! [B: real,A: real] :
% 0.35/0.66 ( ( dvd_dvd_real @ B @ A )
% 0.35/0.66 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.66 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_neg_div
% 0.35/0.66 thf(fact_7664_dvd__neg__div,axiom,
% 0.35/0.66 ! [B: complex,A: complex] :
% 0.35/0.66 ( ( dvd_dvd_complex @ B @ A )
% 0.35/0.66 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_neg_div
% 0.35/0.66 thf(fact_7665_dvd__neg__div,axiom,
% 0.35/0.66 ! [B: code_integer,A: code_integer] :
% 0.35/0.66 ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.66 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_neg_div
% 0.35/0.66 thf(fact_7666_dvd__neg__div,axiom,
% 0.35/0.66 ! [B: rat,A: rat] :
% 0.35/0.66 ( ( dvd_dvd_rat @ B @ A )
% 0.35/0.66 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.66 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_neg_div
% 0.35/0.66 thf(fact_7667_dvd__div__neg,axiom,
% 0.35/0.66 ! [B: int,A: int] :
% 0.35/0.66 ( ( dvd_dvd_int @ B @ A )
% 0.35/0.66 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.66 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_div_neg
% 0.35/0.66 thf(fact_7668_dvd__div__neg,axiom,
% 0.35/0.66 ! [B: real,A: real] :
% 0.35/0.66 ( ( dvd_dvd_real @ B @ A )
% 0.35/0.66 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 0.35/0.66 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_div_neg
% 0.35/0.66 thf(fact_7669_dvd__div__neg,axiom,
% 0.35/0.66 ! [B: complex,A: complex] :
% 0.35/0.66 ( ( dvd_dvd_complex @ B @ A )
% 0.35/0.66 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_div_neg
% 0.35/0.66 thf(fact_7670_dvd__div__neg,axiom,
% 0.35/0.66 ! [B: code_integer,A: code_integer] :
% 0.35/0.66 ( ( dvd_dvd_Code_integer @ B @ A )
% 0.35/0.66 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_div_neg
% 0.35/0.66 thf(fact_7671_dvd__div__neg,axiom,
% 0.35/0.66 ! [B: rat,A: rat] :
% 0.35/0.66 ( ( dvd_dvd_rat @ B @ A )
% 0.35/0.66 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 0.35/0.66 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_div_neg
% 0.35/0.66 thf(fact_7672_fact__dvd,axiom,
% 0.35/0.66 ! [N: nat,M2: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.66 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_dvd
% 0.35/0.66 thf(fact_7673_fact__dvd,axiom,
% 0.35/0.66 ! [N: nat,M2: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.66 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_dvd
% 0.35/0.66 thf(fact_7674_fact__dvd,axiom,
% 0.35/0.66 ! [N: nat,M2: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.66 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_dvd
% 0.35/0.66 thf(fact_7675_real__minus__mult__self__le,axiom,
% 0.35/0.66 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 0.35/0.66
% 0.35/0.66 % real_minus_mult_self_le
% 0.35/0.66 thf(fact_7676_int__of__nat__induct,axiom,
% 0.35/0.66 ! [P2: int > $o,Z3: int] :
% 0.35/0.66 ( ! [N3: nat] : ( P2 @ ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.66 => ( ! [N3: nat] : ( P2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 0.35/0.66 => ( P2 @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % int_of_nat_induct
% 0.35/0.66 thf(fact_7677_int__cases,axiom,
% 0.35/0.66 ! [Z3: int] :
% 0.35/0.66 ( ! [N3: nat] :
% 0.35/0.66 ( Z3
% 0.35/0.66 != ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.66 => ~ ! [N3: nat] :
% 0.35/0.66 ( Z3
% 0.35/0.66 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % int_cases
% 0.35/0.66 thf(fact_7678_zmult__eq__1__iff,axiom,
% 0.35/0.66 ! [M2: int,N: int] :
% 0.35/0.66 ( ( ( times_times_int @ M2 @ N )
% 0.35/0.66 = one_one_int )
% 0.35/0.66 = ( ( ( M2 = one_one_int )
% 0.35/0.66 & ( N = one_one_int ) )
% 0.35/0.66 | ( ( M2
% 0.35/0.66 = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.66 & ( N
% 0.35/0.66 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zmult_eq_1_iff
% 0.35/0.66 thf(fact_7679_pos__zmult__eq__1__iff__lemma,axiom,
% 0.35/0.66 ! [M2: int,N: int] :
% 0.35/0.66 ( ( ( times_times_int @ M2 @ N )
% 0.35/0.66 = one_one_int )
% 0.35/0.66 => ( ( M2 = one_one_int )
% 0.35/0.66 | ( M2
% 0.35/0.66 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pos_zmult_eq_1_iff_lemma
% 0.35/0.66 thf(fact_7680_zmod__zminus1__not__zero,axiom,
% 0.35/0.66 ! [K2: int,L: int] :
% 0.35/0.66 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K2 ) @ L )
% 0.35/0.66 != zero_zero_int )
% 0.35/0.66 => ( ( modulo_modulo_int @ K2 @ L )
% 0.35/0.66 != zero_zero_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % zmod_zminus1_not_zero
% 0.35/0.66 thf(fact_7681_zmod__zminus2__not__zero,axiom,
% 0.35/0.66 ! [K2: int,L: int] :
% 0.35/0.66 ( ( ( modulo_modulo_int @ K2 @ ( uminus_uminus_int @ L ) )
% 0.35/0.66 != zero_zero_int )
% 0.35/0.66 => ( ( modulo_modulo_int @ K2 @ L )
% 0.35/0.66 != zero_zero_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % zmod_zminus2_not_zero
% 0.35/0.66 thf(fact_7682_pochhammer__same,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 0.35/0.66 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_same
% 0.35/0.66 thf(fact_7683_pochhammer__same,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 0.35/0.66 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_same
% 0.35/0.66 thf(fact_7684_pochhammer__same,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 0.35/0.66 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_same
% 0.35/0.66 thf(fact_7685_pochhammer__same,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 0.35/0.66 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_same
% 0.35/0.66 thf(fact_7686_pochhammer__same,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 0.35/0.66 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_same
% 0.35/0.66 thf(fact_7687_fact__ge__Suc__0__nat,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_ge_Suc_0_nat
% 0.35/0.66 thf(fact_7688_dvd__fact,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 0.35/0.66 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % dvd_fact
% 0.35/0.66 thf(fact_7689_not__zero__le__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_le_neg_numeral
% 0.35/0.66 thf(fact_7690_not__zero__le__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_le_neg_numeral
% 0.35/0.66 thf(fact_7691_not__zero__le__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_le_neg_numeral
% 0.35/0.66 thf(fact_7692_not__zero__le__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_le_neg_numeral
% 0.35/0.66 thf(fact_7693_neg__numeral__le__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_zero
% 0.35/0.66 thf(fact_7694_neg__numeral__le__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_zero
% 0.35/0.66 thf(fact_7695_neg__numeral__le__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_zero
% 0.35/0.66 thf(fact_7696_neg__numeral__le__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_zero
% 0.35/0.66 thf(fact_7697_not__zero__less__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_less_neg_numeral
% 0.35/0.66 thf(fact_7698_not__zero__less__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_less_neg_numeral
% 0.35/0.66 thf(fact_7699_not__zero__less__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_less_neg_numeral
% 0.35/0.66 thf(fact_7700_not__zero__less__neg__numeral,axiom,
% 0.35/0.66 ! [N: num] :
% 0.35/0.66 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zero_less_neg_numeral
% 0.35/0.66 thf(fact_7701_neg__numeral__less__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_zero
% 0.35/0.66 thf(fact_7702_neg__numeral__less__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_zero
% 0.35/0.66 thf(fact_7703_neg__numeral__less__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_zero
% 0.35/0.66 thf(fact_7704_neg__numeral__less__zero,axiom,
% 0.35/0.66 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_zero
% 0.35/0.66 thf(fact_7705_le__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(1)
% 0.35/0.66 thf(fact_7706_le__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(1)
% 0.35/0.66 thf(fact_7707_le__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(1)
% 0.35/0.66 thf(fact_7708_le__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(1)
% 0.35/0.66 thf(fact_7709_le__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(3)
% 0.35/0.66 thf(fact_7710_le__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(3)
% 0.35/0.66 thf(fact_7711_le__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(3)
% 0.35/0.66 thf(fact_7712_le__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_one_simps(3)
% 0.35/0.66 thf(fact_7713_less__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(1)
% 0.35/0.66 thf(fact_7714_less__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(1)
% 0.35/0.66 thf(fact_7715_less__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(1)
% 0.35/0.66 thf(fact_7716_less__minus__one__simps_I1_J,axiom,
% 0.35/0.66 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(1)
% 0.35/0.66 thf(fact_7717_less__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(3)
% 0.35/0.66 thf(fact_7718_less__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(3)
% 0.35/0.66 thf(fact_7719_less__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(3)
% 0.35/0.66 thf(fact_7720_less__minus__one__simps_I3_J,axiom,
% 0.35/0.66 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_one_simps(3)
% 0.35/0.66 thf(fact_7721_not__one__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_le_neg_numeral
% 0.35/0.66 thf(fact_7722_not__one__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_le_neg_numeral
% 0.35/0.66 thf(fact_7723_not__one__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_le_neg_numeral
% 0.35/0.66 thf(fact_7724_not__one__le__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_le_neg_numeral
% 0.35/0.66 thf(fact_7725_not__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_one
% 0.35/0.66 thf(fact_7726_not__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_one
% 0.35/0.66 thf(fact_7727_not__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_one
% 0.35/0.66 thf(fact_7728_not__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_le_neg_one
% 0.35/0.66 thf(fact_7729_neg__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_neg_one
% 0.35/0.66 thf(fact_7730_neg__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_neg_one
% 0.35/0.66 thf(fact_7731_neg__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_neg_one
% 0.35/0.66 thf(fact_7732_neg__numeral__le__neg__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_neg_one
% 0.35/0.66 thf(fact_7733_neg__one__le__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_le_numeral
% 0.35/0.66 thf(fact_7734_neg__one__le__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_le_numeral
% 0.35/0.66 thf(fact_7735_neg__one__le__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_le_numeral
% 0.35/0.66 thf(fact_7736_neg__one__le__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_le_numeral
% 0.35/0.66 thf(fact_7737_neg__numeral__le__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_one
% 0.35/0.66 thf(fact_7738_neg__numeral__le__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_one
% 0.35/0.66 thf(fact_7739_neg__numeral__le__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_one
% 0.35/0.66 thf(fact_7740_neg__numeral__le__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_le_one
% 0.35/0.66 thf(fact_7741_gbinomial__pochhammer,axiom,
% 0.35/0.66 ( gbinomial_complex
% 0.35/0.66 = ( ^ [A5: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A5 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % gbinomial_pochhammer
% 0.35/0.66 thf(fact_7742_gbinomial__pochhammer,axiom,
% 0.35/0.66 ( gbinomial_rat
% 0.35/0.66 = ( ^ [A5: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A5 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % gbinomial_pochhammer
% 0.35/0.66 thf(fact_7743_gbinomial__pochhammer,axiom,
% 0.35/0.66 ( gbinomial_real
% 0.35/0.66 = ( ^ [A5: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A5 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % gbinomial_pochhammer
% 0.35/0.66 thf(fact_7744_neg__numeral__less__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_one
% 0.35/0.66 thf(fact_7745_neg__numeral__less__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_one
% 0.35/0.66 thf(fact_7746_neg__numeral__less__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_one
% 0.35/0.66 thf(fact_7747_neg__numeral__less__one,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 0.35/0.66
% 0.35/0.66 % neg_numeral_less_one
% 0.35/0.66 thf(fact_7748_neg__one__less__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_less_numeral
% 0.35/0.66 thf(fact_7749_neg__one__less__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_less_numeral
% 0.35/0.66 thf(fact_7750_neg__one__less__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_less_numeral
% 0.35/0.66 thf(fact_7751_neg__one__less__numeral,axiom,
% 0.35/0.66 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_one_less_numeral
% 0.35/0.66 thf(fact_7752_not__numeral__less__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_one
% 0.35/0.66 thf(fact_7753_not__numeral__less__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_one
% 0.35/0.66 thf(fact_7754_not__numeral__less__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_one
% 0.35/0.66 thf(fact_7755_not__numeral__less__neg__one,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_numeral_less_neg_one
% 0.35/0.66 thf(fact_7756_not__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_less_neg_numeral
% 0.35/0.66 thf(fact_7757_not__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_less_neg_numeral
% 0.35/0.66 thf(fact_7758_not__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_less_neg_numeral
% 0.35/0.66 thf(fact_7759_not__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_one_less_neg_numeral
% 0.35/0.66 thf(fact_7760_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_less_neg_numeral
% 0.35/0.66 thf(fact_7761_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_less_neg_numeral
% 0.35/0.66 thf(fact_7762_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_less_neg_numeral
% 0.35/0.66 thf(fact_7763_not__neg__one__less__neg__numeral,axiom,
% 0.35/0.66 ! [M2: num] :
% 0.35/0.66 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_neg_one_less_neg_numeral
% 0.35/0.66 thf(fact_7764_eq__minus__divide__eq,axiom,
% 0.35/0.66 ! [A: real,B: real,C2: real] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_real )
% 0.35/0.66 => ( ( times_times_real @ A @ C2 )
% 0.35/0.66 = ( uminus_uminus_real @ B ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_real )
% 0.35/0.66 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_minus_divide_eq
% 0.35/0.66 thf(fact_7765_eq__minus__divide__eq,axiom,
% 0.35/0.66 ! [A: complex,B: complex,C2: complex] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C2 ) ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.66 => ( ( times_times_complex @ A @ C2 )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_complex )
% 0.35/0.66 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_minus_divide_eq
% 0.35/0.66 thf(fact_7766_eq__minus__divide__eq,axiom,
% 0.35/0.66 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.66 ( ( A
% 0.35/0.66 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.66 => ( ( times_times_rat @ A @ C2 )
% 0.35/0.66 = ( uminus_uminus_rat @ B ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_rat )
% 0.35/0.66 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_minus_divide_eq
% 0.35/0.66 thf(fact_7767_minus__divide__eq__eq,axiom,
% 0.35/0.66 ! [B: real,C2: real,A: real] :
% 0.35/0.66 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.66 = A )
% 0.35/0.66 = ( ( ( C2 != zero_zero_real )
% 0.35/0.66 => ( ( uminus_uminus_real @ B )
% 0.35/0.66 = ( times_times_real @ A @ C2 ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_real )
% 0.35/0.66 => ( A = zero_zero_real ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_eq_eq
% 0.35/0.66 thf(fact_7768_minus__divide__eq__eq,axiom,
% 0.35/0.66 ! [B: complex,C2: complex,A: complex] :
% 0.35/0.66 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.66 = A )
% 0.35/0.66 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.66 => ( ( uminus1482373934393186551omplex @ B )
% 0.35/0.66 = ( times_times_complex @ A @ C2 ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_complex )
% 0.35/0.66 => ( A = zero_zero_complex ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_eq_eq
% 0.35/0.66 thf(fact_7769_minus__divide__eq__eq,axiom,
% 0.35/0.66 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.66 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.66 = A )
% 0.35/0.66 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.66 => ( ( uminus_uminus_rat @ B )
% 0.35/0.66 = ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_rat )
% 0.35/0.66 => ( A = zero_zero_rat ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_eq_eq
% 0.35/0.66 thf(fact_7770_nonzero__neg__divide__eq__eq,axiom,
% 0.35/0.66 ! [B: real,A: real,C2: real] :
% 0.35/0.66 ( ( B != zero_zero_real )
% 0.35/0.66 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.66 = C2 )
% 0.35/0.66 = ( ( uminus_uminus_real @ A )
% 0.35/0.66 = ( times_times_real @ C2 @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_neg_divide_eq_eq
% 0.35/0.66 thf(fact_7771_nonzero__neg__divide__eq__eq,axiom,
% 0.35/0.66 ! [B: complex,A: complex,C2: complex] :
% 0.35/0.66 ( ( B != zero_zero_complex )
% 0.35/0.66 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.66 = C2 )
% 0.35/0.66 = ( ( uminus1482373934393186551omplex @ A )
% 0.35/0.66 = ( times_times_complex @ C2 @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_neg_divide_eq_eq
% 0.35/0.66 thf(fact_7772_nonzero__neg__divide__eq__eq,axiom,
% 0.35/0.66 ! [B: rat,A: rat,C2: rat] :
% 0.35/0.66 ( ( B != zero_zero_rat )
% 0.35/0.66 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.66 = C2 )
% 0.35/0.66 = ( ( uminus_uminus_rat @ A )
% 0.35/0.66 = ( times_times_rat @ C2 @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_neg_divide_eq_eq
% 0.35/0.66 thf(fact_7773_nonzero__neg__divide__eq__eq2,axiom,
% 0.35/0.66 ! [B: real,C2: real,A: real] :
% 0.35/0.66 ( ( B != zero_zero_real )
% 0.35/0.66 => ( ( C2
% 0.35/0.66 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 0.35/0.66 = ( ( times_times_real @ C2 @ B )
% 0.35/0.66 = ( uminus_uminus_real @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_neg_divide_eq_eq2
% 0.35/0.66 thf(fact_7774_nonzero__neg__divide__eq__eq2,axiom,
% 0.35/0.66 ! [B: complex,C2: complex,A: complex] :
% 0.35/0.66 ( ( B != zero_zero_complex )
% 0.35/0.66 => ( ( C2
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.66 = ( ( times_times_complex @ C2 @ B )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_neg_divide_eq_eq2
% 0.35/0.66 thf(fact_7775_nonzero__neg__divide__eq__eq2,axiom,
% 0.35/0.66 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.66 ( ( B != zero_zero_rat )
% 0.35/0.66 => ( ( C2
% 0.35/0.66 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 0.35/0.66 = ( ( times_times_rat @ C2 @ B )
% 0.35/0.66 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % nonzero_neg_divide_eq_eq2
% 0.35/0.66 thf(fact_7776_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.66 ! [B: int] :
% 0.35/0.66 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 0.35/0.66 = ( uminus_uminus_int @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(1)
% 0.35/0.66 thf(fact_7777_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.66 ! [B: real] :
% 0.35/0.66 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 0.35/0.66 = ( uminus_uminus_real @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(1)
% 0.35/0.66 thf(fact_7778_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.66 ! [B: complex] :
% 0.35/0.66 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(1)
% 0.35/0.66 thf(fact_7779_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.66 ! [B: code_integer] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(1)
% 0.35/0.66 thf(fact_7780_mult__1s__ring__1_I1_J,axiom,
% 0.35/0.66 ! [B: rat] :
% 0.35/0.66 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 0.35/0.66 = ( uminus_uminus_rat @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(1)
% 0.35/0.66 thf(fact_7781_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.66 ! [B: int] :
% 0.35/0.66 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 0.35/0.66 = ( uminus_uminus_int @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(2)
% 0.35/0.66 thf(fact_7782_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.66 ! [B: real] :
% 0.35/0.66 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 0.35/0.66 = ( uminus_uminus_real @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(2)
% 0.35/0.66 thf(fact_7783_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.66 ! [B: complex] :
% 0.35/0.66 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(2)
% 0.35/0.66 thf(fact_7784_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.66 ! [B: code_integer] :
% 0.35/0.66 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(2)
% 0.35/0.66 thf(fact_7785_mult__1s__ring__1_I2_J,axiom,
% 0.35/0.66 ! [B: rat] :
% 0.35/0.66 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 0.35/0.66 = ( uminus_uminus_rat @ B ) ) ).
% 0.35/0.66
% 0.35/0.66 % mult_1s_ring_1(2)
% 0.35/0.66 thf(fact_7786_divide__eq__minus__1__iff,axiom,
% 0.35/0.66 ! [A: real,B: real] :
% 0.35/0.66 ( ( ( divide_divide_real @ A @ B )
% 0.35/0.66 = ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.66 = ( ( B != zero_zero_real )
% 0.35/0.66 & ( A
% 0.35/0.66 = ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_minus_1_iff
% 0.35/0.66 thf(fact_7787_divide__eq__minus__1__iff,axiom,
% 0.35/0.66 ! [A: complex,B: complex] :
% 0.35/0.66 ( ( ( divide1717551699836669952omplex @ A @ B )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.66 = ( ( B != zero_zero_complex )
% 0.35/0.66 & ( A
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_minus_1_iff
% 0.35/0.66 thf(fact_7788_divide__eq__minus__1__iff,axiom,
% 0.35/0.66 ! [A: rat,B: rat] :
% 0.35/0.66 ( ( ( divide_divide_rat @ A @ B )
% 0.35/0.66 = ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.66 = ( ( B != zero_zero_rat )
% 0.35/0.66 & ( A
% 0.35/0.66 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_minus_1_iff
% 0.35/0.66 thf(fact_7789_uminus__numeral__One,axiom,
% 0.35/0.66 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 0.35/0.66 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % uminus_numeral_One
% 0.35/0.66 thf(fact_7790_uminus__numeral__One,axiom,
% 0.35/0.66 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 0.35/0.66 = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % uminus_numeral_One
% 0.35/0.66 thf(fact_7791_uminus__numeral__One,axiom,
% 0.35/0.66 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % uminus_numeral_One
% 0.35/0.66 thf(fact_7792_uminus__numeral__One,axiom,
% 0.35/0.66 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 0.35/0.66 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.66
% 0.35/0.66 % uminus_numeral_One
% 0.35/0.66 thf(fact_7793_uminus__numeral__One,axiom,
% 0.35/0.66 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 0.35/0.66 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % uminus_numeral_One
% 0.35/0.66 thf(fact_7794_fact__less__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.66 => ( ( ord_less_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_less_mono
% 0.35/0.66 thf(fact_7795_fact__less__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.66 => ( ( ord_less_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_less_mono
% 0.35/0.66 thf(fact_7796_fact__less__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.66 => ( ( ord_less_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_less_mono
% 0.35/0.66 thf(fact_7797_fact__less__mono,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.66 => ( ( ord_less_nat @ M2 @ N )
% 0.35/0.66 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_less_mono
% 0.35/0.66 thf(fact_7798_power__minus,axiom,
% 0.35/0.66 ! [A: int,N: nat] :
% 0.35/0.66 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 0.35/0.66 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus
% 0.35/0.66 thf(fact_7799_power__minus,axiom,
% 0.35/0.66 ! [A: real,N: nat] :
% 0.35/0.66 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 0.35/0.66 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus
% 0.35/0.66 thf(fact_7800_power__minus,axiom,
% 0.35/0.66 ! [A: complex,N: nat] :
% 0.35/0.66 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 0.35/0.66 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus
% 0.35/0.66 thf(fact_7801_power__minus,axiom,
% 0.35/0.66 ! [A: code_integer,N: nat] :
% 0.35/0.66 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 0.35/0.66 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus
% 0.35/0.66 thf(fact_7802_power__minus,axiom,
% 0.35/0.66 ! [A: rat,N: nat] :
% 0.35/0.66 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 0.35/0.66 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % power_minus
% 0.35/0.66 thf(fact_7803_inf__shunt,axiom,
% 0.35/0.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 0.35/0.66 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 0.35/0.66 = bot_bo2099793752762293965at_nat )
% 0.35/0.66 = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % inf_shunt
% 0.35/0.66 thf(fact_7804_inf__shunt,axiom,
% 0.35/0.66 ! [X: set_int,Y: set_int] :
% 0.35/0.66 ( ( ( inf_inf_set_int @ X @ Y )
% 0.35/0.66 = bot_bot_set_int )
% 0.35/0.66 = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % inf_shunt
% 0.35/0.66 thf(fact_7805_inf__shunt,axiom,
% 0.35/0.66 ! [X: set_real,Y: set_real] :
% 0.35/0.66 ( ( ( inf_inf_set_real @ X @ Y )
% 0.35/0.66 = bot_bot_set_real )
% 0.35/0.66 = ( ord_less_eq_set_real @ X @ ( uminus612125837232591019t_real @ Y ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % inf_shunt
% 0.35/0.66 thf(fact_7806_inf__shunt,axiom,
% 0.35/0.66 ! [X: set_nat,Y: set_nat] :
% 0.35/0.66 ( ( ( inf_inf_set_nat @ X @ Y )
% 0.35/0.66 = bot_bot_set_nat )
% 0.35/0.66 = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % inf_shunt
% 0.35/0.66 thf(fact_7807_fact__fact__dvd__fact,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_fact_dvd_fact
% 0.35/0.66 thf(fact_7808_fact__fact__dvd__fact,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_fact_dvd_fact
% 0.35/0.66 thf(fact_7809_fact__fact__dvd__fact,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_fact_dvd_fact
% 0.35/0.66 thf(fact_7810_fact__fact__dvd__fact,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_fact_dvd_fact
% 0.35/0.66 thf(fact_7811_fact__mod,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) )
% 0.35/0.66 = zero_zero_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mod
% 0.35/0.66 thf(fact_7812_fact__mod,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri2447717529341329178atural @ M2 ) )
% 0.35/0.66 = zero_z2226904508553997617atural ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mod
% 0.35/0.66 thf(fact_7813_fact__mod,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.66 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) )
% 0.35/0.66 = zero_zero_nat ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_mod
% 0.35/0.66 thf(fact_7814_sup__neg__inf,axiom,
% 0.35/0.66 ! [P: set_Pr1261947904930325089at_nat,Q2: set_Pr1261947904930325089at_nat,R3: set_Pr1261947904930325089at_nat] :
% 0.35/0.66 ( ( ord_le3146513528884898305at_nat @ P @ ( sup_su6327502436637775413at_nat @ Q2 @ R3 ) )
% 0.35/0.66 = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P @ ( uminus6524753893492686040at_nat @ Q2 ) ) @ R3 ) ) ).
% 0.35/0.66
% 0.35/0.66 % sup_neg_inf
% 0.35/0.66 thf(fact_7815_sup__neg__inf,axiom,
% 0.35/0.66 ! [P: set_nat,Q2: set_nat,R3: set_nat] :
% 0.35/0.66 ( ( ord_less_eq_set_nat @ P @ ( sup_sup_set_nat @ Q2 @ R3 ) )
% 0.35/0.66 = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P @ ( uminus5710092332889474511et_nat @ Q2 ) ) @ R3 ) ) ).
% 0.35/0.66
% 0.35/0.66 % sup_neg_inf
% 0.35/0.66 thf(fact_7816_shunt2,axiom,
% 0.35/0.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 0.35/0.66 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z3 )
% 0.35/0.66 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % shunt2
% 0.35/0.66 thf(fact_7817_shunt2,axiom,
% 0.35/0.66 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.35/0.66 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z3 )
% 0.35/0.66 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % shunt2
% 0.35/0.66 thf(fact_7818_shunt1,axiom,
% 0.35/0.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 0.35/0.66 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z3 )
% 0.35/0.66 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % shunt1
% 0.35/0.66 thf(fact_7819_shunt1,axiom,
% 0.35/0.66 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 0.35/0.66 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z3 )
% 0.35/0.66 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % shunt1
% 0.35/0.66 thf(fact_7820_fact__le__power,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_le_power
% 0.35/0.66 thf(fact_7821_fact__le__power,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_le_power
% 0.35/0.66 thf(fact_7822_fact__le__power,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_le_power
% 0.35/0.66 thf(fact_7823_fact__le__power,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_le_power
% 0.35/0.66 thf(fact_7824_int__cases4,axiom,
% 0.35/0.66 ! [M2: int] :
% 0.35/0.66 ( ! [N3: nat] :
% 0.35/0.66 ( M2
% 0.35/0.66 != ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.66 => ~ ! [N3: nat] :
% 0.35/0.66 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.66 => ( M2
% 0.35/0.66 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % int_cases4
% 0.35/0.66 thf(fact_7825_int__zle__neg,axiom,
% 0.35/0.66 ! [N: nat,M2: nat] :
% 0.35/0.66 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 0.35/0.66 = ( ( N = zero_zero_nat )
% 0.35/0.66 & ( M2 = zero_zero_nat ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % int_zle_neg
% 0.35/0.66 thf(fact_7826_zmod__zminus1__eq__if,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.66 = zero_zero_int )
% 0.35/0.66 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.66 = zero_zero_int ) )
% 0.35/0.66 & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.66 != zero_zero_int )
% 0.35/0.66 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.66 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zmod_zminus1_eq_if
% 0.35/0.66 thf(fact_7827_zmod__zminus2__eq__if,axiom,
% 0.35/0.66 ! [A: int,B: int] :
% 0.35/0.66 ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.66 = zero_zero_int )
% 0.35/0.66 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.66 = zero_zero_int ) )
% 0.35/0.66 & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.66 != zero_zero_int )
% 0.35/0.66 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.66 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % zmod_zminus2_eq_if
% 0.35/0.66 thf(fact_7828_fact__div__fact__le__pow,axiom,
% 0.35/0.66 ! [R3: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ R3 @ N )
% 0.35/0.66 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R3 ) ) ) @ ( power_power_nat @ N @ R3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % fact_div_fact_le_pow
% 0.35/0.66 thf(fact_7829_binomial__fact__lemma,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( binomial @ N @ K2 ) )
% 0.35/0.66 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % binomial_fact_lemma
% 0.35/0.66 thf(fact_7830_subset__decode__imp__le,axiom,
% 0.35/0.66 ! [M2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M2 ) @ ( nat_set_decode @ N ) )
% 0.35/0.66 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.66
% 0.35/0.66 % subset_decode_imp_le
% 0.35/0.66 thf(fact_7831_less__minus__divide__eq,axiom,
% 0.35/0.66 ! [A: real,B: real,C2: real] :
% 0.35/0.66 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 0.35/0.66 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_divide_eq
% 0.35/0.66 thf(fact_7832_less__minus__divide__eq,axiom,
% 0.35/0.66 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.66 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 0.35/0.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % less_minus_divide_eq
% 0.35/0.66 thf(fact_7833_minus__divide__less__eq,axiom,
% 0.35/0.66 ! [B: real,C2: real,A: real] :
% 0.35/0.66 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_less_eq
% 0.35/0.66 thf(fact_7834_minus__divide__less__eq,axiom,
% 0.35/0.66 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.66 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_less_eq
% 0.35/0.66 thf(fact_7835_neg__less__minus__divide__eq,axiom,
% 0.35/0.66 ! [C2: real,A: real,B: real] :
% 0.35/0.66 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 0.35/0.66 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_less_minus_divide_eq
% 0.35/0.66 thf(fact_7836_neg__less__minus__divide__eq,axiom,
% 0.35/0.66 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 0.35/0.66 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_less_minus_divide_eq
% 0.35/0.66 thf(fact_7837_neg__minus__divide__less__eq,axiom,
% 0.35/0.66 ! [C2: real,B: real,A: real] :
% 0.35/0.66 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_minus_divide_less_eq
% 0.35/0.66 thf(fact_7838_neg__minus__divide__less__eq,axiom,
% 0.35/0.66 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.66 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_minus_divide_less_eq
% 0.35/0.66 thf(fact_7839_pos__less__minus__divide__eq,axiom,
% 0.35/0.66 ! [C2: real,A: real,B: real] :
% 0.35/0.66 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 0.35/0.66 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pos_less_minus_divide_eq
% 0.35/0.66 thf(fact_7840_pos__less__minus__divide__eq,axiom,
% 0.35/0.66 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 0.35/0.66 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pos_less_minus_divide_eq
% 0.35/0.66 thf(fact_7841_pos__minus__divide__less__eq,axiom,
% 0.35/0.66 ! [C2: real,B: real,A: real] :
% 0.35/0.66 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pos_minus_divide_less_eq
% 0.35/0.66 thf(fact_7842_pos__minus__divide__less__eq,axiom,
% 0.35/0.66 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.66 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pos_minus_divide_less_eq
% 0.35/0.66 thf(fact_7843_eq__divide__eq__numeral_I2_J,axiom,
% 0.35/0.66 ! [W2: num,B: real,C2: real] :
% 0.35/0.66 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.66 = ( divide_divide_real @ B @ C2 ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_real )
% 0.35/0.66 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( C2 = zero_zero_real )
% 0.35/0.66 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.66 = zero_zero_real ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_divide_eq_numeral(2)
% 0.35/0.66 thf(fact_7844_eq__divide__eq__numeral_I2_J,axiom,
% 0.35/0.66 ! [W2: num,B: complex,C2: complex] :
% 0.35/0.66 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.66 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.66 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C2 )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( C2 = zero_zero_complex )
% 0.35/0.66 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.66 = zero_zero_complex ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_divide_eq_numeral(2)
% 0.35/0.66 thf(fact_7845_eq__divide__eq__numeral_I2_J,axiom,
% 0.35/0.66 ! [W2: num,B: rat,C2: rat] :
% 0.35/0.66 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.66 = ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.66 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( C2 = zero_zero_rat )
% 0.35/0.66 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.66 = zero_zero_rat ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % eq_divide_eq_numeral(2)
% 0.35/0.66 thf(fact_7846_divide__eq__eq__numeral_I2_J,axiom,
% 0.35/0.66 ! [B: real,C2: real,W2: num] :
% 0.35/0.66 ( ( ( divide_divide_real @ B @ C2 )
% 0.35/0.66 = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_real )
% 0.35/0.66 => ( B
% 0.35/0.66 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_real )
% 0.35/0.66 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 0.35/0.66 = zero_zero_real ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_eq_numeral(2)
% 0.35/0.66 thf(fact_7847_divide__eq__eq__numeral_I2_J,axiom,
% 0.35/0.66 ! [B: complex,C2: complex,W2: num] :
% 0.35/0.66 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_complex )
% 0.35/0.66 => ( B
% 0.35/0.66 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C2 ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_complex )
% 0.35/0.66 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 0.35/0.66 = zero_zero_complex ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_eq_numeral(2)
% 0.35/0.66 thf(fact_7848_divide__eq__eq__numeral_I2_J,axiom,
% 0.35/0.66 ! [B: rat,C2: rat,W2: num] :
% 0.35/0.66 ( ( ( divide_divide_rat @ B @ C2 )
% 0.35/0.66 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.66 = ( ( ( C2 != zero_zero_rat )
% 0.35/0.66 => ( B
% 0.35/0.66 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 0.35/0.66 & ( ( C2 = zero_zero_rat )
% 0.35/0.66 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 0.35/0.66 = zero_zero_rat ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % divide_eq_eq_numeral(2)
% 0.35/0.66 thf(fact_7849_add__divide__eq__if__simps_I3_J,axiom,
% 0.35/0.66 ! [Z3: real,A: real,B: real] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_real )
% 0.35/0.66 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_real )
% 0.35/0.66 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(3)
% 0.35/0.66 thf(fact_7850_add__divide__eq__if__simps_I3_J,axiom,
% 0.35/0.66 ! [Z3: complex,A: complex,B: complex] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_complex )
% 0.35/0.66 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_complex )
% 0.35/0.66 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(3)
% 0.35/0.66 thf(fact_7851_add__divide__eq__if__simps_I3_J,axiom,
% 0.35/0.66 ! [Z3: rat,A: rat,B: rat] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_rat )
% 0.35/0.66 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 0.35/0.66 = B ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_rat )
% 0.35/0.66 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(3)
% 0.35/0.66 thf(fact_7852_minus__divide__add__eq__iff,axiom,
% 0.35/0.66 ! [Z3: real,X: real,Y: real] :
% 0.35/0.66 ( ( Z3 != zero_zero_real )
% 0.35/0.66 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 0.35/0.66 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_add_eq_iff
% 0.35/0.66 thf(fact_7853_minus__divide__add__eq__iff,axiom,
% 0.35/0.66 ! [Z3: complex,X: complex,Y: complex] :
% 0.35/0.66 ( ( Z3 != zero_zero_complex )
% 0.35/0.66 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 0.35/0.66 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_add_eq_iff
% 0.35/0.66 thf(fact_7854_minus__divide__add__eq__iff,axiom,
% 0.35/0.66 ! [Z3: rat,X: rat,Y: rat] :
% 0.35/0.66 ( ( Z3 != zero_zero_rat )
% 0.35/0.66 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z3 ) ) @ Y )
% 0.35/0.66 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_add_eq_iff
% 0.35/0.66 thf(fact_7855_signed__take__bit__int__greater__eq,axiom,
% 0.35/0.66 ! [K2: int,N: nat] :
% 0.35/0.66 ( ( ord_less_int @ K2 @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.66 => ( ord_less_eq_int @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K2 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % signed_take_bit_int_greater_eq
% 0.35/0.66 thf(fact_7856_add__divide__eq__if__simps_I6_J,axiom,
% 0.35/0.66 ! [Z3: real,A: real,B: real] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_real )
% 0.35/0.66 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( uminus_uminus_real @ B ) ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_real )
% 0.35/0.66 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(6)
% 0.35/0.66 thf(fact_7857_add__divide__eq__if__simps_I6_J,axiom,
% 0.35/0.66 ! [Z3: complex,A: complex,B: complex] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_complex )
% 0.35/0.66 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_complex )
% 0.35/0.66 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(6)
% 0.35/0.66 thf(fact_7858_add__divide__eq__if__simps_I6_J,axiom,
% 0.35/0.66 ! [Z3: rat,A: rat,B: rat] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_rat )
% 0.35/0.66 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( uminus_uminus_rat @ B ) ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_rat )
% 0.35/0.66 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 0.35/0.66 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(6)
% 0.35/0.66 thf(fact_7859_add__divide__eq__if__simps_I5_J,axiom,
% 0.35/0.66 ! [Z3: real,A: real,B: real] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_real )
% 0.35/0.66 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 0.35/0.66 = ( uminus_uminus_real @ B ) ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_real )
% 0.35/0.66 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 0.35/0.66 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(5)
% 0.35/0.66 thf(fact_7860_add__divide__eq__if__simps_I5_J,axiom,
% 0.35/0.66 ! [Z3: complex,A: complex,B: complex] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_complex )
% 0.35/0.66 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 0.35/0.66 = ( uminus1482373934393186551omplex @ B ) ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_complex )
% 0.35/0.66 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 0.35/0.66 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(5)
% 0.35/0.66 thf(fact_7861_add__divide__eq__if__simps_I5_J,axiom,
% 0.35/0.66 ! [Z3: rat,A: rat,B: rat] :
% 0.35/0.66 ( ( ( Z3 = zero_zero_rat )
% 0.35/0.66 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 0.35/0.66 = ( uminus_uminus_rat @ B ) ) )
% 0.35/0.66 & ( ( Z3 != zero_zero_rat )
% 0.35/0.66 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 0.35/0.66 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % add_divide_eq_if_simps(5)
% 0.35/0.66 thf(fact_7862_minus__divide__diff__eq__iff,axiom,
% 0.35/0.66 ! [Z3: real,X: real,Y: real] :
% 0.35/0.66 ( ( Z3 != zero_zero_real )
% 0.35/0.66 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 0.35/0.66 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_diff_eq_iff
% 0.35/0.66 thf(fact_7863_minus__divide__diff__eq__iff,axiom,
% 0.35/0.66 ! [Z3: complex,X: complex,Y: complex] :
% 0.35/0.66 ( ( Z3 != zero_zero_complex )
% 0.35/0.66 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 0.35/0.66 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_diff_eq_iff
% 0.35/0.66 thf(fact_7864_minus__divide__diff__eq__iff,axiom,
% 0.35/0.66 ! [Z3: rat,X: rat,Y: rat] :
% 0.35/0.66 ( ( Z3 != zero_zero_rat )
% 0.35/0.66 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z3 ) ) @ Y )
% 0.35/0.66 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_diff_eq_iff
% 0.35/0.66 thf(fact_7865_choose__dvd,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % choose_dvd
% 0.35/0.66 thf(fact_7866_choose__dvd,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % choose_dvd
% 0.35/0.66 thf(fact_7867_choose__dvd,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % choose_dvd
% 0.35/0.66 thf(fact_7868_choose__dvd,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % choose_dvd
% 0.35/0.66 thf(fact_7869_int__cases3,axiom,
% 0.35/0.66 ! [K2: int] :
% 0.35/0.66 ( ( K2 != zero_zero_int )
% 0.35/0.66 => ( ! [N3: nat] :
% 0.35/0.66 ( ( K2
% 0.35/0.66 = ( semiri1314217659103216013at_int @ N3 ) )
% 0.35/0.66 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 0.35/0.66 => ~ ! [N3: nat] :
% 0.35/0.66 ( ( K2
% 0.35/0.66 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.35/0.66 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % int_cases3
% 0.35/0.66 thf(fact_7870_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ord_less_nat @ N @ K2 )
% 0.35/0.66 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66 thf(fact_7871_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ord_less_nat @ N @ K2 )
% 0.35/0.66 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 0.35/0.66 = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66 thf(fact_7872_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ord_less_nat @ N @ K2 )
% 0.35/0.66 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66 thf(fact_7873_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ord_less_nat @ N @ K2 )
% 0.35/0.66 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66 thf(fact_7874_pochhammer__of__nat__eq__0__lemma,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ord_less_nat @ N @ K2 )
% 0.35/0.66 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma
% 0.35/0.66 thf(fact_7875_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_complex )
% 0.35/0.66 = ( ord_less_nat @ N @ K2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_iff
% 0.35/0.66 thf(fact_7876_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 0.35/0.66 = zero_z3403309356797280102nteger )
% 0.35/0.66 = ( ord_less_nat @ N @ K2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_iff
% 0.35/0.66 thf(fact_7877_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_rat )
% 0.35/0.66 = ( ord_less_nat @ N @ K2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_iff
% 0.35/0.66 thf(fact_7878_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_real )
% 0.35/0.66 = ( ord_less_nat @ N @ K2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_iff
% 0.35/0.66 thf(fact_7879_pochhammer__of__nat__eq__0__iff,axiom,
% 0.35/0.66 ! [N: nat,K2: nat] :
% 0.35/0.66 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 0.35/0.66 = zero_zero_int )
% 0.35/0.66 = ( ord_less_nat @ N @ K2 ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_iff
% 0.35/0.66 thf(fact_7880_pochhammer__eq__0__iff,axiom,
% 0.35/0.66 ! [A: complex,N: nat] :
% 0.35/0.66 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 0.35/0.66 = zero_zero_complex )
% 0.35/0.66 = ( ? [K3: nat] :
% 0.35/0.66 ( ( ord_less_nat @ K3 @ N )
% 0.35/0.66 & ( A
% 0.35/0.66 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_eq_0_iff
% 0.35/0.66 thf(fact_7881_pochhammer__eq__0__iff,axiom,
% 0.35/0.66 ! [A: rat,N: nat] :
% 0.35/0.66 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 0.35/0.66 = zero_zero_rat )
% 0.35/0.66 = ( ? [K3: nat] :
% 0.35/0.66 ( ( ord_less_nat @ K3 @ N )
% 0.35/0.66 & ( A
% 0.35/0.66 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_eq_0_iff
% 0.35/0.66 thf(fact_7882_pochhammer__eq__0__iff,axiom,
% 0.35/0.66 ! [A: real,N: nat] :
% 0.35/0.66 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 0.35/0.66 = zero_zero_real )
% 0.35/0.66 = ( ? [K3: nat] :
% 0.35/0.66 ( ( ord_less_nat @ K3 @ N )
% 0.35/0.66 & ( A
% 0.35/0.66 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_eq_0_iff
% 0.35/0.66 thf(fact_7883_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 0.35/0.66 != zero_zero_complex ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66 thf(fact_7884_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 0.35/0.66 != zero_z3403309356797280102nteger ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66 thf(fact_7885_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 0.35/0.66 != zero_zero_rat ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66 thf(fact_7886_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 0.35/0.66 != zero_zero_real ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66 thf(fact_7887_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 0.35/0.66 != zero_zero_int ) ) ).
% 0.35/0.66
% 0.35/0.66 % pochhammer_of_nat_eq_0_lemma'
% 0.35/0.66 thf(fact_7888_not__zle__0__negative,axiom,
% 0.35/0.66 ! [N: nat] :
% 0.35/0.66 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % not_zle_0_negative
% 0.35/0.66 thf(fact_7889_negD,axiom,
% 0.35/0.66 ! [X: int] :
% 0.35/0.66 ( ( ord_less_int @ X @ zero_zero_int )
% 0.35/0.66 => ? [N3: nat] :
% 0.35/0.66 ( X
% 0.35/0.66 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % negD
% 0.35/0.66 thf(fact_7890_negative__zless__0,axiom,
% 0.35/0.66 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 0.35/0.66
% 0.35/0.66 % negative_zless_0
% 0.35/0.66 thf(fact_7891_div__eq__minus1,axiom,
% 0.35/0.66 ! [B: int] :
% 0.35/0.66 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.66 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.35/0.66 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % div_eq_minus1
% 0.35/0.66 thf(fact_7892_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_real,P2: real > $o,H: real > real,G2: real > real] :
% 0.35/0.66 ( ( finite_finite_real @ A4 )
% 0.35/0.66 => ( ( groups1681761925125756287l_real
% 0.35/0.66 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_real @ ( groups1681761925125756287l_real @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups1681761925125756287l_real @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7893_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_int,P2: int > $o,H: int > real,G2: int > real] :
% 0.35/0.66 ( ( finite_finite_int @ A4 )
% 0.35/0.66 => ( ( groups2316167850115554303t_real
% 0.35/0.66 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_real @ ( groups2316167850115554303t_real @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7894_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_complex,P2: complex > $o,H: complex > real,G2: complex > real] :
% 0.35/0.66 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.66 => ( ( groups766887009212190081x_real
% 0.35/0.66 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_real @ ( groups766887009212190081x_real @ H @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7895_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_nat,P2: nat > $o,H: nat > real,G2: nat > real] :
% 0.35/0.66 ( ( finite_finite_nat @ A4 )
% 0.35/0.66 => ( ( groups129246275422532515t_real
% 0.35/0.66 @ ^ [X4: nat] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_real @ ( groups129246275422532515t_real @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7896_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_real,P2: real > $o,H: real > rat,G2: real > rat] :
% 0.35/0.66 ( ( finite_finite_real @ A4 )
% 0.35/0.66 => ( ( groups4061424788464935467al_rat
% 0.35/0.66 @ ^ [X4: real] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_rat @ ( groups4061424788464935467al_rat @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups4061424788464935467al_rat @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7897_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_int,P2: int > $o,H: int > rat,G2: int > rat] :
% 0.35/0.66 ( ( finite_finite_int @ A4 )
% 0.35/0.66 => ( ( groups1072433553688619179nt_rat
% 0.35/0.66 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7898_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_complex,P2: complex > $o,H: complex > rat,G2: complex > rat] :
% 0.35/0.66 ( ( finite3207457112153483333omplex @ A4 )
% 0.35/0.66 => ( ( groups225925009352817453ex_rat
% 0.35/0.66 @ ^ [X4: complex] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_rat @ ( groups225925009352817453ex_rat @ H @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7899_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_nat,P2: nat > $o,H: nat > rat,G2: nat > rat] :
% 0.35/0.66 ( ( finite_finite_nat @ A4 )
% 0.35/0.66 => ( ( groups73079841787564623at_rat
% 0.35/0.66 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_rat @ ( groups73079841787564623at_rat @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7900_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_real,P2: real > $o,H: real > nat,G2: real > nat] :
% 0.35/0.66 ( ( finite_finite_real @ A4 )
% 0.35/0.66 => ( ( groups4696554848551431203al_nat
% 0.35/0.66 @ ^ [X4: real] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_nat @ ( groups4696554848551431203al_nat @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups4696554848551431203al_nat @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7901_prod_OIf__cases,axiom,
% 0.35/0.66 ! [A4: set_int,P2: int > $o,H: int > nat,G2: int > nat] :
% 0.35/0.66 ( ( finite_finite_int @ A4 )
% 0.35/0.66 => ( ( groups1707563613775114915nt_nat
% 0.35/0.66 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 0.35/0.66 @ A4 )
% 0.35/0.66 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % prod.If_cases
% 0.35/0.66 thf(fact_7902_binomial__altdef__nat,axiom,
% 0.35/0.66 ! [K2: nat,N: nat] :
% 0.35/0.66 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.66 => ( ( binomial @ N @ K2 )
% 0.35/0.66 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % binomial_altdef_nat
% 0.35/0.66 thf(fact_7903_le__minus__divide__eq,axiom,
% 0.35/0.66 ! [A: real,B: real,C2: real] :
% 0.35/0.66 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 0.35/0.66 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_divide_eq
% 0.35/0.66 thf(fact_7904_le__minus__divide__eq,axiom,
% 0.35/0.66 ! [A: rat,B: rat,C2: rat] :
% 0.35/0.66 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 0.35/0.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % le_minus_divide_eq
% 0.35/0.66 thf(fact_7905_minus__divide__le__eq,axiom,
% 0.35/0.66 ! [B: real,C2: real,A: real] :
% 0.35/0.66 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.66 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_le_eq
% 0.35/0.66 thf(fact_7906_minus__divide__le__eq,axiom,
% 0.35/0.66 ! [B: rat,C2: rat,A: rat] :
% 0.35/0.66 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.66 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 0.35/0.66 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % minus_divide_le_eq
% 0.35/0.66 thf(fact_7907_neg__le__minus__divide__eq,axiom,
% 0.35/0.66 ! [C2: real,A: real,B: real] :
% 0.35/0.66 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 0.35/0.66 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_le_minus_divide_eq
% 0.35/0.66 thf(fact_7908_neg__le__minus__divide__eq,axiom,
% 0.35/0.66 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.66 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 0.35/0.66 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_le_minus_divide_eq
% 0.35/0.66 thf(fact_7909_neg__minus__divide__le__eq,axiom,
% 0.35/0.66 ! [C2: real,B: real,A: real] :
% 0.35/0.66 ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.66 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 0.35/0.66 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.66
% 0.35/0.66 % neg_minus_divide_le_eq
% 0.35/0.66 thf(fact_7910_neg__minus__divide__le__eq,axiom,
% 0.35/0.66 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.66 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.66 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 0.35/0.67 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % neg_minus_divide_le_eq
% 0.35/0.67 thf(fact_7911_pos__le__minus__divide__eq,axiom,
% 0.35/0.67 ! [C2: real,A: real,B: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 0.35/0.67 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pos_le_minus_divide_eq
% 0.35/0.67 thf(fact_7912_pos__le__minus__divide__eq,axiom,
% 0.35/0.67 ! [C2: rat,A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 0.35/0.67 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pos_le_minus_divide_eq
% 0.35/0.67 thf(fact_7913_pos__minus__divide__le__eq,axiom,
% 0.35/0.67 ! [C2: real,B: real,A: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 0.35/0.67 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pos_minus_divide_le_eq
% 0.35/0.67 thf(fact_7914_pos__minus__divide__le__eq,axiom,
% 0.35/0.67 ! [C2: rat,B: rat,A: rat] :
% 0.35/0.67 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 0.35/0.67 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pos_minus_divide_le_eq
% 0.35/0.67 thf(fact_7915_divide__less__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [B: real,C2: real,W2: num] :
% 0.35/0.67 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.67 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_less_eq_numeral(2)
% 0.35/0.67 thf(fact_7916_divide__less__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [B: rat,C2: rat,W2: num] :
% 0.35/0.67 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.67 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_less_eq_numeral(2)
% 0.35/0.67 thf(fact_7917_less__divide__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [W2: num,B: real,C2: real] :
% 0.35/0.67 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.67 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % less_divide_eq_numeral(2)
% 0.35/0.67 thf(fact_7918_less__divide__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [W2: num,B: rat,C2: rat] :
% 0.35/0.67 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.67 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % less_divide_eq_numeral(2)
% 0.35/0.67 thf(fact_7919_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K2 ) )
% 0.35/0.67 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.67 thf(fact_7920_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K2 ) )
% 0.35/0.67 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.67 thf(fact_7921_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K2 ) )
% 0.35/0.67 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.67 thf(fact_7922_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K2 ) )
% 0.35/0.67 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.67 thf(fact_7923_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K2 ) )
% 0.35/0.67 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % neg_one_power_add_eq_neg_one_power_diff
% 0.35/0.67 thf(fact_7924_neg__int__cases,axiom,
% 0.35/0.67 ! [K2: int] :
% 0.35/0.67 ( ( ord_less_int @ K2 @ zero_zero_int )
% 0.35/0.67 => ~ ! [N3: nat] :
% 0.35/0.67 ( ( K2
% 0.35/0.67 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 0.35/0.67 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % neg_int_cases
% 0.35/0.67 thf(fact_7925_minus__mod__int__eq,axiom,
% 0.35/0.67 ! [L: int,K2: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 0.35/0.67 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K2 ) @ L )
% 0.35/0.67 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K2 @ one_one_int ) @ L ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_mod_int_eq
% 0.35/0.67 thf(fact_7926_zmod__minus1,axiom,
% 0.35/0.67 ! [B: int] :
% 0.35/0.67 ( ( ord_less_int @ zero_zero_int @ B )
% 0.35/0.67 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 0.35/0.67 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zmod_minus1
% 0.35/0.67 thf(fact_7927_zdiv__zminus1__eq__if,axiom,
% 0.35/0.67 ! [B: int,A: int] :
% 0.35/0.67 ( ( B != zero_zero_int )
% 0.35/0.67 => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.67 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.35/0.67 & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.67 != zero_zero_int )
% 0.35/0.67 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.67 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zdiv_zminus1_eq_if
% 0.35/0.67 thf(fact_7928_zdiv__zminus2__eq__if,axiom,
% 0.35/0.67 ! [B: int,A: int] :
% 0.35/0.67 ( ( B != zero_zero_int )
% 0.35/0.67 => ( ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.67 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 0.35/0.67 & ( ( ( modulo_modulo_int @ A @ B )
% 0.35/0.67 != zero_zero_int )
% 0.35/0.67 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 0.35/0.67 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zdiv_zminus2_eq_if
% 0.35/0.67 thf(fact_7929_fact__eq__fact__times,axiom,
% 0.35/0.67 ! [N: nat,M2: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.67 => ( ( semiri1408675320244567234ct_nat @ M2 )
% 0.35/0.67 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 0.35/0.67 @ ( groups708209901874060359at_nat
% 0.35/0.67 @ ^ [X4: nat] : X4
% 0.35/0.67 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_eq_fact_times
% 0.35/0.67 thf(fact_7930_signed__take__bit__rec,axiom,
% 0.35/0.67 ( bit_ri6519982836138164636nteger
% 0.35/0.67 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_rec
% 0.35/0.67 thf(fact_7931_signed__take__bit__rec,axiom,
% 0.35/0.67 ( bit_ri631733984087533419it_int
% 0.35/0.67 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_rec
% 0.35/0.67 thf(fact_7932_square__fact__le__2__fact,axiom,
% 0.35/0.67 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % square_fact_le_2_fact
% 0.35/0.67 thf(fact_7933_zminus1__lemma,axiom,
% 0.35/0.67 ! [A: int,B: int,Q2: int,R3: int] :
% 0.35/0.67 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 0.35/0.67 => ( ( B != zero_zero_int )
% 0.35/0.67 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zminus1_lemma
% 0.35/0.67 thf(fact_7934_divide__le__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [B: real,C2: real,W2: num] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 0.35/0.67 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_le_eq_numeral(2)
% 0.35/0.67 thf(fact_7935_divide__le__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [B: rat,C2: rat,W2: num] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 0.35/0.67 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_le_eq_numeral(2)
% 0.35/0.67 thf(fact_7936_le__divide__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [W2: num,B: real,C2: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C2 ) )
% 0.35/0.67 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 0.35/0.67 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 0.35/0.67 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % le_divide_eq_numeral(2)
% 0.35/0.67 thf(fact_7937_le__divide__eq__numeral_I2_J,axiom,
% 0.35/0.67 ! [W2: num,B: rat,C2: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 0.35/0.67 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 0.35/0.67 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 0.35/0.67 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 0.35/0.67 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % le_divide_eq_numeral(2)
% 0.35/0.67 thf(fact_7938_square__le__1,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.67 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.67 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % square_le_1
% 0.35/0.67 thf(fact_7939_square__le__1,axiom,
% 0.35/0.67 ! [X: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 0.35/0.67 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % square_le_1
% 0.35/0.67 thf(fact_7940_square__le__1,axiom,
% 0.35/0.67 ! [X: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 0.35/0.67 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 0.35/0.67 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % square_le_1
% 0.35/0.67 thf(fact_7941_square__le__1,axiom,
% 0.35/0.67 ! [X: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 0.35/0.67 => ( ( ord_less_eq_int @ X @ one_one_int )
% 0.35/0.67 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % square_le_1
% 0.35/0.67 thf(fact_7942_minus__power__mult__self,axiom,
% 0.35/0.67 ! [A: int,N: nat] :
% 0.35/0.67 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 0.35/0.67 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_power_mult_self
% 0.35/0.67 thf(fact_7943_minus__power__mult__self,axiom,
% 0.35/0.67 ! [A: real,N: nat] :
% 0.35/0.67 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 0.35/0.67 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_power_mult_self
% 0.35/0.67 thf(fact_7944_minus__power__mult__self,axiom,
% 0.35/0.67 ! [A: complex,N: nat] :
% 0.35/0.67 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 0.35/0.67 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_power_mult_self
% 0.35/0.67 thf(fact_7945_minus__power__mult__self,axiom,
% 0.35/0.67 ! [A: code_integer,N: nat] :
% 0.35/0.67 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 0.35/0.67 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_power_mult_self
% 0.35/0.67 thf(fact_7946_minus__power__mult__self,axiom,
% 0.35/0.67 ! [A: rat,N: nat] :
% 0.35/0.67 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 0.35/0.67 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_power_mult_self
% 0.35/0.67 thf(fact_7947_fact__num__eq__if,axiom,
% 0.35/0.67 ( semiri3624122377584611663nteger
% 0.35/0.67 = ( ^ [M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M6 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_num_eq_if
% 0.35/0.67 thf(fact_7948_fact__num__eq__if,axiom,
% 0.35/0.67 ( semiri5044797733671781792omplex
% 0.35/0.67 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_num_eq_if
% 0.35/0.67 thf(fact_7949_fact__num__eq__if,axiom,
% 0.35/0.67 ( semiri773545260158071498ct_rat
% 0.35/0.67 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_num_eq_if
% 0.35/0.67 thf(fact_7950_fact__num__eq__if,axiom,
% 0.35/0.67 ( semiri1406184849735516958ct_int
% 0.35/0.67 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_num_eq_if
% 0.35/0.67 thf(fact_7951_fact__num__eq__if,axiom,
% 0.35/0.67 ( semiri1408675320244567234ct_nat
% 0.35/0.67 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_num_eq_if
% 0.35/0.67 thf(fact_7952_fact__num__eq__if,axiom,
% 0.35/0.67 ( semiri2265585572941072030t_real
% 0.35/0.67 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_num_eq_if
% 0.35/0.67 thf(fact_7953_fact__code,axiom,
% 0.35/0.67 ( semiri1406184849735516958ct_int
% 0.35/0.67 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_code
% 0.35/0.67 thf(fact_7954_fact__code,axiom,
% 0.35/0.67 ( semiri1408675320244567234ct_nat
% 0.35/0.67 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_code
% 0.35/0.67 thf(fact_7955_fact__code,axiom,
% 0.35/0.67 ( semiri2265585572941072030t_real
% 0.35/0.67 = ( ^ [N4: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_code
% 0.35/0.67 thf(fact_7956_fact__reduce,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ( semiri773545260158071498ct_rat @ N )
% 0.35/0.67 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_reduce
% 0.35/0.67 thf(fact_7957_fact__reduce,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ( semiri1406184849735516958ct_int @ N )
% 0.35/0.67 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_reduce
% 0.35/0.67 thf(fact_7958_fact__reduce,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ( semiri1408675320244567234ct_nat @ N )
% 0.35/0.67 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_reduce
% 0.35/0.67 thf(fact_7959_fact__reduce,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ( semiri2265585572941072030t_real @ N )
% 0.35/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_reduce
% 0.35/0.67 thf(fact_7960_pochhammer__absorb__comp,axiom,
% 0.35/0.67 ! [R3: complex,K2: nat] :
% 0.35/0.67 ( ( times_times_complex @ ( minus_minus_complex @ R3 @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R3 ) @ K2 ) )
% 0.35/0.67 = ( times_times_complex @ R3 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R3 ) @ one_one_complex ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_absorb_comp
% 0.35/0.67 thf(fact_7961_pochhammer__absorb__comp,axiom,
% 0.35/0.67 ! [R3: code_integer,K2: nat] :
% 0.35/0.67 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K2 ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K2 ) )
% 0.35/0.67 = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_absorb_comp
% 0.35/0.67 thf(fact_7962_pochhammer__absorb__comp,axiom,
% 0.35/0.67 ! [R3: rat,K2: nat] :
% 0.35/0.67 ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K2 ) )
% 0.35/0.67 = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_absorb_comp
% 0.35/0.67 thf(fact_7963_pochhammer__absorb__comp,axiom,
% 0.35/0.67 ! [R3: real,K2: nat] :
% 0.35/0.67 ( ( times_times_real @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R3 ) @ K2 ) )
% 0.35/0.67 = ( times_times_real @ R3 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R3 ) @ one_one_real ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_absorb_comp
% 0.35/0.67 thf(fact_7964_pochhammer__absorb__comp,axiom,
% 0.35/0.67 ! [R3: int,K2: nat] :
% 0.35/0.67 ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K2 ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K2 ) )
% 0.35/0.67 = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_absorb_comp
% 0.35/0.67 thf(fact_7965_gbinomial__index__swap,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K2 ) )
% 0.35/0.67 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_index_swap
% 0.35/0.67 thf(fact_7966_gbinomial__index__swap,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K2 ) )
% 0.35/0.67 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_index_swap
% 0.35/0.67 thf(fact_7967_gbinomial__index__swap,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K2 ) )
% 0.35/0.67 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_index_swap
% 0.35/0.67 thf(fact_7968_gbinomial__negated__upper,axiom,
% 0.35/0.67 ( gbinomial_complex
% 0.35/0.67 = ( ^ [A5: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A5 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_negated_upper
% 0.35/0.67 thf(fact_7969_gbinomial__negated__upper,axiom,
% 0.35/0.67 ( gbinomial_rat
% 0.35/0.67 = ( ^ [A5: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A5 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_negated_upper
% 0.35/0.67 thf(fact_7970_gbinomial__negated__upper,axiom,
% 0.35/0.67 ( gbinomial_real
% 0.35/0.67 = ( ^ [A5: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A5 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_negated_upper
% 0.35/0.67 thf(fact_7971_binomial__fact,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) )
% 0.35/0.67 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % binomial_fact
% 0.35/0.67 thf(fact_7972_binomial__fact,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) )
% 0.35/0.67 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % binomial_fact
% 0.35/0.67 thf(fact_7973_binomial__fact,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) )
% 0.35/0.67 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % binomial_fact
% 0.35/0.67 thf(fact_7974_fact__binomial,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K2 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) ) )
% 0.35/0.67 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_binomial
% 0.35/0.67 thf(fact_7975_fact__binomial,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) )
% 0.35/0.67 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_binomial
% 0.35/0.67 thf(fact_7976_fact__binomial,axiom,
% 0.35/0.67 ! [K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ K2 @ N )
% 0.35/0.67 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) )
% 0.35/0.67 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_binomial
% 0.35/0.67 thf(fact_7977_Bernoulli__inequality,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 0.35/0.67 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Bernoulli_inequality
% 0.35/0.67 thf(fact_7978_fact__div__fact,axiom,
% 0.35/0.67 ! [N: nat,M2: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.67 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 0.35/0.67 = ( groups708209901874060359at_nat
% 0.35/0.67 @ ^ [X4: nat] : X4
% 0.35/0.67 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_div_fact
% 0.35/0.67 thf(fact_7979_power__minus1__odd,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.67 = ( uminus_uminus_int @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_minus1_odd
% 0.35/0.67 thf(fact_7980_power__minus1__odd,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.67 = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_minus1_odd
% 0.35/0.67 thf(fact_7981_power__minus1__odd,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.67 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_minus1_odd
% 0.35/0.67 thf(fact_7982_power__minus1__odd,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.67 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_minus1_odd
% 0.35/0.67 thf(fact_7983_power__minus1__odd,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.67 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_minus1_odd
% 0.35/0.67 thf(fact_7984_gbinomial__minus,axiom,
% 0.35/0.67 ! [A: complex,K2: nat] :
% 0.35/0.67 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K2 )
% 0.35/0.67 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_minus
% 0.35/0.67 thf(fact_7985_gbinomial__minus,axiom,
% 0.35/0.67 ! [A: rat,K2: nat] :
% 0.35/0.67 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K2 )
% 0.35/0.67 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_minus
% 0.35/0.67 thf(fact_7986_gbinomial__minus,axiom,
% 0.35/0.67 ! [A: real,K2: nat] :
% 0.35/0.67 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K2 )
% 0.35/0.67 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_minus
% 0.35/0.67 thf(fact_7987_signed__take__bit__int__less__eq,axiom,
% 0.35/0.67 ! [N: nat,K2: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K2 )
% 0.35/0.67 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_int_less_eq
% 0.35/0.67 thf(fact_7988_pochhammer__minus_H,axiom,
% 0.35/0.67 ! [B: complex,K2: nat] :
% 0.35/0.67 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 )
% 0.35/0.67 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus'
% 0.35/0.67 thf(fact_7989_pochhammer__minus_H,axiom,
% 0.35/0.67 ! [B: code_integer,K2: nat] :
% 0.35/0.67 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 )
% 0.35/0.67 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus'
% 0.35/0.67 thf(fact_7990_pochhammer__minus_H,axiom,
% 0.35/0.67 ! [B: rat,K2: nat] :
% 0.35/0.67 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 )
% 0.35/0.67 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus'
% 0.35/0.67 thf(fact_7991_pochhammer__minus_H,axiom,
% 0.35/0.67 ! [B: real,K2: nat] :
% 0.35/0.67 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 )
% 0.35/0.67 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus'
% 0.35/0.67 thf(fact_7992_pochhammer__minus_H,axiom,
% 0.35/0.67 ! [B: int,K2: nat] :
% 0.35/0.67 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 )
% 0.35/0.67 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus'
% 0.35/0.67 thf(fact_7993_pochhammer__minus,axiom,
% 0.35/0.67 ! [B: complex,K2: nat] :
% 0.35/0.67 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K2 )
% 0.35/0.67 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus
% 0.35/0.67 thf(fact_7994_pochhammer__minus,axiom,
% 0.35/0.67 ! [B: code_integer,K2: nat] :
% 0.35/0.67 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 )
% 0.35/0.67 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus
% 0.35/0.67 thf(fact_7995_pochhammer__minus,axiom,
% 0.35/0.67 ! [B: rat,K2: nat] :
% 0.35/0.67 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 )
% 0.35/0.67 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus
% 0.35/0.67 thf(fact_7996_pochhammer__minus,axiom,
% 0.35/0.67 ! [B: real,K2: nat] :
% 0.35/0.67 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K2 )
% 0.35/0.67 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus
% 0.35/0.67 thf(fact_7997_pochhammer__minus,axiom,
% 0.35/0.67 ! [B: int,K2: nat] :
% 0.35/0.67 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 )
% 0.35/0.67 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pochhammer_minus
% 0.35/0.67 thf(fact_7998_int__bit__induct,axiom,
% 0.35/0.67 ! [P2: int > $o,K2: int] :
% 0.35/0.67 ( ( P2 @ zero_zero_int )
% 0.35/0.67 => ( ( P2 @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.67 => ( ! [K: int] :
% 0.35/0.67 ( ( P2 @ K )
% 0.35/0.67 => ( ( K != zero_zero_int )
% 0.35/0.67 => ( P2 @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.67 => ( ! [K: int] :
% 0.35/0.67 ( ( P2 @ K )
% 0.35/0.67 => ( ( K
% 0.35/0.67 != ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.67 => ( P2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 0.35/0.67 => ( P2 @ K2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % int_bit_induct
% 0.35/0.67 thf(fact_7999_gbinomial__sum__lower__neg,axiom,
% 0.35/0.67 ! [A: complex,M2: nat] :
% 0.35/0.67 ( ( groups2073611262835488442omplex
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.67 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_sum_lower_neg
% 0.35/0.67 thf(fact_8000_gbinomial__sum__lower__neg,axiom,
% 0.35/0.67 ! [A: rat,M2: nat] :
% 0.35/0.67 ( ( groups2906978787729119204at_rat
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.67 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_sum_lower_neg
% 0.35/0.67 thf(fact_8001_gbinomial__sum__lower__neg,axiom,
% 0.35/0.67 ! [A: real,M2: nat] :
% 0.35/0.67 ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.67 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M2 ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_sum_lower_neg
% 0.35/0.67 thf(fact_8002_gbinomial__Suc,axiom,
% 0.35/0.67 ! [A: complex,K2: nat] :
% 0.35/0.67 ( ( gbinomial_complex @ A @ ( suc @ K2 ) )
% 0.35/0.67 = ( divide1717551699836669952omplex
% 0.35/0.67 @ ( groups6464643781859351333omplex
% 0.35/0.67 @ ^ [I: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I ) )
% 0.35/0.67 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 0.35/0.67 @ ( semiri5044797733671781792omplex @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_Suc
% 0.35/0.67 thf(fact_8003_gbinomial__Suc,axiom,
% 0.35/0.67 ! [A: rat,K2: nat] :
% 0.35/0.67 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 0.35/0.67 = ( divide_divide_rat
% 0.35/0.67 @ ( groups73079841787564623at_rat
% 0.35/0.67 @ ^ [I: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 0.35/0.67 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 0.35/0.67 @ ( semiri773545260158071498ct_rat @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_Suc
% 0.35/0.67 thf(fact_8004_gbinomial__Suc,axiom,
% 0.35/0.67 ! [A: real,K2: nat] :
% 0.35/0.67 ( ( gbinomial_real @ A @ ( suc @ K2 ) )
% 0.35/0.67 = ( divide_divide_real
% 0.35/0.67 @ ( groups129246275422532515t_real
% 0.35/0.67 @ ^ [I: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I ) )
% 0.35/0.67 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 0.35/0.67 @ ( semiri2265585572941072030t_real @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_Suc
% 0.35/0.67 thf(fact_8005_gbinomial__Suc,axiom,
% 0.35/0.67 ! [A: int,K2: nat] :
% 0.35/0.67 ( ( gbinomial_int @ A @ ( suc @ K2 ) )
% 0.35/0.67 = ( divide_divide_int
% 0.35/0.67 @ ( groups705719431365010083at_int
% 0.35/0.67 @ ^ [I: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 0.35/0.67 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 0.35/0.67 @ ( semiri1406184849735516958ct_int @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_Suc
% 0.35/0.67 thf(fact_8006_gbinomial__Suc,axiom,
% 0.35/0.67 ! [A: nat,K2: nat] :
% 0.35/0.67 ( ( gbinomial_nat @ A @ ( suc @ K2 ) )
% 0.35/0.67 = ( divide_divide_nat
% 0.35/0.67 @ ( groups708209901874060359at_nat
% 0.35/0.67 @ ^ [I: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 0.35/0.67 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 0.35/0.67 @ ( semiri1408675320244567234ct_nat @ ( suc @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_Suc
% 0.35/0.67 thf(fact_8007_gbinomial__partial__sum__poly,axiom,
% 0.35/0.67 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 0.35/0.67 ( ( groups2073611262835488442omplex
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.67 = ( groups2073611262835488442omplex
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_partial_sum_poly
% 0.35/0.67 thf(fact_8008_gbinomial__partial__sum__poly,axiom,
% 0.35/0.67 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 0.35/0.67 ( ( groups2906978787729119204at_rat
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.67 = ( groups2906978787729119204at_rat
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_partial_sum_poly
% 0.35/0.67 thf(fact_8009_gbinomial__partial__sum__poly,axiom,
% 0.35/0.67 ! [M2: nat,A: real,X: real,Y: real] :
% 0.35/0.67 ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) )
% 0.35/0.67 = ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % gbinomial_partial_sum_poly
% 0.35/0.67 thf(fact_8010_root__polyfun,axiom,
% 0.35/0.67 ! [N: nat,Z3: int,A: int] :
% 0.35/0.67 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.67 => ( ( ( power_power_int @ Z3 @ N )
% 0.35/0.67 = A )
% 0.35/0.67 = ( ( groups3539618377306564664at_int
% 0.35/0.67 @ ^ [I: nat] : ( times_times_int @ ( if_int @ ( I = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z3 @ I ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % root_polyfun
% 0.35/0.67 thf(fact_8011_root__polyfun,axiom,
% 0.35/0.67 ! [N: nat,Z3: complex,A: complex] :
% 0.35/0.67 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.67 => ( ( ( power_power_complex @ Z3 @ N )
% 0.35/0.67 = A )
% 0.35/0.67 = ( ( groups2073611262835488442omplex
% 0.35/0.67 @ ^ [I: nat] : ( times_times_complex @ ( if_complex @ ( I = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z3 @ I ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_complex ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % root_polyfun
% 0.35/0.67 thf(fact_8012_root__polyfun,axiom,
% 0.35/0.67 ! [N: nat,Z3: code_integer,A: code_integer] :
% 0.35/0.67 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.67 => ( ( ( power_8256067586552552935nteger @ Z3 @ N )
% 0.35/0.67 = A )
% 0.35/0.67 = ( ( groups7501900531339628137nteger
% 0.35/0.67 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z3 @ I ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_z3403309356797280102nteger ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % root_polyfun
% 0.35/0.67 thf(fact_8013_root__polyfun,axiom,
% 0.35/0.67 ! [N: nat,Z3: rat,A: rat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.67 => ( ( ( power_power_rat @ Z3 @ N )
% 0.35/0.67 = A )
% 0.35/0.67 = ( ( groups2906978787729119204at_rat
% 0.35/0.67 @ ^ [I: nat] : ( times_times_rat @ ( if_rat @ ( I = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z3 @ I ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_rat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % root_polyfun
% 0.35/0.67 thf(fact_8014_root__polyfun,axiom,
% 0.35/0.67 ! [N: nat,Z3: real,A: real] :
% 0.35/0.67 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 0.35/0.67 => ( ( ( power_power_real @ Z3 @ N )
% 0.35/0.67 = A )
% 0.35/0.67 = ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [I: nat] : ( times_times_real @ ( if_real @ ( I = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z3 @ I ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_real ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % root_polyfun
% 0.35/0.67 thf(fact_8015_set__decode__plus__power__2,axiom,
% 0.35/0.67 ! [N: nat,Z3: nat] :
% 0.35/0.67 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z3 ) )
% 0.35/0.67 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z3 ) )
% 0.35/0.67 = ( insert_nat @ N @ ( nat_set_decode @ Z3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % set_decode_plus_power_2
% 0.35/0.67 thf(fact_8016_choose__alternating__linear__sum,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( N != one_one_nat )
% 0.35/0.67 => ( ( groups2073611262835488442omplex
% 0.35/0.67 @ ^ [I: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I ) @ ( semiri8010041392384452111omplex @ I ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_complex ) ) ).
% 0.35/0.67
% 0.35/0.67 % choose_alternating_linear_sum
% 0.35/0.67 thf(fact_8017_choose__alternating__linear__sum,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( N != one_one_nat )
% 0.35/0.67 => ( ( groups7501900531339628137nteger
% 0.35/0.67 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ I ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.67
% 0.35/0.67 % choose_alternating_linear_sum
% 0.35/0.67 thf(fact_8018_choose__alternating__linear__sum,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( N != one_one_nat )
% 0.35/0.67 => ( ( groups2906978787729119204at_rat
% 0.35/0.67 @ ^ [I: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ I ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % choose_alternating_linear_sum
% 0.35/0.67 thf(fact_8019_choose__alternating__linear__sum,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( N != one_one_nat )
% 0.35/0.67 => ( ( groups3539618377306564664at_int
% 0.35/0.67 @ ^ [I: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ I ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % choose_alternating_linear_sum
% 0.35/0.67 thf(fact_8020_choose__alternating__linear__sum,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( N != one_one_nat )
% 0.35/0.67 => ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [I: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( semiri5074537144036343181t_real @ I ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) )
% 0.35/0.67 @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.67 = zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % choose_alternating_linear_sum
% 0.35/0.67 thf(fact_8021_set__decode__def,axiom,
% 0.35/0.67 ( nat_set_decode
% 0.35/0.67 = ( ^ [X4: nat] :
% 0.35/0.67 ( collect_nat
% 0.35/0.67 @ ^ [N4: nat] :
% 0.35/0.67 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % set_decode_def
% 0.35/0.67 thf(fact_8022_fact__double,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_double
% 0.35/0.67 thf(fact_8023_fact__double,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.67 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_double
% 0.35/0.67 thf(fact_8024_fact__double,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_double
% 0.35/0.67 thf(fact_8025_binomial__code,axiom,
% 0.35/0.67 ( binomial
% 0.35/0.67 = ( ^ [N4: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K3 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % binomial_code
% 0.35/0.67 thf(fact_8026_Maclaurin__lemma,axiom,
% 0.35/0.67 ! [H: real,F2: real > real,J2: nat > real,N: nat] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ H )
% 0.35/0.67 => ? [B8: real] :
% 0.35/0.67 ( ( F2 @ H )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_lemma
% 0.35/0.67 thf(fact_8027_Maclaurin__zero,axiom,
% 0.35/0.67 ! [X: real,N: nat,Diff: nat > complex > real] :
% 0.35/0.67 ( ( X = zero_zero_real )
% 0.35/0.67 => ( ( N != zero_zero_nat )
% 0.35/0.67 => ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_zero
% 0.35/0.67 thf(fact_8028_Maclaurin__zero,axiom,
% 0.35/0.67 ! [X: real,N: nat,Diff: nat > real > real] :
% 0.35/0.67 ( ( X = zero_zero_real )
% 0.35/0.67 => ( ( N != zero_zero_nat )
% 0.35/0.67 => ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_zero
% 0.35/0.67 thf(fact_8029_Maclaurin__zero,axiom,
% 0.35/0.67 ! [X: real,N: nat,Diff: nat > rat > real] :
% 0.35/0.67 ( ( X = zero_zero_real )
% 0.35/0.67 => ( ( N != zero_zero_nat )
% 0.35/0.67 => ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_zero
% 0.35/0.67 thf(fact_8030_Maclaurin__zero,axiom,
% 0.35/0.67 ! [X: real,N: nat,Diff: nat > nat > real] :
% 0.35/0.67 ( ( X = zero_zero_real )
% 0.35/0.67 => ( ( N != zero_zero_nat )
% 0.35/0.67 => ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_zero
% 0.35/0.67 thf(fact_8031_Maclaurin__zero,axiom,
% 0.35/0.67 ! [X: real,N: nat,Diff: nat > int > real] :
% 0.35/0.67 ( ( X = zero_zero_real )
% 0.35/0.67 => ( ( N != zero_zero_nat )
% 0.35/0.67 => ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_zero
% 0.35/0.67 thf(fact_8032_sin__coeff__def,axiom,
% 0.35/0.67 ( sin_coeff
% 0.35/0.67 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_coeff_def
% 0.35/0.67 thf(fact_8033_fact__diff__Suc,axiom,
% 0.35/0.67 ! [N: nat,M2: nat] :
% 0.35/0.67 ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 0.35/0.67 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) )
% 0.35/0.67 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_diff_Suc
% 0.35/0.67 thf(fact_8034_sin__paired,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( sums_real
% 0.35/0.67 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 0.35/0.67 @ ( sin_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_paired
% 0.35/0.67 thf(fact_8035_and__int_Osimps,axiom,
% 0.35/0.67 ( bit_se725231765392027082nd_int
% 0.35/0.67 = ( ^ [K3: int,L2: int] :
% 0.35/0.67 ( if_int
% 0.35/0.67 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.67 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.67 @ ( uminus_uminus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.35/0.67 @ ( plus_plus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.35/0.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_int.simps
% 0.35/0.67 thf(fact_8036_sin__zero,axiom,
% 0.35/0.67 ( ( sin_complex @ zero_zero_complex )
% 0.35/0.67 = zero_zero_complex ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero
% 0.35/0.67 thf(fact_8037_sin__zero,axiom,
% 0.35/0.67 ( ( sin_real @ zero_zero_real )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero
% 0.35/0.67 thf(fact_8038_bit_Oconj__zero__right,axiom,
% 0.35/0.67 ! [X: int] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % bit.conj_zero_right
% 0.35/0.67 thf(fact_8039_bit_Oconj__zero__left,axiom,
% 0.35/0.67 ! [X: int] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % bit.conj_zero_left
% 0.35/0.67 thf(fact_8040_zero__and__eq,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % zero_and_eq
% 0.35/0.67 thf(fact_8041_zero__and__eq,axiom,
% 0.35/0.67 ! [A: nat] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 0.35/0.67 = zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % zero_and_eq
% 0.35/0.67 thf(fact_8042_and__zero__eq,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % and_zero_eq
% 0.35/0.67 thf(fact_8043_and__zero__eq,axiom,
% 0.35/0.67 ! [A: nat] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 0.35/0.67 = zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % and_zero_eq
% 0.35/0.67 thf(fact_8044_sin__coeff__0,axiom,
% 0.35/0.67 ( ( sin_coeff @ zero_zero_nat )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_coeff_0
% 0.35/0.67 thf(fact_8045_and__numerals_I5_J,axiom,
% 0.35/0.67 ! [X: num] :
% 0.35/0.67 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 0.35/0.67 = zero_z3403309356797280102nteger ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(5)
% 0.35/0.67 thf(fact_8046_and__numerals_I5_J,axiom,
% 0.35/0.67 ! [X: num] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(5)
% 0.35/0.67 thf(fact_8047_and__numerals_I5_J,axiom,
% 0.35/0.67 ! [X: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 0.35/0.67 = zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(5)
% 0.35/0.67 thf(fact_8048_and__numerals_I1_J,axiom,
% 0.35/0.67 ! [Y: num] :
% 0.35/0.67 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 0.35/0.67 = zero_z3403309356797280102nteger ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(1)
% 0.35/0.67 thf(fact_8049_and__numerals_I1_J,axiom,
% 0.35/0.67 ! [Y: num] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(1)
% 0.35/0.67 thf(fact_8050_and__numerals_I1_J,axiom,
% 0.35/0.67 ! [Y: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.35/0.67 = zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(1)
% 0.35/0.67 thf(fact_8051_and__numerals_I3_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.35/0.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(3)
% 0.35/0.67 thf(fact_8052_and__numerals_I3_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.35/0.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(3)
% 0.35/0.67 thf(fact_8053_and__int__rec,axiom,
% 0.35/0.67 ( bit_se725231765392027082nd_int
% 0.35/0.67 = ( ^ [K3: int,L2: int] :
% 0.35/0.67 ( plus_plus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.35/0.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_int_rec
% 0.35/0.67 thf(fact_8054_and__int__unfold,axiom,
% 0.35/0.67 ( bit_se725231765392027082nd_int
% 0.35/0.67 = ( ^ [K3: int,L2: int] :
% 0.35/0.67 ( if_int
% 0.35/0.67 @ ( ( K3 = zero_zero_int )
% 0.35/0.67 | ( L2 = zero_zero_int ) )
% 0.35/0.67 @ zero_zero_int
% 0.35/0.67 @ ( if_int
% 0.35/0.67 @ ( K3
% 0.35/0.67 = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.67 @ L2
% 0.35/0.67 @ ( if_int
% 0.35/0.67 @ ( L2
% 0.35/0.67 = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.67 @ K3
% 0.35/0.67 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_int_unfold
% 0.35/0.67 thf(fact_8055_and__int_Oelims,axiom,
% 0.35/0.67 ! [X: int,Xa2: int,Y: int] :
% 0.35/0.67 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 0.35/0.67 = Y )
% 0.35/0.67 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.67 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.67 => ( Y
% 0.35/0.67 = ( uminus_uminus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.35/0.67 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.67 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.67 => ( Y
% 0.35/0.67 = ( plus_plus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.35/0.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_int.elims
% 0.35/0.67 thf(fact_8056_Maclaurin__sin__expansion3,axiom,
% 0.35/0.67 ! [N: nat,X: real] :
% 0.35/0.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ? [T6: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.67 & ( ord_less_real @ T6 @ X )
% 0.35/0.67 & ( ( sin_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_sin_expansion3
% 0.35/0.67 thf(fact_8057_Maclaurin__sin__expansion4,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ? [T6: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.67 & ( ord_less_eq_real @ T6 @ X )
% 0.35/0.67 & ( ( sin_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_sin_expansion4
% 0.35/0.67 thf(fact_8058_sumr__cos__zero__one,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % sumr_cos_zero_one
% 0.35/0.67 thf(fact_8059_sin__cos__npi,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_cos_npi
% 0.35/0.67 thf(fact_8060_Maclaurin__sin__expansion,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ? [T6: real] :
% 0.35/0.67 ( ( sin_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_sin_expansion
% 0.35/0.67 thf(fact_8061_signed__take__bit__Suc__minus__bit1,axiom,
% 0.35/0.67 ! [N: nat,K2: num] :
% 0.35/0.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_Suc_minus_bit1
% 0.35/0.67 thf(fact_8062_semiring__norm_I15_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 0.35/0.67 = ( bit0 @ ( times_times_num @ ( bit1 @ M2 ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % semiring_norm(15)
% 0.35/0.67 thf(fact_8063_semiring__norm_I14_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( times_times_num @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( bit0 @ ( times_times_num @ M2 @ ( bit1 @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % semiring_norm(14)
% 0.35/0.67 thf(fact_8064_cos__coeff__0,axiom,
% 0.35/0.67 ( ( cos_coeff @ zero_zero_nat )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % cos_coeff_0
% 0.35/0.67 thf(fact_8065_dbl__inc__simps_I5_J,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K2 ) )
% 0.35/0.67 = ( numera6690914467698888265omplex @ ( bit1 @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_inc_simps(5)
% 0.35/0.67 thf(fact_8066_dbl__inc__simps_I5_J,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K2 ) )
% 0.35/0.67 = ( numeral_numeral_real @ ( bit1 @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_inc_simps(5)
% 0.35/0.67 thf(fact_8067_dbl__inc__simps_I5_J,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K2 ) )
% 0.35/0.67 = ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_inc_simps(5)
% 0.35/0.67 thf(fact_8068_and__nat__numerals_I1_J,axiom,
% 0.35/0.67 ! [Y: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.35/0.67 = zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % and_nat_numerals(1)
% 0.35/0.67 thf(fact_8069_and__nat__numerals_I3_J,axiom,
% 0.35/0.67 ! [X: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.67 = zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % and_nat_numerals(3)
% 0.35/0.67 thf(fact_8070_zdiv__numeral__Bit1,axiom,
% 0.35/0.67 ! [V2: num,W2: num] :
% 0.35/0.67 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.35/0.67 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zdiv_numeral_Bit1
% 0.35/0.67 thf(fact_8071_semiring__norm_I16_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M2 @ N ) @ ( bit0 @ ( times_times_num @ M2 @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % semiring_norm(16)
% 0.35/0.67 thf(fact_8072_and__nat__numerals_I4_J,axiom,
% 0.35/0.67 ! [X: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.67 = one_one_nat ) ).
% 0.35/0.67
% 0.35/0.67 % and_nat_numerals(4)
% 0.35/0.67 thf(fact_8073_and__nat__numerals_I2_J,axiom,
% 0.35/0.67 ! [Y: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.35/0.67 = one_one_nat ) ).
% 0.35/0.67
% 0.35/0.67 % and_nat_numerals(2)
% 0.35/0.67 thf(fact_8074_sin__npi2,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_npi2
% 0.35/0.67 thf(fact_8075_sin__npi,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_npi
% 0.35/0.67 thf(fact_8076_dbl__inc__simps_I3_J,axiom,
% 0.35/0.67 ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 0.35/0.67 = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_inc_simps(3)
% 0.35/0.67 thf(fact_8077_dbl__inc__simps_I3_J,axiom,
% 0.35/0.67 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 0.35/0.67 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_inc_simps(3)
% 0.35/0.67 thf(fact_8078_dbl__inc__simps_I3_J,axiom,
% 0.35/0.67 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 0.35/0.67 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_inc_simps(3)
% 0.35/0.67 thf(fact_8079_dbl__inc__simps_I3_J,axiom,
% 0.35/0.67 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 0.35/0.67 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_inc_simps(3)
% 0.35/0.67 thf(fact_8080_and__numerals_I4_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.35/0.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(4)
% 0.35/0.67 thf(fact_8081_and__numerals_I4_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.35/0.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(4)
% 0.35/0.67 thf(fact_8082_and__numerals_I6_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 0.35/0.67 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(6)
% 0.35/0.67 thf(fact_8083_and__numerals_I6_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.35/0.67 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(6)
% 0.35/0.67 thf(fact_8084_Suc__0__and__eq,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.67 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Suc_0_and_eq
% 0.35/0.67 thf(fact_8085_and__Suc__0__eq,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.67 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_Suc_0_eq
% 0.35/0.67 thf(fact_8086_div__Suc__eq__div__add3,axiom,
% 0.35/0.67 ! [M2: nat,N: nat] :
% 0.35/0.67 ( ( divide_divide_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.35/0.67 = ( divide_divide_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % div_Suc_eq_div_add3
% 0.35/0.67 thf(fact_8087_Suc__div__eq__add3__div__numeral,axiom,
% 0.35/0.67 ! [M2: nat,V2: num] :
% 0.35/0.67 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 0.35/0.67 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Suc_div_eq_add3_div_numeral
% 0.35/0.67 thf(fact_8088_mod__Suc__eq__mod__add3,axiom,
% 0.35/0.67 ! [M2: nat,N: nat] :
% 0.35/0.67 ( ( modulo_modulo_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 0.35/0.67 = ( modulo_modulo_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % mod_Suc_eq_mod_add3
% 0.35/0.67 thf(fact_8089_Suc__mod__eq__add3__mod__numeral,axiom,
% 0.35/0.67 ! [M2: nat,V2: num] :
% 0.35/0.67 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 0.35/0.67 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Suc_mod_eq_add3_mod_numeral
% 0.35/0.67 thf(fact_8090_dbl__dec__simps_I4_J,axiom,
% 0.35/0.67 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.67 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_dec_simps(4)
% 0.35/0.67 thf(fact_8091_dbl__dec__simps_I4_J,axiom,
% 0.35/0.67 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.67 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_dec_simps(4)
% 0.35/0.67 thf(fact_8092_dbl__dec__simps_I4_J,axiom,
% 0.35/0.67 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 0.35/0.67 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_dec_simps(4)
% 0.35/0.67 thf(fact_8093_dbl__dec__simps_I4_J,axiom,
% 0.35/0.67 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.67 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_dec_simps(4)
% 0.35/0.67 thf(fact_8094_dbl__dec__simps_I4_J,axiom,
% 0.35/0.67 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.67 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dbl_dec_simps(4)
% 0.35/0.67 thf(fact_8095_sin__two__pi,axiom,
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_two_pi
% 0.35/0.67 thf(fact_8096_sin__2pi__minus,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 0.35/0.67 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_2pi_minus
% 0.35/0.67 thf(fact_8097_sin__periodic,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.67 = ( sin_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_periodic
% 0.35/0.67 thf(fact_8098_and__numerals_I7_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 0.35/0.67 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(7)
% 0.35/0.67 thf(fact_8099_and__numerals_I7_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 0.35/0.67 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(7)
% 0.35/0.67 thf(fact_8100_and__numerals_I7_J,axiom,
% 0.35/0.67 ! [X: num,Y: num] :
% 0.35/0.67 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.35/0.67 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_numerals(7)
% 0.35/0.67 thf(fact_8101_zmod__numeral__Bit1,axiom,
% 0.35/0.67 ! [V2: num,W2: num] :
% 0.35/0.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % zmod_numeral_Bit1
% 0.35/0.67 thf(fact_8102_sin__2npi,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_2npi
% 0.35/0.67 thf(fact_8103_signed__take__bit__Suc__bit1,axiom,
% 0.35/0.67 ! [N: nat,K2: num] :
% 0.35/0.67 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_Suc_bit1
% 0.35/0.67 thf(fact_8104_sin__3over2__pi,axiom,
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.35/0.67 = ( uminus_uminus_real @ one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_3over2_pi
% 0.35/0.67 thf(fact_8105_num_Oexhaust,axiom,
% 0.35/0.67 ! [Y: num] :
% 0.35/0.67 ( ( Y != one )
% 0.35/0.67 => ( ! [X23: num] :
% 0.35/0.67 ( Y
% 0.35/0.67 != ( bit0 @ X23 ) )
% 0.35/0.67 => ~ ! [X32: num] :
% 0.35/0.67 ( Y
% 0.35/0.67 != ( bit1 @ X32 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % num.exhaust
% 0.35/0.67 thf(fact_8106_numeral__Bit1,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_Bit1
% 0.35/0.67 thf(fact_8107_numeral__Bit1,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_Bit1
% 0.35/0.67 thf(fact_8108_numeral__Bit1,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numera1916890842035813515d_enat @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) @ one_on7984719198319812577d_enat ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_Bit1
% 0.35/0.67 thf(fact_8109_numeral__Bit1,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_Bit1
% 0.35/0.67 thf(fact_8110_numeral__Bit1,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_Bit1
% 0.35/0.67 thf(fact_8111_numeral__Bit1,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_Bit1
% 0.35/0.67 thf(fact_8112_numeral__Bit1,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_Bit1
% 0.35/0.67 thf(fact_8113_eval__nat__numeral_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.35/0.67 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % eval_nat_numeral(3)
% 0.35/0.67 thf(fact_8114_cong__exp__iff__simps_I13_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num,N: num] :
% 0.35/0.67 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.67 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(13)
% 0.35/0.67 thf(fact_8115_cong__exp__iff__simps_I13_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num,N: num] :
% 0.35/0.67 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.67 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(13)
% 0.35/0.67 thf(fact_8116_cong__exp__iff__simps_I12_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num,N: num] :
% 0.35/0.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(12)
% 0.35/0.67 thf(fact_8117_cong__exp__iff__simps_I12_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num,N: num] :
% 0.35/0.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(12)
% 0.35/0.67 thf(fact_8118_cong__exp__iff__simps_I10_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num,N: num] :
% 0.35/0.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(10)
% 0.35/0.67 thf(fact_8119_cong__exp__iff__simps_I10_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num,N: num] :
% 0.35/0.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(10)
% 0.35/0.67 thf(fact_8120_numeral__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_code(3)
% 0.35/0.67 thf(fact_8121_numeral__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_code(3)
% 0.35/0.67 thf(fact_8122_numeral__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numera1916890842035813515d_enat @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) @ one_on7984719198319812577d_enat ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_code(3)
% 0.35/0.67 thf(fact_8123_numeral__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_code(3)
% 0.35/0.67 thf(fact_8124_numeral__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_code(3)
% 0.35/0.67 thf(fact_8125_numeral__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_code(3)
% 0.35/0.67 thf(fact_8126_numeral__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 0.35/0.67 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_code(3)
% 0.35/0.67 thf(fact_8127_power__numeral__odd,axiom,
% 0.35/0.67 ! [Z3: complex,W2: num] :
% 0.35/0.67 ( ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ Z3 @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_numeral_odd
% 0.35/0.67 thf(fact_8128_power__numeral__odd,axiom,
% 0.35/0.67 ! [Z3: real,W2: num] :
% 0.35/0.67 ( ( power_power_real @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ Z3 @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_numeral_odd
% 0.35/0.67 thf(fact_8129_power__numeral__odd,axiom,
% 0.35/0.67 ! [Z3: rat,W2: num] :
% 0.35/0.67 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 0.35/0.67 = ( times_times_rat @ ( times_times_rat @ Z3 @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_numeral_odd
% 0.35/0.67 thf(fact_8130_power__numeral__odd,axiom,
% 0.35/0.67 ! [Z3: nat,W2: num] :
% 0.35/0.67 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 0.35/0.67 = ( times_times_nat @ ( times_times_nat @ Z3 @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_numeral_odd
% 0.35/0.67 thf(fact_8131_power__numeral__odd,axiom,
% 0.35/0.67 ! [Z3: int,W2: num] :
% 0.35/0.67 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 0.35/0.67 = ( times_times_int @ ( times_times_int @ Z3 @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_numeral_odd
% 0.35/0.67 thf(fact_8132_cong__exp__iff__simps_I3_J,axiom,
% 0.35/0.67 ! [N: num,Q2: num] :
% 0.35/0.67 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 != zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(3)
% 0.35/0.67 thf(fact_8133_cong__exp__iff__simps_I3_J,axiom,
% 0.35/0.67 ! [N: num,Q2: num] :
% 0.35/0.67 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 != zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(3)
% 0.35/0.67 thf(fact_8134_power3__eq__cube,axiom,
% 0.35/0.67 ! [A: complex] :
% 0.35/0.67 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % power3_eq_cube
% 0.35/0.67 thf(fact_8135_power3__eq__cube,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % power3_eq_cube
% 0.35/0.67 thf(fact_8136_power3__eq__cube,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % power3_eq_cube
% 0.35/0.67 thf(fact_8137_power3__eq__cube,axiom,
% 0.35/0.67 ! [A: nat] :
% 0.35/0.67 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % power3_eq_cube
% 0.35/0.67 thf(fact_8138_power3__eq__cube,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % power3_eq_cube
% 0.35/0.67 thf(fact_8139_numeral__3__eq__3,axiom,
% 0.35/0.67 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 0.35/0.67 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_3_eq_3
% 0.35/0.67 thf(fact_8140_Suc3__eq__add__3,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 0.35/0.67 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % Suc3_eq_add_3
% 0.35/0.67 thf(fact_8141_num_Osize_I6_J,axiom,
% 0.35/0.67 ! [X33: num] :
% 0.35/0.67 ( ( size_size_num @ ( bit1 @ X33 ) )
% 0.35/0.67 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % num.size(6)
% 0.35/0.67 thf(fact_8142_cong__exp__iff__simps_I7_J,axiom,
% 0.35/0.67 ! [Q2: num,N: num] :
% 0.35/0.67 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.67 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.67 = zero_zero_nat ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(7)
% 0.35/0.67 thf(fact_8143_cong__exp__iff__simps_I7_J,axiom,
% 0.35/0.67 ! [Q2: num,N: num] :
% 0.35/0.67 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.67 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.67 = zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(7)
% 0.35/0.67 thf(fact_8144_cong__exp__iff__simps_I11_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num] :
% 0.35/0.67 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.67 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.67 = zero_zero_nat ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(11)
% 0.35/0.67 thf(fact_8145_cong__exp__iff__simps_I11_J,axiom,
% 0.35/0.67 ! [M2: num,Q2: num] :
% 0.35/0.67 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 0.35/0.67 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 0.35/0.67 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 0.35/0.67 = zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % cong_exp_iff_simps(11)
% 0.35/0.67 thf(fact_8146_Suc__div__eq__add3__div,axiom,
% 0.35/0.67 ! [M2: nat,N: nat] :
% 0.35/0.67 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 0.35/0.67 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % Suc_div_eq_add3_div
% 0.35/0.67 thf(fact_8147_card__3__iff,axiom,
% 0.35/0.67 ! [S3: set_complex] :
% 0.35/0.67 ( ( ( finite_card_complex @ S3 )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( ? [X4: complex,Y4: complex,Z4: complex] :
% 0.35/0.67 ( ( S3
% 0.35/0.67 = ( insert_complex @ X4 @ ( insert_complex @ Y4 @ ( insert_complex @ Z4 @ bot_bot_set_complex ) ) ) )
% 0.35/0.67 & ( X4 != Y4 )
% 0.35/0.67 & ( Y4 != Z4 )
% 0.35/0.67 & ( X4 != Z4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % card_3_iff
% 0.35/0.67 thf(fact_8148_card__3__iff,axiom,
% 0.35/0.67 ! [S3: set_list_nat] :
% 0.35/0.67 ( ( ( finite_card_list_nat @ S3 )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( ? [X4: list_nat,Y4: list_nat,Z4: list_nat] :
% 0.35/0.67 ( ( S3
% 0.35/0.67 = ( insert_list_nat @ X4 @ ( insert_list_nat @ Y4 @ ( insert_list_nat @ Z4 @ bot_bot_set_list_nat ) ) ) )
% 0.35/0.67 & ( X4 != Y4 )
% 0.35/0.67 & ( Y4 != Z4 )
% 0.35/0.67 & ( X4 != Z4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % card_3_iff
% 0.35/0.67 thf(fact_8149_card__3__iff,axiom,
% 0.35/0.67 ! [S3: set_set_nat] :
% 0.35/0.67 ( ( ( finite_card_set_nat @ S3 )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( ? [X4: set_nat,Y4: set_nat,Z4: set_nat] :
% 0.35/0.67 ( ( S3
% 0.35/0.67 = ( insert_set_nat @ X4 @ ( insert_set_nat @ Y4 @ ( insert_set_nat @ Z4 @ bot_bot_set_set_nat ) ) ) )
% 0.35/0.67 & ( X4 != Y4 )
% 0.35/0.67 & ( Y4 != Z4 )
% 0.35/0.67 & ( X4 != Z4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % card_3_iff
% 0.35/0.67 thf(fact_8150_card__3__iff,axiom,
% 0.35/0.67 ! [S3: set_nat] :
% 0.35/0.67 ( ( ( finite_card_nat @ S3 )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( ? [X4: nat,Y4: nat,Z4: nat] :
% 0.35/0.67 ( ( S3
% 0.35/0.67 = ( insert_nat @ X4 @ ( insert_nat @ Y4 @ ( insert_nat @ Z4 @ bot_bot_set_nat ) ) ) )
% 0.35/0.67 & ( X4 != Y4 )
% 0.35/0.67 & ( Y4 != Z4 )
% 0.35/0.67 & ( X4 != Z4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % card_3_iff
% 0.35/0.67 thf(fact_8151_card__3__iff,axiom,
% 0.35/0.67 ! [S3: set_int] :
% 0.35/0.67 ( ( ( finite_card_int @ S3 )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( ? [X4: int,Y4: int,Z4: int] :
% 0.35/0.67 ( ( S3
% 0.35/0.67 = ( insert_int @ X4 @ ( insert_int @ Y4 @ ( insert_int @ Z4 @ bot_bot_set_int ) ) ) )
% 0.35/0.67 & ( X4 != Y4 )
% 0.35/0.67 & ( Y4 != Z4 )
% 0.35/0.67 & ( X4 != Z4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % card_3_iff
% 0.35/0.67 thf(fact_8152_card__3__iff,axiom,
% 0.35/0.67 ! [S3: set_real] :
% 0.35/0.67 ( ( ( finite_card_real @ S3 )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 = ( ? [X4: real,Y4: real,Z4: real] :
% 0.35/0.67 ( ( S3
% 0.35/0.67 = ( insert_real @ X4 @ ( insert_real @ Y4 @ ( insert_real @ Z4 @ bot_bot_set_real ) ) ) )
% 0.35/0.67 & ( X4 != Y4 )
% 0.35/0.67 & ( Y4 != Z4 )
% 0.35/0.67 & ( X4 != Z4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % card_3_iff
% 0.35/0.67 thf(fact_8153_Suc__mod__eq__add3__mod,axiom,
% 0.35/0.67 ! [M2: nat,N: nat] :
% 0.35/0.67 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 0.35/0.67 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % Suc_mod_eq_add3_mod
% 0.35/0.67 thf(fact_8154_mod__exhaust__less__4,axiom,
% 0.35/0.67 ! [M2: nat] :
% 0.35/0.67 ( ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = zero_zero_nat )
% 0.35/0.67 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = one_one_nat )
% 0.35/0.67 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.67 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % mod_exhaust_less_4
% 0.35/0.67 thf(fact_8155_m2pi__less__pi,axiom,
% 0.35/0.67 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 0.35/0.67
% 0.35/0.67 % m2pi_less_pi
% 0.35/0.67 thf(fact_8156_sin__pi__divide__n__ge__0,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( N != zero_zero_nat )
% 0.35/0.67 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_pi_divide_n_ge_0
% 0.35/0.67 thf(fact_8157_sin__coeff__Suc,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( sin_coeff @ ( suc @ N ) )
% 0.35/0.67 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_coeff_Suc
% 0.35/0.67 thf(fact_8158_sin__lt__zero,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_real @ pi @ X )
% 0.35/0.67 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_lt_zero
% 0.35/0.67 thf(fact_8159_and__nat__unfold,axiom,
% 0.35/0.67 ( bit_se727722235901077358nd_nat
% 0.35/0.67 = ( ^ [M6: nat,N4: nat] :
% 0.35/0.67 ( if_nat
% 0.35/0.67 @ ( ( M6 = zero_zero_nat )
% 0.35/0.67 | ( N4 = zero_zero_nat ) )
% 0.35/0.67 @ zero_zero_nat
% 0.35/0.67 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_nat_unfold
% 0.35/0.67 thf(fact_8160_and__nat__rec,axiom,
% 0.35/0.67 ( bit_se727722235901077358nd_nat
% 0.35/0.67 = ( ^ [M6: nat,N4: nat] :
% 0.35/0.67 ( plus_plus_nat
% 0.35/0.67 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.67 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 0.35/0.67 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.35/0.67 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_nat_rec
% 0.35/0.67 thf(fact_8161_sin__le__zero,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ pi @ X )
% 0.35/0.67 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_le_zero
% 0.35/0.67 thf(fact_8162_cos__coeff__Suc,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( cos_coeff @ ( suc @ N ) )
% 0.35/0.67 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_coeff_Suc
% 0.35/0.67 thf(fact_8163_odd__mod__4__div__2,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 0.35/0.67 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % odd_mod_4_div_2
% 0.35/0.67 thf(fact_8164_sin__pi__divide__n__gt__0,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_pi_divide_n_gt_0
% 0.35/0.67 thf(fact_8165_sin__zero__lemma,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ( sin_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 => ? [N3: nat] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero_lemma
% 0.35/0.67 thf(fact_8166_sin__zero__iff,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( sin_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 = ( ? [N4: nat] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.67 | ? [N4: nat] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero_iff
% 0.35/0.67 thf(fact_8167_Maclaurin__minus__cos__expansion,axiom,
% 0.35/0.67 ! [N: nat,X: real] :
% 0.35/0.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.67 => ? [T6: real] :
% 0.35/0.67 ( ( ord_less_real @ X @ T6 )
% 0.35/0.67 & ( ord_less_real @ T6 @ zero_zero_real )
% 0.35/0.67 & ( ( cos_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_minus_cos_expansion
% 0.35/0.67 thf(fact_8168_Maclaurin__cos__expansion2,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ? [T6: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.67 & ( ord_less_real @ T6 @ X )
% 0.35/0.67 & ( ( cos_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_cos_expansion2
% 0.35/0.67 thf(fact_8169_Maclaurin__sin__expansion2,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ? [T6: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.67 & ( ( sin_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_sin_expansion2
% 0.35/0.67 thf(fact_8170_signed__take__bit__numeral__minus__bit1,axiom,
% 0.35/0.67 ! [L: num,K2: num] :
% 0.35/0.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_numeral_minus_bit1
% 0.35/0.67 thf(fact_8171_divmod__algorithm__code_I8_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( ( ord_less_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) ) ) )
% 0.35/0.67 & ( ~ ( ord_less_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(8)
% 0.35/0.67 thf(fact_8172_divmod__algorithm__code_I8_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( ( ord_less_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) ) ) )
% 0.35/0.67 & ( ~ ( ord_less_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(8)
% 0.35/0.67 thf(fact_8173_divmod__algorithm__code_I8_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( ( ord_less_num @ M2 @ N )
% 0.35/0.67 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M2 ) ) ) ) )
% 0.35/0.67 & ( ~ ( ord_less_num @ M2 @ N )
% 0.35/0.67 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(8)
% 0.35/0.67 thf(fact_8174_divmod__algorithm__code_I7_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( ( ord_less_eq_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) ) ) )
% 0.35/0.67 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(7)
% 0.35/0.67 thf(fact_8175_divmod__algorithm__code_I7_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( ( ord_less_eq_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ) )
% 0.35/0.67 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 0.35/0.67 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(7)
% 0.35/0.67 thf(fact_8176_divmod__algorithm__code_I7_J,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( ( ord_less_eq_num @ M2 @ N )
% 0.35/0.67 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M2 ) ) ) ) )
% 0.35/0.67 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 0.35/0.67 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 0.35/0.67 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(7)
% 0.35/0.67 thf(fact_8177_abs__idempotent,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.35/0.67 = ( abs_abs_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_idempotent
% 0.35/0.67 thf(fact_8178_abs__idempotent,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.35/0.67 = ( abs_abs_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_idempotent
% 0.35/0.67 thf(fact_8179_abs__idempotent,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.35/0.67 = ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_idempotent
% 0.35/0.67 thf(fact_8180_abs__idempotent,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.35/0.67 = ( abs_abs_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_idempotent
% 0.35/0.67 thf(fact_8181_abs__abs,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 0.35/0.67 = ( abs_abs_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_abs
% 0.35/0.67 thf(fact_8182_abs__abs,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 0.35/0.67 = ( abs_abs_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_abs
% 0.35/0.67 thf(fact_8183_abs__abs,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 0.35/0.67 = ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_abs
% 0.35/0.67 thf(fact_8184_abs__abs,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 0.35/0.67 = ( abs_abs_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_abs
% 0.35/0.67 thf(fact_8185_abs__0,axiom,
% 0.35/0.67 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.35/0.67 = zero_z3403309356797280102nteger ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0
% 0.35/0.67 thf(fact_8186_abs__0,axiom,
% 0.35/0.67 ( ( abs_abs_complex @ zero_zero_complex )
% 0.35/0.67 = zero_zero_complex ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0
% 0.35/0.67 thf(fact_8187_abs__0,axiom,
% 0.35/0.67 ( ( abs_abs_real @ zero_zero_real )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0
% 0.35/0.67 thf(fact_8188_abs__0,axiom,
% 0.35/0.67 ( ( abs_abs_rat @ zero_zero_rat )
% 0.35/0.67 = zero_zero_rat ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0
% 0.35/0.67 thf(fact_8189_abs__0,axiom,
% 0.35/0.67 ( ( abs_abs_int @ zero_zero_int )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0
% 0.35/0.67 thf(fact_8190_abs__0__eq,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( zero_z3403309356797280102nteger
% 0.35/0.67 = ( abs_abs_Code_integer @ A ) )
% 0.35/0.67 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0_eq
% 0.35/0.67 thf(fact_8191_abs__0__eq,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( zero_zero_real
% 0.35/0.67 = ( abs_abs_real @ A ) )
% 0.35/0.67 = ( A = zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0_eq
% 0.35/0.67 thf(fact_8192_abs__0__eq,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( zero_zero_rat
% 0.35/0.67 = ( abs_abs_rat @ A ) )
% 0.35/0.67 = ( A = zero_zero_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0_eq
% 0.35/0.67 thf(fact_8193_abs__0__eq,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( zero_zero_int
% 0.35/0.67 = ( abs_abs_int @ A ) )
% 0.35/0.67 = ( A = zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_0_eq
% 0.35/0.67 thf(fact_8194_abs__eq__0,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ( abs_abs_Code_integer @ A )
% 0.35/0.67 = zero_z3403309356797280102nteger )
% 0.35/0.67 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0
% 0.35/0.67 thf(fact_8195_abs__eq__0,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ( abs_abs_real @ A )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 = ( A = zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0
% 0.35/0.67 thf(fact_8196_abs__eq__0,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ( abs_abs_rat @ A )
% 0.35/0.67 = zero_zero_rat )
% 0.35/0.67 = ( A = zero_zero_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0
% 0.35/0.67 thf(fact_8197_abs__eq__0,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ( abs_abs_int @ A )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 = ( A = zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0
% 0.35/0.67 thf(fact_8198_abs__zero,axiom,
% 0.35/0.67 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 0.35/0.67 = zero_z3403309356797280102nteger ) ).
% 0.35/0.67
% 0.35/0.67 % abs_zero
% 0.35/0.67 thf(fact_8199_abs__zero,axiom,
% 0.35/0.67 ( ( abs_abs_real @ zero_zero_real )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % abs_zero
% 0.35/0.67 thf(fact_8200_abs__zero,axiom,
% 0.35/0.67 ( ( abs_abs_rat @ zero_zero_rat )
% 0.35/0.67 = zero_zero_rat ) ).
% 0.35/0.67
% 0.35/0.67 % abs_zero
% 0.35/0.67 thf(fact_8201_abs__zero,axiom,
% 0.35/0.67 ( ( abs_abs_int @ zero_zero_int )
% 0.35/0.67 = zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % abs_zero
% 0.35/0.67 thf(fact_8202_abs__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 0.35/0.67 = ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_numeral
% 0.35/0.67 thf(fact_8203_abs__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 0.35/0.67 = ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_numeral
% 0.35/0.67 thf(fact_8204_abs__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 0.35/0.67 = ( numeral_numeral_real @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_numeral
% 0.35/0.67 thf(fact_8205_abs__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 0.35/0.67 = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_numeral
% 0.35/0.67 thf(fact_8206_abs__mult__self__eq,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 0.35/0.67 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_self_eq
% 0.35/0.67 thf(fact_8207_abs__mult__self__eq,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 0.35/0.67 = ( times_times_real @ A @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_self_eq
% 0.35/0.67 thf(fact_8208_abs__mult__self__eq,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 0.35/0.67 = ( times_times_rat @ A @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_self_eq
% 0.35/0.67 thf(fact_8209_abs__mult__self__eq,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 0.35/0.67 = ( times_times_int @ A @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_self_eq
% 0.35/0.67 thf(fact_8210_abs__add__abs,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 0.35/0.67 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_abs
% 0.35/0.67 thf(fact_8211_abs__add__abs,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 0.35/0.67 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_abs
% 0.35/0.67 thf(fact_8212_abs__add__abs,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 0.35/0.67 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_abs
% 0.35/0.67 thf(fact_8213_abs__add__abs,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_abs
% 0.35/0.67 thf(fact_8214_abs__1,axiom,
% 0.35/0.67 ( ( abs_abs_rat @ one_one_rat )
% 0.35/0.67 = one_one_rat ) ).
% 0.35/0.67
% 0.35/0.67 % abs_1
% 0.35/0.67 thf(fact_8215_abs__1,axiom,
% 0.35/0.67 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.35/0.67 = one_one_Code_integer ) ).
% 0.35/0.67
% 0.35/0.67 % abs_1
% 0.35/0.67 thf(fact_8216_abs__1,axiom,
% 0.35/0.67 ( ( abs_abs_complex @ one_one_complex )
% 0.35/0.67 = one_one_complex ) ).
% 0.35/0.67
% 0.35/0.67 % abs_1
% 0.35/0.67 thf(fact_8217_abs__1,axiom,
% 0.35/0.67 ( ( abs_abs_real @ one_one_real )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % abs_1
% 0.35/0.67 thf(fact_8218_abs__1,axiom,
% 0.35/0.67 ( ( abs_abs_int @ one_one_int )
% 0.35/0.67 = one_one_int ) ).
% 0.35/0.67
% 0.35/0.67 % abs_1
% 0.35/0.67 thf(fact_8219_abs__minus__cancel,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.35/0.67 = ( abs_abs_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_cancel
% 0.35/0.67 thf(fact_8220_abs__minus__cancel,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.35/0.67 = ( abs_abs_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_cancel
% 0.35/0.67 thf(fact_8221_abs__minus__cancel,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.67 = ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_cancel
% 0.35/0.67 thf(fact_8222_abs__minus__cancel,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.35/0.67 = ( abs_abs_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_cancel
% 0.35/0.67 thf(fact_8223_abs__minus,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 0.35/0.67 = ( abs_abs_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus
% 0.35/0.67 thf(fact_8224_abs__minus,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 0.35/0.67 = ( abs_abs_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus
% 0.35/0.67 thf(fact_8225_abs__minus,axiom,
% 0.35/0.67 ! [A: complex] :
% 0.35/0.67 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 0.35/0.67 = ( abs_abs_complex @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus
% 0.35/0.67 thf(fact_8226_abs__minus,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 0.35/0.67 = ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus
% 0.35/0.67 thf(fact_8227_abs__minus,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 0.35/0.67 = ( abs_abs_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus
% 0.35/0.67 thf(fact_8228_dvd__abs__iff,axiom,
% 0.35/0.67 ! [M2: real,K2: real] :
% 0.35/0.67 ( ( dvd_dvd_real @ M2 @ ( abs_abs_real @ K2 ) )
% 0.35/0.67 = ( dvd_dvd_real @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_abs_iff
% 0.35/0.67 thf(fact_8229_dvd__abs__iff,axiom,
% 0.35/0.67 ! [M2: int,K2: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ M2 @ ( abs_abs_int @ K2 ) )
% 0.35/0.67 = ( dvd_dvd_int @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_abs_iff
% 0.35/0.67 thf(fact_8230_dvd__abs__iff,axiom,
% 0.35/0.67 ! [M2: code_integer,K2: code_integer] :
% 0.35/0.67 ( ( dvd_dvd_Code_integer @ M2 @ ( abs_abs_Code_integer @ K2 ) )
% 0.35/0.67 = ( dvd_dvd_Code_integer @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_abs_iff
% 0.35/0.67 thf(fact_8231_dvd__abs__iff,axiom,
% 0.35/0.67 ! [M2: rat,K2: rat] :
% 0.35/0.67 ( ( dvd_dvd_rat @ M2 @ ( abs_abs_rat @ K2 ) )
% 0.35/0.67 = ( dvd_dvd_rat @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_abs_iff
% 0.35/0.67 thf(fact_8232_abs__dvd__iff,axiom,
% 0.35/0.67 ! [M2: real,K2: real] :
% 0.35/0.67 ( ( dvd_dvd_real @ ( abs_abs_real @ M2 ) @ K2 )
% 0.35/0.67 = ( dvd_dvd_real @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_dvd_iff
% 0.35/0.67 thf(fact_8233_abs__dvd__iff,axiom,
% 0.35/0.67 ! [M2: int,K2: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ ( abs_abs_int @ M2 ) @ K2 )
% 0.35/0.67 = ( dvd_dvd_int @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_dvd_iff
% 0.35/0.67 thf(fact_8234_abs__dvd__iff,axiom,
% 0.35/0.67 ! [M2: code_integer,K2: code_integer] :
% 0.35/0.67 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M2 ) @ K2 )
% 0.35/0.67 = ( dvd_dvd_Code_integer @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_dvd_iff
% 0.35/0.67 thf(fact_8235_abs__dvd__iff,axiom,
% 0.35/0.67 ! [M2: rat,K2: rat] :
% 0.35/0.67 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M2 ) @ K2 )
% 0.35/0.67 = ( dvd_dvd_rat @ M2 @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_dvd_iff
% 0.35/0.67 thf(fact_8236_abs__of__nat,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 0.35/0.67 = ( semiri4939895301339042750nteger @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nat
% 0.35/0.67 thf(fact_8237_abs__of__nat,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 0.35/0.67 = ( semiri681578069525770553at_rat @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nat
% 0.35/0.67 thf(fact_8238_abs__of__nat,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.67 = ( semiri5074537144036343181t_real @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nat
% 0.35/0.67 thf(fact_8239_abs__of__nat,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.67 = ( semiri1314217659103216013at_int @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nat
% 0.35/0.67 thf(fact_8240_abs__bool__eq,axiom,
% 0.35/0.67 ! [P2: $o] :
% 0.35/0.67 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P2 ) )
% 0.35/0.67 = ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_bool_eq
% 0.35/0.67 thf(fact_8241_abs__bool__eq,axiom,
% 0.35/0.67 ! [P2: $o] :
% 0.35/0.67 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 0.35/0.67 = ( zero_n2052037380579107095ol_rat @ P2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_bool_eq
% 0.35/0.67 thf(fact_8242_abs__bool__eq,axiom,
% 0.35/0.67 ! [P2: $o] :
% 0.35/0.67 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 0.35/0.67 = ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_bool_eq
% 0.35/0.67 thf(fact_8243_abs__bool__eq,axiom,
% 0.35/0.67 ! [P2: $o] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) )
% 0.35/0.67 = ( zero_n356916108424825756nteger @ P2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_bool_eq
% 0.35/0.67 thf(fact_8244_abs__of__nonneg,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.67 => ( ( abs_abs_Code_integer @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonneg
% 0.35/0.67 thf(fact_8245_abs__of__nonneg,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.67 => ( ( abs_abs_real @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonneg
% 0.35/0.67 thf(fact_8246_abs__of__nonneg,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.67 => ( ( abs_abs_rat @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonneg
% 0.35/0.67 thf(fact_8247_abs__of__nonneg,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.67 => ( ( abs_abs_int @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonneg
% 0.35/0.67 thf(fact_8248_abs__le__self__iff,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 0.35/0.67 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_self_iff
% 0.35/0.67 thf(fact_8249_abs__le__self__iff,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 0.35/0.67 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_self_iff
% 0.35/0.67 thf(fact_8250_abs__le__self__iff,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 0.35/0.67 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_self_iff
% 0.35/0.67 thf(fact_8251_abs__le__self__iff,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 0.35/0.67 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_self_iff
% 0.35/0.67 thf(fact_8252_abs__le__zero__iff,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 0.35/0.67 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_zero_iff
% 0.35/0.67 thf(fact_8253_abs__le__zero__iff,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 0.35/0.67 = ( A = zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_zero_iff
% 0.35/0.67 thf(fact_8254_abs__le__zero__iff,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 0.35/0.67 = ( A = zero_zero_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_zero_iff
% 0.35/0.67 thf(fact_8255_abs__le__zero__iff,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 0.35/0.67 = ( A = zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_zero_iff
% 0.35/0.67 thf(fact_8256_zero__less__abs__iff,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 0.35/0.67 = ( A != zero_z3403309356797280102nteger ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_abs_iff
% 0.35/0.67 thf(fact_8257_zero__less__abs__iff,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 0.35/0.67 = ( A != zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_abs_iff
% 0.35/0.67 thf(fact_8258_zero__less__abs__iff,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 0.35/0.67 = ( A != zero_zero_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_abs_iff
% 0.35/0.67 thf(fact_8259_zero__less__abs__iff,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 0.35/0.67 = ( A != zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_abs_iff
% 0.35/0.67 thf(fact_8260_abs__neg__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.67 = ( numeral_numeral_int @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_numeral
% 0.35/0.67 thf(fact_8261_abs__neg__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 0.35/0.67 = ( numeral_numeral_real @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_numeral
% 0.35/0.67 thf(fact_8262_abs__neg__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 0.35/0.67 = ( numera6620942414471956472nteger @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_numeral
% 0.35/0.67 thf(fact_8263_abs__neg__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 0.35/0.67 = ( numeral_numeral_rat @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_numeral
% 0.35/0.67 thf(fact_8264_abs__neg__one,axiom,
% 0.35/0.67 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.67 = one_one_int ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_one
% 0.35/0.67 thf(fact_8265_abs__neg__one,axiom,
% 0.35/0.67 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_one
% 0.35/0.67 thf(fact_8266_abs__neg__one,axiom,
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 0.35/0.67 = one_one_Code_integer ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_one
% 0.35/0.67 thf(fact_8267_abs__neg__one,axiom,
% 0.35/0.67 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 0.35/0.67 = one_one_rat ) ).
% 0.35/0.67
% 0.35/0.67 % abs_neg_one
% 0.35/0.67 thf(fact_8268_cos__zero,axiom,
% 0.35/0.67 ( ( cos_complex @ zero_zero_complex )
% 0.35/0.67 = one_one_complex ) ).
% 0.35/0.67
% 0.35/0.67 % cos_zero
% 0.35/0.67 thf(fact_8269_cos__zero,axiom,
% 0.35/0.67 ( ( cos_real @ zero_zero_real )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % cos_zero
% 0.35/0.67 thf(fact_8270_pred__numeral__simps_I1_J,axiom,
% 0.35/0.67 ( ( pred_numeral @ one )
% 0.35/0.67 = zero_zero_nat ) ).
% 0.35/0.67
% 0.35/0.67 % pred_numeral_simps(1)
% 0.35/0.67 thf(fact_8271_eq__numeral__Suc,axiom,
% 0.35/0.67 ! [K2: num,N: nat] :
% 0.35/0.67 ( ( ( numeral_numeral_nat @ K2 )
% 0.35/0.67 = ( suc @ N ) )
% 0.35/0.67 = ( ( pred_numeral @ K2 )
% 0.35/0.67 = N ) ) ).
% 0.35/0.67
% 0.35/0.67 % eq_numeral_Suc
% 0.35/0.67 thf(fact_8272_Suc__eq__numeral,axiom,
% 0.35/0.67 ! [N: nat,K2: num] :
% 0.35/0.67 ( ( ( suc @ N )
% 0.35/0.67 = ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( N
% 0.35/0.67 = ( pred_numeral @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Suc_eq_numeral
% 0.35/0.67 thf(fact_8273_sum__abs,axiom,
% 0.35/0.67 ! [F2: int > int,A4: set_int] :
% 0.35/0.67 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) )
% 0.35/0.67 @ ( groups4538972089207619220nt_int
% 0.35/0.67 @ ^ [I: int] : ( abs_abs_int @ ( F2 @ I ) )
% 0.35/0.67 @ A4 ) ) ).
% 0.35/0.67
% 0.35/0.67 % sum_abs
% 0.35/0.67 thf(fact_8274_sum__abs,axiom,
% 0.35/0.67 ! [F2: nat > real,A4: set_nat] :
% 0.35/0.67 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) )
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [I: nat] : ( abs_abs_real @ ( F2 @ I ) )
% 0.35/0.67 @ A4 ) ) ).
% 0.35/0.67
% 0.35/0.67 % sum_abs
% 0.35/0.67 thf(fact_8275_divide__le__0__abs__iff,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 0.35/0.67 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.35/0.67 | ( B = zero_zero_real ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_le_0_abs_iff
% 0.35/0.67 thf(fact_8276_divide__le__0__abs__iff,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 0.35/0.67 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.35/0.67 | ( B = zero_zero_rat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_le_0_abs_iff
% 0.35/0.67 thf(fact_8277_zero__le__divide__abs__iff,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 0.35/0.67 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.67 | ( B = zero_zero_real ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_le_divide_abs_iff
% 0.35/0.67 thf(fact_8278_zero__le__divide__abs__iff,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 0.35/0.67 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.67 | ( B = zero_zero_rat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_le_divide_abs_iff
% 0.35/0.67 thf(fact_8279_abs__of__nonpos,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 0.35/0.67 => ( ( abs_abs_real @ A )
% 0.35/0.67 = ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonpos
% 0.35/0.67 thf(fact_8280_abs__of__nonpos,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 0.35/0.67 => ( ( abs_abs_Code_integer @ A )
% 0.35/0.67 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonpos
% 0.35/0.67 thf(fact_8281_abs__of__nonpos,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 0.35/0.67 => ( ( abs_abs_rat @ A )
% 0.35/0.67 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonpos
% 0.35/0.67 thf(fact_8282_abs__of__nonpos,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.35/0.67 => ( ( abs_abs_int @ A )
% 0.35/0.67 = ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_nonpos
% 0.35/0.67 thf(fact_8283_less__Suc__numeral,axiom,
% 0.35/0.67 ! [N: nat,K2: num] :
% 0.35/0.67 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( ord_less_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % less_Suc_numeral
% 0.35/0.67 thf(fact_8284_less__numeral__Suc,axiom,
% 0.35/0.67 ! [K2: num,N: nat] :
% 0.35/0.67 ( ( ord_less_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 0.35/0.67 = ( ord_less_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % less_numeral_Suc
% 0.35/0.67 thf(fact_8285_pred__numeral__simps_I3_J,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( pred_numeral @ ( bit1 @ K2 ) )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bit0 @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pred_numeral_simps(3)
% 0.35/0.67 thf(fact_8286_le__numeral__Suc,axiom,
% 0.35/0.67 ! [K2: num,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 0.35/0.67 = ( ord_less_eq_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % le_numeral_Suc
% 0.35/0.67 thf(fact_8287_le__Suc__numeral,axiom,
% 0.35/0.67 ! [N: nat,K2: num] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % le_Suc_numeral
% 0.35/0.67 thf(fact_8288_diff__numeral__Suc,axiom,
% 0.35/0.67 ! [K2: num,N: nat] :
% 0.35/0.67 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 0.35/0.67 = ( minus_minus_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % diff_numeral_Suc
% 0.35/0.67 thf(fact_8289_diff__Suc__numeral,axiom,
% 0.35/0.67 ! [N: nat,K2: num] :
% 0.35/0.67 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( minus_minus_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % diff_Suc_numeral
% 0.35/0.67 thf(fact_8290_max__Suc__numeral,axiom,
% 0.35/0.67 ! [N: nat,K2: num] :
% 0.35/0.67 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % max_Suc_numeral
% 0.35/0.67 thf(fact_8291_max__numeral__Suc,axiom,
% 0.35/0.67 ! [K2: num,N: nat] :
% 0.35/0.67 ( ( ord_max_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 0.35/0.67 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K2 ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % max_numeral_Suc
% 0.35/0.67 thf(fact_8292_sum__abs__ge__zero,axiom,
% 0.35/0.67 ! [F2: int > int,A4: set_int] :
% 0.35/0.67 ( ord_less_eq_int @ zero_zero_int
% 0.35/0.67 @ ( groups4538972089207619220nt_int
% 0.35/0.67 @ ^ [I: int] : ( abs_abs_int @ ( F2 @ I ) )
% 0.35/0.67 @ A4 ) ) ).
% 0.35/0.67
% 0.35/0.67 % sum_abs_ge_zero
% 0.35/0.67 thf(fact_8293_sum__abs__ge__zero,axiom,
% 0.35/0.67 ! [F2: nat > real,A4: set_nat] :
% 0.35/0.67 ( ord_less_eq_real @ zero_zero_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [I: nat] : ( abs_abs_real @ ( F2 @ I ) )
% 0.35/0.67 @ A4 ) ) ).
% 0.35/0.67
% 0.35/0.67 % sum_abs_ge_zero
% 0.35/0.67 thf(fact_8294_minus__numeral__div__numeral,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.67 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_numeral_div_numeral
% 0.35/0.67 thf(fact_8295_numeral__div__minus__numeral,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.67 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_div_minus_numeral
% 0.35/0.67 thf(fact_8296_zero__less__power__abs__iff,axiom,
% 0.35/0.67 ! [A: code_integer,N: nat] :
% 0.35/0.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 0.35/0.67 = ( ( A != zero_z3403309356797280102nteger )
% 0.35/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_power_abs_iff
% 0.35/0.67 thf(fact_8297_zero__less__power__abs__iff,axiom,
% 0.35/0.67 ! [A: real,N: nat] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.35/0.67 = ( ( A != zero_zero_real )
% 0.35/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_power_abs_iff
% 0.35/0.67 thf(fact_8298_zero__less__power__abs__iff,axiom,
% 0.35/0.67 ! [A: rat,N: nat] :
% 0.35/0.67 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 0.35/0.67 = ( ( A != zero_zero_rat )
% 0.35/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_power_abs_iff
% 0.35/0.67 thf(fact_8299_zero__less__power__abs__iff,axiom,
% 0.35/0.67 ! [A: int,N: nat] :
% 0.35/0.67 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 0.35/0.67 = ( ( A != zero_zero_int )
% 0.35/0.67 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_less_power_abs_iff
% 0.35/0.67 thf(fact_8300_sin__cos__squared__add3,axiom,
% 0.35/0.67 ! [X: complex] :
% 0.35/0.67 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 0.35/0.67 = one_one_complex ) ).
% 0.35/0.67
% 0.35/0.67 % sin_cos_squared_add3
% 0.35/0.67 thf(fact_8301_sin__cos__squared__add3,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_cos_squared_add3
% 0.35/0.67 thf(fact_8302_dvd__numeral__simp,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.67 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_numeral_simp
% 0.35/0.67 thf(fact_8303_dvd__numeral__simp,axiom,
% 0.35/0.67 ! [M2: num,N: num] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.67 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_numeral_simp
% 0.35/0.67 thf(fact_8304_divmod__algorithm__code_I2_J,axiom,
% 0.35/0.67 ! [M2: num] :
% 0.35/0.67 ( ( unique3479559517661332726nteger @ M2 @ one )
% 0.35/0.67 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M2 ) @ zero_z3403309356797280102nteger ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(2)
% 0.35/0.67 thf(fact_8305_divmod__algorithm__code_I2_J,axiom,
% 0.35/0.67 ! [M2: num] :
% 0.35/0.67 ( ( unique5052692396658037445od_int @ M2 @ one )
% 0.35/0.67 = ( product_Pair_int_int @ ( numeral_numeral_int @ M2 ) @ zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(2)
% 0.35/0.67 thf(fact_8306_divmod__algorithm__code_I2_J,axiom,
% 0.35/0.67 ! [M2: num] :
% 0.35/0.67 ( ( unique5055182867167087721od_nat @ M2 @ one )
% 0.35/0.67 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M2 ) @ zero_zero_nat ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(2)
% 0.35/0.67 thf(fact_8307_divmod__algorithm__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 0.35/0.67 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(3)
% 0.35/0.67 thf(fact_8308_divmod__algorithm__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 0.35/0.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(3)
% 0.35/0.67 thf(fact_8309_divmod__algorithm__code_I3_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 0.35/0.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(3)
% 0.35/0.67 thf(fact_8310_divmod__algorithm__code_I4_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 0.35/0.67 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(4)
% 0.35/0.67 thf(fact_8311_divmod__algorithm__code_I4_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 0.35/0.67 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(4)
% 0.35/0.67 thf(fact_8312_divmod__algorithm__code_I4_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 0.35/0.67 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_algorithm_code(4)
% 0.35/0.67 thf(fact_8313_one__div__minus__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.67 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % one_div_minus_numeral
% 0.35/0.67 thf(fact_8314_minus__one__div__numeral,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.67 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % minus_one_div_numeral
% 0.35/0.67 thf(fact_8315_cos__two__pi,axiom,
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % cos_two_pi
% 0.35/0.67 thf(fact_8316_cos__periodic,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.67 = ( cos_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_periodic
% 0.35/0.67 thf(fact_8317_cos__2pi__minus,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 0.35/0.67 = ( cos_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_2pi_minus
% 0.35/0.67 thf(fact_8318_signed__take__bit__numeral__bit0,axiom,
% 0.35/0.67 ! [L: num,K2: num] :
% 0.35/0.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) )
% 0.35/0.67 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_numeral_bit0
% 0.35/0.67 thf(fact_8319_cos__npi,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.67 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_npi
% 0.35/0.67 thf(fact_8320_cos__npi2,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.67 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_npi2
% 0.35/0.67 thf(fact_8321_cos__2npi,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % cos_2npi
% 0.35/0.67 thf(fact_8322_signed__take__bit__numeral__minus__bit0,axiom,
% 0.35/0.67 ! [L: num,K2: num] :
% 0.35/0.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 0.35/0.67 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_numeral_minus_bit0
% 0.35/0.67 thf(fact_8323_cos__3over2__pi,axiom,
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % cos_3over2_pi
% 0.35/0.67 thf(fact_8324_signed__take__bit__numeral__bit1,axiom,
% 0.35/0.67 ! [L: num,K2: num] :
% 0.35/0.67 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % signed_take_bit_numeral_bit1
% 0.35/0.67 thf(fact_8325_cos__pi__eq__zero,axiom,
% 0.35/0.67 ! [M2: nat] :
% 0.35/0.67 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % cos_pi_eq_zero
% 0.35/0.67 thf(fact_8326_abs__ge__self,axiom,
% 0.35/0.67 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_self
% 0.35/0.67 thf(fact_8327_abs__ge__self,axiom,
% 0.35/0.67 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_self
% 0.35/0.67 thf(fact_8328_abs__ge__self,axiom,
% 0.35/0.67 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_self
% 0.35/0.67 thf(fact_8329_abs__ge__self,axiom,
% 0.35/0.67 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_self
% 0.35/0.67 thf(fact_8330_abs__le__D1,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_real @ A @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D1
% 0.35/0.67 thf(fact_8331_abs__le__D1,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D1
% 0.35/0.67 thf(fact_8332_abs__le__D1,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_rat @ A @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D1
% 0.35/0.67 thf(fact_8333_abs__le__D1,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_int @ A @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D1
% 0.35/0.67 thf(fact_8334_abs__eq__0__iff,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ( abs_abs_Code_integer @ A )
% 0.35/0.67 = zero_z3403309356797280102nteger )
% 0.35/0.67 = ( A = zero_z3403309356797280102nteger ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0_iff
% 0.35/0.67 thf(fact_8335_abs__eq__0__iff,axiom,
% 0.35/0.67 ! [A: complex] :
% 0.35/0.67 ( ( ( abs_abs_complex @ A )
% 0.35/0.67 = zero_zero_complex )
% 0.35/0.67 = ( A = zero_zero_complex ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0_iff
% 0.35/0.67 thf(fact_8336_abs__eq__0__iff,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ( abs_abs_real @ A )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 = ( A = zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0_iff
% 0.35/0.67 thf(fact_8337_abs__eq__0__iff,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ( abs_abs_rat @ A )
% 0.35/0.67 = zero_zero_rat )
% 0.35/0.67 = ( A = zero_zero_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0_iff
% 0.35/0.67 thf(fact_8338_abs__eq__0__iff,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ( abs_abs_int @ A )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 = ( A = zero_zero_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_0_iff
% 0.35/0.67 thf(fact_8339_abs__mult,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.35/0.67 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult
% 0.35/0.67 thf(fact_8340_abs__mult,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.35/0.67 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult
% 0.35/0.67 thf(fact_8341_abs__mult,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.67 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult
% 0.35/0.67 thf(fact_8342_abs__mult,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.35/0.67 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult
% 0.35/0.67 thf(fact_8343_abs__one,axiom,
% 0.35/0.67 ( ( abs_abs_rat @ one_one_rat )
% 0.35/0.67 = one_one_rat ) ).
% 0.35/0.67
% 0.35/0.67 % abs_one
% 0.35/0.67 thf(fact_8344_abs__one,axiom,
% 0.35/0.67 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 0.35/0.67 = one_one_Code_integer ) ).
% 0.35/0.67
% 0.35/0.67 % abs_one
% 0.35/0.67 thf(fact_8345_abs__one,axiom,
% 0.35/0.67 ( ( abs_abs_real @ one_one_real )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % abs_one
% 0.35/0.67 thf(fact_8346_abs__one,axiom,
% 0.35/0.67 ( ( abs_abs_int @ one_one_int )
% 0.35/0.67 = one_one_int ) ).
% 0.35/0.67
% 0.35/0.67 % abs_one
% 0.35/0.67 thf(fact_8347_abs__minus__commute,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 0.35/0.67 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_commute
% 0.35/0.67 thf(fact_8348_abs__minus__commute,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 0.35/0.67 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_commute
% 0.35/0.67 thf(fact_8349_abs__minus__commute,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 0.35/0.67 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_commute
% 0.35/0.67 thf(fact_8350_abs__minus__commute,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 0.35/0.67 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_commute
% 0.35/0.67 thf(fact_8351_abs__eq__iff,axiom,
% 0.35/0.67 ! [X: int,Y: int] :
% 0.35/0.67 ( ( ( abs_abs_int @ X )
% 0.35/0.67 = ( abs_abs_int @ Y ) )
% 0.35/0.67 = ( ( X = Y )
% 0.35/0.67 | ( X
% 0.35/0.67 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff
% 0.35/0.67 thf(fact_8352_abs__eq__iff,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( ( abs_abs_real @ X )
% 0.35/0.67 = ( abs_abs_real @ Y ) )
% 0.35/0.67 = ( ( X = Y )
% 0.35/0.67 | ( X
% 0.35/0.67 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff
% 0.35/0.67 thf(fact_8353_abs__eq__iff,axiom,
% 0.35/0.67 ! [X: code_integer,Y: code_integer] :
% 0.35/0.67 ( ( ( abs_abs_Code_integer @ X )
% 0.35/0.67 = ( abs_abs_Code_integer @ Y ) )
% 0.35/0.67 = ( ( X = Y )
% 0.35/0.67 | ( X
% 0.35/0.67 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff
% 0.35/0.67 thf(fact_8354_abs__eq__iff,axiom,
% 0.35/0.67 ! [X: rat,Y: rat] :
% 0.35/0.67 ( ( ( abs_abs_rat @ X )
% 0.35/0.67 = ( abs_abs_rat @ Y ) )
% 0.35/0.67 = ( ( X = Y )
% 0.35/0.67 | ( X
% 0.35/0.67 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff
% 0.35/0.67 thf(fact_8355_dvd__if__abs__eq,axiom,
% 0.35/0.67 ! [L: real,K2: real] :
% 0.35/0.67 ( ( ( abs_abs_real @ L )
% 0.35/0.67 = ( abs_abs_real @ K2 ) )
% 0.35/0.67 => ( dvd_dvd_real @ L @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_if_abs_eq
% 0.35/0.67 thf(fact_8356_dvd__if__abs__eq,axiom,
% 0.35/0.67 ! [L: int,K2: int] :
% 0.35/0.67 ( ( ( abs_abs_int @ L )
% 0.35/0.67 = ( abs_abs_int @ K2 ) )
% 0.35/0.67 => ( dvd_dvd_int @ L @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_if_abs_eq
% 0.35/0.67 thf(fact_8357_dvd__if__abs__eq,axiom,
% 0.35/0.67 ! [L: code_integer,K2: code_integer] :
% 0.35/0.67 ( ( ( abs_abs_Code_integer @ L )
% 0.35/0.67 = ( abs_abs_Code_integer @ K2 ) )
% 0.35/0.67 => ( dvd_dvd_Code_integer @ L @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_if_abs_eq
% 0.35/0.67 thf(fact_8358_dvd__if__abs__eq,axiom,
% 0.35/0.67 ! [L: rat,K2: rat] :
% 0.35/0.67 ( ( ( abs_abs_rat @ L )
% 0.35/0.67 = ( abs_abs_rat @ K2 ) )
% 0.35/0.67 => ( dvd_dvd_rat @ L @ K2 ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_if_abs_eq
% 0.35/0.67 thf(fact_8359_abs__ge__zero,axiom,
% 0.35/0.67 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_zero
% 0.35/0.67 thf(fact_8360_abs__ge__zero,axiom,
% 0.35/0.67 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_zero
% 0.35/0.67 thf(fact_8361_abs__ge__zero,axiom,
% 0.35/0.67 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_zero
% 0.35/0.67 thf(fact_8362_abs__ge__zero,axiom,
% 0.35/0.67 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_zero
% 0.35/0.67 thf(fact_8363_abs__not__less__zero,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.67
% 0.35/0.67 % abs_not_less_zero
% 0.35/0.67 thf(fact_8364_abs__not__less__zero,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % abs_not_less_zero
% 0.35/0.67 thf(fact_8365_abs__not__less__zero,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 0.35/0.67
% 0.35/0.67 % abs_not_less_zero
% 0.35/0.67 thf(fact_8366_abs__not__less__zero,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % abs_not_less_zero
% 0.35/0.67 thf(fact_8367_abs__of__pos,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.67 => ( ( abs_abs_Code_integer @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_pos
% 0.35/0.67 thf(fact_8368_abs__of__pos,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67 => ( ( abs_abs_real @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_pos
% 0.35/0.67 thf(fact_8369_abs__of__pos,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ord_less_rat @ zero_zero_rat @ A )
% 0.35/0.67 => ( ( abs_abs_rat @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_pos
% 0.35/0.67 thf(fact_8370_abs__of__pos,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ord_less_int @ zero_zero_int @ A )
% 0.35/0.67 => ( ( abs_abs_int @ A )
% 0.35/0.67 = A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_pos
% 0.35/0.67 thf(fact_8371_abs__triangle__ineq,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq
% 0.35/0.67 thf(fact_8372_abs__triangle__ineq,axiom,
% 0.35/0.67 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq
% 0.35/0.67 thf(fact_8373_abs__triangle__ineq,axiom,
% 0.35/0.67 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq
% 0.35/0.67 thf(fact_8374_abs__triangle__ineq,axiom,
% 0.35/0.67 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq
% 0.35/0.67 thf(fact_8375_abs__mult__less,axiom,
% 0.35/0.67 ! [A: code_integer,C2: code_integer,B: code_integer,D: code_integer] :
% 0.35/0.67 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C2 )
% 0.35/0.67 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 0.35/0.67 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C2 @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_less
% 0.35/0.67 thf(fact_8376_abs__mult__less,axiom,
% 0.35/0.67 ! [A: real,C2: real,B: real,D: real] :
% 0.35/0.67 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C2 )
% 0.35/0.67 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 0.35/0.67 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C2 @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_less
% 0.35/0.67 thf(fact_8377_abs__mult__less,axiom,
% 0.35/0.67 ! [A: rat,C2: rat,B: rat,D: rat] :
% 0.35/0.67 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C2 )
% 0.35/0.67 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 0.35/0.67 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C2 @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_less
% 0.35/0.67 thf(fact_8378_abs__mult__less,axiom,
% 0.35/0.67 ! [A: int,C2: int,B: int,D: int] :
% 0.35/0.67 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C2 )
% 0.35/0.67 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 0.35/0.67 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C2 @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_less
% 0.35/0.67 thf(fact_8379_abs__triangle__ineq2__sym,axiom,
% 0.35/0.67 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2_sym
% 0.35/0.67 thf(fact_8380_abs__triangle__ineq2__sym,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2_sym
% 0.35/0.67 thf(fact_8381_abs__triangle__ineq2__sym,axiom,
% 0.35/0.67 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2_sym
% 0.35/0.67 thf(fact_8382_abs__triangle__ineq2__sym,axiom,
% 0.35/0.67 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2_sym
% 0.35/0.67 thf(fact_8383_abs__triangle__ineq3,axiom,
% 0.35/0.67 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq3
% 0.35/0.67 thf(fact_8384_abs__triangle__ineq3,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq3
% 0.35/0.67 thf(fact_8385_abs__triangle__ineq3,axiom,
% 0.35/0.67 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq3
% 0.35/0.67 thf(fact_8386_abs__triangle__ineq3,axiom,
% 0.35/0.67 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq3
% 0.35/0.67 thf(fact_8387_abs__triangle__ineq2,axiom,
% 0.35/0.67 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2
% 0.35/0.67 thf(fact_8388_abs__triangle__ineq2,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2
% 0.35/0.67 thf(fact_8389_abs__triangle__ineq2,axiom,
% 0.35/0.67 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2
% 0.35/0.67 thf(fact_8390_abs__triangle__ineq2,axiom,
% 0.35/0.67 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq2
% 0.35/0.67 thf(fact_8391_nonzero__abs__divide,axiom,
% 0.35/0.67 ! [B: real,A: real] :
% 0.35/0.67 ( ( B != zero_zero_real )
% 0.35/0.67 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 0.35/0.67 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % nonzero_abs_divide
% 0.35/0.67 thf(fact_8392_nonzero__abs__divide,axiom,
% 0.35/0.67 ! [B: rat,A: rat] :
% 0.35/0.67 ( ( B != zero_zero_rat )
% 0.35/0.67 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 0.35/0.67 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % nonzero_abs_divide
% 0.35/0.67 thf(fact_8393_abs__leI,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ A @ B )
% 0.35/0.67 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_leI
% 0.35/0.67 thf(fact_8394_abs__leI,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.35/0.67 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_leI
% 0.35/0.67 thf(fact_8395_abs__leI,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.67 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_leI
% 0.35/0.67 thf(fact_8396_abs__leI,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ A @ B )
% 0.35/0.67 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_leI
% 0.35/0.67 thf(fact_8397_abs__le__D2,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D2
% 0.35/0.67 thf(fact_8398_abs__le__D2,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D2
% 0.35/0.67 thf(fact_8399_abs__le__D2,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D2
% 0.35/0.67 thf(fact_8400_abs__le__D2,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.67 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_D2
% 0.35/0.67 thf(fact_8401_abs__le__iff,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.67 = ( ( ord_less_eq_real @ A @ B )
% 0.35/0.67 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_iff
% 0.35/0.67 thf(fact_8402_abs__le__iff,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.67 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 0.35/0.67 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_iff
% 0.35/0.67 thf(fact_8403_abs__le__iff,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 0.35/0.67 = ( ( ord_less_eq_rat @ A @ B )
% 0.35/0.67 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_iff
% 0.35/0.67 thf(fact_8404_abs__le__iff,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.67 = ( ( ord_less_eq_int @ A @ B )
% 0.35/0.67 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_iff
% 0.35/0.67 thf(fact_8405_abs__ge__minus__self,axiom,
% 0.35/0.67 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_minus_self
% 0.35/0.67 thf(fact_8406_abs__ge__minus__self,axiom,
% 0.35/0.67 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_minus_self
% 0.35/0.67 thf(fact_8407_abs__ge__minus__self,axiom,
% 0.35/0.67 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_minus_self
% 0.35/0.67 thf(fact_8408_abs__ge__minus__self,axiom,
% 0.35/0.67 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ge_minus_self
% 0.35/0.67 thf(fact_8409_abs__less__iff,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 0.35/0.67 = ( ( ord_less_int @ A @ B )
% 0.35/0.67 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_less_iff
% 0.35/0.67 thf(fact_8410_abs__less__iff,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 0.35/0.67 = ( ( ord_less_real @ A @ B )
% 0.35/0.67 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_less_iff
% 0.35/0.67 thf(fact_8411_abs__less__iff,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 0.35/0.67 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 0.35/0.67 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_less_iff
% 0.35/0.67 thf(fact_8412_abs__less__iff,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 0.35/0.67 = ( ( ord_less_rat @ A @ B )
% 0.35/0.67 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_less_iff
% 0.35/0.67 thf(fact_8413_polar__Ex,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ? [R4: real,A3: real] :
% 0.35/0.67 ( ( X
% 0.35/0.67 = ( times_times_real @ R4 @ ( cos_real @ A3 ) ) )
% 0.35/0.67 & ( Y
% 0.35/0.67 = ( times_times_real @ R4 @ ( sin_real @ A3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % polar_Ex
% 0.35/0.67 thf(fact_8414_numeral__eq__Suc,axiom,
% 0.35/0.67 ( numeral_numeral_nat
% 0.35/0.67 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % numeral_eq_Suc
% 0.35/0.67 thf(fact_8415_sin__cos__le1,axiom,
% 0.35/0.67 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_cos_le1
% 0.35/0.67 thf(fact_8416_dense__eq0__I,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ! [E2: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 0.35/0.67 => ( X = zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % dense_eq0_I
% 0.35/0.67 thf(fact_8417_dense__eq0__I,axiom,
% 0.35/0.67 ! [X: rat] :
% 0.35/0.67 ( ! [E2: rat] :
% 0.35/0.67 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 0.35/0.67 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 0.35/0.67 => ( X = zero_zero_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % dense_eq0_I
% 0.35/0.67 thf(fact_8418_abs__mult__pos,axiom,
% 0.35/0.67 ! [X: code_integer,Y: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 0.35/0.67 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 0.35/0.67 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_pos
% 0.35/0.67 thf(fact_8419_abs__mult__pos,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 0.35/0.67 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_pos
% 0.35/0.67 thf(fact_8420_abs__mult__pos,axiom,
% 0.35/0.67 ! [X: rat,Y: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 0.35/0.67 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 0.35/0.67 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_pos
% 0.35/0.67 thf(fact_8421_abs__mult__pos,axiom,
% 0.35/0.67 ! [X: int,Y: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.35/0.67 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 0.35/0.67 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_mult_pos
% 0.35/0.67 thf(fact_8422_abs__eq__mult,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.67 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 0.35/0.67 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.35/0.67 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 0.35/0.67 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 0.35/0.67 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_mult
% 0.35/0.67 thf(fact_8423_abs__eq__mult,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.67 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 0.35/0.67 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.35/0.67 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 0.35/0.67 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 0.35/0.67 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_mult
% 0.35/0.67 thf(fact_8424_abs__eq__mult,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.67 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 0.35/0.67 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.35/0.67 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 0.35/0.67 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 0.35/0.67 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_mult
% 0.35/0.67 thf(fact_8425_abs__eq__mult,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.67 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 0.35/0.67 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.35/0.67 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 0.35/0.67 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 0.35/0.67 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_mult
% 0.35/0.67 thf(fact_8426_cos__one__sin__zero,axiom,
% 0.35/0.67 ! [X: complex] :
% 0.35/0.67 ( ( ( cos_complex @ X )
% 0.35/0.67 = one_one_complex )
% 0.35/0.67 => ( ( sin_complex @ X )
% 0.35/0.67 = zero_zero_complex ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_one_sin_zero
% 0.35/0.67 thf(fact_8427_cos__one__sin__zero,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( cos_real @ X )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 => ( ( sin_real @ X )
% 0.35/0.67 = zero_zero_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_one_sin_zero
% 0.35/0.67 thf(fact_8428_abs__minus__le__zero,axiom,
% 0.35/0.67 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_le_zero
% 0.35/0.67 thf(fact_8429_abs__minus__le__zero,axiom,
% 0.35/0.67 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_le_zero
% 0.35/0.67 thf(fact_8430_abs__minus__le__zero,axiom,
% 0.35/0.67 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_le_zero
% 0.35/0.67 thf(fact_8431_abs__minus__le__zero,axiom,
% 0.35/0.67 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 0.35/0.67
% 0.35/0.67 % abs_minus_le_zero
% 0.35/0.67 thf(fact_8432_eq__abs__iff_H,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( A
% 0.35/0.67 = ( abs_abs_real @ B ) )
% 0.35/0.67 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 0.35/0.67 & ( ( B = A )
% 0.35/0.67 | ( B
% 0.35/0.67 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % eq_abs_iff'
% 0.35/0.67 thf(fact_8433_eq__abs__iff_H,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( A
% 0.35/0.67 = ( abs_abs_Code_integer @ B ) )
% 0.35/0.67 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 0.35/0.67 & ( ( B = A )
% 0.35/0.67 | ( B
% 0.35/0.67 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % eq_abs_iff'
% 0.35/0.67 thf(fact_8434_eq__abs__iff_H,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( A
% 0.35/0.67 = ( abs_abs_rat @ B ) )
% 0.35/0.67 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 0.35/0.67 & ( ( B = A )
% 0.35/0.67 | ( B
% 0.35/0.67 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % eq_abs_iff'
% 0.35/0.67 thf(fact_8435_eq__abs__iff_H,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( A
% 0.35/0.67 = ( abs_abs_int @ B ) )
% 0.35/0.67 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.35/0.67 & ( ( B = A )
% 0.35/0.67 | ( B
% 0.35/0.67 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % eq_abs_iff'
% 0.35/0.67 thf(fact_8436_abs__eq__iff_H,axiom,
% 0.35/0.67 ! [A: real,B: real] :
% 0.35/0.67 ( ( ( abs_abs_real @ A )
% 0.35/0.67 = B )
% 0.35/0.67 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 0.35/0.67 & ( ( A = B )
% 0.35/0.67 | ( A
% 0.35/0.67 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff'
% 0.35/0.67 thf(fact_8437_abs__eq__iff_H,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( ( abs_abs_Code_integer @ A )
% 0.35/0.67 = B )
% 0.35/0.67 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 0.35/0.67 & ( ( A = B )
% 0.35/0.67 | ( A
% 0.35/0.67 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff'
% 0.35/0.67 thf(fact_8438_abs__eq__iff_H,axiom,
% 0.35/0.67 ! [A: rat,B: rat] :
% 0.35/0.67 ( ( ( abs_abs_rat @ A )
% 0.35/0.67 = B )
% 0.35/0.67 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 0.35/0.67 & ( ( A = B )
% 0.35/0.67 | ( A
% 0.35/0.67 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff'
% 0.35/0.67 thf(fact_8439_abs__eq__iff_H,axiom,
% 0.35/0.67 ! [A: int,B: int] :
% 0.35/0.67 ( ( ( abs_abs_int @ A )
% 0.35/0.67 = B )
% 0.35/0.67 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.35/0.67 & ( ( A = B )
% 0.35/0.67 | ( A
% 0.35/0.67 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_eq_iff'
% 0.35/0.67 thf(fact_8440_abs__div__pos,axiom,
% 0.35/0.67 ! [Y: real,X: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.67 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 0.35/0.67 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_div_pos
% 0.35/0.67 thf(fact_8441_abs__div__pos,axiom,
% 0.35/0.67 ! [Y: rat,X: rat] :
% 0.35/0.67 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 0.35/0.67 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 0.35/0.67 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_div_pos
% 0.35/0.67 thf(fact_8442_zero__le__power__abs,axiom,
% 0.35/0.67 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_le_power_abs
% 0.35/0.67 thf(fact_8443_zero__le__power__abs,axiom,
% 0.35/0.67 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_le_power_abs
% 0.35/0.67 thf(fact_8444_zero__le__power__abs,axiom,
% 0.35/0.67 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_le_power_abs
% 0.35/0.67 thf(fact_8445_zero__le__power__abs,axiom,
% 0.35/0.67 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % zero_le_power_abs
% 0.35/0.67 thf(fact_8446_abs__if__raw,axiom,
% 0.35/0.67 ( abs_abs_int
% 0.35/0.67 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if_raw
% 0.35/0.67 thf(fact_8447_abs__if__raw,axiom,
% 0.35/0.67 ( abs_abs_real
% 0.35/0.67 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if_raw
% 0.35/0.67 thf(fact_8448_abs__if__raw,axiom,
% 0.35/0.67 ( abs_abs_Code_integer
% 0.35/0.67 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if_raw
% 0.35/0.67 thf(fact_8449_abs__if__raw,axiom,
% 0.35/0.67 ( abs_abs_rat
% 0.35/0.67 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if_raw
% 0.35/0.67 thf(fact_8450_abs__if,axiom,
% 0.35/0.67 ( abs_abs_int
% 0.35/0.67 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if
% 0.35/0.67 thf(fact_8451_abs__if,axiom,
% 0.35/0.67 ( abs_abs_real
% 0.35/0.67 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if
% 0.35/0.67 thf(fact_8452_abs__if,axiom,
% 0.35/0.67 ( abs_abs_Code_integer
% 0.35/0.67 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if
% 0.35/0.67 thf(fact_8453_abs__if,axiom,
% 0.35/0.67 ( abs_abs_rat
% 0.35/0.67 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_if
% 0.35/0.67 thf(fact_8454_abs__of__neg,axiom,
% 0.35/0.67 ! [A: int] :
% 0.35/0.67 ( ( ord_less_int @ A @ zero_zero_int )
% 0.35/0.67 => ( ( abs_abs_int @ A )
% 0.35/0.67 = ( uminus_uminus_int @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_neg
% 0.35/0.67 thf(fact_8455_abs__of__neg,axiom,
% 0.35/0.67 ! [A: real] :
% 0.35/0.67 ( ( ord_less_real @ A @ zero_zero_real )
% 0.35/0.67 => ( ( abs_abs_real @ A )
% 0.35/0.67 = ( uminus_uminus_real @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_neg
% 0.35/0.67 thf(fact_8456_abs__of__neg,axiom,
% 0.35/0.67 ! [A: code_integer] :
% 0.35/0.67 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 0.35/0.67 => ( ( abs_abs_Code_integer @ A )
% 0.35/0.67 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_neg
% 0.35/0.67 thf(fact_8457_abs__of__neg,axiom,
% 0.35/0.67 ! [A: rat] :
% 0.35/0.67 ( ( ord_less_rat @ A @ zero_zero_rat )
% 0.35/0.67 => ( ( abs_abs_rat @ A )
% 0.35/0.67 = ( uminus_uminus_rat @ A ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_of_neg
% 0.35/0.67 thf(fact_8458_sin__add,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 0.35/0.67 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_add
% 0.35/0.67 thf(fact_8459_abs__diff__le__iff,axiom,
% 0.35/0.67 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_le_iff
% 0.35/0.67 thf(fact_8460_abs__diff__le__iff,axiom,
% 0.35/0.67 ! [X: real,A: real,R3: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_le_iff
% 0.35/0.67 thf(fact_8461_abs__diff__le__iff,axiom,
% 0.35/0.67 ! [X: rat,A: rat,R3: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_le_iff
% 0.35/0.67 thf(fact_8462_abs__diff__le__iff,axiom,
% 0.35/0.67 ! [X: int,A: int,R3: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_le_iff
% 0.35/0.67 thf(fact_8463_abs__diff__triangle__ineq,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C2 @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C2 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_triangle_ineq
% 0.35/0.67 thf(fact_8464_abs__diff__triangle__ineq,axiom,
% 0.35/0.67 ! [A: real,B: real,C2: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C2 @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C2 ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_triangle_ineq
% 0.35/0.67 thf(fact_8465_abs__diff__triangle__ineq,axiom,
% 0.35/0.67 ! [A: rat,B: rat,C2: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C2 @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C2 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_triangle_ineq
% 0.35/0.67 thf(fact_8466_abs__diff__triangle__ineq,axiom,
% 0.35/0.67 ! [A: int,B: int,C2: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C2 @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_triangle_ineq
% 0.35/0.67 thf(fact_8467_abs__triangle__ineq4,axiom,
% 0.35/0.67 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq4
% 0.35/0.67 thf(fact_8468_abs__triangle__ineq4,axiom,
% 0.35/0.67 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq4
% 0.35/0.67 thf(fact_8469_abs__triangle__ineq4,axiom,
% 0.35/0.67 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq4
% 0.35/0.67 thf(fact_8470_abs__triangle__ineq4,axiom,
% 0.35/0.67 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_triangle_ineq4
% 0.35/0.67 thf(fact_8471_sin__diff,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( sin_real @ ( minus_minus_real @ X @ Y ) )
% 0.35/0.67 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_diff
% 0.35/0.67 thf(fact_8472_abs__diff__less__iff,axiom,
% 0.35/0.67 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 0.35/0.67 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_less_iff
% 0.35/0.67 thf(fact_8473_abs__diff__less__iff,axiom,
% 0.35/0.67 ! [X: real,A: real,R3: real] :
% 0.35/0.67 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_less_real @ ( minus_minus_real @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_less_iff
% 0.35/0.67 thf(fact_8474_abs__diff__less__iff,axiom,
% 0.35/0.67 ! [X: rat,A: rat,R3: rat] :
% 0.35/0.67 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_less_iff
% 0.35/0.67 thf(fact_8475_abs__diff__less__iff,axiom,
% 0.35/0.67 ! [X: int,A: int,R3: int] :
% 0.35/0.67 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 0.35/0.67 = ( ( ord_less_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 0.35/0.67 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_diff_less_iff
% 0.35/0.67 thf(fact_8476_pred__numeral__def,axiom,
% 0.35/0.67 ( pred_numeral
% 0.35/0.67 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pred_numeral_def
% 0.35/0.67 thf(fact_8477_lessThan__nat__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( insert_nat @ ( pred_numeral @ K2 ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % lessThan_nat_numeral
% 0.35/0.67 thf(fact_8478_atMost__nat__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( insert_nat @ ( numeral_numeral_nat @ K2 ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % atMost_nat_numeral
% 0.35/0.67 thf(fact_8479_cos__add,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 0.35/0.67 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_add
% 0.35/0.67 thf(fact_8480_cos__diff,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 0.35/0.67 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_diff
% 0.35/0.67 thf(fact_8481_abs__add__one__gt__zero,axiom,
% 0.35/0.67 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_one_gt_zero
% 0.35/0.67 thf(fact_8482_abs__add__one__gt__zero,axiom,
% 0.35/0.67 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_one_gt_zero
% 0.35/0.67 thf(fact_8483_abs__add__one__gt__zero,axiom,
% 0.35/0.67 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_one_gt_zero
% 0.35/0.67 thf(fact_8484_abs__add__one__gt__zero,axiom,
% 0.35/0.67 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_add_one_gt_zero
% 0.35/0.67 thf(fact_8485_sin__zero__norm__cos__one,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( sin_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 0.35/0.67 = one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero_norm_cos_one
% 0.35/0.67 thf(fact_8486_sin__zero__norm__cos__one,axiom,
% 0.35/0.67 ! [X: complex] :
% 0.35/0.67 ( ( ( sin_complex @ X )
% 0.35/0.67 = zero_zero_complex )
% 0.35/0.67 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 0.35/0.67 = one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero_norm_cos_one
% 0.35/0.67 thf(fact_8487_fact__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( times_times_rat @ ( numeral_numeral_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_numeral
% 0.35/0.67 thf(fact_8488_fact__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ K2 ) @ ( semiri4449623510593786356d_enat @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_numeral
% 0.35/0.67 thf(fact_8489_fact__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( times_times_complex @ ( numera6690914467698888265omplex @ K2 ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_numeral
% 0.35/0.67 thf(fact_8490_fact__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( times_times_int @ ( numeral_numeral_int @ K2 ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_numeral
% 0.35/0.67 thf(fact_8491_fact__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( times_times_nat @ ( numeral_numeral_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_numeral
% 0.35/0.67 thf(fact_8492_fact__numeral,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.67 = ( times_times_real @ ( numeral_numeral_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % fact_numeral
% 0.35/0.67 thf(fact_8493_sin__double,axiom,
% 0.35/0.67 ! [X: complex] :
% 0.35/0.67 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_double
% 0.35/0.67 thf(fact_8494_sin__double,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_double
% 0.35/0.67 thf(fact_8495_abs__le__square__iff,axiom,
% 0.35/0.67 ! [X: code_integer,Y: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 0.35/0.67 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_square_iff
% 0.35/0.67 thf(fact_8496_abs__le__square__iff,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 0.35/0.67 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_square_iff
% 0.35/0.67 thf(fact_8497_abs__le__square__iff,axiom,
% 0.35/0.67 ! [X: rat,Y: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 0.35/0.67 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_square_iff
% 0.35/0.67 thf(fact_8498_abs__le__square__iff,axiom,
% 0.35/0.67 ! [X: int,Y: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 0.35/0.67 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_le_square_iff
% 0.35/0.67 thf(fact_8499_divmod__int__def,axiom,
% 0.35/0.67 ( unique5052692396658037445od_int
% 0.35/0.67 = ( ^ [M6: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_int_def
% 0.35/0.67 thf(fact_8500_abs__sqrt__wlog,axiom,
% 0.35/0.67 ! [P2: code_integer > code_integer > $o,X: code_integer] :
% 0.35/0.67 ( ! [X3: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 0.35/0.67 => ( P2 @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67 => ( P2 @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_sqrt_wlog
% 0.35/0.67 thf(fact_8501_abs__sqrt__wlog,axiom,
% 0.35/0.67 ! [P2: real > real > $o,X: real] :
% 0.35/0.67 ( ! [X3: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 0.35/0.67 => ( P2 @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67 => ( P2 @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_sqrt_wlog
% 0.35/0.67 thf(fact_8502_abs__sqrt__wlog,axiom,
% 0.35/0.67 ! [P2: rat > rat > $o,X: rat] :
% 0.35/0.67 ( ! [X3: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 0.35/0.67 => ( P2 @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67 => ( P2 @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_sqrt_wlog
% 0.35/0.67 thf(fact_8503_abs__sqrt__wlog,axiom,
% 0.35/0.67 ! [P2: int > int > $o,X: int] :
% 0.35/0.67 ( ! [X3: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 0.35/0.67 => ( P2 @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67 => ( P2 @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_sqrt_wlog
% 0.35/0.67 thf(fact_8504_power2__le__iff__abs__le,axiom,
% 0.35/0.67 ! [Y: code_integer,X: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 0.35/0.67 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power2_le_iff_abs_le
% 0.35/0.67 thf(fact_8505_power2__le__iff__abs__le,axiom,
% 0.35/0.67 ! [Y: real,X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.67 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power2_le_iff_abs_le
% 0.35/0.67 thf(fact_8506_power2__le__iff__abs__le,axiom,
% 0.35/0.67 ! [Y: rat,X: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 0.35/0.67 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power2_le_iff_abs_le
% 0.35/0.67 thf(fact_8507_power2__le__iff__abs__le,axiom,
% 0.35/0.67 ! [Y: int,X: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.35/0.67 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power2_le_iff_abs_le
% 0.35/0.67 thf(fact_8508_abs__square__le__1,axiom,
% 0.35/0.67 ! [X: code_integer] :
% 0.35/0.67 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 0.35/0.67 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_square_le_1
% 0.35/0.67 thf(fact_8509_abs__square__le__1,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 0.35/0.67 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_square_le_1
% 0.35/0.67 thf(fact_8510_abs__square__le__1,axiom,
% 0.35/0.67 ! [X: rat] :
% 0.35/0.67 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 0.35/0.67 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_square_le_1
% 0.35/0.67 thf(fact_8511_abs__square__le__1,axiom,
% 0.35/0.67 ! [X: int] :
% 0.35/0.67 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 0.35/0.67 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_square_le_1
% 0.35/0.67 thf(fact_8512_divmod__def,axiom,
% 0.35/0.67 ( unique3479559517661332726nteger
% 0.35/0.67 = ( ^ [M6: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_def
% 0.35/0.67 thf(fact_8513_divmod__def,axiom,
% 0.35/0.67 ( unique5052692396658037445od_int
% 0.35/0.67 = ( ^ [M6: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_def
% 0.35/0.67 thf(fact_8514_divmod__def,axiom,
% 0.35/0.67 ( unique5055182867167087721od_nat
% 0.35/0.67 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_def
% 0.35/0.67 thf(fact_8515_divmod_H__nat__def,axiom,
% 0.35/0.67 ( unique5055182867167087721od_nat
% 0.35/0.67 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod'_nat_def
% 0.35/0.67 thf(fact_8516_power__mono__even,axiom,
% 0.35/0.67 ! [N: nat,A: code_integer,B: code_integer] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_mono_even
% 0.35/0.67 thf(fact_8517_power__mono__even,axiom,
% 0.35/0.67 ! [N: nat,A: real,B: real] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 0.35/0.67 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_mono_even
% 0.35/0.67 thf(fact_8518_power__mono__even,axiom,
% 0.35/0.67 ! [N: nat,A: rat,B: rat] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 0.35/0.67 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_mono_even
% 0.35/0.67 thf(fact_8519_power__mono__even,axiom,
% 0.35/0.67 ! [N: nat,A: int,B: int] :
% 0.35/0.67 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 0.35/0.67 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % power_mono_even
% 0.35/0.67 thf(fact_8520_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.67 ( ! [I3: complex] :
% 0.35/0.67 ( ( member_complex @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups6621422865394947399nteger @ X @ I5 )
% 0.35/0.67 = one_one_Code_integer )
% 0.35/0.67 => ( ! [I3: complex] :
% 0.35/0.67 ( ( member_complex @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_le3102999989581377725nteger
% 0.35/0.67 @ ( abs_abs_Code_integer
% 0.35/0.67 @ ( minus_8373710615458151222nteger
% 0.35/0.67 @ ( groups6621422865394947399nteger
% 0.35/0.67 @ ^ [I: complex] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8521_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.67 ( ! [I3: real] :
% 0.35/0.67 ( ( member_real @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups7713935264441627589nteger @ X @ I5 )
% 0.35/0.67 = one_one_Code_integer )
% 0.35/0.67 => ( ! [I3: real] :
% 0.35/0.67 ( ( member_real @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_le3102999989581377725nteger
% 0.35/0.67 @ ( abs_abs_Code_integer
% 0.35/0.67 @ ( minus_8373710615458151222nteger
% 0.35/0.67 @ ( groups7713935264441627589nteger
% 0.35/0.67 @ ^ [I: real] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8522_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.67 ( ! [I3: nat] :
% 0.35/0.67 ( ( member_nat @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 0.35/0.67 = one_one_Code_integer )
% 0.35/0.67 => ( ! [I3: nat] :
% 0.35/0.67 ( ( member_nat @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_le3102999989581377725nteger
% 0.35/0.67 @ ( abs_abs_Code_integer
% 0.35/0.67 @ ( minus_8373710615458151222nteger
% 0.35/0.67 @ ( groups7501900531339628137nteger
% 0.35/0.67 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8523_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 0.35/0.67 ( ! [I3: int] :
% 0.35/0.67 ( ( member_int @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 0.35/0.67 = one_one_Code_integer )
% 0.35/0.67 => ( ! [I3: int] :
% 0.35/0.67 ( ( member_int @ I3 @ I5 )
% 0.35/0.67 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_le3102999989581377725nteger
% 0.35/0.67 @ ( abs_abs_Code_integer
% 0.35/0.67 @ ( minus_8373710615458151222nteger
% 0.35/0.67 @ ( groups7873554091576472773nteger
% 0.35/0.67 @ ^ [I: int] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8524_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 0.35/0.67 ( ! [I3: complex] :
% 0.35/0.67 ( ( member_complex @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups5808333547571424918x_real @ X @ I5 )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 => ( ! [I3: complex] :
% 0.35/0.67 ( ( member_complex @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_less_eq_real
% 0.35/0.67 @ ( abs_abs_real
% 0.35/0.67 @ ( minus_minus_real
% 0.35/0.67 @ ( groups5808333547571424918x_real
% 0.35/0.67 @ ^ [I: complex] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8525_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 0.35/0.67 ( ! [I3: real] :
% 0.35/0.67 ( ( member_real @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups8097168146408367636l_real @ X @ I5 )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 => ( ! [I3: real] :
% 0.35/0.67 ( ( member_real @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_less_eq_real
% 0.35/0.67 @ ( abs_abs_real
% 0.35/0.67 @ ( minus_minus_real
% 0.35/0.67 @ ( groups8097168146408367636l_real
% 0.35/0.67 @ ^ [I: real] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8526_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 0.35/0.67 ( ! [I3: int] :
% 0.35/0.67 ( ( member_int @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups8778361861064173332t_real @ X @ I5 )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 => ( ! [I3: int] :
% 0.35/0.67 ( ( member_int @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_less_eq_real
% 0.35/0.67 @ ( abs_abs_real
% 0.35/0.67 @ ( minus_minus_real
% 0.35/0.67 @ ( groups8778361861064173332t_real
% 0.35/0.67 @ ^ [I: int] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8527_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 0.35/0.67 ( ! [I3: complex] :
% 0.35/0.67 ( ( member_complex @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups5058264527183730370ex_rat @ X @ I5 )
% 0.35/0.67 = one_one_rat )
% 0.35/0.67 => ( ! [I3: complex] :
% 0.35/0.67 ( ( member_complex @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_less_eq_rat
% 0.35/0.67 @ ( abs_abs_rat
% 0.35/0.67 @ ( minus_minus_rat
% 0.35/0.67 @ ( groups5058264527183730370ex_rat
% 0.35/0.67 @ ^ [I: complex] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8528_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 0.35/0.67 ( ! [I3: real] :
% 0.35/0.67 ( ( member_real @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups1300246762558778688al_rat @ X @ I5 )
% 0.35/0.67 = one_one_rat )
% 0.35/0.67 => ( ! [I3: real] :
% 0.35/0.67 ( ( member_real @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_less_eq_rat
% 0.35/0.67 @ ( abs_abs_rat
% 0.35/0.67 @ ( minus_minus_rat
% 0.35/0.67 @ ( groups1300246762558778688al_rat
% 0.35/0.67 @ ^ [I: real] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8529_convex__sum__bound__le,axiom,
% 0.35/0.67 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 0.35/0.67 ( ! [I3: nat] :
% 0.35/0.67 ( ( member_nat @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 0.35/0.67 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 0.35/0.67 = one_one_rat )
% 0.35/0.67 => ( ! [I3: nat] :
% 0.35/0.67 ( ( member_nat @ I3 @ I5 )
% 0.35/0.67 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 0.35/0.67 => ( ord_less_eq_rat
% 0.35/0.67 @ ( abs_abs_rat
% 0.35/0.67 @ ( minus_minus_rat
% 0.35/0.67 @ ( groups2906978787729119204at_rat
% 0.35/0.67 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 0.35/0.67 @ I5 )
% 0.35/0.67 @ B ) )
% 0.35/0.67 @ Delta ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % convex_sum_bound_le
% 0.35/0.67 thf(fact_8530_cos__plus__cos,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( plus_plus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_plus_cos
% 0.35/0.67 thf(fact_8531_cos__plus__cos,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( plus_plus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_plus_cos
% 0.35/0.67 thf(fact_8532_cos__times__cos,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 0.35/0.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_times_cos
% 0.35/0.67 thf(fact_8533_cos__times__cos,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( times_times_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 0.35/0.67 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_times_cos
% 0.35/0.67 thf(fact_8534_cos__double__less__one,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.67 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_double_less_one
% 0.35/0.67 thf(fact_8535_cos__double__cos,axiom,
% 0.35/0.67 ! [W2: complex] :
% 0.35/0.67 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W2 ) )
% 0.35/0.67 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_double_cos
% 0.35/0.67 thf(fact_8536_cos__double__cos,axiom,
% 0.35/0.67 ! [W2: real] :
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W2 ) )
% 0.35/0.67 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_double_cos
% 0.35/0.67 thf(fact_8537_cos__treble__cos,axiom,
% 0.35/0.67 ! [X: complex] :
% 0.35/0.67 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 0.35/0.67 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_treble_cos
% 0.35/0.67 thf(fact_8538_cos__treble__cos,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 0.35/0.67 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_treble_cos
% 0.35/0.67 thf(fact_8539_cos__diff__cos,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( minus_minus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z3 @ W2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_diff_cos
% 0.35/0.67 thf(fact_8540_cos__diff__cos,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( minus_minus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z3 @ W2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_diff_cos
% 0.35/0.67 thf(fact_8541_sin__diff__sin,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( minus_minus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_diff_sin
% 0.35/0.67 thf(fact_8542_sin__diff__sin,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( minus_minus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_diff_sin
% 0.35/0.67 thf(fact_8543_sin__plus__sin,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( plus_plus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 0.35/0.67 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_plus_sin
% 0.35/0.67 thf(fact_8544_sin__plus__sin,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( plus_plus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_plus_sin
% 0.35/0.67 thf(fact_8545_cos__times__sin,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 0.35/0.67 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_times_sin
% 0.35/0.67 thf(fact_8546_cos__times__sin,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( times_times_real @ ( cos_real @ W2 ) @ ( sin_real @ Z3 ) )
% 0.35/0.67 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_times_sin
% 0.35/0.67 thf(fact_8547_sin__times__cos,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 0.35/0.67 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_times_cos
% 0.35/0.67 thf(fact_8548_sin__times__cos,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( times_times_real @ ( sin_real @ W2 ) @ ( cos_real @ Z3 ) )
% 0.35/0.67 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_times_cos
% 0.35/0.67 thf(fact_8549_sin__times__sin,axiom,
% 0.35/0.67 ! [W2: complex,Z3: complex] :
% 0.35/0.67 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 0.35/0.67 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_times_sin
% 0.35/0.67 thf(fact_8550_sin__times__sin,axiom,
% 0.35/0.67 ! [W2: real,Z3: real] :
% 0.35/0.67 ( ( times_times_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 0.35/0.67 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_times_sin
% 0.35/0.67 thf(fact_8551_Maclaurin__cos__expansion,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ? [T6: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.67 & ( ( cos_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_cos_expansion
% 0.35/0.67 thf(fact_8552_cos__one__2pi,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( cos_real @ X )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 = ( ? [X4: nat] :
% 0.35/0.67 ( X
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 0.35/0.67 | ? [X4: nat] :
% 0.35/0.67 ( X
% 0.35/0.67 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_one_2pi
% 0.35/0.67 thf(fact_8553_sin__expansion__lemma,axiom,
% 0.35/0.67 ! [X: real,M2: nat] :
% 0.35/0.67 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_expansion_lemma
% 0.35/0.67 thf(fact_8554_cos__zero__lemma,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ( cos_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 => ? [N3: nat] :
% 0.35/0.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_zero_lemma
% 0.35/0.67 thf(fact_8555_cos__zero__iff,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( cos_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 = ( ? [N4: nat] :
% 0.35/0.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.67 | ? [N4: nat] :
% 0.35/0.67 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_zero_iff
% 0.35/0.67 thf(fact_8556_cos__expansion__lemma,axiom,
% 0.35/0.67 ! [X: real,M2: nat] :
% 0.35/0.67 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 0.35/0.67 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_expansion_lemma
% 0.35/0.67 thf(fact_8557_cos__paired,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( sums_real
% 0.35/0.67 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.35/0.67 @ ( cos_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_paired
% 0.35/0.67 thf(fact_8558_sincos__total__2pi__le,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 => ? [T6: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.67 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( cos_real @ T6 ) )
% 0.35/0.67 & ( Y
% 0.35/0.67 = ( sin_real @ T6 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sincos_total_2pi_le
% 0.35/0.67 thf(fact_8559_sincos__total__2pi,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 => ~ ! [T6: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.67 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67 => ( ( X
% 0.35/0.67 = ( cos_real @ T6 ) )
% 0.35/0.67 => ( Y
% 0.35/0.67 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sincos_total_2pi
% 0.35/0.67 thf(fact_8560_monoseq__arctan__series,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.67 => ( topolo6980174941875973593q_real
% 0.35/0.67 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % monoseq_arctan_series
% 0.35/0.67 thf(fact_8561_summable__arctan__series,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.67 => ( summable_real
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % summable_arctan_series
% 0.35/0.67 thf(fact_8562_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.67 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 0.35/0.67 thf(fact_8563_pi__series,axiom,
% 0.35/0.67 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( suminf_real
% 0.35/0.67 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pi_series
% 0.35/0.67 thf(fact_8564_and__int_Opsimps,axiom,
% 0.35/0.67 ! [K2: int,L: int] :
% 0.35/0.67 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L ) )
% 0.35/0.67 => ( ( ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.67 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.67 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 0.35/0.67 = ( uminus_uminus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 0.35/0.67 & ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.67 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.67 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 0.35/0.67 = ( plus_plus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 0.35/0.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_int.psimps
% 0.35/0.67 thf(fact_8565_tan__npi,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % tan_npi
% 0.35/0.67 thf(fact_8566_tan__periodic__n,axiom,
% 0.35/0.67 ! [X: real,N: num] :
% 0.35/0.67 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 0.35/0.67 = ( tan_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % tan_periodic_n
% 0.35/0.67 thf(fact_8567_tan__periodic__nat,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 0.35/0.67 = ( tan_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % tan_periodic_nat
% 0.35/0.67 thf(fact_8568_tan__periodic,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.67 = ( tan_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % tan_periodic
% 0.35/0.67 thf(fact_8569_abs__zmult__eq__1,axiom,
% 0.35/0.67 ! [M2: int,N: int] :
% 0.35/0.67 ( ( ( abs_abs_int @ ( times_times_int @ M2 @ N ) )
% 0.35/0.67 = one_one_int )
% 0.35/0.67 => ( ( abs_abs_int @ M2 )
% 0.35/0.67 = one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_zmult_eq_1
% 0.35/0.67 thf(fact_8570_abs__div,axiom,
% 0.35/0.67 ! [Y: int,X: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ Y @ X )
% 0.35/0.67 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 0.35/0.67 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_div
% 0.35/0.67 thf(fact_8571_summable__rabs__comparison__test,axiom,
% 0.35/0.67 ! [F2: nat > real,G2: nat > real] :
% 0.35/0.67 ( ? [N7: nat] :
% 0.35/0.67 ! [N3: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( F2 @ N3 ) ) @ ( G2 @ N3 ) ) )
% 0.35/0.67 => ( ( summable_real @ G2 )
% 0.35/0.67 => ( summable_real
% 0.35/0.67 @ ^ [N4: nat] : ( abs_abs_real @ ( F2 @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % summable_rabs_comparison_test
% 0.35/0.67 thf(fact_8572_ln__mult,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.67 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 0.35/0.67 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % ln_mult
% 0.35/0.67 thf(fact_8573_zdvd__mult__cancel1,axiom,
% 0.35/0.67 ! [M2: int,N: int] :
% 0.35/0.67 ( ( M2 != zero_zero_int )
% 0.35/0.67 => ( ( dvd_dvd_int @ ( times_times_int @ M2 @ N ) @ M2 )
% 0.35/0.67 = ( ( abs_abs_int @ N )
% 0.35/0.67 = one_one_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % zdvd_mult_cancel1
% 0.35/0.67 thf(fact_8574_sum__pos__lt__pair,axiom,
% 0.35/0.67 ! [F2: nat > real,K2: nat] :
% 0.35/0.67 ( ( summable_real @ F2 )
% 0.35/0.67 => ( ! [D5: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F2 @ ( plus_plus_nat @ K2 @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) ) ) @ ( F2 @ ( plus_plus_nat @ K2 @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) @ one_one_nat ) ) ) ) )
% 0.35/0.67 => ( ord_less_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ K2 ) ) @ ( suminf_real @ F2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sum_pos_lt_pair
% 0.35/0.67 thf(fact_8575_ln__realpow,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 0.35/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % ln_realpow
% 0.35/0.67 thf(fact_8576_summable__power__series,axiom,
% 0.35/0.67 ! [F2: nat > real,Z3: real] :
% 0.35/0.67 ( ! [I3: nat] : ( ord_less_eq_real @ ( F2 @ I3 ) @ one_one_real )
% 0.35/0.67 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 0.35/0.67 => ( ( ord_less_eq_real @ zero_zero_real @ Z3 )
% 0.35/0.67 => ( ( ord_less_real @ Z3 @ one_one_real )
% 0.35/0.67 => ( summable_real
% 0.35/0.67 @ ^ [I: nat] : ( times_times_real @ ( F2 @ I ) @ ( power_power_real @ Z3 @ I ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % summable_power_series
% 0.35/0.67 thf(fact_8577_nat__intermed__int__val,axiom,
% 0.35/0.67 ! [M2: nat,N: nat,F2: nat > int,K2: int] :
% 0.35/0.67 ( ! [I3: nat] :
% 0.35/0.67 ( ( ( ord_less_eq_nat @ M2 @ I3 )
% 0.35/0.67 & ( ord_less_nat @ I3 @ N ) )
% 0.35/0.67 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 0.35/0.67 => ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.67 => ( ( ord_less_eq_int @ ( F2 @ M2 ) @ K2 )
% 0.35/0.67 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 0.35/0.67 => ? [I3: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ M2 @ I3 )
% 0.35/0.67 & ( ord_less_eq_nat @ I3 @ N )
% 0.35/0.67 & ( ( F2 @ I3 )
% 0.35/0.67 = K2 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % nat_intermed_int_val
% 0.35/0.67 thf(fact_8578_incr__lemma,axiom,
% 0.35/0.67 ! [D: int,Z3: int,X: int] :
% 0.35/0.67 ( ( ord_less_int @ zero_zero_int @ D )
% 0.35/0.67 => ( ord_less_int @ Z3 @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % incr_lemma
% 0.35/0.67 thf(fact_8579_decr__lemma,axiom,
% 0.35/0.67 ! [D: int,X: int,Z3: int] :
% 0.35/0.67 ( ( ord_less_int @ zero_zero_int @ D )
% 0.35/0.67 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D ) ) @ Z3 ) ) ).
% 0.35/0.67
% 0.35/0.67 % decr_lemma
% 0.35/0.67 thf(fact_8580_ln__series,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.67 => ( ( ln_ln_real @ X )
% 0.35/0.67 = ( suminf_real
% 0.35/0.67 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % ln_series
% 0.35/0.67 thf(fact_8581_nat__ivt__aux,axiom,
% 0.35/0.67 ! [N: nat,F2: nat > int,K2: int] :
% 0.35/0.67 ( ! [I3: nat] :
% 0.35/0.67 ( ( ord_less_nat @ I3 @ N )
% 0.35/0.67 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 0.35/0.67 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K2 )
% 0.35/0.67 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 0.35/0.67 => ? [I3: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ I3 @ N )
% 0.35/0.67 & ( ( F2 @ I3 )
% 0.35/0.67 = K2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % nat_ivt_aux
% 0.35/0.67 thf(fact_8582_nat0__intermed__int__val,axiom,
% 0.35/0.67 ! [N: nat,F2: nat > int,K2: int] :
% 0.35/0.67 ( ! [I3: nat] :
% 0.35/0.67 ( ( ord_less_nat @ I3 @ N )
% 0.35/0.67 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 0.35/0.67 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K2 )
% 0.35/0.67 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 0.35/0.67 => ? [I3: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ I3 @ N )
% 0.35/0.67 & ( ( F2 @ I3 )
% 0.35/0.67 = K2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % nat0_intermed_int_val
% 0.35/0.67 thf(fact_8583_ln__one__minus__pos__lower__bound,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % ln_one_minus_pos_lower_bound
% 0.35/0.67 thf(fact_8584_abs__ln__one__plus__x__minus__x__bound,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % abs_ln_one_plus_x_minus_x_bound
% 0.35/0.67 thf(fact_8585_and__int_Opelims,axiom,
% 0.35/0.67 ! [X: int,Xa2: int,Y: int] :
% 0.35/0.67 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 0.35/0.67 = Y )
% 0.35/0.67 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 0.35/0.67 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.67 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.67 => ( Y
% 0.35/0.67 = ( uminus_uminus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 0.35/0.67 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 0.35/0.67 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 0.35/0.67 => ( Y
% 0.35/0.67 = ( plus_plus_int
% 0.35/0.67 @ ( zero_n2684676970156552555ol_int
% 0.35/0.67 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 0.35/0.67 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 0.35/0.67 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.35/0.67 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % and_int.pelims
% 0.35/0.67 thf(fact_8586_arctan__series,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.67 => ( ( arctan @ X )
% 0.35/0.67 = ( suminf_real
% 0.35/0.67 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % arctan_series
% 0.35/0.67 thf(fact_8587_Maclaurin__exp__lt,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ( X != zero_zero_real )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ? [T6: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.35/0.67 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.67 & ( ( exp_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_exp_lt
% 0.35/0.67 thf(fact_8588_arctan__double,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.67 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 0.35/0.67 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % arctan_double
% 0.35/0.67 thf(fact_8589_real__exp__bound__lemma,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.67 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % real_exp_bound_lemma
% 0.35/0.67 thf(fact_8590_exp__ge__one__plus__x__over__n__power__n,axiom,
% 0.35/0.67 ! [N: nat,X: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % exp_ge_one_plus_x_over_n_power_n
% 0.35/0.67 thf(fact_8591_exp__ge__one__minus__x__over__n__power__n,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.67 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % exp_ge_one_minus_x_over_n_power_n
% 0.35/0.67 thf(fact_8592_arctan__add,axiom,
% 0.35/0.67 ! [X: real,Y: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.67 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 0.35/0.67 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 0.35/0.67 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % arctan_add
% 0.35/0.67 thf(fact_8593_Maclaurin__exp__le,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ? [T6: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.67 & ( ( exp_real @ X )
% 0.35/0.67 = ( plus_plus_real
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.67 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_exp_le
% 0.35/0.67 thf(fact_8594_machin__Euler,axiom,
% 0.35/0.67 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.67 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % machin_Euler
% 0.35/0.67 thf(fact_8595_machin,axiom,
% 0.35/0.67 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 0.35/0.67 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % machin
% 0.35/0.67 thf(fact_8596_tanh__real__altdef,axiom,
% 0.35/0.67 ( tanh_real
% 0.35/0.67 = ( ^ [X4: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % tanh_real_altdef
% 0.35/0.67 thf(fact_8597_Maclaurin__sin__bound,axiom,
% 0.35/0.67 ! [X: real,N: nat] :
% 0.35/0.67 ( ord_less_eq_real
% 0.35/0.67 @ ( abs_abs_real
% 0.35/0.67 @ ( minus_minus_real @ ( sin_real @ X )
% 0.35/0.67 @ ( groups6591440286371151544t_real
% 0.35/0.67 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.67 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 0.35/0.67 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Maclaurin_sin_bound
% 0.35/0.67 thf(fact_8598_divmod__BitM__2__eq,axiom,
% 0.35/0.67 ! [M2: num] :
% 0.35/0.67 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 0.35/0.67 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_BitM_2_eq
% 0.35/0.67 thf(fact_8599_pred__numeral__simps_I2_J,axiom,
% 0.35/0.67 ! [K2: num] :
% 0.35/0.67 ( ( pred_numeral @ ( bit0 @ K2 ) )
% 0.35/0.67 = ( numeral_numeral_nat @ ( bitM @ K2 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % pred_numeral_simps(2)
% 0.35/0.67 thf(fact_8600_sin__npi__int,axiom,
% 0.35/0.67 ! [N: int] :
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_npi_int
% 0.35/0.67 thf(fact_8601_tan__periodic__int,axiom,
% 0.35/0.67 ! [X: real,I2: int] :
% 0.35/0.67 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 0.35/0.67 = ( tan_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % tan_periodic_int
% 0.35/0.67 thf(fact_8602_sin__int__2pin,axiom,
% 0.35/0.67 ! [N: int] :
% 0.35/0.67 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % sin_int_2pin
% 0.35/0.67 thf(fact_8603_cos__int__2pin,axiom,
% 0.35/0.67 ! [N: int] :
% 0.35/0.67 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.67 = one_one_real ) ).
% 0.35/0.67
% 0.35/0.67 % cos_int_2pin
% 0.35/0.67 thf(fact_8604_cos__npi__int,axiom,
% 0.35/0.67 ! [N: int] :
% 0.35/0.67 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.67 = one_one_real ) )
% 0.35/0.67 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 0.35/0.67 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_npi_int
% 0.35/0.67 thf(fact_8605_real__scaleR__def,axiom,
% 0.35/0.67 real_V1485227260804924795R_real = times_times_real ).
% 0.35/0.67
% 0.35/0.67 % real_scaleR_def
% 0.35/0.67 thf(fact_8606_divide__real__def,axiom,
% 0.35/0.67 ( divide_divide_real
% 0.35/0.67 = ( ^ [X4: real,Y4: real] : ( times_times_real @ X4 @ ( inverse_inverse_real @ Y4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_real_def
% 0.35/0.67 thf(fact_8607_eval__nat__numeral_I2_J,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 0.35/0.67 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % eval_nat_numeral(2)
% 0.35/0.67 thf(fact_8608_BitM__plus__one,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 0.35/0.67 = ( bit0 @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % BitM_plus_one
% 0.35/0.67 thf(fact_8609_one__plus__BitM,axiom,
% 0.35/0.67 ! [N: num] :
% 0.35/0.67 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 0.35/0.67 = ( bit0 @ N ) ) ).
% 0.35/0.67
% 0.35/0.67 % one_plus_BitM
% 0.35/0.67 thf(fact_8610_forall__pos__mono__1,axiom,
% 0.35/0.67 ! [P2: real > $o,E: real] :
% 0.35/0.67 ( ! [D5: real,E2: real] :
% 0.35/0.67 ( ( ord_less_real @ D5 @ E2 )
% 0.35/0.67 => ( ( P2 @ D5 )
% 0.35/0.67 => ( P2 @ E2 ) ) )
% 0.35/0.67 => ( ! [N3: nat] : ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.67 => ( P2 @ E ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % forall_pos_mono_1
% 0.35/0.67 thf(fact_8611_forall__pos__mono,axiom,
% 0.35/0.67 ! [P2: real > $o,E: real] :
% 0.35/0.67 ( ! [D5: real,E2: real] :
% 0.35/0.67 ( ( ord_less_real @ D5 @ E2 )
% 0.35/0.67 => ( ( P2 @ D5 )
% 0.35/0.67 => ( P2 @ E2 ) ) )
% 0.35/0.67 => ( ! [N3: nat] :
% 0.35/0.67 ( ( N3 != zero_zero_nat )
% 0.35/0.67 => ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.67 => ( P2 @ E ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % forall_pos_mono
% 0.35/0.67 thf(fact_8612_real__arch__inverse,axiom,
% 0.35/0.67 ! [E: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ E )
% 0.35/0.67 = ( ? [N4: nat] :
% 0.35/0.67 ( ( N4 != zero_zero_nat )
% 0.35/0.67 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 0.35/0.67 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ E ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % real_arch_inverse
% 0.35/0.67 thf(fact_8613_sin__zero__iff__int2,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( sin_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 = ( ? [I: int] :
% 0.35/0.67 ( X
% 0.35/0.67 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero_iff_int2
% 0.35/0.67 thf(fact_8614_cos__one__2pi__int,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( cos_real @ X )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 = ( ? [X4: int] :
% 0.35/0.67 ( X
% 0.35/0.67 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_one_2pi_int
% 0.35/0.67 thf(fact_8615_cos__zero__iff__int,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( cos_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 = ( ? [I: int] :
% 0.35/0.67 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % cos_zero_iff_int
% 0.35/0.67 thf(fact_8616_sin__zero__iff__int,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ( sin_real @ X )
% 0.35/0.67 = zero_zero_real )
% 0.35/0.67 = ( ? [I: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I )
% 0.35/0.67 & ( X
% 0.35/0.67 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sin_zero_iff_int
% 0.35/0.67 thf(fact_8617_complex__unimodular__polar,axiom,
% 0.35/0.67 ! [Z3: complex] :
% 0.35/0.67 ( ( ( real_V1022390504157884413omplex @ Z3 )
% 0.35/0.67 = one_one_real )
% 0.35/0.67 => ~ ! [T6: real] :
% 0.35/0.67 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.67 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.67 => ( Z3
% 0.35/0.67 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % complex_unimodular_polar
% 0.35/0.67 thf(fact_8618_arccos__cos__eq__abs__2pi,axiom,
% 0.35/0.67 ! [Theta: real] :
% 0.35/0.67 ~ ! [K: int] :
% 0.35/0.67 ( ( arccos @ ( cos_real @ Theta ) )
% 0.35/0.67 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % arccos_cos_eq_abs_2pi
% 0.35/0.67 thf(fact_8619_log__base__10__eq1,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.67 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log_base_10_eq1
% 0.35/0.67 thf(fact_8620_complex__scaleR,axiom,
% 0.35/0.67 ! [R3: real,A: real,B: real] :
% 0.35/0.67 ( ( real_V2046097035970521341omplex @ R3 @ ( complex2 @ A @ B ) )
% 0.35/0.67 = ( complex2 @ ( times_times_real @ R3 @ A ) @ ( times_times_real @ R3 @ B ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % complex_scaleR
% 0.35/0.67 thf(fact_8621_complex__mult,axiom,
% 0.35/0.67 ! [A: real,B: real,C2: real,D: real] :
% 0.35/0.67 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C2 @ D ) )
% 0.35/0.67 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % complex_mult
% 0.35/0.67 thf(fact_8622_log__mult,axiom,
% 0.35/0.67 ! [A: real,X: real,Y: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67 => ( ( A != one_one_real )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.35/0.67 => ( ( log2 @ A @ ( times_times_real @ X @ Y ) )
% 0.35/0.67 = ( plus_plus_real @ ( log2 @ A @ X ) @ ( log2 @ A @ Y ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log_mult
% 0.35/0.67 thf(fact_8623_log__nat__power,axiom,
% 0.35/0.67 ! [X: real,B: real,N: nat] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( log2 @ B @ ( power_power_real @ X @ N ) )
% 0.35/0.67 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log_nat_power
% 0.35/0.67 thf(fact_8624_log__of__power__less,axiom,
% 0.35/0.67 ! [M2: nat,B: real,N: nat] :
% 0.35/0.67 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 0.35/0.67 => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.67 => ( ord_less_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log_of_power_less
% 0.35/0.67 thf(fact_8625_log__eq__div__ln__mult__log,axiom,
% 0.35/0.67 ! [A: real,B: real,X: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.67 => ( ( A != one_one_real )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.67 => ( ( B != one_one_real )
% 0.35/0.67 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( log2 @ A @ X )
% 0.35/0.67 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log2 @ B @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log_eq_div_ln_mult_log
% 0.35/0.67 thf(fact_8626_log__of__power__le,axiom,
% 0.35/0.67 ! [M2: nat,B: real,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 0.35/0.67 => ( ( ord_less_real @ one_one_real @ B )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.67 => ( ord_less_eq_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log_of_power_le
% 0.35/0.67 thf(fact_8627_le__log2__of__power,axiom,
% 0.35/0.67 ! [N: nat,M2: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 )
% 0.35/0.67 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % le_log2_of_power
% 0.35/0.67 thf(fact_8628_divmod__step__nat__def,axiom,
% 0.35/0.67 ( unique5026877609467782581ep_nat
% 0.35/0.67 = ( ^ [L2: num] :
% 0.35/0.67 ( produc2626176000494625587at_nat
% 0.35/0.67 @ ^ [Q5: nat,R: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_step_nat_def
% 0.35/0.67 thf(fact_8629_log2__of__power__less,axiom,
% 0.35/0.67 ! [M2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.67 => ( ord_less_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log2_of_power_less
% 0.35/0.67 thf(fact_8630_divmod__step__int__def,axiom,
% 0.35/0.67 ( unique5024387138958732305ep_int
% 0.35/0.67 = ( ^ [L2: num] :
% 0.35/0.67 ( produc4245557441103728435nt_int
% 0.35/0.67 @ ^ [Q5: int,R: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_step_int_def
% 0.35/0.67 thf(fact_8631_log2__of__power__le,axiom,
% 0.35/0.67 ! [M2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.67 => ( ord_less_eq_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log2_of_power_le
% 0.35/0.67 thf(fact_8632_log__base__10__eq2,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.67 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 0.35/0.67 = ( times_times_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % log_base_10_eq2
% 0.35/0.67 thf(fact_8633_ceiling__log__nat__eq__powr__iff,axiom,
% 0.35/0.67 ! [B: nat,K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.67 => ( ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 0.35/0.67 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 0.35/0.67 & ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % ceiling_log_nat_eq_powr_iff
% 0.35/0.67 thf(fact_8634_ceiling__log__nat__eq__if,axiom,
% 0.35/0.67 ! [B: nat,N: nat,K2: nat] :
% 0.35/0.67 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 0.35/0.67 => ( ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.35/0.67 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.67 => ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % ceiling_log_nat_eq_if
% 0.35/0.67 thf(fact_8635_ceiling__log2__div2,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( archim7802044766580827645g_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % ceiling_log2_div2
% 0.35/0.67 thf(fact_8636_divmod__nat__if,axiom,
% 0.35/0.67 ( divmod_nat
% 0.35/0.67 = ( ^ [M6: nat,N4: nat] :
% 0.35/0.67 ( if_Pro6206227464963214023at_nat
% 0.35/0.67 @ ( ( N4 = zero_zero_nat )
% 0.35/0.67 | ( ord_less_nat @ M6 @ N4 ) )
% 0.35/0.67 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 0.35/0.67 @ ( produc2626176000494625587at_nat
% 0.35/0.67 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 0.35/0.67 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_nat_if
% 0.35/0.67 thf(fact_8637_floor__log__nat__eq__powr__iff,axiom,
% 0.35/0.67 ! [B: nat,K2: nat,N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.67 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 0.35/0.67 => ( ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 0.35/0.67 = ( semiri1314217659103216013at_int @ N ) )
% 0.35/0.67 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 0.35/0.67 & ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % floor_log_nat_eq_powr_iff
% 0.35/0.67 thf(fact_8638_divide__complex__def,axiom,
% 0.35/0.67 ( divide1717551699836669952omplex
% 0.35/0.67 = ( ^ [X4: complex,Y4: complex] : ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divide_complex_def
% 0.35/0.67 thf(fact_8639_prod__encode__def,axiom,
% 0.35/0.67 ( nat_prod_encode
% 0.35/0.67 = ( produc6842872674320459806at_nat
% 0.35/0.67 @ ^ [M6: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N4 ) ) @ M6 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % prod_encode_def
% 0.35/0.67 thf(fact_8640_Divides_Oadjust__div__def,axiom,
% 0.35/0.67 ( adjust_div
% 0.35/0.67 = ( produc8211389475949308722nt_int
% 0.35/0.67 @ ^ [Q5: int,R: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % Divides.adjust_div_def
% 0.35/0.67 thf(fact_8641_divmod__nat__def,axiom,
% 0.35/0.67 ( divmod_nat
% 0.35/0.67 = ( ^ [M6: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N4 ) @ ( modulo_modulo_nat @ M6 @ N4 ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % divmod_nat_def
% 0.35/0.67 thf(fact_8642_floor__log2__div2,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.67 => ( ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.67 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % floor_log2_div2
% 0.35/0.67 thf(fact_8643_floor__log__nat__eq__if,axiom,
% 0.35/0.67 ! [B: nat,N: nat,K2: nat] :
% 0.35/0.67 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 0.35/0.67 => ( ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 0.35/0.67 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 0.35/0.67 => ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 0.35/0.67 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % floor_log_nat_eq_if
% 0.35/0.67 thf(fact_8644_cot__periodic,axiom,
% 0.35/0.67 ! [X: real] :
% 0.35/0.67 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.67 = ( cot_real @ X ) ) ).
% 0.35/0.67
% 0.35/0.67 % cot_periodic
% 0.35/0.67 thf(fact_8645_modulo__int__unfold,axiom,
% 0.35/0.67 ! [L: int,K2: int,N: nat,M2: nat] :
% 0.35/0.67 ( ( ( ( ( sgn_sgn_int @ L )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 | ( ( sgn_sgn_int @ K2 )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 | ( N = zero_zero_nat ) )
% 0.35/0.67 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67 = ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) )
% 0.35/0.67 & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 | ( ( sgn_sgn_int @ K2 )
% 0.35/0.67 = zero_zero_int )
% 0.35/0.67 | ( N = zero_zero_nat ) )
% 0.35/0.67 => ( ( ( ( sgn_sgn_int @ K2 )
% 0.35/0.67 = ( sgn_sgn_int @ L ) )
% 0.35/0.67 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) )
% 0.35/0.67 & ( ( ( sgn_sgn_int @ K2 )
% 0.35/0.67 != ( sgn_sgn_int @ L ) )
% 0.35/0.67 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.67 = ( times_times_int @ ( sgn_sgn_int @ L )
% 0.35/0.67 @ ( minus_minus_int
% 0.35/0.67 @ ( semiri1314217659103216013at_int
% 0.35/0.67 @ ( times_times_nat @ N
% 0.35/0.67 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.67 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) )
% 0.35/0.67 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % modulo_int_unfold
% 0.35/0.67 thf(fact_8646_dvd__mult__sgn__iff,axiom,
% 0.35/0.67 ! [L: int,K2: int,R3: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ L @ ( times_times_int @ K2 @ ( sgn_sgn_int @ R3 ) ) )
% 0.35/0.67 = ( ( dvd_dvd_int @ L @ K2 )
% 0.35/0.67 | ( R3 = zero_zero_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_mult_sgn_iff
% 0.35/0.67 thf(fact_8647_dvd__sgn__mult__iff,axiom,
% 0.35/0.67 ! [L: int,R3: int,K2: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R3 ) @ K2 ) )
% 0.35/0.67 = ( ( dvd_dvd_int @ L @ K2 )
% 0.35/0.67 | ( R3 = zero_zero_int ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % dvd_sgn_mult_iff
% 0.35/0.67 thf(fact_8648_mult__sgn__dvd__iff,axiom,
% 0.35/0.67 ! [L: int,R3: int,K2: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R3 ) ) @ K2 )
% 0.35/0.67 = ( ( dvd_dvd_int @ L @ K2 )
% 0.35/0.67 & ( ( R3 = zero_zero_int )
% 0.35/0.67 => ( K2 = zero_zero_int ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % mult_sgn_dvd_iff
% 0.35/0.67 thf(fact_8649_sgn__mult__dvd__iff,axiom,
% 0.35/0.67 ! [R3: int,L: int,K2: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R3 ) @ L ) @ K2 )
% 0.35/0.67 = ( ( dvd_dvd_int @ L @ K2 )
% 0.35/0.67 & ( ( R3 = zero_zero_int )
% 0.35/0.67 => ( K2 = zero_zero_int ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % sgn_mult_dvd_iff
% 0.35/0.67 thf(fact_8650_cot__npi,axiom,
% 0.35/0.67 ! [N: nat] :
% 0.35/0.67 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 0.35/0.67 = zero_zero_real ) ).
% 0.35/0.67
% 0.35/0.67 % cot_npi
% 0.35/0.67 thf(fact_8651_int__sgnE,axiom,
% 0.35/0.67 ! [K2: int] :
% 0.35/0.67 ~ ! [N3: nat,L4: int] :
% 0.35/0.67 ( K2
% 0.35/0.67 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % int_sgnE
% 0.35/0.67 thf(fact_8652_div__eq__sgn__abs,axiom,
% 0.35/0.67 ! [K2: int,L: int] :
% 0.35/0.67 ( ( ( sgn_sgn_int @ K2 )
% 0.35/0.67 = ( sgn_sgn_int @ L ) )
% 0.35/0.67 => ( ( divide_divide_int @ K2 @ L )
% 0.35/0.67 = ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % div_eq_sgn_abs
% 0.35/0.67 thf(fact_8653_div__sgn__abs__cancel,axiom,
% 0.35/0.67 ! [V2: int,K2: int,L: int] :
% 0.35/0.67 ( ( V2 != zero_zero_int )
% 0.35/0.67 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ K2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ L ) ) )
% 0.35/0.67 = ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % div_sgn_abs_cancel
% 0.35/0.67 thf(fact_8654_div__dvd__sgn__abs,axiom,
% 0.35/0.67 ! [L: int,K2: int] :
% 0.35/0.67 ( ( dvd_dvd_int @ L @ K2 )
% 0.35/0.67 => ( ( divide_divide_int @ K2 @ L )
% 0.35/0.67 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % div_dvd_sgn_abs
% 0.35/0.67 thf(fact_8655_eucl__rel__int__remainderI,axiom,
% 0.35/0.67 ! [R3: int,L: int,K2: int,Q2: int] :
% 0.35/0.67 ( ( ( sgn_sgn_int @ R3 )
% 0.35/0.67 = ( sgn_sgn_int @ L ) )
% 0.35/0.67 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 0.35/0.67 => ( ( K2
% 0.35/0.67 = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R3 ) )
% 0.35/0.67 => ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) ) ) ) ) ).
% 0.35/0.67
% 0.35/0.67 % eucl_rel_int_remainderI
% 0.35/0.68 thf(fact_8656_eucl__rel__int_Osimps,axiom,
% 0.35/0.68 ( eucl_rel_int
% 0.35/0.68 = ( ^ [A13: int,A24: int,A32: product_prod_int_int] :
% 0.35/0.68 ( ? [K3: int] :
% 0.35/0.68 ( ( A13 = K3 )
% 0.35/0.68 & ( A24 = zero_zero_int )
% 0.35/0.68 & ( A32
% 0.35/0.68 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 0.35/0.68 | ? [L2: int,K3: int,Q5: int] :
% 0.35/0.68 ( ( A13 = K3 )
% 0.35/0.68 & ( A24 = L2 )
% 0.35/0.68 & ( A32
% 0.35/0.68 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 0.35/0.68 & ( L2 != zero_zero_int )
% 0.35/0.68 & ( K3
% 0.35/0.68 = ( times_times_int @ Q5 @ L2 ) ) )
% 0.35/0.68 | ? [R: int,L2: int,K3: int,Q5: int] :
% 0.35/0.68 ( ( A13 = K3 )
% 0.35/0.68 & ( A24 = L2 )
% 0.35/0.68 & ( A32
% 0.35/0.68 = ( product_Pair_int_int @ Q5 @ R ) )
% 0.35/0.68 & ( ( sgn_sgn_int @ R )
% 0.35/0.68 = ( sgn_sgn_int @ L2 ) )
% 0.35/0.68 & ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 0.35/0.68 & ( K3
% 0.35/0.68 = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % eucl_rel_int.simps
% 0.35/0.68 thf(fact_8657_eucl__rel__int_Ocases,axiom,
% 0.35/0.68 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 0.35/0.68 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 0.35/0.68 => ( ( ( A23 = zero_zero_int )
% 0.35/0.68 => ( A33
% 0.35/0.68 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 0.35/0.68 => ( ! [Q3: int] :
% 0.35/0.68 ( ( A33
% 0.35/0.68 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 0.35/0.68 => ( ( A23 != zero_zero_int )
% 0.35/0.68 => ( A12
% 0.35/0.68 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 0.35/0.68 => ~ ! [R4: int,Q3: int] :
% 0.35/0.68 ( ( A33
% 0.35/0.68 = ( product_Pair_int_int @ Q3 @ R4 ) )
% 0.35/0.68 => ( ( ( sgn_sgn_int @ R4 )
% 0.35/0.68 = ( sgn_sgn_int @ A23 ) )
% 0.35/0.68 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ A23 ) )
% 0.35/0.68 => ( A12
% 0.35/0.68 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R4 ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % eucl_rel_int.cases
% 0.35/0.68 thf(fact_8658_div__noneq__sgn__abs,axiom,
% 0.35/0.68 ! [L: int,K2: int] :
% 0.35/0.68 ( ( L != zero_zero_int )
% 0.35/0.68 => ( ( ( sgn_sgn_int @ K2 )
% 0.35/0.68 != ( sgn_sgn_int @ L ) )
% 0.35/0.68 => ( ( divide_divide_int @ K2 @ L )
% 0.35/0.68 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) )
% 0.35/0.68 @ ( zero_n2684676970156552555ol_int
% 0.35/0.68 @ ~ ( dvd_dvd_int @ L @ K2 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % div_noneq_sgn_abs
% 0.35/0.68 thf(fact_8659_divide__int__unfold,axiom,
% 0.35/0.68 ! [L: int,K2: int,N: nat,M2: nat] :
% 0.35/0.68 ( ( ( ( ( sgn_sgn_int @ L )
% 0.35/0.68 = zero_zero_int )
% 0.35/0.68 | ( ( sgn_sgn_int @ K2 )
% 0.35/0.68 = zero_zero_int )
% 0.35/0.68 | ( N = zero_zero_nat ) )
% 0.35/0.68 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.68 = zero_zero_int ) )
% 0.35/0.68 & ( ~ ( ( ( sgn_sgn_int @ L )
% 0.35/0.68 = zero_zero_int )
% 0.35/0.68 | ( ( sgn_sgn_int @ K2 )
% 0.35/0.68 = zero_zero_int )
% 0.35/0.68 | ( N = zero_zero_nat ) )
% 0.35/0.68 => ( ( ( ( sgn_sgn_int @ K2 )
% 0.35/0.68 = ( sgn_sgn_int @ L ) )
% 0.35/0.68 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.68 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) ) ) )
% 0.35/0.68 & ( ( ( sgn_sgn_int @ K2 )
% 0.35/0.68 != ( sgn_sgn_int @ L ) )
% 0.35/0.68 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.68 = ( uminus_uminus_int
% 0.35/0.68 @ ( semiri1314217659103216013at_int
% 0.35/0.68 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N )
% 0.35/0.68 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % divide_int_unfold
% 0.35/0.68 thf(fact_8660_natLess__def,axiom,
% 0.35/0.68 ( bNF_Ca8459412986667044542atLess
% 0.35/0.68 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % natLess_def
% 0.35/0.68 thf(fact_8661_modulo__int__def,axiom,
% 0.35/0.68 ( modulo_modulo_int
% 0.35/0.68 = ( ^ [K3: int,L2: int] :
% 0.35/0.68 ( if_int @ ( L2 = zero_zero_int ) @ K3
% 0.35/0.68 @ ( if_int
% 0.35/0.68 @ ( ( sgn_sgn_int @ K3 )
% 0.35/0.68 = ( sgn_sgn_int @ L2 ) )
% 0.35/0.68 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 0.35/0.68 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 0.35/0.68 @ ( minus_minus_int
% 0.35/0.68 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 0.35/0.68 @ ( zero_n2684676970156552555ol_int
% 0.35/0.68 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 0.35/0.68 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % modulo_int_def
% 0.35/0.68 thf(fact_8662_num_Osize__gen_I3_J,axiom,
% 0.35/0.68 ! [X33: num] :
% 0.35/0.68 ( ( size_num @ ( bit1 @ X33 ) )
% 0.35/0.68 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % num.size_gen(3)
% 0.35/0.68 thf(fact_8663_mask__nat__positive__iff,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.35/0.68 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % mask_nat_positive_iff
% 0.35/0.68 thf(fact_8664_nat__1,axiom,
% 0.35/0.68 ( ( nat2 @ one_one_int )
% 0.35/0.68 = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_1
% 0.35/0.68 thf(fact_8665_nat__0__iff,axiom,
% 0.35/0.68 ! [I2: int] :
% 0.35/0.68 ( ( ( nat2 @ I2 )
% 0.35/0.68 = zero_zero_nat )
% 0.35/0.68 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_0_iff
% 0.35/0.68 thf(fact_8666_nat__le__0,axiom,
% 0.35/0.68 ! [Z3: int] :
% 0.35/0.68 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 0.35/0.68 => ( ( nat2 @ Z3 )
% 0.35/0.68 = zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_le_0
% 0.35/0.68 thf(fact_8667_nat__neg__numeral,axiom,
% 0.35/0.68 ! [K2: num] :
% 0.35/0.68 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % nat_neg_numeral
% 0.35/0.68 thf(fact_8668_nat__zminus__int,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % nat_zminus_int
% 0.35/0.68 thf(fact_8669_take__bit__of__Suc__0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_of_Suc_0
% 0.35/0.68 thf(fact_8670_zero__less__nat__eq,axiom,
% 0.35/0.68 ! [Z3: int] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z3 ) )
% 0.35/0.68 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % zero_less_nat_eq
% 0.35/0.68 thf(fact_8671_card__atLeastAtMost__int,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 0.35/0.68 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_atLeastAtMost_int
% 0.35/0.68 thf(fact_8672_nat__ceiling__le__eq,axiom,
% 0.35/0.68 ! [X: real,A: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 0.35/0.68 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_ceiling_le_eq
% 0.35/0.68 thf(fact_8673_one__less__nat__eq,axiom,
% 0.35/0.68 ! [Z3: int] :
% 0.35/0.68 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z3 ) )
% 0.35/0.68 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % one_less_nat_eq
% 0.35/0.68 thf(fact_8674_numeral__power__le__nat__cancel__iff,axiom,
% 0.35/0.68 ! [X: num,N: nat,A: int] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 0.35/0.68 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 0.35/0.68
% 0.35/0.68 % numeral_power_le_nat_cancel_iff
% 0.35/0.68 thf(fact_8675_nat__le__numeral__power__cancel__iff,axiom,
% 0.35/0.68 ! [A: int,X: num,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 0.35/0.68 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_le_numeral_power_cancel_iff
% 0.35/0.68 thf(fact_8676_take__bit__tightened__less__eq__nat,axiom,
% 0.35/0.68 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M2 @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_tightened_less_eq_nat
% 0.35/0.68 thf(fact_8677_take__bit__nat__less__eq__self,axiom,
% 0.35/0.68 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_nat_less_eq_self
% 0.35/0.68 thf(fact_8678_take__bit__mult,axiom,
% 0.35/0.68 ! [N: nat,K2: int,L: int] :
% 0.35/0.68 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K2 ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 0.35/0.68 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K2 @ L ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_mult
% 0.35/0.68 thf(fact_8679_less__eq__mask,axiom,
% 0.35/0.68 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % less_eq_mask
% 0.35/0.68 thf(fact_8680_nat__zero__as__int,axiom,
% 0.35/0.68 ( zero_zero_nat
% 0.35/0.68 = ( nat2 @ zero_zero_int ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_zero_as_int
% 0.35/0.68 thf(fact_8681_take__bit__tightened__less__eq__int,axiom,
% 0.35/0.68 ! [M2: nat,N: nat,K2: int] :
% 0.35/0.68 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M2 @ K2 ) @ ( bit_se2923211474154528505it_int @ N @ K2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_tightened_less_eq_int
% 0.35/0.68 thf(fact_8682_nat__mono,axiom,
% 0.35/0.68 ! [X: int,Y: int] :
% 0.35/0.68 ( ( ord_less_eq_int @ X @ Y )
% 0.35/0.68 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_mono
% 0.35/0.68 thf(fact_8683_nat__le__iff,axiom,
% 0.35/0.68 ! [X: int,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 0.35/0.68 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_le_iff
% 0.35/0.68 thf(fact_8684_nat__abs__mult__distrib,axiom,
% 0.35/0.68 ! [W2: int,Z3: int] :
% 0.35/0.68 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z3 ) ) )
% 0.35/0.68 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_abs_mult_distrib
% 0.35/0.68 thf(fact_8685_nat__times__as__int,axiom,
% 0.35/0.68 ( times_times_nat
% 0.35/0.68 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_times_as_int
% 0.35/0.68 thf(fact_8686_less__mask,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.68 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % less_mask
% 0.35/0.68 thf(fact_8687_nat__le__eq__zle,axiom,
% 0.35/0.68 ! [W2: int,Z3: int] :
% 0.35/0.68 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 0.35/0.68 | ( ord_less_eq_int @ zero_zero_int @ Z3 ) )
% 0.35/0.68 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 0.35/0.68 = ( ord_less_eq_int @ W2 @ Z3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_le_eq_zle
% 0.35/0.68 thf(fact_8688_nat__eq__iff2,axiom,
% 0.35/0.68 ! [M2: nat,W2: int] :
% 0.35/0.68 ( ( M2
% 0.35/0.68 = ( nat2 @ W2 ) )
% 0.35/0.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.35/0.68 => ( W2
% 0.35/0.68 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.35/0.68 => ( M2 = zero_zero_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_eq_iff2
% 0.35/0.68 thf(fact_8689_nat__eq__iff,axiom,
% 0.35/0.68 ! [W2: int,M2: nat] :
% 0.35/0.68 ( ( ( nat2 @ W2 )
% 0.35/0.68 = M2 )
% 0.35/0.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.35/0.68 => ( W2
% 0.35/0.68 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 0.35/0.68 => ( M2 = zero_zero_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_eq_iff
% 0.35/0.68 thf(fact_8690_split__nat,axiom,
% 0.35/0.68 ! [P2: nat > $o,I2: int] :
% 0.35/0.68 ( ( P2 @ ( nat2 @ I2 ) )
% 0.35/0.68 = ( ! [N4: nat] :
% 0.35/0.68 ( ( I2
% 0.35/0.68 = ( semiri1314217659103216013at_int @ N4 ) )
% 0.35/0.68 => ( P2 @ N4 ) )
% 0.35/0.68 & ( ( ord_less_int @ I2 @ zero_zero_int )
% 0.35/0.68 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % split_nat
% 0.35/0.68 thf(fact_8691_le__nat__iff,axiom,
% 0.35/0.68 ! [K2: int,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 0.35/0.68 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K2 ) )
% 0.35/0.68 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % le_nat_iff
% 0.35/0.68 thf(fact_8692_nat__mult__distrib,axiom,
% 0.35/0.68 ! [Z3: int,Z6: int] :
% 0.35/0.68 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 0.35/0.68 => ( ( nat2 @ ( times_times_int @ Z3 @ Z6 ) )
% 0.35/0.68 = ( times_times_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_mult_distrib
% 0.35/0.68 thf(fact_8693_Suc__as__int,axiom,
% 0.35/0.68 ( suc
% 0.35/0.68 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_as_int
% 0.35/0.68 thf(fact_8694_nat__abs__triangle__ineq,axiom,
% 0.35/0.68 ! [K2: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K2 @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_abs_triangle_ineq
% 0.35/0.68 thf(fact_8695_nat__floor__neg,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 0.35/0.68 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.68 = zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_floor_neg
% 0.35/0.68 thf(fact_8696_div__abs__eq__div__nat,axiom,
% 0.35/0.68 ! [K2: int,L: int] :
% 0.35/0.68 ( ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) )
% 0.35/0.68 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % div_abs_eq_div_nat
% 0.35/0.68 thf(fact_8697_floor__eq3,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.35/0.68 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.35/0.68 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.68 = N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % floor_eq3
% 0.35/0.68 thf(fact_8698_le__nat__floor,axiom,
% 0.35/0.68 ! [X: nat,A: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 0.35/0.68 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % le_nat_floor
% 0.35/0.68 thf(fact_8699_mod__abs__eq__div__nat,axiom,
% 0.35/0.68 ! [K2: int,L: int] :
% 0.35/0.68 ( ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) )
% 0.35/0.68 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % mod_abs_eq_div_nat
% 0.35/0.68 thf(fact_8700_nat__2,axiom,
% 0.35/0.68 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.68 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_2
% 0.35/0.68 thf(fact_8701_sgn__power__injE,axiom,
% 0.35/0.68 ! [A: real,N: nat,X: real,B: real] :
% 0.35/0.68 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 0.35/0.68 = X )
% 0.35/0.68 => ( ( X
% 0.35/0.68 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 0.35/0.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( A = B ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sgn_power_injE
% 0.35/0.68 thf(fact_8702_Suc__nat__eq__nat__zadd1,axiom,
% 0.35/0.68 ! [Z3: int] :
% 0.35/0.68 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 0.35/0.68 => ( ( suc @ ( nat2 @ Z3 ) )
% 0.35/0.68 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_nat_eq_nat_zadd1
% 0.35/0.68 thf(fact_8703_nat__mult__distrib__neg,axiom,
% 0.35/0.68 ! [Z3: int,Z6: int] :
% 0.35/0.68 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 0.35/0.68 => ( ( nat2 @ ( times_times_int @ Z3 @ Z6 ) )
% 0.35/0.68 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z3 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_mult_distrib_neg
% 0.35/0.68 thf(fact_8704_nat__abs__int__diff,axiom,
% 0.35/0.68 ! [A: nat,B: nat] :
% 0.35/0.68 ( ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.68 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.35/0.68 = ( minus_minus_nat @ B @ A ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_nat @ A @ B )
% 0.35/0.68 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 0.35/0.68 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_abs_int_diff
% 0.35/0.68 thf(fact_8705_floor__eq4,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 0.35/0.68 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 0.35/0.68 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 0.35/0.68 = N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % floor_eq4
% 0.35/0.68 thf(fact_8706_num_Osize__gen_I1_J,axiom,
% 0.35/0.68 ( ( size_num @ one )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % num.size_gen(1)
% 0.35/0.68 thf(fact_8707_diff__nat__eq__if,axiom,
% 0.35/0.68 ! [Z6: int,Z3: int] :
% 0.35/0.68 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 0.35/0.68 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) )
% 0.35/0.68 = ( nat2 @ Z3 ) ) )
% 0.35/0.68 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 0.35/0.68 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) )
% 0.35/0.68 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z3 @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z3 @ Z6 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % diff_nat_eq_if
% 0.35/0.68 thf(fact_8708_take__bit__nat__less__self__iff,axiom,
% 0.35/0.68 ! [N: nat,M2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 )
% 0.35/0.68 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_nat_less_self_iff
% 0.35/0.68 thf(fact_8709_Suc__mask__eq__exp,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_mask_eq_exp
% 0.35/0.68 thf(fact_8710_take__bit__Suc__minus__bit0,axiom,
% 0.35/0.68 ! [N: nat,K2: num] :
% 0.35/0.68 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 0.35/0.68 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_Suc_minus_bit0
% 0.35/0.68 thf(fact_8711_nat__dvd__iff,axiom,
% 0.35/0.68 ! [Z3: int,M2: nat] :
% 0.35/0.68 ( ( dvd_dvd_nat @ ( nat2 @ Z3 ) @ M2 )
% 0.35/0.68 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 0.35/0.68 => ( dvd_dvd_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 0.35/0.68 => ( M2 = zero_zero_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_dvd_iff
% 0.35/0.68 thf(fact_8712_take__bit__numeral__minus__bit0,axiom,
% 0.35/0.68 ! [L: num,K2: num] :
% 0.35/0.68 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 0.35/0.68 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_numeral_minus_bit0
% 0.35/0.68 thf(fact_8713_take__bit__int__less__eq,axiom,
% 0.35/0.68 ! [N: nat,K2: int] :
% 0.35/0.68 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K2 )
% 0.35/0.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_int_less_eq
% 0.35/0.68 thf(fact_8714_signed__take__bit__eq__take__bit__shift,axiom,
% 0.35/0.68 ( bit_ri631733984087533419it_int
% 0.35/0.68 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % signed_take_bit_eq_take_bit_shift
% 0.35/0.68 thf(fact_8715_arctan__inverse,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( X != zero_zero_real )
% 0.35/0.68 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 0.35/0.68 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % arctan_inverse
% 0.35/0.68 thf(fact_8716_num_Osize__gen_I2_J,axiom,
% 0.35/0.68 ! [X2: num] :
% 0.35/0.68 ( ( size_num @ ( bit0 @ X2 ) )
% 0.35/0.68 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % num.size_gen(2)
% 0.35/0.68 thf(fact_8717_take__bit__numeral__minus__bit1,axiom,
% 0.35/0.68 ! [L: num,K2: num] :
% 0.35/0.68 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 0.35/0.68 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_numeral_minus_bit1
% 0.35/0.68 thf(fact_8718_take__bit__Suc__minus__bit1,axiom,
% 0.35/0.68 ! [N: nat,K2: num] :
% 0.35/0.68 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 0.35/0.68 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_Suc_minus_bit1
% 0.35/0.68 thf(fact_8719_or__int__unfold,axiom,
% 0.35/0.68 ( bit_se1409905431419307370or_int
% 0.35/0.68 = ( ^ [K3: int,L2: int] :
% 0.35/0.68 ( if_int
% 0.35/0.68 @ ( ( K3
% 0.35/0.68 = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.68 | ( L2
% 0.35/0.68 = ( uminus_uminus_int @ one_one_int ) ) )
% 0.35/0.68 @ ( uminus_uminus_int @ one_one_int )
% 0.35/0.68 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_int_unfold
% 0.35/0.68 thf(fact_8720_arctan__half,axiom,
% 0.35/0.68 ( arctan
% 0.35/0.68 = ( ^ [X4: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X4 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % arctan_half
% 0.35/0.68 thf(fact_8721_real__sqrt__mult__self,axiom,
% 0.35/0.68 ! [A: real] :
% 0.35/0.68 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 0.35/0.68 = ( abs_abs_real @ A ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_sqrt_mult_self
% 0.35/0.68 thf(fact_8722_real__sqrt__abs2,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 0.35/0.68 = ( abs_abs_real @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_sqrt_abs2
% 0.35/0.68 thf(fact_8723_pred__numeral__inc,axiom,
% 0.35/0.68 ! [K2: num] :
% 0.35/0.68 ( ( pred_numeral @ ( inc @ K2 ) )
% 0.35/0.68 = ( numeral_numeral_nat @ K2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % pred_numeral_inc
% 0.35/0.68 thf(fact_8724_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 0.35/0.68 ! [X: real,Y: real,Xa2: real,Ya: real] :
% 0.35/0.68 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.68 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_sqrt_sum_squares_mult_squared_eq
% 0.35/0.68 thf(fact_8725_real__sqrt__mult,axiom,
% 0.35/0.68 ! [X: real,Y: real] :
% 0.35/0.68 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 0.35/0.68 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_sqrt_mult
% 0.35/0.68 thf(fact_8726_num__induct,axiom,
% 0.35/0.68 ! [P2: num > $o,X: num] :
% 0.35/0.68 ( ( P2 @ one )
% 0.35/0.68 => ( ! [X3: num] :
% 0.35/0.68 ( ( P2 @ X3 )
% 0.35/0.68 => ( P2 @ ( inc @ X3 ) ) )
% 0.35/0.68 => ( P2 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % num_induct
% 0.35/0.68 thf(fact_8727_add__inc,axiom,
% 0.35/0.68 ! [X: num,Y: num] :
% 0.35/0.68 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 0.35/0.68 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % add_inc
% 0.35/0.68 thf(fact_8728_inc_Osimps_I1_J,axiom,
% 0.35/0.68 ( ( inc @ one )
% 0.35/0.68 = ( bit0 @ one ) ) ).
% 0.35/0.68
% 0.35/0.68 % inc.simps(1)
% 0.35/0.68 thf(fact_8729_inc_Osimps_I2_J,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( inc @ ( bit0 @ X ) )
% 0.35/0.68 = ( bit1 @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % inc.simps(2)
% 0.35/0.68 thf(fact_8730_inc_Osimps_I3_J,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( inc @ ( bit1 @ X ) )
% 0.35/0.68 = ( bit0 @ ( inc @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % inc.simps(3)
% 0.35/0.68 thf(fact_8731_add__One,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( plus_plus_num @ X @ one )
% 0.35/0.68 = ( inc @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % add_One
% 0.35/0.68 thf(fact_8732_le__real__sqrt__sumsq,axiom,
% 0.35/0.68 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % le_real_sqrt_sumsq
% 0.35/0.68 thf(fact_8733_inc__BitM__eq,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ( ( inc @ ( bitM @ N ) )
% 0.35/0.68 = ( bit0 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % inc_BitM_eq
% 0.35/0.68 thf(fact_8734_BitM__inc__eq,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ( ( bitM @ ( inc @ N ) )
% 0.35/0.68 = ( bit1 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % BitM_inc_eq
% 0.35/0.68 thf(fact_8735_mult__inc,axiom,
% 0.35/0.68 ! [X: num,Y: num] :
% 0.35/0.68 ( ( times_times_num @ X @ ( inc @ Y ) )
% 0.35/0.68 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % mult_inc
% 0.35/0.68 thf(fact_8736_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 0.35/0.68 ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_sqrt_sum_squares_mult_ge_zero
% 0.35/0.68 thf(fact_8737_arith__geo__mean__sqrt,axiom,
% 0.35/0.68 ! [X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.68 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % arith_geo_mean_sqrt
% 0.35/0.68 thf(fact_8738_or__int__rec,axiom,
% 0.35/0.68 ( bit_se1409905431419307370or_int
% 0.35/0.68 = ( ^ [K3: int,L2: int] :
% 0.35/0.68 ( plus_plus_int
% 0.35/0.68 @ ( zero_n2684676970156552555ol_int
% 0.35/0.68 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 0.35/0.68 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 0.35/0.68 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_int_rec
% 0.35/0.68 thf(fact_8739_signed__take__bit__eq__take__bit__minus,axiom,
% 0.35/0.68 ( bit_ri631733984087533419it_int
% 0.35/0.68 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % signed_take_bit_eq_take_bit_minus
% 0.35/0.68 thf(fact_8740_cis__2pi,axiom,
% 0.35/0.68 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 0.35/0.68 = one_one_complex ) ).
% 0.35/0.68
% 0.35/0.68 % cis_2pi
% 0.35/0.68 thf(fact_8741_take__bit__Suc__from__most,axiom,
% 0.35/0.68 ! [N: nat,K2: int] :
% 0.35/0.68 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K2 )
% 0.35/0.68 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_Suc_from_most
% 0.35/0.68 thf(fact_8742_pi__def,axiom,
% 0.35/0.68 ( pi
% 0.35/0.68 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 0.35/0.68 @ ( the_real
% 0.35/0.68 @ ^ [X4: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 0.35/0.68 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 0.35/0.68 & ( ( cos_real @ X4 )
% 0.35/0.68 = zero_zero_real ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % pi_def
% 0.35/0.68 thf(fact_8743_or__nat__numerals_I4_J,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_nat_numerals(4)
% 0.35/0.68 thf(fact_8744_or__nat__numerals_I2_J,axiom,
% 0.35/0.68 ! [Y: num] :
% 0.35/0.68 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_nat_numerals(2)
% 0.35/0.68 thf(fact_8745_or__nat__numerals_I1_J,axiom,
% 0.35/0.68 ! [Y: num] :
% 0.35/0.68 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_nat_numerals(1)
% 0.35/0.68 thf(fact_8746_or__nat__numerals_I3_J,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_nat_numerals(3)
% 0.35/0.68 thf(fact_8747_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 0.35/0.68 ! [W2: num,N: nat] :
% 0.35/0.68 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( suc @ N ) )
% 0.35/0.68 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % bit_minus_numeral_Bit0_Suc_iff
% 0.35/0.68 thf(fact_8748_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 0.35/0.68 ! [W2: num,N: nat] :
% 0.35/0.68 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( suc @ N ) )
% 0.35/0.68 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bit_minus_numeral_Bit1_Suc_iff
% 0.35/0.68 thf(fact_8749_cis__mult,axiom,
% 0.35/0.68 ! [A: real,B: real] :
% 0.35/0.68 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 0.35/0.68 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % cis_mult
% 0.35/0.68 thf(fact_8750_DeMoivre,axiom,
% 0.35/0.68 ! [A: real,N: nat] :
% 0.35/0.68 ( ( power_power_complex @ ( cis @ A ) @ N )
% 0.35/0.68 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DeMoivre
% 0.35/0.68 thf(fact_8751_bit__concat__bit__iff,axiom,
% 0.35/0.68 ! [M2: nat,K2: int,L: int,N: nat] :
% 0.35/0.68 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M2 @ K2 @ L ) @ N )
% 0.35/0.68 = ( ( ( ord_less_nat @ N @ M2 )
% 0.35/0.68 & ( bit_se1146084159140164899it_int @ K2 @ N ) )
% 0.35/0.68 | ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bit_concat_bit_iff
% 0.35/0.68 thf(fact_8752_int__bit__bound,axiom,
% 0.35/0.68 ! [K2: int] :
% 0.35/0.68 ~ ! [N3: nat] :
% 0.35/0.68 ( ! [M3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ N3 @ M3 )
% 0.35/0.68 => ( ( bit_se1146084159140164899it_int @ K2 @ M3 )
% 0.35/0.68 = ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) )
% 0.35/0.68 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 0.35/0.68 => ( ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 0.35/0.68 = ( ~ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % int_bit_bound
% 0.35/0.68 thf(fact_8753_set__bit__eq,axiom,
% 0.35/0.68 ( bit_se7879613467334960850it_int
% 0.35/0.68 = ( ^ [N4: nat,K3: int] :
% 0.35/0.68 ( plus_plus_int @ K3
% 0.35/0.68 @ ( times_times_int
% 0.35/0.68 @ ( zero_n2684676970156552555ol_int
% 0.35/0.68 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N4 ) )
% 0.35/0.68 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % set_bit_eq
% 0.35/0.68 thf(fact_8754_unset__bit__eq,axiom,
% 0.35/0.68 ( bit_se4203085406695923979it_int
% 0.35/0.68 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % unset_bit_eq
% 0.35/0.68 thf(fact_8755_or__Suc__0__eq,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_Suc_0_eq
% 0.35/0.68 thf(fact_8756_Suc__0__or__eq,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.68 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_0_or_eq
% 0.35/0.68 thf(fact_8757_or__nat__rec,axiom,
% 0.35/0.68 ( bit_se1412395901928357646or_nat
% 0.35/0.68 = ( ^ [M6: nat,N4: nat] :
% 0.35/0.68 ( plus_plus_nat
% 0.35/0.68 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 0.35/0.68 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.35/0.68 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_nat_rec
% 0.35/0.68 thf(fact_8758_or__nat__unfold,axiom,
% 0.35/0.68 ( bit_se1412395901928357646or_nat
% 0.35/0.68 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_nat_unfold
% 0.35/0.68 thf(fact_8759_bij__betw__roots__unity,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( bij_betw_nat_complex
% 0.35/0.68 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N )
% 0.35/0.68 @ ( collect_complex
% 0.35/0.68 @ ^ [Z4: complex] :
% 0.35/0.68 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.68 = one_one_complex ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bij_betw_roots_unity
% 0.35/0.68 thf(fact_8760_cis__multiple__2pi,axiom,
% 0.35/0.68 ! [N: real] :
% 0.35/0.68 ( ( member_real @ N @ ring_1_Ints_real )
% 0.35/0.68 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.35/0.68 = one_one_complex ) ) ).
% 0.35/0.68
% 0.35/0.68 % cis_multiple_2pi
% 0.35/0.68 thf(fact_8761_not__bit__Suc__0__Suc,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % not_bit_Suc_0_Suc
% 0.35/0.68 thf(fact_8762_bit__Suc__0__iff,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.68 = ( N = zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % bit_Suc_0_iff
% 0.35/0.68 thf(fact_8763_not__bit__Suc__0__numeral,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % not_bit_Suc_0_numeral
% 0.35/0.68 thf(fact_8764_sin__times__pi__eq__0,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % sin_times_pi_eq_0
% 0.35/0.68 thf(fact_8765_sin__integer__2pi,axiom,
% 0.35/0.68 ! [N: real] :
% 0.35/0.68 ( ( member_real @ N @ ring_1_Ints_real )
% 0.35/0.68 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.35/0.68 = zero_zero_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % sin_integer_2pi
% 0.35/0.68 thf(fact_8766_cos__integer__2pi,axiom,
% 0.35/0.68 ! [N: real] :
% 0.35/0.68 ( ( member_real @ N @ ring_1_Ints_real )
% 0.35/0.68 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 0.35/0.68 = one_one_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % cos_integer_2pi
% 0.35/0.68 thf(fact_8767_i__even__power,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % i_even_power
% 0.35/0.68 thf(fact_8768_Suc__0__xor__eq,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.68 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.68 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_0_xor_eq
% 0.35/0.68 thf(fact_8769_xor__Suc__0__eq,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.68 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_Suc_0_eq
% 0.35/0.68 thf(fact_8770_horner__sum__of__bool__2__less,axiom,
% 0.35/0.68 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % horner_sum_of_bool_2_less
% 0.35/0.68 thf(fact_8771_complex__i__mult__minus,axiom,
% 0.35/0.68 ! [X: complex] :
% 0.35/0.68 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 0.35/0.68 = ( uminus1482373934393186551omplex @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_i_mult_minus
% 0.35/0.68 thf(fact_8772_divide__numeral__i,axiom,
% 0.35/0.68 ! [Z3: complex,N: num] :
% 0.35/0.68 ( ( divide1717551699836669952omplex @ Z3 @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 0.35/0.68 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z3 ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % divide_numeral_i
% 0.35/0.68 thf(fact_8773_divide__i,axiom,
% 0.35/0.68 ! [X: complex] :
% 0.35/0.68 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 0.35/0.68 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % divide_i
% 0.35/0.68 thf(fact_8774_i__squared,axiom,
% 0.35/0.68 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 0.35/0.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.68
% 0.35/0.68 % i_squared
% 0.35/0.68 thf(fact_8775_xor__nat__numerals_I1_J,axiom,
% 0.35/0.68 ! [Y: num] :
% 0.35/0.68 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_nat_numerals(1)
% 0.35/0.68 thf(fact_8776_xor__nat__numerals_I2_J,axiom,
% 0.35/0.68 ! [Y: num] :
% 0.35/0.68 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_nat_numerals(2)
% 0.35/0.68 thf(fact_8777_xor__nat__numerals_I3_J,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_nat_numerals(3)
% 0.35/0.68 thf(fact_8778_xor__nat__numerals_I4_J,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_nat_numerals(4)
% 0.35/0.68 thf(fact_8779_i__times__eq__iff,axiom,
% 0.35/0.68 ! [W2: complex,Z3: complex] :
% 0.35/0.68 ( ( ( times_times_complex @ imaginary_unit @ W2 )
% 0.35/0.68 = Z3 )
% 0.35/0.68 = ( W2
% 0.35/0.68 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % i_times_eq_iff
% 0.35/0.68 thf(fact_8780_i__mult__Complex,axiom,
% 0.35/0.68 ! [A: real,B: real] :
% 0.35/0.68 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 0.35/0.68 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.35/0.68
% 0.35/0.68 % i_mult_Complex
% 0.35/0.68 thf(fact_8781_Complex__mult__i,axiom,
% 0.35/0.68 ! [A: real,B: real] :
% 0.35/0.68 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 0.35/0.68 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 0.35/0.68
% 0.35/0.68 % Complex_mult_i
% 0.35/0.68 thf(fact_8782_xor__nat__unfold,axiom,
% 0.35/0.68 ( bit_se6528837805403552850or_nat
% 0.35/0.68 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_nat_unfold
% 0.35/0.68 thf(fact_8783_xor__nat__rec,axiom,
% 0.35/0.68 ( bit_se6528837805403552850or_nat
% 0.35/0.68 = ( ^ [M6: nat,N4: nat] :
% 0.35/0.68 ( plus_plus_nat
% 0.35/0.68 @ ( zero_n2687167440665602831ol_nat
% 0.35/0.68 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 0.35/0.68 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 0.35/0.68 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_nat_rec
% 0.35/0.68 thf(fact_8784_Sum__Ico__nat,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( groups3542108847815614940at_nat
% 0.35/0.68 @ ^ [X4: nat] : X4
% 0.35/0.68 @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 0.35/0.68 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Sum_Ico_nat
% 0.35/0.68 thf(fact_8785_Least__eq__0,axiom,
% 0.35/0.68 ! [P2: nat > $o] :
% 0.35/0.68 ( ( P2 @ zero_zero_nat )
% 0.35/0.68 => ( ( ord_Least_nat @ P2 )
% 0.35/0.68 = zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % Least_eq_0
% 0.35/0.68 thf(fact_8786_finite__atLeastLessThan,axiom,
% 0.35/0.68 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_atLeastLessThan
% 0.35/0.68 thf(fact_8787_card__atLeastLessThan,axiom,
% 0.35/0.68 ! [L: nat,U: nat] :
% 0.35/0.68 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 0.35/0.68 = ( minus_minus_nat @ U @ L ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_atLeastLessThan
% 0.35/0.68 thf(fact_8788_atLeastLessThan__singleton,axiom,
% 0.35/0.68 ! [M2: nat] :
% 0.35/0.68 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 0.35/0.68 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastLessThan_singleton
% 0.35/0.68 thf(fact_8789_all__nat__less__eq,axiom,
% 0.35/0.68 ! [N: nat,P2: nat > $o] :
% 0.35/0.68 ( ( ! [M6: nat] :
% 0.35/0.68 ( ( ord_less_nat @ M6 @ N )
% 0.35/0.68 => ( P2 @ M6 ) ) )
% 0.35/0.68 = ( ! [X4: nat] :
% 0.35/0.68 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68 => ( P2 @ X4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % all_nat_less_eq
% 0.35/0.68 thf(fact_8790_ex__nat__less__eq,axiom,
% 0.35/0.68 ! [N: nat,P2: nat > $o] :
% 0.35/0.68 ( ( ? [M6: nat] :
% 0.35/0.68 ( ( ord_less_nat @ M6 @ N )
% 0.35/0.68 & ( P2 @ M6 ) ) )
% 0.35/0.68 = ( ? [X4: nat] :
% 0.35/0.68 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68 & ( P2 @ X4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % ex_nat_less_eq
% 0.35/0.68 thf(fact_8791_atLeastLessThanSuc__atLeastAtMost,axiom,
% 0.35/0.68 ! [L: nat,U: nat] :
% 0.35/0.68 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 0.35/0.68 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastLessThanSuc_atLeastAtMost
% 0.35/0.68 thf(fact_8792_lessThan__atLeast0,axiom,
% 0.35/0.68 ( set_ord_lessThan_nat
% 0.35/0.68 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % lessThan_atLeast0
% 0.35/0.68 thf(fact_8793_atLeastLessThan0,axiom,
% 0.35/0.68 ! [M2: nat] :
% 0.35/0.68 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 0.35/0.68 = bot_bot_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastLessThan0
% 0.35/0.68 thf(fact_8794_Least__Suc2,axiom,
% 0.35/0.68 ! [P2: nat > $o,N: nat,Q: nat > $o,M2: nat] :
% 0.35/0.68 ( ( P2 @ N )
% 0.35/0.68 => ( ( Q @ M2 )
% 0.35/0.68 => ( ~ ( P2 @ zero_zero_nat )
% 0.35/0.68 => ( ! [K: nat] :
% 0.35/0.68 ( ( P2 @ ( suc @ K ) )
% 0.35/0.68 = ( Q @ K ) )
% 0.35/0.68 => ( ( ord_Least_nat @ P2 )
% 0.35/0.68 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Least_Suc2
% 0.35/0.68 thf(fact_8795_Least__Suc,axiom,
% 0.35/0.68 ! [P2: nat > $o,N: nat] :
% 0.35/0.68 ( ( P2 @ N )
% 0.35/0.68 => ( ~ ( P2 @ zero_zero_nat )
% 0.35/0.68 => ( ( ord_Least_nat @ P2 )
% 0.35/0.68 = ( suc
% 0.35/0.68 @ ( ord_Least_nat
% 0.35/0.68 @ ^ [M6: nat] : ( P2 @ ( suc @ M6 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Least_Suc
% 0.35/0.68 thf(fact_8796_atLeast0__lessThan__Suc,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.68 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast0_lessThan_Suc
% 0.35/0.68 thf(fact_8797_subset__eq__atLeast0__lessThan__finite,axiom,
% 0.35/0.68 ! [N6: set_nat,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68 => ( finite_finite_nat @ N6 ) ) ).
% 0.35/0.68
% 0.35/0.68 % subset_eq_atLeast0_lessThan_finite
% 0.35/0.68 thf(fact_8798_subset__card__intvl__is__intvl,axiom,
% 0.35/0.68 ! [A4: set_nat,K2: nat] :
% 0.35/0.68 ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) )
% 0.35/0.68 => ( A4
% 0.35/0.68 = ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % subset_card_intvl_is_intvl
% 0.35/0.68 thf(fact_8799_atLeastLessThan__add__Un,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat,K2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.68 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 0.35/0.68 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) @ ( set_or4665077453230672383an_nat @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastLessThan_add_Un
% 0.35/0.68 thf(fact_8800_atLeastLessThanSuc,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 0.35/0.68 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 0.35/0.68 = bot_bot_set_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastLessThanSuc
% 0.35/0.68 thf(fact_8801_prod__Suc__Suc__fact,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 0.35/0.68 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % prod_Suc_Suc_fact
% 0.35/0.68 thf(fact_8802_prod__Suc__fact,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % prod_Suc_fact
% 0.35/0.68 thf(fact_8803_subset__eq__atLeast0__lessThan__card,axiom,
% 0.35/0.68 ! [N6: set_nat,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 0.35/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ N6 ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % subset_eq_atLeast0_lessThan_card
% 0.35/0.68 thf(fact_8804_card__sum__le__nat__sum,axiom,
% 0.35/0.68 ! [S3: set_nat] :
% 0.35/0.68 ( ord_less_eq_nat
% 0.35/0.68 @ ( groups3542108847815614940at_nat
% 0.35/0.68 @ ^ [X4: nat] : X4
% 0.35/0.68 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 0.35/0.68 @ ( groups3542108847815614940at_nat
% 0.35/0.68 @ ^ [X4: nat] : X4
% 0.35/0.68 @ S3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_sum_le_nat_sum
% 0.35/0.68 thf(fact_8805_atLeastLessThan__nat__numeral,axiom,
% 0.35/0.68 ! [M2: nat,K2: num] :
% 0.35/0.68 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K2 ) )
% 0.35/0.68 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.68 = ( insert_nat @ ( pred_numeral @ K2 ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K2 ) ) ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K2 ) )
% 0.35/0.68 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.68 = bot_bot_set_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastLessThan_nat_numeral
% 0.35/0.68 thf(fact_8806_atLeast1__lessThan__eq__remove0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 0.35/0.68 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast1_lessThan_eq_remove0
% 0.35/0.68 thf(fact_8807_xor__int__rec,axiom,
% 0.35/0.68 ( bit_se6526347334894502574or_int
% 0.35/0.68 = ( ^ [K3: int,L2: int] :
% 0.35/0.68 ( plus_plus_int
% 0.35/0.68 @ ( zero_n2684676970156552555ol_int
% 0.35/0.68 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 0.35/0.68 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 0.35/0.68 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_int_rec
% 0.35/0.68 thf(fact_8808_sum__power2,axiom,
% 0.35/0.68 ! [K2: nat] :
% 0.35/0.68 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K2 ) )
% 0.35/0.68 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) @ one_one_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % sum_power2
% 0.35/0.68 thf(fact_8809_Chebyshev__sum__upper__nat,axiom,
% 0.35/0.68 ! [N: nat,A: nat > nat,B: nat > nat] :
% 0.35/0.68 ( ! [I3: nat,J3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.35/0.68 => ( ( ord_less_nat @ J3 @ N )
% 0.35/0.68 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J3 ) ) ) )
% 0.35/0.68 => ( ! [I3: nat,J3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ I3 @ J3 )
% 0.35/0.68 => ( ( ord_less_nat @ J3 @ N )
% 0.35/0.68 => ( ord_less_eq_nat @ ( B @ J3 ) @ ( B @ I3 ) ) ) )
% 0.35/0.68 => ( ord_less_eq_nat
% 0.35/0.68 @ ( times_times_nat @ N
% 0.35/0.68 @ ( groups3542108847815614940at_nat
% 0.35/0.68 @ ^ [I: nat] : ( times_times_nat @ ( A @ I ) @ ( B @ I ) )
% 0.35/0.68 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 0.35/0.68 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Chebyshev_sum_upper_nat
% 0.35/0.68 thf(fact_8810_xor__int__unfold,axiom,
% 0.35/0.68 ( bit_se6526347334894502574or_int
% 0.35/0.68 = ( ^ [K3: int,L2: int] :
% 0.35/0.68 ( if_int
% 0.35/0.68 @ ( K3
% 0.35/0.68 = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.68 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 0.35/0.68 @ ( if_int
% 0.35/0.68 @ ( L2
% 0.35/0.68 = ( uminus_uminus_int @ one_one_int ) )
% 0.35/0.68 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 0.35/0.68 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % xor_int_unfold
% 0.35/0.68 thf(fact_8811_exp__two__pi__i_H,axiom,
% 0.35/0.68 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 = one_one_complex ) ).
% 0.35/0.68
% 0.35/0.68 % exp_two_pi_i'
% 0.35/0.68 thf(fact_8812_finite__atLeastLessThan__int,axiom,
% 0.35/0.68 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_atLeastLessThan_int
% 0.35/0.68 thf(fact_8813_card__atLeastLessThan__int,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 0.35/0.68 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_atLeastLessThan_int
% 0.35/0.68 thf(fact_8814_exp__pi__i_H,axiom,
% 0.35/0.68 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 0.35/0.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.68
% 0.35/0.68 % exp_pi_i'
% 0.35/0.68 thf(fact_8815_exp__pi__i,axiom,
% 0.35/0.68 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 0.35/0.68 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 0.35/0.68
% 0.35/0.68 % exp_pi_i
% 0.35/0.68 thf(fact_8816_exp__two__pi__i,axiom,
% 0.35/0.68 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 0.35/0.68 = one_one_complex ) ).
% 0.35/0.68
% 0.35/0.68 % exp_two_pi_i
% 0.35/0.68 thf(fact_8817_complex__exp__exists,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ? [A3: complex,R4: real] :
% 0.35/0.68 ( Z3
% 0.35/0.68 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) @ ( exp_complex @ A3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_exp_exists
% 0.35/0.68 thf(fact_8818_finite__atLeastZeroLessThan__int,axiom,
% 0.35/0.68 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_atLeastZeroLessThan_int
% 0.35/0.68 thf(fact_8819_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 0.35/0.68 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastLessThanPlusOne_atLeastAtMost_int
% 0.35/0.68 thf(fact_8820_Complex__mult__complex__of__real,axiom,
% 0.35/0.68 ! [X: real,Y: real,R3: real] :
% 0.35/0.68 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R3 ) )
% 0.35/0.68 = ( complex2 @ ( times_times_real @ X @ R3 ) @ ( times_times_real @ Y @ R3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Complex_mult_complex_of_real
% 0.35/0.68 thf(fact_8821_complex__of__real__mult__Complex,axiom,
% 0.35/0.68 ! [R3: real,X: real,Y: real] :
% 0.35/0.68 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( complex2 @ X @ Y ) )
% 0.35/0.68 = ( complex2 @ ( times_times_real @ R3 @ X ) @ ( times_times_real @ R3 @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_of_real_mult_Complex
% 0.35/0.68 thf(fact_8822_Complex__eq,axiom,
% 0.35/0.68 ( complex2
% 0.35/0.68 = ( ^ [A5: real,B4: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A5 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Complex_eq
% 0.35/0.68 thf(fact_8823_cis__conv__exp,axiom,
% 0.35/0.68 ( cis
% 0.35/0.68 = ( ^ [B4: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % cis_conv_exp
% 0.35/0.68 thf(fact_8824_card__atLeastZeroLessThan__int,axiom,
% 0.35/0.68 ! [U: int] :
% 0.35/0.68 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 0.35/0.68 = ( nat2 @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_atLeastZeroLessThan_int
% 0.35/0.68 thf(fact_8825_complex__of__real__i,axiom,
% 0.35/0.68 ! [R3: real] :
% 0.35/0.68 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ imaginary_unit )
% 0.35/0.68 = ( complex2 @ zero_zero_real @ R3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_of_real_i
% 0.35/0.68 thf(fact_8826_i__complex__of__real,axiom,
% 0.35/0.68 ! [R3: real] :
% 0.35/0.68 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R3 ) )
% 0.35/0.68 = ( complex2 @ zero_zero_real @ R3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % i_complex_of_real
% 0.35/0.68 thf(fact_8827_complex__split__polar,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ? [R4: real,A3: real] :
% 0.35/0.68 ( Z3
% 0.35/0.68 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_split_polar
% 0.35/0.68 thf(fact_8828_and__not__numerals_I5_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % and_not_numerals(5)
% 0.35/0.68 thf(fact_8829_and__not__numerals_I6_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % and_not_numerals(6)
% 0.35/0.68 thf(fact_8830_and__not__numerals_I9_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % and_not_numerals(9)
% 0.35/0.68 thf(fact_8831_or__not__numerals_I6_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_not_numerals(6)
% 0.35/0.68 thf(fact_8832_cmod__unit__one,axiom,
% 0.35/0.68 ! [A: real] :
% 0.35/0.68 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 0.35/0.68 = one_one_real ) ).
% 0.35/0.68
% 0.35/0.68 % cmod_unit_one
% 0.35/0.68 thf(fact_8833_cmod__complex__polar,axiom,
% 0.35/0.68 ! [R3: real,A: real] :
% 0.35/0.68 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 0.35/0.68 = ( abs_abs_real @ R3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % cmod_complex_polar
% 0.35/0.68 thf(fact_8834_or__not__numerals_I5_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_not_numerals(5)
% 0.35/0.68 thf(fact_8835_and__not__numerals_I8_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % and_not_numerals(8)
% 0.35/0.68 thf(fact_8836_or__not__numerals_I8_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 0.35/0.68 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_not_numerals(8)
% 0.35/0.68 thf(fact_8837_or__not__numerals_I9_J,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 0.35/0.68 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % or_not_numerals(9)
% 0.35/0.68 thf(fact_8838_not__int__rec,axiom,
% 0.35/0.68 ( bit_ri7919022796975470100ot_int
% 0.35/0.68 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % not_int_rec
% 0.35/0.68 thf(fact_8839_Cauchy__iff2,axiom,
% 0.35/0.68 ( topolo4055970368930404560y_real
% 0.35/0.68 = ( ^ [X7: nat > real] :
% 0.35/0.68 ! [J: nat] :
% 0.35/0.68 ? [M9: nat] :
% 0.35/0.68 ! [M6: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ M9 @ M6 )
% 0.35/0.68 => ! [N4: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ M9 @ N4 )
% 0.35/0.68 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X7 @ M6 ) @ ( X7 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Cauchy_iff2
% 0.35/0.68 thf(fact_8840_VEBT_Osize__gen_I1_J,axiom,
% 0.35/0.68 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.35/0.68 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.35/0.68 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT.size_gen(1)
% 0.35/0.68 thf(fact_8841_VEBT_Osize_I3_J,axiom,
% 0.35/0.68 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 0.35/0.68 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 0.35/0.68 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT.size(3)
% 0.35/0.68 thf(fact_8842_divmod__step__integer__def,axiom,
% 0.35/0.68 ( unique4921790084139445826nteger
% 0.35/0.68 = ( ^ [L2: num] :
% 0.35/0.68 ( produc6916734918728496179nteger
% 0.35/0.68 @ ^ [Q5: code_integer,R: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % divmod_step_integer_def
% 0.35/0.68 thf(fact_8843_complex__div__cnj,axiom,
% 0.35/0.68 ( divide1717551699836669952omplex
% 0.35/0.68 = ( ^ [A5: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A5 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_div_cnj
% 0.35/0.68 thf(fact_8844_list__decode_Opsimps_I2_J,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 0.35/0.68 => ( ( nat_list_decode @ ( suc @ N ) )
% 0.35/0.68 = ( produc2761476792215241774st_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 0.35/0.68 @ ( nat_prod_decode @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode.psimps(2)
% 0.35/0.68 thf(fact_8845_complex__cnj__mult,axiom,
% 0.35/0.68 ! [X: complex,Y: complex] :
% 0.35/0.68 ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 0.35/0.68 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_cnj_mult
% 0.35/0.68 thf(fact_8846_list__decode__eq,axiom,
% 0.35/0.68 ! [X: nat,Y: nat] :
% 0.35/0.68 ( ( ( nat_list_decode @ X )
% 0.35/0.68 = ( nat_list_decode @ Y ) )
% 0.35/0.68 = ( X = Y ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode_eq
% 0.35/0.68 thf(fact_8847_times__integer__code_I1_J,axiom,
% 0.35/0.68 ! [K2: code_integer] :
% 0.35/0.68 ( ( times_3573771949741848930nteger @ K2 @ zero_z3403309356797280102nteger )
% 0.35/0.68 = zero_z3403309356797280102nteger ) ).
% 0.35/0.68
% 0.35/0.68 % times_integer_code(1)
% 0.35/0.68 thf(fact_8848_times__integer__code_I2_J,axiom,
% 0.35/0.68 ! [L: code_integer] :
% 0.35/0.68 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 0.35/0.68 = zero_z3403309356797280102nteger ) ).
% 0.35/0.68
% 0.35/0.68 % times_integer_code(2)
% 0.35/0.68 thf(fact_8849_zero__natural_Orsp,axiom,
% 0.35/0.68 zero_zero_nat = zero_zero_nat ).
% 0.35/0.68
% 0.35/0.68 % zero_natural.rsp
% 0.35/0.68 thf(fact_8850_list__decode_Osimps_I2_J,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( nat_list_decode @ ( suc @ N ) )
% 0.35/0.68 = ( produc2761476792215241774st_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 0.35/0.68 @ ( nat_prod_decode @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode.simps(2)
% 0.35/0.68 thf(fact_8851_complex__mod__mult__cnj,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) )
% 0.35/0.68 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_mod_mult_cnj
% 0.35/0.68 thf(fact_8852_complex__norm__square,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68 = ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_norm_square
% 0.35/0.68 thf(fact_8853_integer__of__int__code,axiom,
% 0.35/0.68 ( code_integer_of_int
% 0.35/0.68 = ( ^ [K3: int] :
% 0.35/0.68 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 0.35/0.68 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 0.35/0.68 @ ( if_Code_integer
% 0.35/0.68 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 0.35/0.68 = zero_zero_int )
% 0.35/0.68 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % integer_of_int_code
% 0.35/0.68 thf(fact_8854_list__decode_Opelims,axiom,
% 0.35/0.68 ! [X: nat,Y: list_nat] :
% 0.35/0.68 ( ( ( nat_list_decode @ X )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 0.35/0.68 => ( ( ( X = zero_zero_nat )
% 0.35/0.68 => ( ( Y = nil_nat )
% 0.35/0.68 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 0.35/0.68 => ~ ! [N3: nat] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( suc @ N3 ) )
% 0.35/0.68 => ( ( Y
% 0.35/0.68 = ( produc2761476792215241774st_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 0.35/0.68 @ ( nat_prod_decode @ N3 ) ) )
% 0.35/0.68 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode.pelims
% 0.35/0.68 thf(fact_8855_list__decode_Oelims,axiom,
% 0.35/0.68 ! [X: nat,Y: list_nat] :
% 0.35/0.68 ( ( ( nat_list_decode @ X )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( ( X = zero_zero_nat )
% 0.35/0.68 => ( Y != nil_nat ) )
% 0.35/0.68 => ~ ! [N3: nat] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( suc @ N3 ) )
% 0.35/0.68 => ( Y
% 0.35/0.68 != ( produc2761476792215241774st_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 0.35/0.68 @ ( nat_prod_decode @ N3 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode.elims
% 0.35/0.68 thf(fact_8856_cnj__add__mult__eq__Re,axiom,
% 0.35/0.68 ! [Z3: complex,W2: complex] :
% 0.35/0.68 ( ( plus_plus_complex @ ( times_times_complex @ Z3 @ ( cnj @ W2 ) ) @ ( times_times_complex @ ( cnj @ Z3 ) @ W2 ) )
% 0.35/0.68 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z3 @ ( cnj @ W2 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % cnj_add_mult_eq_Re
% 0.35/0.68 thf(fact_8857_list__encode_Ocases,axiom,
% 0.35/0.68 ! [X: list_nat] :
% 0.35/0.68 ( ( X != nil_nat )
% 0.35/0.68 => ~ ! [X3: nat,Xs3: list_nat] :
% 0.35/0.68 ( X
% 0.35/0.68 != ( cons_nat @ X3 @ Xs3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_encode.cases
% 0.35/0.68 thf(fact_8858_times__integer_Oabs__eq,axiom,
% 0.35/0.68 ! [Xa2: int,X: int] :
% 0.35/0.68 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 0.35/0.68 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_integer.abs_eq
% 0.35/0.68 thf(fact_8859_scaleR__complex_Osimps_I1_J,axiom,
% 0.35/0.68 ! [R3: real,X: complex] :
% 0.35/0.68 ( ( re @ ( real_V2046097035970521341omplex @ R3 @ X ) )
% 0.35/0.68 = ( times_times_real @ R3 @ ( re @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % scaleR_complex.simps(1)
% 0.35/0.68 thf(fact_8860_list__decode_Osimps_I1_J,axiom,
% 0.35/0.68 ( ( nat_list_decode @ zero_zero_nat )
% 0.35/0.68 = nil_nat ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode.simps(1)
% 0.35/0.68 thf(fact_8861_Re__complex__div__eq__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 0.35/0.68 = zero_zero_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_complex_div_eq_0
% 0.35/0.68 thf(fact_8862_complex__mod__sqrt__Re__mult__cnj,axiom,
% 0.35/0.68 ( real_V1022390504157884413omplex
% 0.35/0.68 = ( ^ [Z4: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z4 @ ( cnj @ Z4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_mod_sqrt_Re_mult_cnj
% 0.35/0.68 thf(fact_8863_Re__complex__div__gt__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_complex_div_gt_0
% 0.35/0.68 thf(fact_8864_Re__complex__div__lt__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_complex_div_lt_0
% 0.35/0.68 thf(fact_8865_Re__complex__div__le__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_complex_div_le_0
% 0.35/0.68 thf(fact_8866_Re__complex__div__ge__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_complex_div_ge_0
% 0.35/0.68 thf(fact_8867_list__decode_Opsimps_I1_J,axiom,
% 0.35/0.68 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 0.35/0.68 => ( ( nat_list_decode @ zero_zero_nat )
% 0.35/0.68 = nil_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode.psimps(1)
% 0.35/0.68 thf(fact_8868_cos__n__Re__cis__pow__n,axiom,
% 0.35/0.68 ! [N: nat,A: real] :
% 0.35/0.68 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.35/0.68 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % cos_n_Re_cis_pow_n
% 0.35/0.68 thf(fact_8869_complex__add__cnj,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( plus_plus_complex @ Z3 @ ( cnj @ Z3 ) )
% 0.35/0.68 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_add_cnj
% 0.35/0.68 thf(fact_8870_list__encode_Oelims,axiom,
% 0.35/0.68 ! [X: list_nat,Y: nat] :
% 0.35/0.68 ( ( ( nat_list_encode @ X )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( ( X = nil_nat )
% 0.35/0.68 => ( Y != zero_zero_nat ) )
% 0.35/0.68 => ~ ! [X3: nat,Xs3: list_nat] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( cons_nat @ X3 @ Xs3 ) )
% 0.35/0.68 => ( Y
% 0.35/0.68 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_encode.elims
% 0.35/0.68 thf(fact_8871_Complex__divide,axiom,
% 0.35/0.68 ( divide1717551699836669952omplex
% 0.35/0.68 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Complex_divide
% 0.35/0.68 thf(fact_8872_Re__Reals__divide,axiom,
% 0.35/0.68 ! [R3: complex,Z3: complex] :
% 0.35/0.68 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 0.35/0.68 => ( ( re @ ( divide1717551699836669952omplex @ R3 @ Z3 ) )
% 0.35/0.68 = ( divide_divide_real @ ( times_times_real @ ( re @ R3 ) @ ( re @ Z3 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_Reals_divide
% 0.35/0.68 thf(fact_8873_list__encode__inverse,axiom,
% 0.35/0.68 ! [X: list_nat] :
% 0.35/0.68 ( ( nat_list_decode @ ( nat_list_encode @ X ) )
% 0.35/0.68 = X ) ).
% 0.35/0.68
% 0.35/0.68 % list_encode_inverse
% 0.35/0.68 thf(fact_8874_list__decode__inverse,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( nat_list_encode @ ( nat_list_decode @ N ) )
% 0.35/0.68 = N ) ).
% 0.35/0.68
% 0.35/0.68 % list_decode_inverse
% 0.35/0.68 thf(fact_8875_complex__In__mult__cnj__zero,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( im @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) )
% 0.35/0.68 = zero_zero_real ) ).
% 0.35/0.68
% 0.35/0.68 % complex_In_mult_cnj_zero
% 0.35/0.68 thf(fact_8876_Im__i__times,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( im @ ( times_times_complex @ imaginary_unit @ Z3 ) )
% 0.35/0.68 = ( re @ Z3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_i_times
% 0.35/0.68 thf(fact_8877_real__eq__imaginary__iff,axiom,
% 0.35/0.68 ! [Y: complex,X: complex] :
% 0.35/0.68 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 0.35/0.68 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 0.35/0.68 => ( ( X
% 0.35/0.68 = ( times_times_complex @ imaginary_unit @ Y ) )
% 0.35/0.68 = ( ( X = zero_zero_complex )
% 0.35/0.68 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_eq_imaginary_iff
% 0.35/0.68 thf(fact_8878_imaginary__eq__real__iff,axiom,
% 0.35/0.68 ! [Y: complex,X: complex] :
% 0.35/0.68 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 0.35/0.68 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 0.35/0.68 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 0.35/0.68 = X )
% 0.35/0.68 = ( ( X = zero_zero_complex )
% 0.35/0.68 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % imaginary_eq_real_iff
% 0.35/0.68 thf(fact_8879_Re__i__times,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( re @ ( times_times_complex @ imaginary_unit @ Z3 ) )
% 0.35/0.68 = ( uminus_uminus_real @ ( im @ Z3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_i_times
% 0.35/0.68 thf(fact_8880_list__encode__eq,axiom,
% 0.35/0.68 ! [X: list_nat,Y: list_nat] :
% 0.35/0.68 ( ( ( nat_list_encode @ X )
% 0.35/0.68 = ( nat_list_encode @ Y ) )
% 0.35/0.68 = ( X = Y ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_encode_eq
% 0.35/0.68 thf(fact_8881_scaleR__complex_Osimps_I2_J,axiom,
% 0.35/0.68 ! [R3: real,X: complex] :
% 0.35/0.68 ( ( im @ ( real_V2046097035970521341omplex @ R3 @ X ) )
% 0.35/0.68 = ( times_times_real @ R3 @ ( im @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % scaleR_complex.simps(2)
% 0.35/0.68 thf(fact_8882_list__encode_Osimps_I1_J,axiom,
% 0.35/0.68 ( ( nat_list_encode @ nil_nat )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % list_encode.simps(1)
% 0.35/0.68 thf(fact_8883_times__complex_Osimps_I2_J,axiom,
% 0.35/0.68 ! [X: complex,Y: complex] :
% 0.35/0.68 ( ( im @ ( times_times_complex @ X @ Y ) )
% 0.35/0.68 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_complex.simps(2)
% 0.35/0.68 thf(fact_8884_times__complex_Osimps_I1_J,axiom,
% 0.35/0.68 ! [X: complex,Y: complex] :
% 0.35/0.68 ( ( re @ ( times_times_complex @ X @ Y ) )
% 0.35/0.68 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_complex.simps(1)
% 0.35/0.68 thf(fact_8885_Im__complex__div__eq__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 0.35/0.68 = zero_zero_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_complex_div_eq_0
% 0.35/0.68 thf(fact_8886_scaleR__complex_Ocode,axiom,
% 0.35/0.68 ( real_V2046097035970521341omplex
% 0.35/0.68 = ( ^ [R: real,X4: complex] : ( complex2 @ ( times_times_real @ R @ ( re @ X4 ) ) @ ( times_times_real @ R @ ( im @ X4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % scaleR_complex.code
% 0.35/0.68 thf(fact_8887_Im__Reals__divide,axiom,
% 0.35/0.68 ! [R3: complex,Z3: complex] :
% 0.35/0.68 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 0.35/0.68 => ( ( im @ ( divide1717551699836669952omplex @ R3 @ Z3 ) )
% 0.35/0.68 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R3 ) ) @ ( im @ Z3 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_Reals_divide
% 0.35/0.68 thf(fact_8888_Im__complex__div__lt__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_complex_div_lt_0
% 0.35/0.68 thf(fact_8889_Im__complex__div__gt__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_complex_div_gt_0
% 0.35/0.68 thf(fact_8890_Im__complex__div__ge__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_complex_div_ge_0
% 0.35/0.68 thf(fact_8891_Im__complex__div__le__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 0.35/0.68 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_complex_div_le_0
% 0.35/0.68 thf(fact_8892_sin__n__Im__cis__pow__n,axiom,
% 0.35/0.68 ! [N: nat,A: real] :
% 0.35/0.68 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 0.35/0.68 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sin_n_Im_cis_pow_n
% 0.35/0.68 thf(fact_8893_Re__exp,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( re @ ( exp_complex @ Z3 ) )
% 0.35/0.68 = ( times_times_real @ ( exp_real @ ( re @ Z3 ) ) @ ( cos_real @ ( im @ Z3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_exp
% 0.35/0.68 thf(fact_8894_Im__exp,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( im @ ( exp_complex @ Z3 ) )
% 0.35/0.68 = ( times_times_real @ ( exp_real @ ( re @ Z3 ) ) @ ( sin_real @ ( im @ Z3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_exp
% 0.35/0.68 thf(fact_8895_complex__eq,axiom,
% 0.35/0.68 ! [A: complex] :
% 0.35/0.68 ( A
% 0.35/0.68 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_eq
% 0.35/0.68 thf(fact_8896_times__complex_Ocode,axiom,
% 0.35/0.68 ( times_times_complex
% 0.35/0.68 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_complex.code
% 0.35/0.68 thf(fact_8897_complex__div__gt__0,axiom,
% 0.35/0.68 ! [A: complex,B: complex] :
% 0.35/0.68 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 0.35/0.68 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 0.35/0.68 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_div_gt_0
% 0.35/0.68 thf(fact_8898_exp__eq__polar,axiom,
% 0.35/0.68 ( exp_complex
% 0.35/0.68 = ( ^ [Z4: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z4 ) ) ) @ ( cis @ ( im @ Z4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % exp_eq_polar
% 0.35/0.68 thf(fact_8899_Im__power2,axiom,
% 0.35/0.68 ! [X: complex] :
% 0.35/0.68 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_power2
% 0.35/0.68 thf(fact_8900_list__encode_Osimps_I2_J,axiom,
% 0.35/0.68 ! [X: nat,Xs2: list_nat] :
% 0.35/0.68 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 0.35/0.68 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_encode.simps(2)
% 0.35/0.68 thf(fact_8901_complex__diff__cnj,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( minus_minus_complex @ Z3 @ ( cnj @ Z3 ) )
% 0.35/0.68 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z3 ) ) ) @ imaginary_unit ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_diff_cnj
% 0.35/0.68 thf(fact_8902_Re__divide,axiom,
% 0.35/0.68 ! [X: complex,Y: complex] :
% 0.35/0.68 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 0.35/0.68 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_divide
% 0.35/0.68 thf(fact_8903_complex__mult__cnj,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( times_times_complex @ Z3 @ ( cnj @ Z3 ) )
% 0.35/0.68 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_mult_cnj
% 0.35/0.68 thf(fact_8904_Im__divide,axiom,
% 0.35/0.68 ! [X: complex,Y: complex] :
% 0.35/0.68 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 0.35/0.68 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_divide
% 0.35/0.68 thf(fact_8905_complex__abs__le__norm,axiom,
% 0.35/0.68 ! [Z3: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z3 ) ) @ ( abs_abs_real @ ( im @ Z3 ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % complex_abs_le_norm
% 0.35/0.68 thf(fact_8906_csqrt_Ocode,axiom,
% 0.35/0.68 ( csqrt
% 0.35/0.68 = ( ^ [Z4: complex] :
% 0.35/0.68 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 0.35/0.68 @ ( times_times_real
% 0.35/0.68 @ ( if_real
% 0.35/0.68 @ ( ( im @ Z4 )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 @ one_one_real
% 0.35/0.68 @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 0.35/0.68 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % csqrt.code
% 0.35/0.68 thf(fact_8907_csqrt_Osimps_I2_J,axiom,
% 0.35/0.68 ! [Z3: complex] :
% 0.35/0.68 ( ( im @ ( csqrt @ Z3 ) )
% 0.35/0.68 = ( times_times_real
% 0.35/0.68 @ ( if_real
% 0.35/0.68 @ ( ( im @ Z3 )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 @ one_one_real
% 0.35/0.68 @ ( sgn_sgn_real @ ( im @ Z3 ) ) )
% 0.35/0.68 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % csqrt.simps(2)
% 0.35/0.68 thf(fact_8908_csqrt__of__real__nonpos,axiom,
% 0.35/0.68 ! [X: complex] :
% 0.35/0.68 ( ( ( im @ X )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 0.35/0.68 => ( ( csqrt @ X )
% 0.35/0.68 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % csqrt_of_real_nonpos
% 0.35/0.68 thf(fact_8909_csqrt__minus,axiom,
% 0.35/0.68 ! [X: complex] :
% 0.35/0.68 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 0.35/0.68 | ( ( ( im @ X )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 0.35/0.68 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 0.35/0.68 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % csqrt_minus
% 0.35/0.68 thf(fact_8910_bezw__0,axiom,
% 0.35/0.68 ! [X: nat] :
% 0.35/0.68 ( ( bezw @ X @ zero_zero_nat )
% 0.35/0.68 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezw_0
% 0.35/0.68 thf(fact_8911_push__bit__of__Suc__0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % push_bit_of_Suc_0
% 0.35/0.68 thf(fact_8912_nat_Odisc__eq__case_I1_J,axiom,
% 0.35/0.68 ! [Nat: nat] :
% 0.35/0.68 ( ( Nat = zero_zero_nat )
% 0.35/0.68 = ( case_nat_o @ $true
% 0.35/0.68 @ ^ [Uu3: nat] : $false
% 0.35/0.68 @ Nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat.disc_eq_case(1)
% 0.35/0.68 thf(fact_8913_nat_Odisc__eq__case_I2_J,axiom,
% 0.35/0.68 ! [Nat: nat] :
% 0.35/0.68 ( ( Nat != zero_zero_nat )
% 0.35/0.68 = ( case_nat_o @ $false
% 0.35/0.68 @ ^ [Uu3: nat] : $true
% 0.35/0.68 @ Nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat.disc_eq_case(2)
% 0.35/0.68 thf(fact_8914_bit__push__bit__iff__int,axiom,
% 0.35/0.68 ! [M2: nat,K2: int,N: nat] :
% 0.35/0.68 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M2 @ K2 ) @ N )
% 0.35/0.68 = ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 & ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bit_push_bit_iff_int
% 0.35/0.68 thf(fact_8915_bit__push__bit__iff__nat,axiom,
% 0.35/0.68 ! [M2: nat,Q2: nat,N: nat] :
% 0.35/0.68 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M2 @ Q2 ) @ N )
% 0.35/0.68 = ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bit_push_bit_iff_nat
% 0.35/0.68 thf(fact_8916_less__eq__nat_Osimps_I2_J,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 0.35/0.68 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M2 ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % less_eq_nat.simps(2)
% 0.35/0.68 thf(fact_8917_max__Suc2,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_max_nat @ M2 @ ( suc @ N ) )
% 0.35/0.68 = ( case_nat_nat @ ( suc @ N )
% 0.35/0.68 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ M7 @ N ) )
% 0.35/0.68 @ M2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % max_Suc2
% 0.35/0.68 thf(fact_8918_max__Suc1,axiom,
% 0.35/0.68 ! [N: nat,M2: nat] :
% 0.35/0.68 ( ( ord_max_nat @ ( suc @ N ) @ M2 )
% 0.35/0.68 = ( case_nat_nat @ ( suc @ N )
% 0.35/0.68 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ N @ M7 ) )
% 0.35/0.68 @ M2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % max_Suc1
% 0.35/0.68 thf(fact_8919_diff__Suc,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 0.35/0.68 = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68 @ ^ [K3: nat] : K3
% 0.35/0.68 @ ( minus_minus_nat @ M2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % diff_Suc
% 0.35/0.68 thf(fact_8920_push__bit__nat__def,axiom,
% 0.35/0.68 ( bit_se547839408752420682it_nat
% 0.35/0.68 = ( ^ [N4: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % push_bit_nat_def
% 0.35/0.68 thf(fact_8921_push__bit__int__def,axiom,
% 0.35/0.68 ( bit_se545348938243370406it_int
% 0.35/0.68 = ( ^ [N4: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % push_bit_int_def
% 0.35/0.68 thf(fact_8922_pred__def,axiom,
% 0.35/0.68 ( pred
% 0.35/0.68 = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68 @ ^ [X24: nat] : X24 ) ) ).
% 0.35/0.68
% 0.35/0.68 % pred_def
% 0.35/0.68 thf(fact_8923_Suc__0__mod__numeral,axiom,
% 0.35/0.68 ! [K2: num] :
% 0.35/0.68 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.68 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_0_mod_numeral
% 0.35/0.68 thf(fact_8924_Suc__0__div__numeral,axiom,
% 0.35/0.68 ! [K2: num] :
% 0.35/0.68 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.68 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_0_div_numeral
% 0.35/0.68 thf(fact_8925_nat__of__integer__code,axiom,
% 0.35/0.68 ( code_nat_of_integer
% 0.35/0.68 = ( ^ [K3: code_integer] :
% 0.35/0.68 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 0.35/0.68 @ ( produc1555791787009142072er_nat
% 0.35/0.68 @ ^ [L2: code_integer,J: code_integer] : ( if_nat @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 0.35/0.68 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_of_integer_code
% 0.35/0.68 thf(fact_8926_drop__bit__of__Suc__0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % drop_bit_of_Suc_0
% 0.35/0.68 thf(fact_8927_drop__bit__Suc__minus__bit0,axiom,
% 0.35/0.68 ! [N: nat,K2: num] :
% 0.35/0.68 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 0.35/0.68 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % drop_bit_Suc_minus_bit0
% 0.35/0.68 thf(fact_8928_fst__divmod__nat,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( product_fst_nat_nat @ ( divmod_nat @ M2 @ N ) )
% 0.35/0.68 = ( divide_divide_nat @ M2 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % fst_divmod_nat
% 0.35/0.68 thf(fact_8929_nat__of__integer__non__positive,axiom,
% 0.35/0.68 ! [K2: code_integer] :
% 0.35/0.68 ( ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger )
% 0.35/0.68 => ( ( code_nat_of_integer @ K2 )
% 0.35/0.68 = zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_of_integer_non_positive
% 0.35/0.68 thf(fact_8930_snd__divmod__nat,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( product_snd_nat_nat @ ( divmod_nat @ M2 @ N ) )
% 0.35/0.68 = ( modulo_modulo_nat @ M2 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % snd_divmod_nat
% 0.35/0.68 thf(fact_8931_drop__bit__Suc__minus__bit1,axiom,
% 0.35/0.68 ! [N: nat,K2: num] :
% 0.35/0.68 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 0.35/0.68 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % drop_bit_Suc_minus_bit1
% 0.35/0.68 thf(fact_8932_nat__of__integer__code__post_I1_J,axiom,
% 0.35/0.68 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % nat_of_integer_code_post(1)
% 0.35/0.68 thf(fact_8933_int__of__integer__code,axiom,
% 0.35/0.68 ( code_int_of_integer
% 0.35/0.68 = ( ^ [K3: code_integer] :
% 0.35/0.68 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 0.35/0.68 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 0.35/0.68 @ ( produc1553301316500091796er_int
% 0.35/0.68 @ ^ [L2: code_integer,J: code_integer] : ( if_int @ ( J = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 0.35/0.68 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % int_of_integer_code
% 0.35/0.68 thf(fact_8934_times__integer_Orep__eq,axiom,
% 0.35/0.68 ! [X: code_integer,Xa2: code_integer] :
% 0.35/0.68 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 0.35/0.68 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_integer.rep_eq
% 0.35/0.68 thf(fact_8935_bezw__non__0,axiom,
% 0.35/0.68 ! [Y: nat,X: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 0.35/0.68 => ( ( bezw @ X @ Y )
% 0.35/0.68 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezw_non_0
% 0.35/0.68 thf(fact_8936_bezw_Oelims,axiom,
% 0.35/0.68 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 0.35/0.68 ( ( ( bezw @ X @ Xa2 )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.35/0.68 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezw.elims
% 0.35/0.68 thf(fact_8937_bezw_Osimps,axiom,
% 0.35/0.68 ( bezw
% 0.35/0.68 = ( ^ [X4: nat,Y4: nat] : ( if_Pro3027730157355071871nt_int @ ( Y4 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y4 ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezw.simps
% 0.35/0.68 thf(fact_8938_one__mod__minus__numeral,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % one_mod_minus_numeral
% 0.35/0.68 thf(fact_8939_minus__one__mod__numeral,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % minus_one_mod_numeral
% 0.35/0.68 thf(fact_8940_numeral__mod__minus__numeral,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 0.35/0.68 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % numeral_mod_minus_numeral
% 0.35/0.68 thf(fact_8941_minus__numeral__mod__numeral,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 0.35/0.68 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % minus_numeral_mod_numeral
% 0.35/0.68 thf(fact_8942_Divides_Oadjust__mod__def,axiom,
% 0.35/0.68 ( adjust_mod
% 0.35/0.68 = ( ^ [L2: int,R: int] : ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Divides.adjust_mod_def
% 0.35/0.68 thf(fact_8943_bezw_Opelims,axiom,
% 0.35/0.68 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 0.35/0.68 ( ( ( bezw @ X @ Xa2 )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.35/0.68 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 0.35/0.68 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 0.35/0.68 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezw.pelims
% 0.35/0.68 thf(fact_8944_card__greaterThanLessThan__int,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 0.35/0.68 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_greaterThanLessThan_int
% 0.35/0.68 thf(fact_8945_finite__greaterThanLessThan__int,axiom,
% 0.35/0.68 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_greaterThanLessThan_int
% 0.35/0.68 thf(fact_8946_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.35/0.68 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 0.35/0.68 thf(fact_8947_prod__decode__aux_Opelims,axiom,
% 0.35/0.68 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 0.35/0.68 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.35/0.68 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 0.35/0.68 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % prod_decode_aux.pelims
% 0.35/0.68 thf(fact_8948_finite__greaterThanLessThan,axiom,
% 0.35/0.68 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_greaterThanLessThan
% 0.35/0.68 thf(fact_8949_Suc__funpow,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( compow_nat_nat @ N @ suc )
% 0.35/0.68 = ( plus_plus_nat @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % Suc_funpow
% 0.35/0.68 thf(fact_8950_card__greaterThanLessThan,axiom,
% 0.35/0.68 ! [L: nat,U: nat] :
% 0.35/0.68 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 0.35/0.68 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_greaterThanLessThan
% 0.35/0.68 thf(fact_8951_atLeastSucLessThan__greaterThanLessThan,axiom,
% 0.35/0.68 ! [L: nat,U: nat] :
% 0.35/0.68 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 0.35/0.68 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastSucLessThan_greaterThanLessThan
% 0.35/0.68 thf(fact_8952_sub__BitM__One__eq,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 0.35/0.68 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sub_BitM_One_eq
% 0.35/0.68 thf(fact_8953_bij__betw__nth__root__unity,axiom,
% 0.35/0.68 ! [C2: complex,N: nat] :
% 0.35/0.68 ( ( C2 != zero_zero_complex )
% 0.35/0.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C2 ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 0.35/0.68 @ ( collect_complex
% 0.35/0.68 @ ^ [Z4: complex] :
% 0.35/0.68 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.68 = one_one_complex ) )
% 0.35/0.68 @ ( collect_complex
% 0.35/0.68 @ ^ [Z4: complex] :
% 0.35/0.68 ( ( power_power_complex @ Z4 @ N )
% 0.35/0.68 = C2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bij_betw_nth_root_unity
% 0.35/0.68 thf(fact_8954_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.35/0.68 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 0.35/0.68
% 0.35/0.68 % max_nat.semilattice_neutr_order_axioms
% 0.35/0.68 thf(fact_8955_real__root__Suc__0,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 0.35/0.68 = X ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_Suc_0
% 0.35/0.68 thf(fact_8956_real__root__eq__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( root @ N @ X )
% 0.35/0.68 = ( root @ N @ Y ) )
% 0.35/0.68 = ( X = Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_eq_iff
% 0.35/0.68 thf(fact_8957_root__0,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( root @ zero_zero_nat @ X )
% 0.35/0.68 = zero_zero_real ) ).
% 0.35/0.68
% 0.35/0.68 % root_0
% 0.35/0.68 thf(fact_8958_real__root__eq__0__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( root @ N @ X )
% 0.35/0.68 = zero_zero_real )
% 0.35/0.68 = ( X = zero_zero_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_eq_0_iff
% 0.35/0.68 thf(fact_8959_real__root__less__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 0.35/0.68 = ( ord_less_real @ X @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_less_iff
% 0.35/0.68 thf(fact_8960_real__root__le__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 0.35/0.68 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_le_iff
% 0.35/0.68 thf(fact_8961_real__root__one,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( root @ N @ one_one_real )
% 0.35/0.68 = one_one_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_one
% 0.35/0.68 thf(fact_8962_real__root__eq__1__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( root @ N @ X )
% 0.35/0.68 = one_one_real )
% 0.35/0.68 = ( X = one_one_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_eq_1_iff
% 0.35/0.68 thf(fact_8963_real__root__gt__0__iff,axiom,
% 0.35/0.68 ! [N: nat,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 0.35/0.68 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_gt_0_iff
% 0.35/0.68 thf(fact_8964_real__root__lt__0__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.35/0.68 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_lt_0_iff
% 0.35/0.68 thf(fact_8965_real__root__ge__0__iff,axiom,
% 0.35/0.68 ! [N: nat,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 0.35/0.68 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_ge_0_iff
% 0.35/0.68 thf(fact_8966_real__root__le__0__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 0.35/0.68 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_le_0_iff
% 0.35/0.68 thf(fact_8967_real__root__gt__1__iff,axiom,
% 0.35/0.68 ! [N: nat,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 0.35/0.68 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_gt_1_iff
% 0.35/0.68 thf(fact_8968_real__root__lt__1__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 0.35/0.68 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_lt_1_iff
% 0.35/0.68 thf(fact_8969_real__root__ge__1__iff,axiom,
% 0.35/0.68 ! [N: nat,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 0.35/0.68 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_ge_1_iff
% 0.35/0.68 thf(fact_8970_real__root__le__1__iff,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 0.35/0.68 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_le_1_iff
% 0.35/0.68 thf(fact_8971_real__root__pow__pos2,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.35/0.68 = X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_pow_pos2
% 0.35/0.68 thf(fact_8972_real__root__mult__exp,axiom,
% 0.35/0.68 ! [M2: nat,N: nat,X: real] :
% 0.35/0.68 ( ( root @ ( times_times_nat @ M2 @ N ) @ X )
% 0.35/0.68 = ( root @ M2 @ ( root @ N @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_mult_exp
% 0.35/0.68 thf(fact_8973_real__root__mult,axiom,
% 0.35/0.68 ! [N: nat,X: real,Y: real] :
% 0.35/0.68 ( ( root @ N @ ( times_times_real @ X @ Y ) )
% 0.35/0.68 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_mult
% 0.35/0.68 thf(fact_8974_real__root__less__mono,axiom,
% 0.35/0.68 ! [N: nat,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ X @ Y )
% 0.35/0.68 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_less_mono
% 0.35/0.68 thf(fact_8975_real__root__le__mono,axiom,
% 0.35/0.68 ! [N: nat,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ X @ Y )
% 0.35/0.68 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_le_mono
% 0.35/0.68 thf(fact_8976_real__root__power,axiom,
% 0.35/0.68 ! [N: nat,X: real,K2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( root @ N @ ( power_power_real @ X @ K2 ) )
% 0.35/0.68 = ( power_power_real @ ( root @ N @ X ) @ K2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_power
% 0.35/0.68 thf(fact_8977_real__root__abs,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 0.35/0.68 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_abs
% 0.35/0.68 thf(fact_8978_sgn__root,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 0.35/0.68 = ( sgn_sgn_real @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sgn_root
% 0.35/0.68 thf(fact_8979_real__root__gt__zero,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_gt_zero
% 0.35/0.68 thf(fact_8980_real__root__strict__decreasing,axiom,
% 0.35/0.68 ! [N: nat,N6: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_nat @ N @ N6 )
% 0.35/0.68 => ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.68 => ( ord_less_real @ ( root @ N6 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_strict_decreasing
% 0.35/0.68 thf(fact_8981_root__abs__power,axiom,
% 0.35/0.68 ! [N: nat,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 0.35/0.68 = ( abs_abs_real @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % root_abs_power
% 0.35/0.68 thf(fact_8982_real__root__pos__pos,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_pos_pos
% 0.35/0.68 thf(fact_8983_real__root__strict__increasing,axiom,
% 0.35/0.68 ! [N: nat,N6: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_nat @ N @ N6 )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( ord_less_real @ X @ one_one_real )
% 0.35/0.68 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_strict_increasing
% 0.35/0.68 thf(fact_8984_real__root__decreasing,axiom,
% 0.35/0.68 ! [N: nat,N6: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_nat @ N @ N6 )
% 0.35/0.68 => ( ( ord_less_eq_real @ one_one_real @ X )
% 0.35/0.68 => ( ord_less_eq_real @ ( root @ N6 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_decreasing
% 0.35/0.68 thf(fact_8985_real__root__pow__pos,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 0.35/0.68 = X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_pow_pos
% 0.35/0.68 thf(fact_8986_real__root__pos__unique,axiom,
% 0.35/0.68 ! [N: nat,Y: real,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.68 => ( ( ( power_power_real @ Y @ N )
% 0.35/0.68 = X )
% 0.35/0.68 => ( ( root @ N @ X )
% 0.35/0.68 = Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_pos_unique
% 0.35/0.68 thf(fact_8987_real__root__power__cancel,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 0.35/0.68 = X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_power_cancel
% 0.35/0.68 thf(fact_8988_real__root__increasing,axiom,
% 0.35/0.68 ! [N: nat,N6: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_eq_nat @ N @ N6 )
% 0.35/0.68 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( ord_less_eq_real @ X @ one_one_real )
% 0.35/0.68 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_root_increasing
% 0.35/0.68 thf(fact_8989_sgn__power__root,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 0.35/0.68 = X ) ) ).
% 0.35/0.68
% 0.35/0.68 % sgn_power_root
% 0.35/0.68 thf(fact_8990_root__sgn__power,axiom,
% 0.35/0.68 ! [N: nat,Y: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 0.35/0.68 = Y ) ) ).
% 0.35/0.68
% 0.35/0.68 % root_sgn_power
% 0.35/0.68 thf(fact_8991_ln__root,axiom,
% 0.35/0.68 ! [N: nat,B: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.68 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 0.35/0.68 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % ln_root
% 0.35/0.68 thf(fact_8992_log__root,axiom,
% 0.35/0.68 ! [N: nat,A: real,B: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.68 => ( ( log2 @ B @ ( root @ N @ A ) )
% 0.35/0.68 = ( divide_divide_real @ ( log2 @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % log_root
% 0.35/0.68 thf(fact_8993_log__base__root,axiom,
% 0.35/0.68 ! [N: nat,B: real,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.68 => ( ( log2 @ ( root @ N @ B ) @ X )
% 0.35/0.68 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % log_base_root
% 0.35/0.68 thf(fact_8994_split__root,axiom,
% 0.35/0.68 ! [P2: real > $o,N: nat,X: real] :
% 0.35/0.68 ( ( P2 @ ( root @ N @ X ) )
% 0.35/0.68 = ( ( ( N = zero_zero_nat )
% 0.35/0.68 => ( P2 @ zero_zero_real ) )
% 0.35/0.68 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ! [Y4: real] :
% 0.35/0.68 ( ( ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 0.35/0.68 = X )
% 0.35/0.68 => ( P2 @ Y4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % split_root
% 0.35/0.68 thf(fact_8995_root__powr__inverse,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( root @ N @ X )
% 0.35/0.68 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % root_powr_inverse
% 0.35/0.68 thf(fact_8996_powr__powr,axiom,
% 0.35/0.68 ! [X: real,A: real,B: real] :
% 0.35/0.68 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 0.35/0.68 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % powr_powr
% 0.35/0.68 thf(fact_8997_powr__mult,axiom,
% 0.35/0.68 ! [X: real,Y: real,A: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 0.35/0.68 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 0.35/0.68 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % powr_mult
% 0.35/0.68 thf(fact_8998_divide__powr__uminus,axiom,
% 0.35/0.68 ! [A: real,B: real,C2: real] :
% 0.35/0.68 ( ( divide_divide_real @ A @ ( powr_real @ B @ C2 ) )
% 0.35/0.68 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % divide_powr_uminus
% 0.35/0.68 thf(fact_8999_ln__powr,axiom,
% 0.35/0.68 ! [X: real,Y: real] :
% 0.35/0.68 ( ( X != zero_zero_real )
% 0.35/0.68 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 0.35/0.68 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % ln_powr
% 0.35/0.68 thf(fact_9000_log__powr,axiom,
% 0.35/0.68 ! [X: real,B: real,Y: real] :
% 0.35/0.68 ( ( X != zero_zero_real )
% 0.35/0.68 => ( ( log2 @ B @ ( powr_real @ X @ Y ) )
% 0.35/0.68 = ( times_times_real @ Y @ ( log2 @ B @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % log_powr
% 0.35/0.68 thf(fact_9001_powr__mult__base,axiom,
% 0.35/0.68 ! [X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 0.35/0.68 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % powr_mult_base
% 0.35/0.68 thf(fact_9002_ln__powr__bound2,axiom,
% 0.35/0.68 ! [X: real,A: real] :
% 0.35/0.68 ( ( ord_less_real @ one_one_real @ X )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.35/0.68 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % ln_powr_bound2
% 0.35/0.68 thf(fact_9003_log__add__eq__powr,axiom,
% 0.35/0.68 ! [B: real,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.68 => ( ( B != one_one_real )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( plus_plus_real @ ( log2 @ B @ X ) @ Y )
% 0.35/0.68 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % log_add_eq_powr
% 0.35/0.68 thf(fact_9004_add__log__eq__powr,axiom,
% 0.35/0.68 ! [B: real,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.68 => ( ( B != one_one_real )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( plus_plus_real @ Y @ ( log2 @ B @ X ) )
% 0.35/0.68 = ( log2 @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % add_log_eq_powr
% 0.35/0.68 thf(fact_9005_log__minus__eq__powr,axiom,
% 0.35/0.68 ! [B: real,X: real,Y: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ B )
% 0.35/0.68 => ( ( B != one_one_real )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( ( minus_minus_real @ ( log2 @ B @ X ) @ Y )
% 0.35/0.68 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % log_minus_eq_powr
% 0.35/0.68 thf(fact_9006_times__int_Oabs__eq,axiom,
% 0.35/0.68 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68 = ( abs_Integ
% 0.35/0.68 @ ( produc27273713700761075at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) )
% 0.35/0.68 @ Xa2
% 0.35/0.68 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_int.abs_eq
% 0.35/0.68 thf(fact_9007_num__of__nat_Osimps_I2_J,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( num_of_nat @ ( suc @ N ) )
% 0.35/0.68 = ( inc @ ( num_of_nat @ N ) ) ) )
% 0.35/0.68 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( num_of_nat @ ( suc @ N ) )
% 0.35/0.68 = one ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % num_of_nat.simps(2)
% 0.35/0.68 thf(fact_9008_num__of__nat__numeral__eq,axiom,
% 0.35/0.68 ! [Q2: num] :
% 0.35/0.68 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 0.35/0.68 = Q2 ) ).
% 0.35/0.68
% 0.35/0.68 % num_of_nat_numeral_eq
% 0.35/0.68 thf(fact_9009_eq__Abs__Integ,axiom,
% 0.35/0.68 ! [Z3: int] :
% 0.35/0.68 ~ ! [X3: nat,Y3: nat] :
% 0.35/0.68 ( Z3
% 0.35/0.68 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % eq_Abs_Integ
% 0.35/0.68 thf(fact_9010_num__of__nat_Osimps_I1_J,axiom,
% 0.35/0.68 ( ( num_of_nat @ zero_zero_nat )
% 0.35/0.68 = one ) ).
% 0.35/0.68
% 0.35/0.68 % num_of_nat.simps(1)
% 0.35/0.68 thf(fact_9011_zero__int__def,axiom,
% 0.35/0.68 ( zero_zero_int
% 0.35/0.68 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % zero_int_def
% 0.35/0.68 thf(fact_9012_int__def,axiom,
% 0.35/0.68 ( semiri1314217659103216013at_int
% 0.35/0.68 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % int_def
% 0.35/0.68 thf(fact_9013_numeral__num__of__nat,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 0.35/0.68 = N ) ) ).
% 0.35/0.68
% 0.35/0.68 % numeral_num_of_nat
% 0.35/0.68 thf(fact_9014_num__of__nat__One,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 0.35/0.68 => ( ( num_of_nat @ N )
% 0.35/0.68 = one ) ) ).
% 0.35/0.68
% 0.35/0.68 % num_of_nat_One
% 0.35/0.68 thf(fact_9015_uminus__int_Oabs__eq,axiom,
% 0.35/0.68 ! [X: product_prod_nat_nat] :
% 0.35/0.68 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 0.35/0.68 = ( abs_Integ
% 0.35/0.68 @ ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 )
% 0.35/0.68 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % uminus_int.abs_eq
% 0.35/0.68 thf(fact_9016_one__int__def,axiom,
% 0.35/0.68 ( one_one_int
% 0.35/0.68 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % one_int_def
% 0.35/0.68 thf(fact_9017_num__of__nat__double,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 0.35/0.68 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % num_of_nat_double
% 0.35/0.68 thf(fact_9018_num__of__nat__plus__distrib,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N ) )
% 0.35/0.68 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % num_of_nat_plus_distrib
% 0.35/0.68 thf(fact_9019_less__eq__int_Oabs__eq,axiom,
% 0.35/0.68 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68 = ( produc8739625826339149834_nat_o
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 0.35/0.68 @ Xa2
% 0.35/0.68 @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % less_eq_int.abs_eq
% 0.35/0.68 thf(fact_9020_plus__int_Oabs__eq,axiom,
% 0.35/0.68 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68 = ( abs_Integ
% 0.35/0.68 @ ( produc27273713700761075at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) )
% 0.35/0.68 @ Xa2
% 0.35/0.68 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % plus_int.abs_eq
% 0.35/0.68 thf(fact_9021_minus__int_Oabs__eq,axiom,
% 0.35/0.68 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 0.35/0.68 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 0.35/0.68 = ( abs_Integ
% 0.35/0.68 @ ( produc27273713700761075at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) )
% 0.35/0.68 @ Xa2
% 0.35/0.68 @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % minus_int.abs_eq
% 0.35/0.68 thf(fact_9022_sorted__list__of__set__atMost__Suc,axiom,
% 0.35/0.68 ! [K2: nat] :
% 0.35/0.68 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K2 ) ) )
% 0.35/0.68 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K2 ) ) @ ( cons_nat @ ( suc @ K2 ) @ nil_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sorted_list_of_set_atMost_Suc
% 0.35/0.68 thf(fact_9023_sorted__list__of__set__lessThan__Suc,axiom,
% 0.35/0.68 ! [K2: nat] :
% 0.35/0.68 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K2 ) ) )
% 0.35/0.68 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K2 ) ) @ ( cons_nat @ K2 @ nil_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sorted_list_of_set_lessThan_Suc
% 0.35/0.68 thf(fact_9024_sorted__list__of__set__greaterThanLessThan,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ ( suc @ I2 ) @ J2 )
% 0.35/0.68 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) )
% 0.35/0.68 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sorted_list_of_set_greaterThanLessThan
% 0.35/0.68 thf(fact_9025_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 0.35/0.68 ! [N: nat,J2: nat,I2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ ( suc @ I2 ) ) )
% 0.35/0.68 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) ) @ N )
% 0.35/0.68 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nth_sorted_list_of_set_greaterThanLessThan
% 0.35/0.68 thf(fact_9026_less__eq__int_Orep__eq,axiom,
% 0.35/0.68 ( ord_less_eq_int
% 0.35/0.68 = ( ^ [X4: int,Xa3: int] :
% 0.35/0.68 ( produc8739625826339149834_nat_o
% 0.35/0.68 @ ^ [Y4: nat,Z4: nat] :
% 0.35/0.68 ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V3 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 0.35/0.68 @ ( rep_Integ @ X4 )
% 0.35/0.68 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % less_eq_int.rep_eq
% 0.35/0.68 thf(fact_9027_image__minus__const__atLeastLessThan__nat,axiom,
% 0.35/0.68 ! [C2: nat,Y: nat,X: nat] :
% 0.35/0.68 ( ( ( ord_less_nat @ C2 @ Y )
% 0.35/0.68 => ( ( image_nat_nat
% 0.35/0.68 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 0.35/0.68 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.35/0.68 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C2 ) @ ( minus_minus_nat @ Y @ C2 ) ) ) )
% 0.35/0.68 & ( ~ ( ord_less_nat @ C2 @ Y )
% 0.35/0.68 => ( ( ( ord_less_nat @ X @ Y )
% 0.35/0.68 => ( ( image_nat_nat
% 0.35/0.68 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 0.35/0.68 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.35/0.68 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 0.35/0.68 & ( ~ ( ord_less_nat @ X @ Y )
% 0.35/0.68 => ( ( image_nat_nat
% 0.35/0.68 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 0.35/0.68 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 0.35/0.68 = bot_bot_set_nat ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_minus_const_atLeastLessThan_nat
% 0.35/0.68 thf(fact_9028_bij__betw__Suc,axiom,
% 0.35/0.68 ! [M5: set_nat,N6: set_nat] :
% 0.35/0.68 ( ( bij_betw_nat_nat @ suc @ M5 @ N6 )
% 0.35/0.68 = ( ( image_nat_nat @ suc @ M5 )
% 0.35/0.68 = N6 ) ) ).
% 0.35/0.68
% 0.35/0.68 % bij_betw_Suc
% 0.35/0.68 thf(fact_9029_image__Suc__atLeastAtMost,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 0.35/0.68 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_Suc_atLeastAtMost
% 0.35/0.68 thf(fact_9030_image__Suc__atLeastLessThan,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) )
% 0.35/0.68 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_Suc_atLeastLessThan
% 0.35/0.68 thf(fact_9031_zero__notin__Suc__image,axiom,
% 0.35/0.68 ! [A4: set_nat] :
% 0.35/0.68 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 0.35/0.68
% 0.35/0.68 % zero_notin_Suc_image
% 0.35/0.68 thf(fact_9032_image__Suc__lessThan,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_Suc_lessThan
% 0.35/0.68 thf(fact_9033_image__Suc__atMost,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 0.35/0.68 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_Suc_atMost
% 0.35/0.68 thf(fact_9034_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.68 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast0_atMost_Suc_eq_insert_0
% 0.35/0.68 thf(fact_9035_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 0.35/0.68 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast0_lessThan_Suc_eq_insert_0
% 0.35/0.68 thf(fact_9036_lessThan__Suc__eq__insert__0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 0.35/0.68 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % lessThan_Suc_eq_insert_0
% 0.35/0.68 thf(fact_9037_atMost__Suc__eq__insert__0,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 0.35/0.68 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atMost_Suc_eq_insert_0
% 0.35/0.68 thf(fact_9038_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 0.35/0.68 ! [N: nat,J2: nat,I2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ I2 ) )
% 0.35/0.68 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) ) @ N )
% 0.35/0.68 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nth_sorted_list_of_set_greaterThanAtMost
% 0.35/0.68 thf(fact_9039_uminus__int__def,axiom,
% 0.35/0.68 ( uminus_uminus_int
% 0.35/0.68 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 0.35/0.68 @ ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % uminus_int_def
% 0.35/0.68 thf(fact_9040_rat__inverse__code,axiom,
% 0.35/0.68 ! [P: rat] :
% 0.35/0.68 ( ( quotient_of @ ( inverse_inverse_rat @ P ) )
% 0.35/0.68 = ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 0.35/0.68 @ ( quotient_of @ P ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rat_inverse_code
% 0.35/0.68 thf(fact_9041_finite__greaterThanAtMost,axiom,
% 0.35/0.68 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_greaterThanAtMost
% 0.35/0.68 thf(fact_9042_card__greaterThanAtMost,axiom,
% 0.35/0.68 ! [L: nat,U: nat] :
% 0.35/0.68 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 0.35/0.68 = ( minus_minus_nat @ U @ L ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_greaterThanAtMost
% 0.35/0.68 thf(fact_9043_divide__rat__def,axiom,
% 0.35/0.68 ( divide_divide_rat
% 0.35/0.68 = ( ^ [Q5: rat,R: rat] : ( times_times_rat @ Q5 @ ( inverse_inverse_rat @ R ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % divide_rat_def
% 0.35/0.68 thf(fact_9044_rat__less__eq__code,axiom,
% 0.35/0.68 ( ord_less_eq_rat
% 0.35/0.68 = ( ^ [P5: rat,Q5: rat] :
% 0.35/0.68 ( produc4947309494688390418_int_o
% 0.35/0.68 @ ^ [A5: int,C3: int] :
% 0.35/0.68 ( produc4947309494688390418_int_o
% 0.35/0.68 @ ^ [B4: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 0.35/0.68 @ ( quotient_of @ Q5 ) )
% 0.35/0.68 @ ( quotient_of @ P5 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rat_less_eq_code
% 0.35/0.68 thf(fact_9045_rat__less__code,axiom,
% 0.35/0.68 ( ord_less_rat
% 0.35/0.68 = ( ^ [P5: rat,Q5: rat] :
% 0.35/0.68 ( produc4947309494688390418_int_o
% 0.35/0.68 @ ^ [A5: int,C3: int] :
% 0.35/0.68 ( produc4947309494688390418_int_o
% 0.35/0.68 @ ^ [B4: int,D2: int] : ( ord_less_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 0.35/0.68 @ ( quotient_of @ Q5 ) )
% 0.35/0.68 @ ( quotient_of @ P5 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rat_less_code
% 0.35/0.68 thf(fact_9046_atLeastSucAtMost__greaterThanAtMost,axiom,
% 0.35/0.68 ! [L: nat,U: nat] :
% 0.35/0.68 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 0.35/0.68 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastSucAtMost_greaterThanAtMost
% 0.35/0.68 thf(fact_9047_image__int__atLeastAtMost,axiom,
% 0.35/0.68 ! [A: nat,B: nat] :
% 0.35/0.68 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 0.35/0.68 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_int_atLeastAtMost
% 0.35/0.68 thf(fact_9048_image__int__atLeastLessThan,axiom,
% 0.35/0.68 ! [A: nat,B: nat] :
% 0.35/0.68 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 0.35/0.68 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_int_atLeastLessThan
% 0.35/0.68 thf(fact_9049_sorted__list__of__set__greaterThanAtMost,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J2 )
% 0.35/0.68 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) )
% 0.35/0.68 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sorted_list_of_set_greaterThanAtMost
% 0.35/0.68 thf(fact_9050_image__add__int__atLeastLessThan,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( image_int_int
% 0.35/0.68 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 0.35/0.68 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 0.35/0.68 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_add_int_atLeastLessThan
% 0.35/0.68 thf(fact_9051_image__atLeastZeroLessThan__int,axiom,
% 0.35/0.68 ! [U: int] :
% 0.35/0.68 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 0.35/0.68 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 0.35/0.68 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % image_atLeastZeroLessThan_int
% 0.35/0.68 thf(fact_9052_times__int__def,axiom,
% 0.35/0.68 ( times_times_int
% 0.35/0.68 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.35/0.68 @ ( produc27273713700761075at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_int_def
% 0.35/0.68 thf(fact_9053_minus__int__def,axiom,
% 0.35/0.68 ( minus_minus_int
% 0.35/0.68 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.35/0.68 @ ( produc27273713700761075at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % minus_int_def
% 0.35/0.68 thf(fact_9054_plus__int__def,axiom,
% 0.35/0.68 ( plus_plus_int
% 0.35/0.68 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 0.35/0.68 @ ( produc27273713700761075at_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( produc2626176000494625587at_nat
% 0.35/0.68 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % plus_int_def
% 0.35/0.68 thf(fact_9055_rat__minus__code,axiom,
% 0.35/0.68 ! [P: rat,Q2: rat] :
% 0.35/0.68 ( ( quotient_of @ ( minus_minus_rat @ P @ Q2 ) )
% 0.35/0.68 = ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [A5: int,C3: int] :
% 0.35/0.68 ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 0.35/0.68 @ ( quotient_of @ Q2 ) )
% 0.35/0.68 @ ( quotient_of @ P ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rat_minus_code
% 0.35/0.68 thf(fact_9056_finite__greaterThanAtMost__int,axiom,
% 0.35/0.68 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_greaterThanAtMost_int
% 0.35/0.68 thf(fact_9057_card__greaterThanAtMost__int,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 0.35/0.68 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_greaterThanAtMost_int
% 0.35/0.68 thf(fact_9058_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 0.35/0.68 ! [L: int,U: int] :
% 0.35/0.68 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 0.35/0.68 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 0.35/0.68 thf(fact_9059_normalize__crossproduct,axiom,
% 0.35/0.68 ! [Q2: int,S2: int,P: int,R3: int] :
% 0.35/0.68 ( ( Q2 != zero_zero_int )
% 0.35/0.68 => ( ( S2 != zero_zero_int )
% 0.35/0.68 => ( ( ( normalize @ ( product_Pair_int_int @ P @ Q2 ) )
% 0.35/0.68 = ( normalize @ ( product_Pair_int_int @ R3 @ S2 ) ) )
% 0.35/0.68 => ( ( times_times_int @ P @ S2 )
% 0.35/0.68 = ( times_times_int @ R3 @ Q2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % normalize_crossproduct
% 0.35/0.68 thf(fact_9060_rat__times__code,axiom,
% 0.35/0.68 ! [P: rat,Q2: rat] :
% 0.35/0.68 ( ( quotient_of @ ( times_times_rat @ P @ Q2 ) )
% 0.35/0.68 = ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [A5: int,C3: int] :
% 0.35/0.68 ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 0.35/0.68 @ ( quotient_of @ Q2 ) )
% 0.35/0.68 @ ( quotient_of @ P ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rat_times_code
% 0.35/0.68 thf(fact_9061_rat__divide__code,axiom,
% 0.35/0.68 ! [P: rat,Q2: rat] :
% 0.35/0.68 ( ( quotient_of @ ( divide_divide_rat @ P @ Q2 ) )
% 0.35/0.68 = ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [A5: int,C3: int] :
% 0.35/0.68 ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) ) )
% 0.35/0.68 @ ( quotient_of @ Q2 ) )
% 0.35/0.68 @ ( quotient_of @ P ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rat_divide_code
% 0.35/0.68 thf(fact_9062_rat__plus__code,axiom,
% 0.35/0.68 ! [P: rat,Q2: rat] :
% 0.35/0.68 ( ( quotient_of @ ( plus_plus_rat @ P @ Q2 ) )
% 0.35/0.68 = ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [A5: int,C3: int] :
% 0.35/0.68 ( produc4245557441103728435nt_int
% 0.35/0.68 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 0.35/0.68 @ ( quotient_of @ Q2 ) )
% 0.35/0.68 @ ( quotient_of @ P ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rat_plus_code
% 0.35/0.68 thf(fact_9063_list__encode_Opelims,axiom,
% 0.35/0.68 ! [X: list_nat,Y: nat] :
% 0.35/0.68 ( ( ( nat_list_encode @ X )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 0.35/0.68 => ( ( ( X = nil_nat )
% 0.35/0.68 => ( ( Y = zero_zero_nat )
% 0.35/0.68 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 0.35/0.68 => ~ ! [X3: nat,Xs3: list_nat] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( cons_nat @ X3 @ Xs3 ) )
% 0.35/0.68 => ( ( Y
% 0.35/0.68 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 0.35/0.68 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % list_encode.pelims
% 0.35/0.68 thf(fact_9064_upt__rec__numeral,axiom,
% 0.35/0.68 ! [M2: num,N: num] :
% 0.35/0.68 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.68 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.68 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 0.35/0.68 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.68 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 0.35/0.68 = nil_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_rec_numeral
% 0.35/0.68 thf(fact_9065_tl__upt,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( tl_nat @ ( upt @ M2 @ N ) )
% 0.35/0.68 = ( upt @ ( suc @ M2 ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % tl_upt
% 0.35/0.68 thf(fact_9066_length__upt,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( size_size_list_nat @ ( upt @ I2 @ J2 ) )
% 0.35/0.68 = ( minus_minus_nat @ J2 @ I2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % length_upt
% 0.35/0.68 thf(fact_9067_take__upt,axiom,
% 0.35/0.68 ! [I2: nat,M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M2 ) @ N )
% 0.35/0.68 => ( ( take_nat @ M2 @ ( upt @ I2 @ N ) )
% 0.35/0.68 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_upt
% 0.35/0.68 thf(fact_9068_upt__conv__Nil,axiom,
% 0.35/0.68 ! [J2: nat,I2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ J2 @ I2 )
% 0.35/0.68 => ( ( upt @ I2 @ J2 )
% 0.35/0.68 = nil_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_conv_Nil
% 0.35/0.68 thf(fact_9069_upt__eq__Nil__conv,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( ( upt @ I2 @ J2 )
% 0.35/0.68 = nil_nat )
% 0.35/0.68 = ( ( J2 = zero_zero_nat )
% 0.35/0.68 | ( ord_less_eq_nat @ J2 @ I2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_eq_Nil_conv
% 0.35/0.68 thf(fact_9070_atLeastAtMost__upt,axiom,
% 0.35/0.68 ( set_or1269000886237332187st_nat
% 0.35/0.68 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ N4 @ ( suc @ M6 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeastAtMost_upt
% 0.35/0.68 thf(fact_9071_atLeast__upt,axiom,
% 0.35/0.68 ( set_ord_lessThan_nat
% 0.35/0.68 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast_upt
% 0.35/0.68 thf(fact_9072_upt__conv__Cons__Cons,axiom,
% 0.35/0.68 ! [M2: nat,N: nat,Ns: list_nat,Q2: nat] :
% 0.35/0.68 ( ( ( cons_nat @ M2 @ ( cons_nat @ N @ Ns ) )
% 0.35/0.68 = ( upt @ M2 @ Q2 ) )
% 0.35/0.68 = ( ( cons_nat @ N @ Ns )
% 0.35/0.68 = ( upt @ ( suc @ M2 ) @ Q2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_conv_Cons_Cons
% 0.35/0.68 thf(fact_9073_upt__0,axiom,
% 0.35/0.68 ! [I2: nat] :
% 0.35/0.68 ( ( upt @ I2 @ zero_zero_nat )
% 0.35/0.68 = nil_nat ) ).
% 0.35/0.68
% 0.35/0.68 % upt_0
% 0.35/0.68 thf(fact_9074_greaterThanAtMost__upt,axiom,
% 0.35/0.68 ( set_or6659071591806873216st_nat
% 0.35/0.68 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ ( suc @ M6 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % greaterThanAtMost_upt
% 0.35/0.68 thf(fact_9075_greaterThanLessThan__upt,axiom,
% 0.35/0.68 ( set_or5834768355832116004an_nat
% 0.35/0.68 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ M6 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % greaterThanLessThan_upt
% 0.35/0.68 thf(fact_9076_atMost__upto,axiom,
% 0.35/0.68 ( set_ord_atMost_nat
% 0.35/0.68 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atMost_upto
% 0.35/0.68 thf(fact_9077_upt__conv__Cons,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I2 @ J2 )
% 0.35/0.68 => ( ( upt @ I2 @ J2 )
% 0.35/0.68 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_conv_Cons
% 0.35/0.68 thf(fact_9078_upt__add__eq__append,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat,K2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.68 => ( ( upt @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 0.35/0.68 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( upt @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_add_eq_append
% 0.35/0.68 thf(fact_9079_upt__rec,axiom,
% 0.35/0.68 ( upt
% 0.35/0.68 = ( ^ [I: nat,J: nat] : ( if_list_nat @ ( ord_less_nat @ I @ J ) @ ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) @ nil_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_rec
% 0.35/0.68 thf(fact_9080_upt__Suc,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.68 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 0.35/0.68 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) )
% 0.35/0.68 & ( ~ ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.68 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 0.35/0.68 = nil_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_Suc
% 0.35/0.68 thf(fact_9081_upt__Suc__append,axiom,
% 0.35/0.68 ! [I2: nat,J2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ I2 @ J2 )
% 0.35/0.68 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 0.35/0.68 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % upt_Suc_append
% 0.35/0.68 thf(fact_9082_mono__Suc,axiom,
% 0.35/0.68 order_mono_nat_nat @ suc ).
% 0.35/0.68
% 0.35/0.68 % mono_Suc
% 0.35/0.68 thf(fact_9083_mono__times__nat,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % mono_times_nat
% 0.35/0.68 thf(fact_9084_mono__ge2__power__minus__self,axiom,
% 0.35/0.68 ! [K2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 0.35/0.68 => ( order_mono_nat_nat
% 0.35/0.68 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K2 @ M6 ) @ M6 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % mono_ge2_power_minus_self
% 0.35/0.68 thf(fact_9085_sum__list__upt,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 => ( ( groups4561878855575611511st_nat @ ( upt @ M2 @ N ) )
% 0.35/0.68 = ( groups3542108847815614940at_nat
% 0.35/0.68 @ ^ [X4: nat] : X4
% 0.35/0.68 @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sum_list_upt
% 0.35/0.68 thf(fact_9086_map__Suc__upt,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( map_nat_nat @ suc @ ( upt @ M2 @ N ) )
% 0.35/0.68 = ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % map_Suc_upt
% 0.35/0.68 thf(fact_9087_map__add__upt,axiom,
% 0.35/0.68 ! [N: nat,M2: nat] :
% 0.35/0.68 ( ( map_nat_nat
% 0.35/0.68 @ ^ [I: nat] : ( plus_plus_nat @ I @ N )
% 0.35/0.68 @ ( upt @ zero_zero_nat @ M2 ) )
% 0.35/0.68 = ( upt @ N @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % map_add_upt
% 0.35/0.68 thf(fact_9088_map__decr__upt,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( map_nat_nat
% 0.35/0.68 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 @ ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 0.35/0.68 = ( upt @ M2 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % map_decr_upt
% 0.35/0.68 thf(fact_9089_card__length__sum__list__rec,axiom,
% 0.35/0.68 ! [M2: nat,N6: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 0.35/0.68 => ( ( finite_card_list_nat
% 0.35/0.68 @ ( collect_list_nat
% 0.35/0.68 @ ^ [L2: list_nat] :
% 0.35/0.68 ( ( ( size_size_list_nat @ L2 )
% 0.35/0.68 = M2 )
% 0.35/0.68 & ( ( groups4561878855575611511st_nat @ L2 )
% 0.35/0.68 = N6 ) ) ) )
% 0.35/0.68 = ( plus_plus_nat
% 0.35/0.68 @ ( finite_card_list_nat
% 0.35/0.68 @ ( collect_list_nat
% 0.35/0.68 @ ^ [L2: list_nat] :
% 0.35/0.68 ( ( ( size_size_list_nat @ L2 )
% 0.35/0.68 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 0.35/0.68 & ( ( groups4561878855575611511st_nat @ L2 )
% 0.35/0.68 = N6 ) ) ) )
% 0.35/0.68 @ ( finite_card_list_nat
% 0.35/0.68 @ ( collect_list_nat
% 0.35/0.68 @ ^ [L2: list_nat] :
% 0.35/0.68 ( ( ( size_size_list_nat @ L2 )
% 0.35/0.68 = M2 )
% 0.35/0.68 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 0.35/0.68 = N6 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_length_sum_list_rec
% 0.35/0.68 thf(fact_9090_card__length__sum__list,axiom,
% 0.35/0.68 ! [M2: nat,N6: nat] :
% 0.35/0.68 ( ( finite_card_list_nat
% 0.35/0.68 @ ( collect_list_nat
% 0.35/0.68 @ ^ [L2: list_nat] :
% 0.35/0.68 ( ( ( size_size_list_nat @ L2 )
% 0.35/0.68 = M2 )
% 0.35/0.68 & ( ( groups4561878855575611511st_nat @ L2 )
% 0.35/0.68 = N6 ) ) ) )
% 0.35/0.68 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N6 @ M2 ) @ one_one_nat ) @ N6 ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_length_sum_list
% 0.35/0.68 thf(fact_9091_range__mod,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( image_nat_nat
% 0.35/0.68 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 0.35/0.68 @ top_top_set_nat )
% 0.35/0.68 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % range_mod
% 0.35/0.68 thf(fact_9092_UNIV__nat__eq,axiom,
% 0.35/0.68 ( top_top_set_nat
% 0.35/0.68 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % UNIV_nat_eq
% 0.35/0.68 thf(fact_9093_range__mult,axiom,
% 0.35/0.68 ! [A: real] :
% 0.35/0.68 ( ( ( A = zero_zero_real )
% 0.35/0.68 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.35/0.68 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 0.35/0.68 & ( ( A != zero_zero_real )
% 0.35/0.68 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 0.35/0.68 = top_top_set_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % range_mult
% 0.35/0.68 thf(fact_9094_sorted__upt,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M2 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % sorted_upt
% 0.35/0.68 thf(fact_9095_surj__prod__decode,axiom,
% 0.35/0.68 ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 0.35/0.68 = top_to4669805908274784177at_nat ) ).
% 0.35/0.68
% 0.35/0.68 % surj_prod_decode
% 0.35/0.68 thf(fact_9096_bij__prod__decode,axiom,
% 0.35/0.68 bij_be8693218025023041337at_nat @ nat_prod_decode @ top_top_set_nat @ top_to4669805908274784177at_nat ).
% 0.35/0.68
% 0.35/0.68 % bij_prod_decode
% 0.35/0.68 thf(fact_9097_surj__list__decode,axiom,
% 0.35/0.68 ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 0.35/0.68 = top_top_set_list_nat ) ).
% 0.35/0.68
% 0.35/0.68 % surj_list_decode
% 0.35/0.68 thf(fact_9098_bij__list__decode,axiom,
% 0.35/0.68 bij_be6293887246118711976st_nat @ nat_list_decode @ top_top_set_nat @ top_top_set_list_nat ).
% 0.35/0.68
% 0.35/0.68 % bij_list_decode
% 0.35/0.68 thf(fact_9099_surj__list__encode,axiom,
% 0.35/0.68 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 0.35/0.68 = top_top_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % surj_list_encode
% 0.35/0.68 thf(fact_9100_bij__list__encode,axiom,
% 0.35/0.68 bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 0.35/0.68
% 0.35/0.68 % bij_list_encode
% 0.35/0.68 thf(fact_9101_surj__prod__encode,axiom,
% 0.35/0.68 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 0.35/0.68 = top_top_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % surj_prod_encode
% 0.35/0.68 thf(fact_9102_bij__prod__encode,axiom,
% 0.35/0.68 bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 0.35/0.68
% 0.35/0.68 % bij_prod_encode
% 0.35/0.68 thf(fact_9103_sorted__wrt__less__idx,axiom,
% 0.35/0.68 ! [Ns: list_nat,I2: nat] :
% 0.35/0.68 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 0.35/0.68 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 0.35/0.68 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sorted_wrt_less_idx
% 0.35/0.68 thf(fact_9104_root__def,axiom,
% 0.35/0.68 ( root
% 0.35/0.68 = ( ^ [N4: nat,X4: real] :
% 0.35/0.68 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 0.35/0.68 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 0.35/0.68 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N4 ) )
% 0.35/0.68 @ X4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % root_def
% 0.35/0.68 thf(fact_9105_DERIV__even__real__root,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_even_real_root
% 0.35/0.68 thf(fact_9106_DERIV__real__root__generic,axiom,
% 0.35/0.68 ! [N: nat,X: real,D3: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( X != zero_zero_real )
% 0.35/0.68 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( D3
% 0.35/0.68 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 0.35/0.68 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68 => ( ( ord_less_real @ X @ zero_zero_real )
% 0.35/0.68 => ( D3
% 0.35/0.68 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 0.35/0.68 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68 => ( D3
% 0.35/0.68 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_real_root_generic
% 0.35/0.68 thf(fact_9107_DERIV__arctan__series,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X9: real] :
% 0.35/0.68 ( suminf_real
% 0.35/0.68 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_arctan_series
% 0.35/0.68 thf(fact_9108_DERIV__fun__pow,axiom,
% 0.35/0.68 ! [G2: real > real,M2: real,X: real,N: nat] :
% 0.35/0.68 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X4: real] : ( power_power_real @ ( G2 @ X4 ) @ N )
% 0.35/0.68 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G2 @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M2 )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_fun_pow
% 0.35/0.68 thf(fact_9109_has__real__derivative__powr,axiom,
% 0.35/0.68 ! [Z3: real,R3: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [Z4: real] : ( powr_real @ Z4 @ R3 )
% 0.35/0.68 @ ( times_times_real @ R3 @ ( powr_real @ Z3 @ ( minus_minus_real @ R3 @ one_one_real ) ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % has_real_derivative_powr
% 0.35/0.68 thf(fact_9110_DERIV__series_H,axiom,
% 0.35/0.68 ! [F2: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 0.35/0.68 ( ! [N3: nat] :
% 0.35/0.68 ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X4: real] : ( F2 @ X4 @ N3 )
% 0.35/0.68 @ ( F5 @ X0 @ N3 )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 0.35/0.68 => ( ! [X3: real] :
% 0.35/0.68 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68 => ( summable_real @ ( F2 @ X3 ) ) )
% 0.35/0.68 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68 => ( ( summable_real @ ( F5 @ X0 ) )
% 0.35/0.68 => ( ( summable_real @ L5 )
% 0.35/0.68 => ( ! [N3: nat,X3: real,Y3: real] :
% 0.35/0.68 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 0.35/0.68 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F2 @ X3 @ N3 ) @ ( F2 @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X4: real] : ( suminf_real @ ( F2 @ X4 ) )
% 0.35/0.68 @ ( suminf_real @ ( F5 @ X0 ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_series'
% 0.35/0.68 thf(fact_9111_DERIV__log,axiom,
% 0.35/0.68 ! [X: real,B: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( log2 @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_log
% 0.35/0.68 thf(fact_9112_DERIV__fun__powr,axiom,
% 0.35/0.68 ! [G2: real > real,M2: real,X: real,R3: real] :
% 0.35/0.68 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ ( G2 @ X ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X4: real] : ( powr_real @ ( G2 @ X4 ) @ R3 )
% 0.35/0.68 @ ( times_times_real @ ( times_times_real @ R3 @ ( powr_real @ ( G2 @ X ) @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M2 )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_fun_powr
% 0.35/0.68 thf(fact_9113_DERIV__powr,axiom,
% 0.35/0.68 ! [G2: real > real,M2: real,X: real,F2: real > real,R3: real] :
% 0.35/0.68 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ ( G2 @ X ) )
% 0.35/0.68 => ( ( has_fi5821293074295781190e_real @ F2 @ R3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X4: real] : ( powr_real @ ( G2 @ X4 ) @ ( F2 @ X4 ) )
% 0.35/0.68 @ ( times_times_real @ ( powr_real @ ( G2 @ X ) @ ( F2 @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R3 @ ( ln_ln_real @ ( G2 @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M2 @ ( F2 @ X ) ) @ ( G2 @ X ) ) ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_powr
% 0.35/0.68 thf(fact_9114_DERIV__power__series_H,axiom,
% 0.35/0.68 ! [R2: real,F2: nat > real,X0: real] :
% 0.35/0.68 ( ! [X3: real] :
% 0.35/0.68 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 0.35/0.68 => ( summable_real
% 0.35/0.68 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F2 @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X3 @ N4 ) ) ) )
% 0.35/0.68 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X4: real] :
% 0.35/0.68 ( suminf_real
% 0.35/0.68 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ ( power_power_real @ X4 @ ( suc @ N4 ) ) ) )
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F2 @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X0 @ N4 ) ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_power_series'
% 0.35/0.68 thf(fact_9115_DERIV__real__root,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ X )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_real_root
% 0.35/0.68 thf(fact_9116_Maclaurin__all__le,axiom,
% 0.35/0.68 ! [Diff: nat > real > real,F2: real > real,X: real,N: nat] :
% 0.35/0.68 ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68 & ( ( F2 @ X )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin_all_le
% 0.35/0.68 thf(fact_9117_Maclaurin__all__le__objl,axiom,
% 0.35/0.68 ! [Diff: nat > real > real,F2: real > real,X: real,N: nat] :
% 0.35/0.68 ( ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 & ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68 & ( ( F2 @ X )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin_all_le_objl
% 0.35/0.68 thf(fact_9118_DERIV__odd__real__root,axiom,
% 0.35/0.68 ! [N: nat,X: real] :
% 0.35/0.68 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68 => ( ( X != zero_zero_real )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_odd_real_root
% 0.35/0.68 thf(fact_9119_Maclaurin__minus,axiom,
% 0.35/0.68 ! [H: real,N: nat,Diff: nat > real > real,F2: real > real] :
% 0.35/0.68 ( ( ord_less_real @ H @ zero_zero_real )
% 0.35/0.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ H @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_real @ H @ T6 )
% 0.35/0.68 & ( ord_less_real @ T6 @ zero_zero_real )
% 0.35/0.68 & ( ( F2 @ H )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin_minus
% 0.35/0.68 thf(fact_9120_Maclaurin2,axiom,
% 0.35/0.68 ! [H: real,Diff: nat > real > real,F2: real > real,N: nat] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ H )
% 0.35/0.68 => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ H ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ H )
% 0.35/0.68 & ( ( F2 @ H )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin2
% 0.35/0.68 thf(fact_9121_Maclaurin,axiom,
% 0.35/0.68 ! [H: real,N: nat,Diff: nat > real > real,F2: real > real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ H )
% 0.35/0.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ H ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ T6 )
% 0.35/0.68 & ( ord_less_real @ T6 @ H )
% 0.35/0.68 & ( ( F2 @ H )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin
% 0.35/0.68 thf(fact_9122_Maclaurin__all__lt,axiom,
% 0.35/0.68 ! [Diff: nat > real > real,F2: real > real,N: nat,X: real] :
% 0.35/0.68 ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( X != zero_zero_real )
% 0.35/0.68 => ( ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 0.35/0.68 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68 & ( ( F2 @ X )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin_all_lt
% 0.35/0.68 thf(fact_9123_Maclaurin__bi__le,axiom,
% 0.35/0.68 ! [Diff: nat > real > real,F2: real > real,N: nat,X: real] :
% 0.35/0.68 ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 0.35/0.68 & ( ( F2 @ X )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin_bi_le
% 0.35/0.68 thf(fact_9124_Taylor__down,axiom,
% 0.35/0.68 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ A @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ B ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ( ( ord_less_real @ A @ C2 )
% 0.35/0.68 => ( ( ord_less_eq_real @ C2 @ B )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_real @ A @ T6 )
% 0.35/0.68 & ( ord_less_real @ T6 @ C2 )
% 0.35/0.68 & ( ( F2 @ A )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Taylor_down
% 0.35/0.68 thf(fact_9125_Taylor__up,axiom,
% 0.35/0.68 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ A @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ B ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ( ( ord_less_eq_real @ A @ C2 )
% 0.35/0.68 => ( ( ord_less_real @ C2 @ B )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ord_less_real @ C2 @ T6 )
% 0.35/0.68 & ( ord_less_real @ T6 @ B )
% 0.35/0.68 & ( ( F2 @ B )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Taylor_up
% 0.35/0.68 thf(fact_9126_Taylor,axiom,
% 0.35/0.68 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real,X: real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( ( Diff @ zero_zero_nat )
% 0.35/0.68 = F2 )
% 0.35/0.68 => ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ A @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ B ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ( ( ord_less_eq_real @ A @ C2 )
% 0.35/0.68 => ( ( ord_less_eq_real @ C2 @ B )
% 0.35/0.68 => ( ( ord_less_eq_real @ A @ X )
% 0.35/0.68 => ( ( ord_less_eq_real @ X @ B )
% 0.35/0.68 => ( ( X != C2 )
% 0.35/0.68 => ? [T6: real] :
% 0.35/0.68 ( ( ( ord_less_real @ X @ C2 )
% 0.35/0.68 => ( ( ord_less_real @ X @ T6 )
% 0.35/0.68 & ( ord_less_real @ T6 @ C2 ) ) )
% 0.35/0.68 & ( ~ ( ord_less_real @ X @ C2 )
% 0.35/0.68 => ( ( ord_less_real @ C2 @ T6 )
% 0.35/0.68 & ( ord_less_real @ T6 @ X ) ) )
% 0.35/0.68 & ( ( F2 @ X )
% 0.35/0.68 = ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ M6 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ N ) )
% 0.35/0.68 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Taylor
% 0.35/0.68 thf(fact_9127_Maclaurin__lemma2,axiom,
% 0.35/0.68 ! [N: nat,H: real,Diff: nat > real > real,K2: nat,B5: real] :
% 0.35/0.68 ( ! [M: nat,T6: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M @ N )
% 0.35/0.68 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 0.35/0.68 & ( ord_less_eq_real @ T6 @ H ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 0.35/0.68 => ( ( N
% 0.35/0.68 = ( suc @ K2 ) )
% 0.35/0.68 => ! [M3: nat,T7: real] :
% 0.35/0.68 ( ( ( ord_less_nat @ M3 @ N )
% 0.35/0.68 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 0.35/0.68 & ( ord_less_eq_real @ T7 @ H ) )
% 0.35/0.68 => ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [U2: real] :
% 0.35/0.68 ( minus_minus_real @ ( Diff @ M3 @ U2 )
% 0.35/0.68 @ ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 0.35/0.68 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 0.35/0.68 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T7 )
% 0.35/0.68 @ ( plus_plus_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 0.35/0.68 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Maclaurin_lemma2
% 0.35/0.68 thf(fact_9128_DERIV__pow,axiom,
% 0.35/0.68 ! [N: nat,X: real,S2: set_real] :
% 0.35/0.68 ( has_fi5821293074295781190e_real
% 0.35/0.68 @ ^ [X4: real] : ( power_power_real @ X4 @ N )
% 0.35/0.68 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ X @ S2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_pow
% 0.35/0.68 thf(fact_9129_DERIV__const__ratio__const,axiom,
% 0.35/0.68 ! [A: real,B: real,F2: real > real,K2: real] :
% 0.35/0.68 ( ( A != B )
% 0.35/0.68 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F2 @ K2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 0.35/0.68 => ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 0.35/0.68 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DERIV_const_ratio_const
% 0.35/0.68 thf(fact_9130_MVT2,axiom,
% 0.35/0.68 ! [A: real,B: real,F2: real > real,F5: real > real] :
% 0.35/0.68 ( ( ord_less_real @ A @ B )
% 0.35/0.68 => ( ! [X3: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68 => ( ( ord_less_eq_real @ X3 @ B )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ F2 @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.68 => ? [Z: real] :
% 0.35/0.68 ( ( ord_less_real @ A @ Z )
% 0.35/0.68 & ( ord_less_real @ Z @ B )
% 0.35/0.68 & ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 0.35/0.68 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % MVT2
% 0.35/0.68 thf(fact_9131_GMVT_H,axiom,
% 0.35/0.68 ! [A: real,B: real,F2: real > real,G2: real > real,G3: real > real,F5: real > real] :
% 0.35/0.68 ( ( ord_less_real @ A @ B )
% 0.35/0.68 => ( ! [Z: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ A @ Z )
% 0.35/0.68 => ( ( ord_less_eq_real @ Z @ B )
% 0.35/0.68 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ F2 ) ) )
% 0.35/0.68 => ( ! [Z: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ A @ Z )
% 0.35/0.68 => ( ( ord_less_eq_real @ Z @ B )
% 0.35/0.68 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ G2 ) ) )
% 0.35/0.68 => ( ! [Z: real] :
% 0.35/0.68 ( ( ord_less_real @ A @ Z )
% 0.35/0.68 => ( ( ord_less_real @ Z @ B )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ G2 @ ( G3 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 0.35/0.68 => ( ! [Z: real] :
% 0.35/0.68 ( ( ord_less_real @ A @ Z )
% 0.35/0.68 => ( ( ord_less_real @ Z @ B )
% 0.35/0.68 => ( has_fi5821293074295781190e_real @ F2 @ ( F5 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 0.35/0.68 => ? [C: real] :
% 0.35/0.68 ( ( ord_less_real @ A @ C )
% 0.35/0.68 & ( ord_less_real @ C @ B )
% 0.35/0.68 & ( ( times_times_real @ ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) ) @ ( G3 @ C ) )
% 0.35/0.68 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ ( F5 @ C ) ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % GMVT'
% 0.35/0.68 thf(fact_9132_summable__Leibniz_I3_J,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 0.35/0.68 => ! [N8: nat] :
% 0.35/0.68 ( member_real
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 0.35/0.68 @ ( set_or1222579329274155063t_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) )
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz(3)
% 0.35/0.68 thf(fact_9133_summable__Leibniz_I2_J,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 0.35/0.68 => ! [N8: nat] :
% 0.35/0.68 ( member_real
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 0.35/0.68 @ ( set_or1222579329274155063t_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz(2)
% 0.35/0.68 thf(fact_9134_summable__Leibniz_H_I4_J,axiom,
% 0.35/0.68 ! [A: nat > real,N: nat] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68 => ( ord_less_eq_real
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz'(4)
% 0.35/0.68 thf(fact_9135_mult__nat__left__at__top,axiom,
% 0.35/0.68 ! [C2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.35/0.68 => ( filterlim_nat_nat @ ( times_times_nat @ C2 ) @ at_top_nat @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % mult_nat_left_at_top
% 0.35/0.68 thf(fact_9136_mult__nat__right__at__top,axiom,
% 0.35/0.68 ! [C2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 0.35/0.68 => ( filterlim_nat_nat
% 0.35/0.68 @ ^ [X4: nat] : ( times_times_nat @ X4 @ C2 )
% 0.35/0.68 @ at_top_nat
% 0.35/0.68 @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % mult_nat_right_at_top
% 0.35/0.68 thf(fact_9137_nested__sequence__unique,axiom,
% 0.35/0.68 ! [F2: nat > real,G2: nat > real] :
% 0.35/0.68 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G2 @ ( suc @ N3 ) ) @ ( G2 @ N3 ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 0.35/0.68 => ( ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ N4 ) @ ( G2 @ N4 ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68 @ at_top_nat )
% 0.35/0.68 => ? [L4: real] :
% 0.35/0.68 ( ! [N8: nat] : ( ord_less_eq_real @ ( F2 @ N8 ) @ L4 )
% 0.35/0.68 & ( filterlim_nat_real @ F2 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 0.35/0.68 & ! [N8: nat] : ( ord_less_eq_real @ L4 @ ( G2 @ N8 ) )
% 0.35/0.68 & ( filterlim_nat_real @ G2 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nested_sequence_unique
% 0.35/0.68 thf(fact_9138_LIMSEQ__inverse__zero,axiom,
% 0.35/0.68 ! [X8: nat > real] :
% 0.35/0.68 ( ! [R4: real] :
% 0.35/0.68 ? [N7: nat] :
% 0.35/0.68 ! [N3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ N7 @ N3 )
% 0.35/0.68 => ( ord_less_real @ R4 @ ( X8 @ N3 ) ) )
% 0.35/0.68 => ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] : ( inverse_inverse_real @ ( X8 @ N4 ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68 @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % LIMSEQ_inverse_zero
% 0.35/0.68 thf(fact_9139_LIMSEQ__inverse__real__of__nat,axiom,
% 0.35/0.68 ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68 @ at_top_nat ) ).
% 0.35/0.68
% 0.35/0.68 % LIMSEQ_inverse_real_of_nat
% 0.35/0.68 thf(fact_9140_LIMSEQ__inverse__real__of__nat__add,axiom,
% 0.35/0.68 ! [R3: real] :
% 0.35/0.68 ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] : ( plus_plus_real @ R3 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ R3 )
% 0.35/0.68 @ at_top_nat ) ).
% 0.35/0.68
% 0.35/0.68 % LIMSEQ_inverse_real_of_nat_add
% 0.35/0.68 thf(fact_9141_increasing__LIMSEQ,axiom,
% 0.35/0.68 ! [F2: nat > real,L: real] :
% 0.35/0.68 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ L )
% 0.35/0.68 => ( ! [E2: real] :
% 0.35/0.68 ( ( ord_less_real @ zero_zero_real @ E2 )
% 0.35/0.68 => ? [N8: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F2 @ N8 ) @ E2 ) ) )
% 0.35/0.68 => ( filterlim_nat_real @ F2 @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % increasing_LIMSEQ
% 0.35/0.68 thf(fact_9142_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 0.35/0.68 ! [R3: real] :
% 0.35/0.68 ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] : ( plus_plus_real @ R3 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ R3 )
% 0.35/0.68 @ at_top_nat ) ).
% 0.35/0.68
% 0.35/0.68 % LIMSEQ_inverse_real_of_nat_add_minus
% 0.35/0.68 thf(fact_9143_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 0.35/0.68 ! [R3: real] :
% 0.35/0.68 ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] : ( times_times_real @ R3 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ R3 )
% 0.35/0.68 @ at_top_nat ) ).
% 0.35/0.68
% 0.35/0.68 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 0.35/0.68 thf(fact_9144_summable__Leibniz_I1_J,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68 => ( summable_real
% 0.35/0.68 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz(1)
% 0.35/0.68 thf(fact_9145_summable,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68 => ( summable_real
% 0.35/0.68 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable
% 0.35/0.68 thf(fact_9146_cos__diff__limit__1,axiom,
% 0.35/0.68 ! [Theta: nat > real,Theta2: real] :
% 0.35/0.68 ( ( filterlim_nat_real
% 0.35/0.68 @ ^ [J: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J ) @ Theta2 ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.35/0.68 @ at_top_nat )
% 0.35/0.68 => ~ ! [K: nat > int] :
% 0.35/0.68 ~ ( filterlim_nat_real
% 0.35/0.68 @ ^ [J: nat] : ( minus_minus_real @ ( Theta @ J ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K @ J ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ Theta2 )
% 0.35/0.68 @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % cos_diff_limit_1
% 0.35/0.68 thf(fact_9147_cos__limit__1,axiom,
% 0.35/0.68 ! [Theta: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real
% 0.35/0.68 @ ^ [J: nat] : ( cos_real @ ( Theta @ J ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ one_one_real )
% 0.35/0.68 @ at_top_nat )
% 0.35/0.68 => ? [K: nat > int] :
% 0.35/0.68 ( filterlim_nat_real
% 0.35/0.68 @ ^ [J: nat] : ( minus_minus_real @ ( Theta @ J ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K @ J ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68 @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % cos_limit_1
% 0.35/0.68 thf(fact_9148_summable__Leibniz_I4_J,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68 => ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] :
% 0.35/0.68 ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 0.35/0.68 @ at_top_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz(4)
% 0.35/0.68 thf(fact_9149_zeroseq__arctan__series,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.35/0.68 => ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 0.35/0.68 @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % zeroseq_arctan_series
% 0.35/0.68 thf(fact_9150_summable__Leibniz_H_I2_J,axiom,
% 0.35/0.68 ! [A: nat > real,N: nat] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68 => ( ord_less_eq_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz'(2)
% 0.35/0.68 thf(fact_9151_summable__Leibniz_H_I3_J,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68 => ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] :
% 0.35/0.68 ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 0.35/0.68 @ at_top_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz'(3)
% 0.35/0.68 thf(fact_9152_sums__alternating__upper__lower,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ? [L4: real] :
% 0.35/0.68 ( ! [N8: nat] :
% 0.35/0.68 ( ord_less_eq_real
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 0.35/0.68 @ L4 )
% 0.35/0.68 & ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] :
% 0.35/0.68 ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ L4 )
% 0.35/0.68 @ at_top_nat )
% 0.35/0.68 & ! [N8: nat] :
% 0.35/0.68 ( ord_less_eq_real @ L4
% 0.35/0.68 @ ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) )
% 0.35/0.68 & ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] :
% 0.35/0.68 ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ L4 )
% 0.35/0.68 @ at_top_nat ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sums_alternating_upper_lower
% 0.35/0.68 thf(fact_9153_summable__Leibniz_I5_J,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ( topolo6980174941875973593q_real @ A )
% 0.35/0.68 => ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] :
% 0.35/0.68 ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 0.35/0.68 @ at_top_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz(5)
% 0.35/0.68 thf(fact_9154_summable__Leibniz_H_I5_J,axiom,
% 0.35/0.68 ! [A: nat > real] :
% 0.35/0.68 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 0.35/0.68 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 0.35/0.68 => ( filterlim_nat_real
% 0.35/0.68 @ ^ [N4: nat] :
% 0.35/0.68 ( groups6591440286371151544t_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 0.35/0.68 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real
% 0.35/0.68 @ ( suminf_real
% 0.35/0.68 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 0.35/0.68 @ at_top_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % summable_Leibniz'(5)
% 0.35/0.68 thf(fact_9155_real__bounded__linear,axiom,
% 0.35/0.68 ( real_V5970128139526366754l_real
% 0.35/0.68 = ( ^ [F4: real > real] :
% 0.35/0.68 ? [C3: real] :
% 0.35/0.68 ( F4
% 0.35/0.68 = ( ^ [X4: real] : ( times_times_real @ X4 @ C3 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % real_bounded_linear
% 0.35/0.68 thf(fact_9156_filterlim__Suc,axiom,
% 0.35/0.68 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 0.35/0.68
% 0.35/0.68 % filterlim_Suc
% 0.35/0.68 thf(fact_9157_tendsto__exp__limit__at__right,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( filterlim_real_real
% 0.35/0.68 @ ^ [Y4: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y4 ) ) @ ( divide_divide_real @ one_one_real @ Y4 ) )
% 0.35/0.68 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 0.35/0.68 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % tendsto_exp_limit_at_right
% 0.35/0.68 thf(fact_9158_GMVT,axiom,
% 0.35/0.68 ! [A: real,B: real,F2: real > real,G2: real > real] :
% 0.35/0.68 ( ( ord_less_real @ A @ B )
% 0.35/0.68 => ( ! [X3: real] :
% 0.35/0.68 ( ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68 & ( ord_less_eq_real @ X3 @ B ) )
% 0.35/0.68 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F2 ) )
% 0.35/0.68 => ( ! [X3: real] :
% 0.35/0.68 ( ( ( ord_less_real @ A @ X3 )
% 0.35/0.68 & ( ord_less_real @ X3 @ B ) )
% 0.35/0.68 => ( differ6690327859849518006l_real @ F2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.68 => ( ! [X3: real] :
% 0.35/0.68 ( ( ( ord_less_eq_real @ A @ X3 )
% 0.35/0.68 & ( ord_less_eq_real @ X3 @ B ) )
% 0.35/0.68 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G2 ) )
% 0.35/0.68 => ( ! [X3: real] :
% 0.35/0.68 ( ( ( ord_less_real @ A @ X3 )
% 0.35/0.68 & ( ord_less_real @ X3 @ B ) )
% 0.35/0.68 => ( differ6690327859849518006l_real @ G2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 0.35/0.68 => ? [G_c: real,F_c: real,C: real] :
% 0.35/0.68 ( ( has_fi5821293074295781190e_real @ G2 @ G_c @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.35/0.68 & ( has_fi5821293074295781190e_real @ F2 @ F_c @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 0.35/0.68 & ( ord_less_real @ A @ C )
% 0.35/0.68 & ( ord_less_real @ C @ B )
% 0.35/0.68 & ( ( times_times_real @ ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) ) @ G_c )
% 0.35/0.68 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % GMVT
% 0.35/0.68 thf(fact_9159_eventually__sequentially__Suc,axiom,
% 0.35/0.68 ! [P2: nat > $o] :
% 0.35/0.68 ( ( eventually_nat
% 0.35/0.68 @ ^ [I: nat] : ( P2 @ ( suc @ I ) )
% 0.35/0.68 @ at_top_nat )
% 0.35/0.68 = ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % eventually_sequentially_Suc
% 0.35/0.68 thf(fact_9160_eventually__sequentially,axiom,
% 0.35/0.68 ! [P2: nat > $o] :
% 0.35/0.68 ( ( eventually_nat @ P2 @ at_top_nat )
% 0.35/0.68 = ( ? [N5: nat] :
% 0.35/0.68 ! [N4: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ N5 @ N4 )
% 0.35/0.68 => ( P2 @ N4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % eventually_sequentially
% 0.35/0.68 thf(fact_9161_eventually__sequentiallyI,axiom,
% 0.35/0.68 ! [C2: nat,P2: nat > $o] :
% 0.35/0.68 ( ! [X3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ C2 @ X3 )
% 0.35/0.68 => ( P2 @ X3 ) )
% 0.35/0.68 => ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % eventually_sequentiallyI
% 0.35/0.68 thf(fact_9162_le__sequentially,axiom,
% 0.35/0.68 ! [F3: filter_nat] :
% 0.35/0.68 ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 0.35/0.68 = ( ! [N5: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N5 ) @ F3 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % le_sequentially
% 0.35/0.68 thf(fact_9163_atLeast__0,axiom,
% 0.35/0.68 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 0.35/0.68 = top_top_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast_0
% 0.35/0.68 thf(fact_9164_atLeast__Suc__greaterThan,axiom,
% 0.35/0.68 ! [K2: nat] :
% 0.35/0.68 ( ( set_ord_atLeast_nat @ ( suc @ K2 ) )
% 0.35/0.68 = ( set_or1210151606488870762an_nat @ K2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast_Suc_greaterThan
% 0.35/0.68 thf(fact_9165_greaterThan__0,axiom,
% 0.35/0.68 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 0.35/0.68 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % greaterThan_0
% 0.35/0.68 thf(fact_9166_greaterThan__Suc,axiom,
% 0.35/0.68 ! [K2: nat] :
% 0.35/0.68 ( ( set_or1210151606488870762an_nat @ ( suc @ K2 ) )
% 0.35/0.68 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K2 ) @ ( insert_nat @ ( suc @ K2 ) @ bot_bot_set_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % greaterThan_Suc
% 0.35/0.68 thf(fact_9167_atLeast__Suc,axiom,
% 0.35/0.68 ! [K2: nat] :
% 0.35/0.68 ( ( set_ord_atLeast_nat @ ( suc @ K2 ) )
% 0.35/0.68 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K2 ) @ ( insert_nat @ K2 @ bot_bot_set_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % atLeast_Suc
% 0.35/0.68 thf(fact_9168_filterlim__pow__at__bot__even,axiom,
% 0.35/0.68 ! [N: nat,F2: real > real,F3: filter_real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( filterlim_real_real @ F2 @ at_bot_real @ F3 )
% 0.35/0.68 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68 => ( filterlim_real_real
% 0.35/0.68 @ ^ [X4: real] : ( power_power_real @ ( F2 @ X4 ) @ N )
% 0.35/0.68 @ at_top_real
% 0.35/0.68 @ F3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % filterlim_pow_at_bot_even
% 0.35/0.68 thf(fact_9169_GreatestI__ex__nat,axiom,
% 0.35/0.68 ! [P2: nat > $o,B: nat] :
% 0.35/0.68 ( ? [X_1: nat] : ( P2 @ X_1 )
% 0.35/0.68 => ( ! [Y3: nat] :
% 0.35/0.68 ( ( P2 @ Y3 )
% 0.35/0.68 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.35/0.68 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % GreatestI_ex_nat
% 0.35/0.68 thf(fact_9170_Greatest__le__nat,axiom,
% 0.35/0.68 ! [P2: nat > $o,K2: nat,B: nat] :
% 0.35/0.68 ( ( P2 @ K2 )
% 0.35/0.68 => ( ! [Y3: nat] :
% 0.35/0.68 ( ( P2 @ Y3 )
% 0.35/0.68 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.35/0.68 => ( ord_less_eq_nat @ K2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Greatest_le_nat
% 0.35/0.68 thf(fact_9171_GreatestI__nat,axiom,
% 0.35/0.68 ! [P2: nat > $o,K2: nat,B: nat] :
% 0.35/0.68 ( ( P2 @ K2 )
% 0.35/0.68 => ( ! [Y3: nat] :
% 0.35/0.68 ( ( P2 @ Y3 )
% 0.35/0.68 => ( ord_less_eq_nat @ Y3 @ B ) )
% 0.35/0.68 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % GreatestI_nat
% 0.35/0.68 thf(fact_9172_filterlim__pow__at__bot__odd,axiom,
% 0.35/0.68 ! [N: nat,F2: real > real,F3: filter_real] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( filterlim_real_real @ F2 @ at_bot_real @ F3 )
% 0.35/0.68 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 0.35/0.68 => ( filterlim_real_real
% 0.35/0.68 @ ^ [X4: real] : ( power_power_real @ ( F2 @ X4 ) @ N )
% 0.35/0.68 @ at_bot_real
% 0.35/0.68 @ F3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % filterlim_pow_at_bot_odd
% 0.35/0.68 thf(fact_9173_MVT,axiom,
% 0.35/0.68 ! [A: real,B: real,F2: real > real] :
% 0.35/0.68 ( ( ord_less_real @ A @ B )
% 0.35/0.68 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F2 )
% 0.35/0.68 => ( ! [X3: real] :
% 0.35/0.68 ( ( ord_less_real @ A @ X3 )
% 0.35/0.68 => ( ( ord_less_real @ X3 @ B )
% 0.35/0.68 => ( differ6690327859849518006l_real @ F2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 0.35/0.68 => ? [L4: real,Z: real] :
% 0.35/0.68 ( ( ord_less_real @ A @ Z )
% 0.35/0.68 & ( ord_less_real @ Z @ B )
% 0.35/0.68 & ( has_fi5821293074295781190e_real @ F2 @ L4 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) )
% 0.35/0.68 & ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 0.35/0.68 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % MVT
% 0.35/0.68 thf(fact_9174_inj__sgn__power,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( inj_on_real_real
% 0.35/0.68 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 0.35/0.68 @ top_top_set_real ) ) ).
% 0.35/0.68
% 0.35/0.68 % inj_sgn_power
% 0.35/0.68 thf(fact_9175_UN__lessThan__UNIV,axiom,
% 0.35/0.68 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 0.35/0.68 = top_top_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % UN_lessThan_UNIV
% 0.35/0.68 thf(fact_9176_UN__atMost__UNIV,axiom,
% 0.35/0.68 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 0.35/0.68 = top_top_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % UN_atMost_UNIV
% 0.35/0.68 thf(fact_9177_UN__atLeast__UNIV,axiom,
% 0.35/0.68 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 0.35/0.68 = top_top_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % UN_atLeast_UNIV
% 0.35/0.68 thf(fact_9178_Sup__nat__empty,axiom,
% 0.35/0.68 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % Sup_nat_empty
% 0.35/0.68 thf(fact_9179_inj__list__encode,axiom,
% 0.35/0.68 ! [A4: set_list_nat] : ( inj_on_list_nat_nat @ nat_list_encode @ A4 ) ).
% 0.35/0.68
% 0.35/0.68 % inj_list_encode
% 0.35/0.68 thf(fact_9180_inj__list__decode,axiom,
% 0.35/0.68 ! [A4: set_nat] : ( inj_on_nat_list_nat @ nat_list_decode @ A4 ) ).
% 0.35/0.68
% 0.35/0.68 % inj_list_decode
% 0.35/0.68 thf(fact_9181_inj__prod__encode,axiom,
% 0.35/0.68 ! [A4: set_Pr1261947904930325089at_nat] : ( inj_on2178005380612969504at_nat @ nat_prod_encode @ A4 ) ).
% 0.35/0.68
% 0.35/0.68 % inj_prod_encode
% 0.35/0.68 thf(fact_9182_inj__Suc,axiom,
% 0.35/0.68 ! [N6: set_nat] : ( inj_on_nat_nat @ suc @ N6 ) ).
% 0.35/0.68
% 0.35/0.68 % inj_Suc
% 0.35/0.68 thf(fact_9183_inj__prod__decode,axiom,
% 0.35/0.68 ! [A4: set_nat] : ( inj_on5538052773655684606at_nat @ nat_prod_decode @ A4 ) ).
% 0.35/0.68
% 0.35/0.68 % inj_prod_decode
% 0.35/0.68 thf(fact_9184_inj__on__diff__nat,axiom,
% 0.35/0.68 ! [N6: set_nat,K2: nat] :
% 0.35/0.68 ( ! [N3: nat] :
% 0.35/0.68 ( ( member_nat @ N3 @ N6 )
% 0.35/0.68 => ( ord_less_eq_nat @ K2 @ N3 ) )
% 0.35/0.68 => ( inj_on_nat_nat
% 0.35/0.68 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ K2 )
% 0.35/0.68 @ N6 ) ) ).
% 0.35/0.68
% 0.35/0.68 % inj_on_diff_nat
% 0.35/0.68 thf(fact_9185_inj__on__set__encode,axiom,
% 0.35/0.68 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 0.35/0.68
% 0.35/0.68 % inj_on_set_encode
% 0.35/0.68 thf(fact_9186_INT__greaterThan__UNIV,axiom,
% 0.35/0.68 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 0.35/0.68 = bot_bot_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % INT_greaterThan_UNIV
% 0.35/0.68 thf(fact_9187_Gcd__eq__Max,axiom,
% 0.35/0.68 ! [M5: set_nat] :
% 0.35/0.68 ( ( finite_finite_nat @ M5 )
% 0.35/0.68 => ( ( M5 != bot_bot_set_nat )
% 0.35/0.68 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 0.35/0.68 => ( ( gcd_Gcd_nat @ M5 )
% 0.35/0.68 = ( lattic8265883725875713057ax_nat
% 0.35/0.68 @ ( comple7806235888213564991et_nat
% 0.35/0.68 @ ( image_nat_set_nat
% 0.35/0.68 @ ^ [M6: nat] :
% 0.35/0.68 ( collect_nat
% 0.35/0.68 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M6 ) )
% 0.35/0.68 @ M5 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Gcd_eq_Max
% 0.35/0.68 thf(fact_9188_Max__divisors__self__nat,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( N != zero_zero_nat )
% 0.35/0.68 => ( ( lattic8265883725875713057ax_nat
% 0.35/0.68 @ ( collect_nat
% 0.35/0.68 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N ) ) )
% 0.35/0.68 = N ) ) ).
% 0.35/0.68
% 0.35/0.68 % Max_divisors_self_nat
% 0.35/0.68 thf(fact_9189_Sup__nat__def,axiom,
% 0.35/0.68 ( complete_Sup_Sup_nat
% 0.35/0.68 = ( ^ [X7: set_nat] : ( if_nat @ ( X7 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X7 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Sup_nat_def
% 0.35/0.68 thf(fact_9190_card__le__Suc__Max,axiom,
% 0.35/0.68 ! [S3: set_nat] :
% 0.35/0.68 ( ( finite_finite_nat @ S3 )
% 0.35/0.68 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % card_le_Suc_Max
% 0.35/0.68 thf(fact_9191_divide__nat__def,axiom,
% 0.35/0.68 ( divide_divide_nat
% 0.35/0.68 = ( ^ [M6: nat,N4: nat] :
% 0.35/0.68 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 0.35/0.68 @ ( lattic8265883725875713057ax_nat
% 0.35/0.68 @ ( collect_nat
% 0.35/0.68 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N4 ) @ M6 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % divide_nat_def
% 0.35/0.68 thf(fact_9192_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 0.35/0.68 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.68 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.68 ( X
% 0.35/0.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( Xa2 != one_one_nat ) ) )
% 0.35/0.68 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( ~ ( ( Deg2 = Xa2 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 & ( case_o184042715313410164at_nat
% 0.35/0.68 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 & ! [I: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 0.35/0.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.68 & ( ( Mi3 = Ma3 )
% 0.35/0.68 => ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 & ( ( Mi3 != Ma3 )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.35/0.68 & ! [X4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 0.35/0.68 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.68 @ Mima ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT_internal.valid'.elims(1)
% 0.35/0.68 thf(fact_9193_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 0.35/0.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.68 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.68 => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.68 ( X
% 0.35/0.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.68 => ( Xa2 != one_one_nat ) )
% 0.35/0.68 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.68 => ~ ( ( Deg2 = Xa2 )
% 0.35/0.68 & ! [X5: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 & ( case_o184042715313410164at_nat
% 0.35/0.68 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 & ! [I: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 0.35/0.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.68 & ( ( Mi3 = Ma3 )
% 0.35/0.68 => ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 & ( ( Mi3 != Ma3 )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.35/0.68 & ! [X4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 0.35/0.68 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.68 @ Mima ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT_internal.valid'.elims(2)
% 0.35/0.68 thf(fact_9194_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 0.35/0.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.68 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.68 => ( ( ? [Uu2: $o,Uv2: $o] :
% 0.35/0.68 ( X
% 0.35/0.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.68 => ( Xa2 = one_one_nat ) )
% 0.35/0.68 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.68 => ( ( Deg2 = Xa2 )
% 0.35/0.68 & ! [X3: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 & ( case_o184042715313410164at_nat
% 0.35/0.68 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 & ! [I: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 0.35/0.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.68 & ( ( Mi3 = Ma3 )
% 0.35/0.68 => ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 & ( ( Mi3 != Ma3 )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.35/0.68 & ! [X4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 0.35/0.68 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.68 @ Mima ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT_internal.valid'.elims(3)
% 0.35/0.68 thf(fact_9195_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 0.35/0.68 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 0.35/0.68 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 0.35/0.68 = ( ( Deg = Deg3 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.68 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 & ( case_o184042715313410164at_nat
% 0.35/0.68 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X7 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.68 & ! [I: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X7 ) )
% 0.35/0.68 = ( vEBT_V8194947554948674370ptions @ Summary @ I ) ) )
% 0.35/0.68 & ( ( Mi3 = Ma3 )
% 0.35/0.68 => ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 & ( ( Mi3 != Ma3 )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 0.35/0.68 & ! [X4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 0.35/0.68 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.68 @ Mima2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT_internal.valid'.simps(2)
% 0.35/0.68 thf(fact_9196_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 0.35/0.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.68 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.68 => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.35/0.68 => ( Xa2 = one_one_nat ) ) )
% 0.35/0.68 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 0.35/0.68 => ( ( Deg2 = Xa2 )
% 0.35/0.68 & ! [X3: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 & ( case_o184042715313410164at_nat
% 0.35/0.68 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 & ! [I: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 0.35/0.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.68 & ( ( Mi3 = Ma3 )
% 0.35/0.68 => ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 & ( ( Mi3 != Ma3 )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.35/0.68 & ! [X4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 0.35/0.68 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.68 @ Mima ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT_internal.valid'.pelims(3)
% 0.35/0.68 thf(fact_9197_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 0.35/0.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 0.35/0.68 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.68 => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 0.35/0.68 => ( Xa2 != one_one_nat ) ) )
% 0.35/0.68 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 0.35/0.68 => ~ ( ( Deg2 = Xa2 )
% 0.35/0.68 & ! [X5: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 & ( case_o184042715313410164at_nat
% 0.35/0.68 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 & ! [I: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 0.35/0.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.68 & ( ( Mi3 = Ma3 )
% 0.35/0.68 => ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 & ( ( Mi3 != Ma3 )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.35/0.68 & ! [X4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 0.35/0.68 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.68 @ Mima ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT_internal.valid'.pelims(2)
% 0.35/0.68 thf(fact_9198_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 0.35/0.68 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 0.35/0.68 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 0.35/0.68 => ( ! [Uu2: $o,Uv2: $o] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 0.35/0.68 => ( ( Y
% 0.35/0.68 = ( Xa2 = one_one_nat ) )
% 0.35/0.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 0.35/0.68 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.68 ( ( X
% 0.35/0.68 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.68 => ( ( Y
% 0.35/0.68 = ( ( Deg2 = Xa2 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 0.35/0.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 & ( case_o184042715313410164at_nat
% 0.35/0.68 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 0.35/0.68 & ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [Mi3: nat,Ma3: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 0.35/0.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 & ! [I: nat] :
% 0.35/0.68 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.68 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 0.35/0.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 0.35/0.68 & ( ( Mi3 = Ma3 )
% 0.35/0.68 => ! [X4: vEBT_VEBT] :
% 0.35/0.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 0.35/0.68 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 0.35/0.68 & ( ( Mi3 != Ma3 )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 0.35/0.68 & ! [X4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 0.35/0.68 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 0.35/0.68 => ( ( ord_less_nat @ Mi3 @ X4 )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 0.35/0.68 @ Mima ) ) )
% 0.35/0.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % VEBT_internal.valid'.pelims(1)
% 0.35/0.68 thf(fact_9199_min__Suc__Suc,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_min_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 0.35/0.68 = ( suc @ ( ord_min_nat @ M2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % min_Suc_Suc
% 0.35/0.68 thf(fact_9200_min__0L,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_min_nat @ zero_zero_nat @ N )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % min_0L
% 0.35/0.68 thf(fact_9201_min__0R,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_min_nat @ N @ zero_zero_nat )
% 0.35/0.68 = zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % min_0R
% 0.35/0.68 thf(fact_9202_take__bit__num__simps_I1_J,axiom,
% 0.35/0.68 ! [M2: num] :
% 0.35/0.68 ( ( bit_take_bit_num @ zero_zero_nat @ M2 )
% 0.35/0.68 = none_num ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_num_simps(1)
% 0.35/0.68 thf(fact_9203_take__bit__num__simps_I2_J,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 0.35/0.68 = ( some_num @ one ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_num_simps(2)
% 0.35/0.68 thf(fact_9204_take__bit__num__simps_I3_J,axiom,
% 0.35/0.68 ! [N: nat,M2: num] :
% 0.35/0.68 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M2 ) )
% 0.35/0.68 = ( case_o6005452278849405969um_num @ none_num
% 0.35/0.68 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 0.35/0.68 @ ( bit_take_bit_num @ N @ M2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_num_simps(3)
% 0.35/0.68 thf(fact_9205_min__numeral__Suc,axiom,
% 0.35/0.68 ! [K2: num,N: nat] :
% 0.35/0.68 ( ( ord_min_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 0.35/0.68 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K2 ) @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % min_numeral_Suc
% 0.35/0.68 thf(fact_9206_min__Suc__numeral,axiom,
% 0.35/0.68 ! [N: nat,K2: num] :
% 0.35/0.68 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 0.35/0.68 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % min_Suc_numeral
% 0.35/0.68 thf(fact_9207_take__bit__num__simps_I4_J,axiom,
% 0.35/0.68 ! [N: nat,M2: num] :
% 0.35/0.68 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M2 ) )
% 0.35/0.68 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M2 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_num_simps(4)
% 0.35/0.68 thf(fact_9208_min__diff,axiom,
% 0.35/0.68 ! [M2: nat,I2: nat,N: nat] :
% 0.35/0.68 ( ( ord_min_nat @ ( minus_minus_nat @ M2 @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 0.35/0.68 = ( minus_minus_nat @ ( ord_min_nat @ M2 @ N ) @ I2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % min_diff
% 0.35/0.68 thf(fact_9209_nat__mult__min__left,axiom,
% 0.35/0.68 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.68 ( ( times_times_nat @ ( ord_min_nat @ M2 @ N ) @ Q2 )
% 0.35/0.68 = ( ord_min_nat @ ( times_times_nat @ M2 @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_mult_min_left
% 0.35/0.68 thf(fact_9210_nat__mult__min__right,axiom,
% 0.35/0.68 ! [M2: nat,N: nat,Q2: nat] :
% 0.35/0.68 ( ( times_times_nat @ M2 @ ( ord_min_nat @ N @ Q2 ) )
% 0.35/0.68 = ( ord_min_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q2 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % nat_mult_min_right
% 0.35/0.68 thf(fact_9211_inf__nat__def,axiom,
% 0.35/0.68 inf_inf_nat = ord_min_nat ).
% 0.35/0.68
% 0.35/0.68 % inf_nat_def
% 0.35/0.68 thf(fact_9212_min__Suc1,axiom,
% 0.35/0.68 ! [N: nat,M2: nat] :
% 0.35/0.68 ( ( ord_min_nat @ ( suc @ N ) @ M2 )
% 0.35/0.68 = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ N @ M7 ) )
% 0.35/0.68 @ M2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % min_Suc1
% 0.35/0.68 thf(fact_9213_min__Suc2,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_min_nat @ M2 @ ( suc @ N ) )
% 0.35/0.68 = ( case_nat_nat @ zero_zero_nat
% 0.35/0.68 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ M7 @ N ) )
% 0.35/0.68 @ M2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % min_Suc2
% 0.35/0.68 thf(fact_9214_take__bit__num__def,axiom,
% 0.35/0.68 ( bit_take_bit_num
% 0.35/0.68 = ( ^ [N4: nat,M6: num] :
% 0.35/0.68 ( if_option_num
% 0.35/0.68 @ ( ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M6 ) )
% 0.35/0.68 = zero_zero_nat )
% 0.35/0.68 @ none_num
% 0.35/0.68 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % take_bit_num_def
% 0.35/0.68 thf(fact_9215_pred__nat__def,axiom,
% 0.35/0.68 ( pred_nat
% 0.35/0.68 = ( collec3392354462482085612at_nat
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [M6: nat,N4: nat] :
% 0.35/0.68 ( N4
% 0.35/0.68 = ( suc @ M6 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % pred_nat_def
% 0.35/0.68 thf(fact_9216_Rats__eq__int__div__nat,axiom,
% 0.35/0.68 ( field_5140801741446780682s_real
% 0.35/0.68 = ( collect_real
% 0.35/0.68 @ ^ [Uu3: real] :
% 0.35/0.68 ? [I: int,N4: nat] :
% 0.35/0.68 ( ( Uu3
% 0.35/0.68 = ( divide_divide_real @ ( ring_1_of_int_real @ I ) @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 0.35/0.68 & ( N4 != zero_zero_nat ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Rats_eq_int_div_nat
% 0.35/0.68 thf(fact_9217_card_Ocomp__fun__commute__on,axiom,
% 0.35/0.68 ( ( comp_nat_nat_nat @ suc @ suc )
% 0.35/0.68 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 0.35/0.68
% 0.35/0.68 % card.comp_fun_commute_on
% 0.35/0.68 thf(fact_9218_divmod__integer__eq__cases,axiom,
% 0.35/0.68 ( code_divmod_integer
% 0.35/0.68 = ( ^ [K3: code_integer,L2: code_integer] :
% 0.35/0.68 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 0.35/0.68 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 0.35/0.68 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 0.35/0.68 @ ( if_Pro6119634080678213985nteger
% 0.35/0.68 @ ( ( sgn_sgn_Code_integer @ K3 )
% 0.35/0.68 = ( sgn_sgn_Code_integer @ L2 ) )
% 0.35/0.68 @ ( code_divmod_abs @ K3 @ L2 )
% 0.35/0.68 @ ( produc6916734918728496179nteger
% 0.35/0.68 @ ^ [R: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 0.35/0.68 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % divmod_integer_eq_cases
% 0.35/0.68 thf(fact_9219_less__eq,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 0.35/0.68 = ( ord_less_nat @ M2 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % less_eq
% 0.35/0.68 thf(fact_9220_pred__nat__trancl__eq__le,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 0.35/0.68 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % pred_nat_trancl_eq_le
% 0.35/0.68 thf(fact_9221_bezw__aux,axiom,
% 0.35/0.68 ! [X: nat,Y: nat] :
% 0.35/0.68 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 0.35/0.68 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezw_aux
% 0.35/0.68 thf(fact_9222_gcd__0__left__nat,axiom,
% 0.35/0.68 ! [X: nat] :
% 0.35/0.68 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 0.35/0.68 = X ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_0_left_nat
% 0.35/0.68 thf(fact_9223_gcd__0__nat,axiom,
% 0.35/0.68 ! [X: nat] :
% 0.35/0.68 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 0.35/0.68 = X ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_0_nat
% 0.35/0.68 thf(fact_9224_gcd__nat_Oright__neutral,axiom,
% 0.35/0.68 ! [A: nat] :
% 0.35/0.68 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 0.35/0.68 = A ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.right_neutral
% 0.35/0.68 thf(fact_9225_gcd__nat_Oneutr__eq__iff,axiom,
% 0.35/0.68 ! [A: nat,B: nat] :
% 0.35/0.68 ( ( zero_zero_nat
% 0.35/0.68 = ( gcd_gcd_nat @ A @ B ) )
% 0.35/0.68 = ( ( A = zero_zero_nat )
% 0.35/0.68 & ( B = zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.neutr_eq_iff
% 0.35/0.68 thf(fact_9226_gcd__nat_Oleft__neutral,axiom,
% 0.35/0.68 ! [A: nat] :
% 0.35/0.68 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 0.35/0.68 = A ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.left_neutral
% 0.35/0.68 thf(fact_9227_gcd__nat_Oeq__neutr__iff,axiom,
% 0.35/0.68 ! [A: nat,B: nat] :
% 0.35/0.68 ( ( ( gcd_gcd_nat @ A @ B )
% 0.35/0.68 = zero_zero_nat )
% 0.35/0.68 = ( ( A = zero_zero_nat )
% 0.35/0.68 & ( B = zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.eq_neutr_iff
% 0.35/0.68 thf(fact_9228_gcd__Suc__0,axiom,
% 0.35/0.68 ! [M2: nat] :
% 0.35/0.68 ( ( gcd_gcd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 0.35/0.68 = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_Suc_0
% 0.35/0.68 thf(fact_9229_gcd__pos__nat,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M2 @ N ) )
% 0.35/0.68 = ( ( M2 != zero_zero_nat )
% 0.35/0.68 | ( N != zero_zero_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_pos_nat
% 0.35/0.68 thf(fact_9230_gcd__diff2__nat,axiom,
% 0.35/0.68 ! [M2: nat,N: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ M2 @ N )
% 0.35/0.68 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M2 ) @ N )
% 0.35/0.68 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_diff2_nat
% 0.35/0.68 thf(fact_9231_gcd__diff1__nat,axiom,
% 0.35/0.68 ! [N: nat,M2: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ N @ M2 )
% 0.35/0.68 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M2 @ N ) @ N )
% 0.35/0.68 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_diff1_nat
% 0.35/0.68 thf(fact_9232_gcd__le1__nat,axiom,
% 0.35/0.68 ! [A: nat,B: nat] :
% 0.35/0.68 ( ( A != zero_zero_nat )
% 0.35/0.68 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_le1_nat
% 0.35/0.68 thf(fact_9233_gcd__le2__nat,axiom,
% 0.35/0.68 ! [B: nat,A: nat] :
% 0.35/0.68 ( ( B != zero_zero_nat )
% 0.35/0.68 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_le2_nat
% 0.35/0.68 thf(fact_9234_gcd__mult__distrib__nat,axiom,
% 0.35/0.68 ! [K2: nat,M2: nat,N: nat] :
% 0.35/0.68 ( ( times_times_nat @ K2 @ ( gcd_gcd_nat @ M2 @ N ) )
% 0.35/0.68 = ( gcd_gcd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_mult_distrib_nat
% 0.35/0.68 thf(fact_9235_gcd__non__0__nat,axiom,
% 0.35/0.68 ! [Y: nat,X: nat] :
% 0.35/0.68 ( ( Y != zero_zero_nat )
% 0.35/0.68 => ( ( gcd_gcd_nat @ X @ Y )
% 0.35/0.68 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_non_0_nat
% 0.35/0.68 thf(fact_9236_gcd__nat_Osimps,axiom,
% 0.35/0.68 ( gcd_gcd_nat
% 0.35/0.68 = ( ^ [X4: nat,Y4: nat] : ( if_nat @ ( Y4 = zero_zero_nat ) @ X4 @ ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.simps
% 0.35/0.68 thf(fact_9237_gcd__nat_Oelims,axiom,
% 0.35/0.68 ! [X: nat,Xa2: nat,Y: nat] :
% 0.35/0.68 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.68 => ( Y = X ) )
% 0.35/0.68 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.elims
% 0.35/0.68 thf(fact_9238_bezout__nat,axiom,
% 0.35/0.68 ! [A: nat,B: nat] :
% 0.35/0.68 ( ( A != zero_zero_nat )
% 0.35/0.68 => ? [X3: nat,Y3: nat] :
% 0.35/0.68 ( ( times_times_nat @ A @ X3 )
% 0.35/0.68 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezout_nat
% 0.35/0.68 thf(fact_9239_bezout__gcd__nat_H,axiom,
% 0.35/0.68 ! [B: nat,A: nat] :
% 0.35/0.68 ? [X3: nat,Y3: nat] :
% 0.35/0.68 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 0.35/0.68 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 0.35/0.68 = ( gcd_gcd_nat @ A @ B ) ) )
% 0.35/0.68 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 0.35/0.68 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 0.35/0.68 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezout_gcd_nat'
% 0.35/0.68 thf(fact_9240_Field__natLeq__on,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( field_nat
% 0.35/0.68 @ ( collec3392354462482085612at_nat
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ N )
% 0.35/0.68 & ( ord_less_nat @ Y4 @ N )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 0.35/0.68 = ( collect_nat
% 0.35/0.68 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Field_natLeq_on
% 0.35/0.68 thf(fact_9241_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 0.35/0.68 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 0.35/0.68 @ ^ [M6: nat,N4: nat] :
% 0.35/0.68 ( ( dvd_dvd_nat @ M6 @ N4 )
% 0.35/0.68 & ( M6 != N4 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.semilattice_neutr_order_axioms
% 0.35/0.68 thf(fact_9242_gcd__is__Max__divisors__nat,axiom,
% 0.35/0.68 ! [N: nat,M2: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( ( gcd_gcd_nat @ M2 @ N )
% 0.35/0.68 = ( lattic8265883725875713057ax_nat
% 0.35/0.68 @ ( collect_nat
% 0.35/0.68 @ ^ [D2: nat] :
% 0.35/0.68 ( ( dvd_dvd_nat @ D2 @ M2 )
% 0.35/0.68 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_is_Max_divisors_nat
% 0.35/0.68 thf(fact_9243_gcd__nat_Opelims,axiom,
% 0.35/0.68 ! [X: nat,Xa2: nat,Y: nat] :
% 0.35/0.68 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 0.35/0.68 = Y )
% 0.35/0.68 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 0.35/0.68 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 0.35/0.68 => ( Y = X ) )
% 0.35/0.68 & ( ( Xa2 != zero_zero_nat )
% 0.35/0.68 => ( Y
% 0.35/0.68 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 0.35/0.68 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.pelims
% 0.35/0.68 thf(fact_9244_gcd__mult__distrib__int,axiom,
% 0.35/0.68 ! [K2: int,M2: int,N: int] :
% 0.35/0.68 ( ( times_times_int @ ( abs_abs_int @ K2 ) @ ( gcd_gcd_int @ M2 @ N ) )
% 0.35/0.68 = ( gcd_gcd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_mult_distrib_int
% 0.35/0.68 thf(fact_9245_bezout__int,axiom,
% 0.35/0.68 ! [X: int,Y: int] :
% 0.35/0.68 ? [U3: int,V: int] :
% 0.35/0.68 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V @ Y ) )
% 0.35/0.68 = ( gcd_gcd_int @ X @ Y ) ) ).
% 0.35/0.68
% 0.35/0.68 % bezout_int
% 0.35/0.68 thf(fact_9246_strict__mono__imp__increasing,axiom,
% 0.35/0.68 ! [F2: nat > nat,N: nat] :
% 0.35/0.68 ( ( order_5726023648592871131at_nat @ F2 )
% 0.35/0.68 => ( ord_less_eq_nat @ N @ ( F2 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % strict_mono_imp_increasing
% 0.35/0.68 thf(fact_9247_DeMoivre2,axiom,
% 0.35/0.68 ! [R3: real,A: real,N: nat] :
% 0.35/0.68 ( ( power_power_complex @ ( rcis @ R3 @ A ) @ N )
% 0.35/0.68 = ( rcis @ ( power_power_real @ R3 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % DeMoivre2
% 0.35/0.68 thf(fact_9248_Re__rcis,axiom,
% 0.35/0.68 ! [R3: real,A: real] :
% 0.35/0.68 ( ( re @ ( rcis @ R3 @ A ) )
% 0.35/0.68 = ( times_times_real @ R3 @ ( cos_real @ A ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Re_rcis
% 0.35/0.68 thf(fact_9249_Im__rcis,axiom,
% 0.35/0.68 ! [R3: real,A: real] :
% 0.35/0.68 ( ( im @ ( rcis @ R3 @ A ) )
% 0.35/0.68 = ( times_times_real @ R3 @ ( sin_real @ A ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Im_rcis
% 0.35/0.68 thf(fact_9250_rcis__mult,axiom,
% 0.35/0.68 ! [R1: real,A: real,R22: real,B: real] :
% 0.35/0.68 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 0.35/0.68 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rcis_mult
% 0.35/0.68 thf(fact_9251_rcis__def,axiom,
% 0.35/0.68 ( rcis
% 0.35/0.68 = ( ^ [R: real,A5: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( cis @ A5 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % rcis_def
% 0.35/0.68 thf(fact_9252_eventually__prod__sequentially,axiom,
% 0.35/0.68 ! [P2: product_prod_nat_nat > $o] :
% 0.35/0.68 ( ( eventu1038000079068216329at_nat @ P2 @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 0.35/0.68 = ( ? [N5: nat] :
% 0.35/0.68 ! [M6: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ N5 @ M6 )
% 0.35/0.68 => ! [N4: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ N5 @ N4 )
% 0.35/0.68 => ( P2 @ ( product_Pair_nat_nat @ N4 @ M6 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % eventually_prod_sequentially
% 0.35/0.68 thf(fact_9253_sqr_Osimps_I3_J,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ( ( sqr @ ( bit1 @ N ) )
% 0.35/0.68 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sqr.simps(3)
% 0.35/0.68 thf(fact_9254_sqr_Osimps_I2_J,axiom,
% 0.35/0.68 ! [N: num] :
% 0.35/0.68 ( ( sqr @ ( bit0 @ N ) )
% 0.35/0.68 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sqr.simps(2)
% 0.35/0.68 thf(fact_9255_sqr_Osimps_I1_J,axiom,
% 0.35/0.68 ( ( sqr @ one )
% 0.35/0.68 = one ) ).
% 0.35/0.68
% 0.35/0.68 % sqr.simps(1)
% 0.35/0.68 thf(fact_9256_sqr__conv__mult,axiom,
% 0.35/0.68 ( sqr
% 0.35/0.68 = ( ^ [X4: num] : ( times_times_num @ X4 @ X4 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % sqr_conv_mult
% 0.35/0.68 thf(fact_9257_pow_Osimps_I3_J,axiom,
% 0.35/0.68 ! [X: num,Y: num] :
% 0.35/0.68 ( ( pow @ X @ ( bit1 @ Y ) )
% 0.35/0.68 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 0.35/0.68
% 0.35/0.68 % pow.simps(3)
% 0.35/0.68 thf(fact_9258_pow_Osimps_I1_J,axiom,
% 0.35/0.68 ! [X: num] :
% 0.35/0.68 ( ( pow @ X @ one )
% 0.35/0.68 = X ) ).
% 0.35/0.68
% 0.35/0.68 % pow.simps(1)
% 0.35/0.68 thf(fact_9259_pow_Osimps_I2_J,axiom,
% 0.35/0.68 ! [X: num,Y: num] :
% 0.35/0.68 ( ( pow @ X @ ( bit0 @ Y ) )
% 0.35/0.68 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % pow.simps(2)
% 0.35/0.68 thf(fact_9260_natLeq__on__wo__rel,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( bNF_We3818239936649020644el_nat
% 0.35/0.68 @ ( collec3392354462482085612at_nat
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ N )
% 0.35/0.68 & ( ord_less_nat @ Y4 @ N )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % natLeq_on_wo_rel
% 0.35/0.68 thf(fact_9261_pairs__le__eq__Sigma,axiom,
% 0.35/0.68 ! [M2: nat] :
% 0.35/0.68 ( ( collec3392354462482085612at_nat
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [I: nat,J: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I @ J ) @ M2 ) ) )
% 0.35/0.68 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M2 )
% 0.35/0.68 @ ^ [R: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M2 @ R ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % pairs_le_eq_Sigma
% 0.35/0.68 thf(fact_9262_finite__vimage__Suc__iff,axiom,
% 0.35/0.68 ! [F3: set_nat] :
% 0.35/0.68 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F3 ) )
% 0.35/0.68 = ( finite_finite_nat @ F3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % finite_vimage_Suc_iff
% 0.35/0.68 thf(fact_9263_coprime__Suc__0__right,axiom,
% 0.35/0.68 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_Suc_0_right
% 0.35/0.68 thf(fact_9264_coprime__Suc__0__left,axiom,
% 0.35/0.68 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_Suc_0_left
% 0.35/0.68 thf(fact_9265_coprime__Suc__left__nat,axiom,
% 0.35/0.68 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_Suc_left_nat
% 0.35/0.68 thf(fact_9266_coprime__Suc__right__nat,axiom,
% 0.35/0.68 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_Suc_right_nat
% 0.35/0.68 thf(fact_9267_coprime__crossproduct__nat,axiom,
% 0.35/0.68 ! [A: nat,D: nat,B: nat,C2: nat] :
% 0.35/0.68 ( ( algebr934650988132801477me_nat @ A @ D )
% 0.35/0.68 => ( ( algebr934650988132801477me_nat @ B @ C2 )
% 0.35/0.68 => ( ( ( times_times_nat @ A @ C2 )
% 0.35/0.68 = ( times_times_nat @ B @ D ) )
% 0.35/0.68 = ( ( A = B )
% 0.35/0.68 & ( C2 = D ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_crossproduct_nat
% 0.35/0.68 thf(fact_9268_vimage__Suc__insert__Suc,axiom,
% 0.35/0.68 ! [N: nat,A4: set_nat] :
% 0.35/0.68 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A4 ) )
% 0.35/0.68 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A4 ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % vimage_Suc_insert_Suc
% 0.35/0.68 thf(fact_9269_vimage__Suc__insert__0,axiom,
% 0.35/0.68 ! [A4: set_nat] :
% 0.35/0.68 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A4 ) )
% 0.35/0.68 = ( vimage_nat_nat @ suc @ A4 ) ) ).
% 0.35/0.68
% 0.35/0.68 % vimage_Suc_insert_0
% 0.35/0.68 thf(fact_9270_coprime__diff__one__left__nat,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_diff_one_left_nat
% 0.35/0.68 thf(fact_9271_coprime__diff__one__right__nat,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.68 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_diff_one_right_nat
% 0.35/0.68 thf(fact_9272_Rats__abs__nat__div__natE,axiom,
% 0.35/0.68 ! [X: real] :
% 0.35/0.68 ( ( member_real @ X @ field_5140801741446780682s_real )
% 0.35/0.68 => ~ ! [M: nat,N3: nat] :
% 0.35/0.68 ( ( N3 != zero_zero_nat )
% 0.35/0.68 => ( ( ( abs_abs_real @ X )
% 0.35/0.68 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 0.35/0.68 => ~ ( algebr934650988132801477me_nat @ M @ N3 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Rats_abs_nat_div_natE
% 0.35/0.68 thf(fact_9273_set__decode__div__2,axiom,
% 0.35/0.68 ! [X: nat] :
% 0.35/0.68 ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 0.35/0.68 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % set_decode_div_2
% 0.35/0.68 thf(fact_9274_set__encode__vimage__Suc,axiom,
% 0.35/0.68 ! [A4: set_nat] :
% 0.35/0.68 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A4 ) )
% 0.35/0.68 = ( divide_divide_nat @ ( nat_set_encode @ A4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % set_encode_vimage_Suc
% 0.35/0.68 thf(fact_9275_Restr__natLeq,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.35/0.68 @ ( produc457027306803732586at_nat
% 0.35/0.68 @ ( collect_nat
% 0.35/0.68 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) )
% 0.35/0.68 @ ^ [Uu3: nat] :
% 0.35/0.68 ( collect_nat
% 0.35/0.68 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) )
% 0.35/0.68 = ( collec3392354462482085612at_nat
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ N )
% 0.35/0.68 & ( ord_less_nat @ Y4 @ N )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Restr_natLeq
% 0.35/0.68 thf(fact_9276_of__nat__eq__id,axiom,
% 0.35/0.68 semiri1316708129612266289at_nat = id_nat ).
% 0.35/0.68
% 0.35/0.68 % of_nat_eq_id
% 0.35/0.68 thf(fact_9277_coprime__crossproduct__int,axiom,
% 0.35/0.68 ! [A: int,D: int,B: int,C2: int] :
% 0.35/0.68 ( ( algebr932160517623751201me_int @ A @ D )
% 0.35/0.68 => ( ( algebr932160517623751201me_int @ B @ C2 )
% 0.35/0.68 => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C2 ) )
% 0.35/0.68 = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D ) ) )
% 0.35/0.68 = ( ( ( abs_abs_int @ A )
% 0.35/0.68 = ( abs_abs_int @ B ) )
% 0.35/0.68 & ( ( abs_abs_int @ C2 )
% 0.35/0.68 = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % coprime_crossproduct_int
% 0.35/0.68 thf(fact_9278_natLeq__Linear__order,axiom,
% 0.35/0.68 order_4473980167227706203on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.68
% 0.35/0.68 % natLeq_Linear_order
% 0.35/0.68 thf(fact_9279_natLeq__Total,axiom,
% 0.35/0.68 total_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.68
% 0.35/0.68 % natLeq_Total
% 0.35/0.68 thf(fact_9280_natLeq__Refl,axiom,
% 0.35/0.68 refl_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.68
% 0.35/0.68 % natLeq_Refl
% 0.35/0.68 thf(fact_9281_natLeq__natLess__Id,axiom,
% 0.35/0.68 ( bNF_Ca8459412986667044542atLess
% 0.35/0.68 = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 0.35/0.68
% 0.35/0.68 % natLeq_natLess_Id
% 0.35/0.68 thf(fact_9282_Field__natLeq,axiom,
% 0.35/0.68 ( ( field_nat @ bNF_Ca8665028551170535155natLeq )
% 0.35/0.68 = top_top_set_nat ) ).
% 0.35/0.68
% 0.35/0.68 % Field_natLeq
% 0.35/0.68 thf(fact_9283_natLeq__def,axiom,
% 0.35/0.68 ( bNF_Ca8665028551170535155natLeq
% 0.35/0.68 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % natLeq_def
% 0.35/0.68 thf(fact_9284_Restr__natLeq2,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 0.35/0.68 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.35/0.68 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 0.35/0.68 = ( collec3392354462482085612at_nat
% 0.35/0.68 @ ( produc6081775807080527818_nat_o
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.68 ( ( ord_less_nat @ X4 @ N )
% 0.35/0.68 & ( ord_less_nat @ Y4 @ N )
% 0.35/0.68 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Restr_natLeq2
% 0.35/0.68 thf(fact_9285_natLeq__underS__less,axiom,
% 0.35/0.68 ! [N: nat] :
% 0.35/0.68 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 0.35/0.68 = ( collect_nat
% 0.35/0.68 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % natLeq_underS_less
% 0.35/0.68 thf(fact_9286_pair__lessI2,axiom,
% 0.35/0.68 ! [A: nat,B: nat,S2: nat,T: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.68 => ( ( ord_less_nat @ S2 @ T )
% 0.35/0.68 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % pair_lessI2
% 0.35/0.68 thf(fact_9287_pair__less__iff1,axiom,
% 0.35/0.68 ! [X: nat,Y: nat,Z3: nat] :
% 0.35/0.68 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z3 ) ) @ fun_pair_less )
% 0.35/0.68 = ( ord_less_nat @ Y @ Z3 ) ) ).
% 0.35/0.68
% 0.35/0.68 % pair_less_iff1
% 0.35/0.68 thf(fact_9288_pair__lessI1,axiom,
% 0.35/0.68 ! [A: nat,B: nat,S2: nat,T: nat] :
% 0.35/0.68 ( ( ord_less_nat @ A @ B )
% 0.35/0.68 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 0.35/0.68
% 0.35/0.68 % pair_lessI1
% 0.35/0.68 thf(fact_9289_pair__leqI2,axiom,
% 0.35/0.68 ! [A: nat,B: nat,S2: nat,T: nat] :
% 0.35/0.68 ( ( ord_less_eq_nat @ A @ B )
% 0.35/0.68 => ( ( ord_less_eq_nat @ S2 @ T )
% 0.35/0.68 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % pair_leqI2
% 0.35/0.68 thf(fact_9290_pair__leqI1,axiom,
% 0.35/0.68 ! [A: nat,B: nat,S2: nat,T: nat] :
% 0.35/0.68 ( ( ord_less_nat @ A @ B )
% 0.35/0.68 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 0.35/0.68
% 0.35/0.68 % pair_leqI1
% 0.35/0.68 thf(fact_9291_length__upto,axiom,
% 0.35/0.68 ! [I2: int,J2: int] :
% 0.35/0.68 ( ( size_size_list_int @ ( upto @ I2 @ J2 ) )
% 0.35/0.68 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J2 @ I2 ) @ one_one_int ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % length_upto
% 0.35/0.68 thf(fact_9292_gcd__nat_Oordering__top__axioms,axiom,
% 0.35/0.68 ( ordering_top_nat @ dvd_dvd_nat
% 0.35/0.68 @ ^ [M6: nat,N4: nat] :
% 0.35/0.68 ( ( dvd_dvd_nat @ M6 @ N4 )
% 0.35/0.68 & ( M6 != N4 ) )
% 0.35/0.68 @ zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % gcd_nat.ordering_top_axioms
% 0.35/0.68 thf(fact_9293_bot__nat__0_Oordering__top__axioms,axiom,
% 0.35/0.68 ( ordering_top_nat
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 0.35/0.68 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 0.35/0.68 @ zero_zero_nat ) ).
% 0.35/0.68
% 0.35/0.68 % bot_nat_0.ordering_top_axioms
% 0.35/0.68 thf(fact_9294_ratrel__iff,axiom,
% 0.35/0.68 ( ratrel
% 0.35/0.68 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 0.35/0.68 ( ( ( product_snd_int_int @ X4 )
% 0.35/0.68 != zero_zero_int )
% 0.35/0.68 & ( ( product_snd_int_int @ Y4 )
% 0.35/0.68 != zero_zero_int )
% 0.35/0.68 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 0.35/0.68 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % ratrel_iff
% 0.35/0.68 thf(fact_9295_ratrel__def,axiom,
% 0.35/0.68 ( ratrel
% 0.35/0.68 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 0.35/0.68 ( ( ( product_snd_int_int @ X4 )
% 0.35/0.68 != zero_zero_int )
% 0.35/0.68 & ( ( product_snd_int_int @ Y4 )
% 0.35/0.68 != zero_zero_int )
% 0.35/0.68 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 0.35/0.68 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % ratrel_def
% 0.35/0.68 thf(fact_9296_plus__rat_Oabs__eq,axiom,
% 0.35/0.68 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 0.35/0.68 ( ( ratrel @ Xa2 @ Xa2 )
% 0.35/0.68 => ( ( ratrel @ X @ X )
% 0.35/0.68 => ( ( plus_plus_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 0.35/0.68 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % plus_rat.abs_eq
% 0.35/0.68 thf(fact_9297_times__rat_Oabs__eq,axiom,
% 0.35/0.68 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 0.35/0.68 ( ( ratrel @ Xa2 @ Xa2 )
% 0.35/0.68 => ( ( ratrel @ X @ X )
% 0.35/0.68 => ( ( times_times_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 0.35/0.68 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % times_rat.abs_eq
% 0.35/0.68 thf(fact_9298_Rat_Opositive_Oabs__eq,axiom,
% 0.35/0.68 ! [X: product_prod_int_int] :
% 0.35/0.68 ( ( ratrel @ X @ X )
% 0.35/0.68 => ( ( positive @ ( abs_Rat @ X ) )
% 0.35/0.68 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Rat.positive.abs_eq
% 0.35/0.68 thf(fact_9299_Rat_Opositive__mult,axiom,
% 0.35/0.68 ! [X: rat,Y: rat] :
% 0.35/0.68 ( ( positive @ X )
% 0.35/0.68 => ( ( positive @ Y )
% 0.35/0.68 => ( positive @ ( times_times_rat @ X @ Y ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Rat.positive_mult
% 0.35/0.68 thf(fact_9300_Rat_Opositive_Orep__eq,axiom,
% 0.35/0.68 ( positive
% 0.35/0.68 = ( ^ [X4: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X4 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X4 ) ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Rat.positive.rep_eq
% 0.35/0.68 thf(fact_9301_Rat_Opositive_Orsp,axiom,
% 0.35/0.68 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 0.35/0.68 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.35/0.68 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 0.35/0.68 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Rat.positive.rsp
% 0.35/0.68 thf(fact_9302_Rat_Opositive__def,axiom,
% 0.35/0.68 ( positive
% 0.35/0.68 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 0.35/0.68 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ).
% 0.35/0.68
% 0.35/0.68 % Rat.positive_def
% 0.35/0.68 thf(fact_9303_less__eq__natural_Orsp,axiom,
% 0.35/0.68 ( bNF_re578469030762574527_nat_o
% 0.35/0.68 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.35/0.68 @ ( bNF_re4705727531993890431at_o_o
% 0.35/0.68 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.35/0.68 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.35/0.68 @ ord_less_eq_nat
% 0.35/0.68 @ ord_less_eq_nat ) ).
% 0.35/0.68
% 0.35/0.68 % less_eq_natural.rsp
% 0.35/0.68 thf(fact_9304_Suc_Orsp,axiom,
% 0.35/0.68 ( bNF_re5653821019739307937at_nat
% 0.35/0.68 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.35/0.68 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.35/0.68 @ suc
% 0.35/0.68 @ suc ) ).
% 0.35/0.68
% 0.35/0.68 % Suc.rsp
% 0.35/0.68 thf(fact_9305_times__integer_Orsp,axiom,
% 0.35/0.68 ( bNF_re711492959462206631nt_int
% 0.35/0.68 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.35/0.68 @ ( bNF_re4712519889275205905nt_int
% 0.35/0.68 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 0.35/0.68 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 0.35/0.68 @ times_times_int
% 0.35/0.68 @ times_times_int ) ).
% 0.35/0.68
% 0.35/0.68 % times_integer.rsp
% 0.35/0.68 thf(fact_9306_times__natural_Orsp,axiom,
% 0.35/0.68 ( bNF_re1345281282404953727at_nat
% 0.35/0.68 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.35/0.68 @ ( bNF_re5653821019739307937at_nat
% 0.35/0.68 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.35/0.68 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 0.35/0.68 @ times_times_nat
% 0.35/0.68 @ times_times_nat ) ).
% 0.35/0.68
% 0.35/0.68 % times_natural.rsp
% 0.35/0.68 thf(fact_9307_times__rat_Orsp,axiom,
% 0.35/0.68 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.35/0.68 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.35/0.69 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_rat.rsp
% 0.35/0.69 thf(fact_9308_plus__rat_Orsp,axiom,
% 0.35/0.69 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 0.35/0.69 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.35/0.69 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % plus_rat.rsp
% 0.35/0.69 thf(fact_9309_plus__rat_Otransfer,axiom,
% 0.35/0.69 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.35/0.69 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.35/0.69 @ plus_plus_rat ) ).
% 0.35/0.69
% 0.35/0.69 % plus_rat.transfer
% 0.35/0.69 thf(fact_9310_Rat_Opositive_Otransfer,axiom,
% 0.35/0.69 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 0.35/0.69 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.35/0.69 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 0.35/0.69 @ positive ) ).
% 0.35/0.69
% 0.35/0.69 % Rat.positive.transfer
% 0.35/0.69 thf(fact_9311_times__rat_Otransfer,axiom,
% 0.35/0.69 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 0.35/0.69 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 0.35/0.69 @ times_times_rat ) ).
% 0.35/0.69
% 0.35/0.69 % times_rat.transfer
% 0.35/0.69 thf(fact_9312_times__int_Otransfer,axiom,
% 0.35/0.69 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 0.35/0.69 @ times_times_int ) ).
% 0.35/0.69
% 0.35/0.69 % times_int.transfer
% 0.35/0.69 thf(fact_9313_minus__int_Otransfer,axiom,
% 0.35/0.69 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 0.35/0.69 @ minus_minus_int ) ).
% 0.35/0.69
% 0.35/0.69 % minus_int.transfer
% 0.35/0.69 thf(fact_9314_zero__int_Otransfer,axiom,
% 0.35/0.69 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 0.35/0.69
% 0.35/0.69 % zero_int.transfer
% 0.35/0.69 thf(fact_9315_int__transfer,axiom,
% 0.35/0.69 ( bNF_re6830278522597306478at_int
% 0.35/0.69 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 0.35/0.69 @ pcr_int
% 0.35/0.69 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 0.35/0.69 @ semiri1314217659103216013at_int ) ).
% 0.35/0.69
% 0.35/0.69 % int_transfer
% 0.35/0.69 thf(fact_9316_uminus__int_Otransfer,axiom,
% 0.35/0.69 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 0.35/0.69 @ ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 0.35/0.69 @ uminus_uminus_int ) ).
% 0.35/0.69
% 0.35/0.69 % uminus_int.transfer
% 0.35/0.69 thf(fact_9317_one__int_Otransfer,axiom,
% 0.35/0.69 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 0.35/0.69
% 0.35/0.69 % one_int.transfer
% 0.35/0.69 thf(fact_9318_less__eq__int_Otransfer,axiom,
% 0.35/0.69 ( bNF_re717283939379294677_int_o @ pcr_int
% 0.35/0.69 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 0.35/0.69 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.35/0.69 @ ( produc8739625826339149834_nat_o
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc6081775807080527818_nat_o
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 0.35/0.69 @ ord_less_eq_int ) ).
% 0.35/0.69
% 0.35/0.69 % less_eq_int.transfer
% 0.35/0.69 thf(fact_9319_plus__int_Otransfer,axiom,
% 0.35/0.69 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 0.35/0.69 @ plus_plus_int ) ).
% 0.35/0.69
% 0.35/0.69 % plus_int.transfer
% 0.35/0.69 thf(fact_9320_times__int_Orsp,axiom,
% 0.35/0.69 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_int.rsp
% 0.35/0.69 thf(fact_9321_minus__int_Orsp,axiom,
% 0.35/0.69 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % minus_int.rsp
% 0.35/0.69 thf(fact_9322_intrel__iff,axiom,
% 0.35/0.69 ! [X: nat,Y: nat,U: nat,V2: nat] :
% 0.35/0.69 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V2 ) )
% 0.35/0.69 = ( ( plus_plus_nat @ X @ V2 )
% 0.35/0.69 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % intrel_iff
% 0.35/0.69 thf(fact_9323_zero__int_Orsp,axiom,
% 0.35/0.69 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % zero_int.rsp
% 0.35/0.69 thf(fact_9324_uminus__int_Orsp,axiom,
% 0.35/0.69 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 0.35/0.69 @ ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 0.35/0.69 @ ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % uminus_int.rsp
% 0.35/0.69 thf(fact_9325_one__int_Orsp,axiom,
% 0.35/0.69 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % one_int.rsp
% 0.35/0.69 thf(fact_9326_less__eq__int_Orsp,axiom,
% 0.35/0.69 ( bNF_re4202695980764964119_nat_o @ intrel
% 0.35/0.69 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 0.35/0.69 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 0.35/0.69 @ ( produc8739625826339149834_nat_o
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc6081775807080527818_nat_o
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 0.35/0.69 @ ( produc8739625826339149834_nat_o
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc6081775807080527818_nat_o
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_eq_int.rsp
% 0.35/0.69 thf(fact_9327_plus__int_Orsp,axiom,
% 0.35/0.69 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 0.35/0.69 @ ( produc27273713700761075at_nat
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc2626176000494625587at_nat
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % plus_int.rsp
% 0.35/0.69 thf(fact_9328_less__eq__enat__def,axiom,
% 0.35/0.69 ( ord_le2932123472753598470d_enat
% 0.35/0.69 = ( ^ [M6: extended_enat] :
% 0.35/0.69 ( extended_case_enat_o
% 0.35/0.69 @ ^ [N1: nat] :
% 0.35/0.69 ( extended_case_enat_o
% 0.35/0.69 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 0.35/0.69 @ $false
% 0.35/0.69 @ M6 )
% 0.35/0.69 @ $true ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_eq_enat_def
% 0.35/0.69 thf(fact_9329_natLeq__Well__order,axiom,
% 0.35/0.69 order_2888998067076097458on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.69
% 0.35/0.69 % natLeq_Well_order
% 0.35/0.69 thf(fact_9330_natLeq__on__well__order__on,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( order_2888998067076097458on_nat
% 0.35/0.69 @ ( collect_nat
% 0.35/0.69 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) )
% 0.35/0.69 @ ( collec3392354462482085612at_nat
% 0.35/0.69 @ ( produc6081775807080527818_nat_o
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( ( ord_less_nat @ X4 @ N )
% 0.35/0.69 & ( ord_less_nat @ Y4 @ N )
% 0.35/0.69 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % natLeq_on_well_order_on
% 0.35/0.69 thf(fact_9331_natLeq__on__Well__order,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( order_2888998067076097458on_nat
% 0.35/0.69 @ ( field_nat
% 0.35/0.69 @ ( collec3392354462482085612at_nat
% 0.35/0.69 @ ( produc6081775807080527818_nat_o
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( ( ord_less_nat @ X4 @ N )
% 0.35/0.69 & ( ord_less_nat @ Y4 @ N )
% 0.35/0.69 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 0.35/0.69 @ ( collec3392354462482085612at_nat
% 0.35/0.69 @ ( produc6081775807080527818_nat_o
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( ( ord_less_nat @ X4 @ N )
% 0.35/0.69 & ( ord_less_nat @ Y4 @ N )
% 0.35/0.69 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % natLeq_on_Well_order
% 0.35/0.69 thf(fact_9332_inj__on__char__of__nat,axiom,
% 0.35/0.69 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % inj_on_char_of_nat
% 0.35/0.69 thf(fact_9333_UNIV__char__of__nat,axiom,
% 0.35/0.69 ( top_top_set_char
% 0.35/0.69 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % UNIV_char_of_nat
% 0.35/0.69 thf(fact_9334_range__nat__of__char,axiom,
% 0.35/0.69 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 0.35/0.69 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % range_nat_of_char
% 0.35/0.69 thf(fact_9335_plus__rat__def,axiom,
% 0.35/0.69 ( plus_plus_rat
% 0.35/0.69 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.35/0.69 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % plus_rat_def
% 0.35/0.69 thf(fact_9336_diff__rat,axiom,
% 0.35/0.69 ! [B: int,D: int,A: int,C2: int] :
% 0.35/0.69 ( ( B != zero_zero_int )
% 0.35/0.69 => ( ( D != zero_zero_int )
% 0.35/0.69 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 0.35/0.69 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C2 @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % diff_rat
% 0.35/0.69 thf(fact_9337_sgn__rat,axiom,
% 0.35/0.69 ! [A: int,B: int] :
% 0.35/0.69 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 0.35/0.69 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % sgn_rat
% 0.35/0.69 thf(fact_9338_mult__rat,axiom,
% 0.35/0.69 ! [A: int,B: int,C2: int,D: int] :
% 0.35/0.69 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 0.35/0.69 = ( fract @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % mult_rat
% 0.35/0.69 thf(fact_9339_divide__rat,axiom,
% 0.35/0.69 ! [A: int,B: int,C2: int,D: int] :
% 0.35/0.69 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 0.35/0.69 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % divide_rat
% 0.35/0.69 thf(fact_9340_less__rat,axiom,
% 0.35/0.69 ! [B: int,D: int,A: int,C2: int] :
% 0.35/0.69 ( ( B != zero_zero_int )
% 0.35/0.69 => ( ( D != zero_zero_int )
% 0.35/0.69 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 0.35/0.69 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_rat
% 0.35/0.69 thf(fact_9341_add__rat,axiom,
% 0.35/0.69 ! [B: int,D: int,A: int,C2: int] :
% 0.35/0.69 ( ( B != zero_zero_int )
% 0.35/0.69 => ( ( D != zero_zero_int )
% 0.35/0.69 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 0.35/0.69 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C2 @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % add_rat
% 0.35/0.69 thf(fact_9342_le__rat,axiom,
% 0.35/0.69 ! [B: int,D: int,A: int,C2: int] :
% 0.35/0.69 ( ( B != zero_zero_int )
% 0.35/0.69 => ( ( D != zero_zero_int )
% 0.35/0.69 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 0.35/0.69 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % le_rat
% 0.35/0.69 thf(fact_9343_mult__rat__cancel,axiom,
% 0.35/0.69 ! [C2: int,A: int,B: int] :
% 0.35/0.69 ( ( C2 != zero_zero_int )
% 0.35/0.69 => ( ( fract @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 0.35/0.69 = ( fract @ A @ B ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % mult_rat_cancel
% 0.35/0.69 thf(fact_9344_eq__rat_I1_J,axiom,
% 0.35/0.69 ! [B: int,D: int,A: int,C2: int] :
% 0.35/0.69 ( ( B != zero_zero_int )
% 0.35/0.69 => ( ( D != zero_zero_int )
% 0.35/0.69 => ( ( ( fract @ A @ B )
% 0.35/0.69 = ( fract @ C2 @ D ) )
% 0.35/0.69 = ( ( times_times_int @ A @ D )
% 0.35/0.69 = ( times_times_int @ C2 @ B ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % eq_rat(1)
% 0.35/0.69 thf(fact_9345_positive__rat,axiom,
% 0.35/0.69 ! [A: int,B: int] :
% 0.35/0.69 ( ( positive @ ( fract @ A @ B ) )
% 0.35/0.69 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % positive_rat
% 0.35/0.69 thf(fact_9346_times__rat__def,axiom,
% 0.35/0.69 ( times_times_rat
% 0.35/0.69 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 0.35/0.69 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_rat_def
% 0.35/0.69 thf(fact_9347_integer__of__char__code,axiom,
% 0.35/0.69 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 0.35/0.69 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 0.35/0.69 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % integer_of_char_code
% 0.35/0.69 thf(fact_9348_char_Osize_I2_J,axiom,
% 0.35/0.69 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 0.35/0.69 ( ( size_size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 0.35/0.69 = zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % char.size(2)
% 0.35/0.69 thf(fact_9349_char_Osize__gen,axiom,
% 0.35/0.69 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 0.35/0.69 ( ( size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 0.35/0.69 = zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % char.size_gen
% 0.35/0.69 thf(fact_9350_numeral__le__enat__iff,axiom,
% 0.35/0.69 ! [M2: num,N: nat] :
% 0.35/0.69 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N ) )
% 0.35/0.69 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 0.35/0.69
% 0.35/0.69 % numeral_le_enat_iff
% 0.35/0.69 thf(fact_9351_idiff__enat__0__right,axiom,
% 0.35/0.69 ! [N: extended_enat] :
% 0.35/0.69 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 0.35/0.69 = N ) ).
% 0.35/0.69
% 0.35/0.69 % idiff_enat_0_right
% 0.35/0.69 thf(fact_9352_idiff__enat__0,axiom,
% 0.35/0.69 ! [N: extended_enat] :
% 0.35/0.69 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 0.35/0.69 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % idiff_enat_0
% 0.35/0.69 thf(fact_9353_times__enat__simps_I1_J,axiom,
% 0.35/0.69 ! [M2: nat,N: nat] :
% 0.35/0.69 ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 0.35/0.69 = ( extended_enat2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_enat_simps(1)
% 0.35/0.69 thf(fact_9354_enat__ord__simps_I1_J,axiom,
% 0.35/0.69 ! [M2: nat,N: nat] :
% 0.35/0.69 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 0.35/0.69 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 0.35/0.69
% 0.35/0.69 % enat_ord_simps(1)
% 0.35/0.69 thf(fact_9355_Suc__ile__eq,axiom,
% 0.35/0.69 ! [M2: nat,N: extended_enat] :
% 0.35/0.69 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M2 ) ) @ N )
% 0.35/0.69 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ N ) ) ).
% 0.35/0.69
% 0.35/0.69 % Suc_ile_eq
% 0.35/0.69 thf(fact_9356_enat__0__iff_I2_J,axiom,
% 0.35/0.69 ! [X: nat] :
% 0.35/0.69 ( ( zero_z5237406670263579293d_enat
% 0.35/0.69 = ( extended_enat2 @ X ) )
% 0.35/0.69 = ( X = zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % enat_0_iff(2)
% 0.35/0.69 thf(fact_9357_enat__0__iff_I1_J,axiom,
% 0.35/0.69 ! [X: nat] :
% 0.35/0.69 ( ( ( extended_enat2 @ X )
% 0.35/0.69 = zero_z5237406670263579293d_enat )
% 0.35/0.69 = ( X = zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % enat_0_iff(1)
% 0.35/0.69 thf(fact_9358_zero__enat__def,axiom,
% 0.35/0.69 ( zero_z5237406670263579293d_enat
% 0.35/0.69 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % zero_enat_def
% 0.35/0.69 thf(fact_9359_iadd__le__enat__iff,axiom,
% 0.35/0.69 ! [X: extended_enat,Y: extended_enat,N: nat] :
% 0.35/0.69 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( extended_enat2 @ N ) )
% 0.35/0.69 = ( ? [Y8: nat,X9: nat] :
% 0.35/0.69 ( ( X
% 0.35/0.69 = ( extended_enat2 @ X9 ) )
% 0.35/0.69 & ( Y
% 0.35/0.69 = ( extended_enat2 @ Y8 ) )
% 0.35/0.69 & ( ord_less_eq_nat @ ( plus_plus_nat @ X9 @ Y8 ) @ N ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % iadd_le_enat_iff
% 0.35/0.69 thf(fact_9360_elimnum,axiom,
% 0.35/0.69 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.35/0.69 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 0.35/0.69 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 0.35/0.69 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % elimnum
% 0.35/0.69 thf(fact_9361_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 0.35/0.69 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 0.35/0.69 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ L ) )
% 0.35/0.69 = ( vEBT_Node @ Info2 @ Deg
% 0.35/0.69 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69 @ ( map_VE8901447254227204932T_VEBT
% 0.35/0.69 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69 @ TreeList2 ) )
% 0.35/0.69 @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.elim_dead.simps(3)
% 0.35/0.69 thf(fact_9362_enat__0__less__mult__iff,axiom,
% 0.35/0.69 ! [M2: extended_enat,N: extended_enat] :
% 0.35/0.69 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M2 @ N ) )
% 0.35/0.69 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M2 )
% 0.35/0.69 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % enat_0_less_mult_iff
% 0.35/0.69 thf(fact_9363_imult__is__0,axiom,
% 0.35/0.69 ! [M2: extended_enat,N: extended_enat] :
% 0.35/0.69 ( ( ( times_7803423173614009249d_enat @ M2 @ N )
% 0.35/0.69 = zero_z5237406670263579293d_enat )
% 0.35/0.69 = ( ( M2 = zero_z5237406670263579293d_enat )
% 0.35/0.69 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % imult_is_0
% 0.35/0.69 thf(fact_9364_VEBT__internal_Oelim__dead_Osimps_I1_J,axiom,
% 0.35/0.69 ! [A: $o,B: $o,Uu: extended_enat] :
% 0.35/0.69 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Leaf @ A @ B ) @ Uu )
% 0.35/0.69 = ( vEBT_Leaf @ A @ B ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.elim_dead.simps(1)
% 0.35/0.69 thf(fact_9365_VEBT__internal_Oelim__dead_Oelims,axiom,
% 0.35/0.69 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 0.35/0.69 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 0.35/0.69 = Y )
% 0.35/0.69 => ( ! [A3: $o,B3: $o] :
% 0.35/0.69 ( ( X
% 0.35/0.69 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.69 => ( Y
% 0.35/0.69 != ( vEBT_Leaf @ A3 @ B3 ) ) )
% 0.35/0.69 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69 ( ( X
% 0.35/0.69 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.69 => ( ( Xa2 = extend5688581933313929465d_enat )
% 0.35/0.69 => ( Y
% 0.35/0.69 != ( vEBT_Node @ Info @ Deg2
% 0.35/0.69 @ ( map_VE8901447254227204932T_VEBT
% 0.35/0.69 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69 @ TreeList )
% 0.35/0.69 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 0.35/0.69 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69 ( ( X
% 0.35/0.69 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.69 => ! [L4: nat] :
% 0.35/0.69 ( ( Xa2
% 0.35/0.69 = ( extended_enat2 @ L4 ) )
% 0.35/0.69 => ( Y
% 0.35/0.69 != ( vEBT_Node @ Info @ Deg2
% 0.35/0.69 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69 @ ( map_VE8901447254227204932T_VEBT
% 0.35/0.69 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69 @ TreeList ) )
% 0.35/0.69 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.elim_dead.elims
% 0.35/0.69 thf(fact_9366_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 0.35/0.69 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 0.35/0.69 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 0.35/0.69 = ( vEBT_Node @ Info2 @ Deg
% 0.35/0.69 @ ( map_VE8901447254227204932T_VEBT
% 0.35/0.69 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69 @ TreeList2 )
% 0.35/0.69 @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.elim_dead.simps(2)
% 0.35/0.69 thf(fact_9367_elimcomplete,axiom,
% 0.35/0.69 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 0.35/0.69 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 0.35/0.69 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 0.35/0.69 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % elimcomplete
% 0.35/0.69 thf(fact_9368_times__enat__simps_I2_J,axiom,
% 0.35/0.69 ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ extend5688581933313929465d_enat )
% 0.35/0.69 = extend5688581933313929465d_enat ) ).
% 0.35/0.69
% 0.35/0.69 % times_enat_simps(2)
% 0.35/0.69 thf(fact_9369_times__enat__simps_I3_J,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( ( ( N = zero_zero_nat )
% 0.35/0.69 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 0.35/0.69 = zero_z5237406670263579293d_enat ) )
% 0.35/0.69 & ( ( N != zero_zero_nat )
% 0.35/0.69 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 0.35/0.69 = extend5688581933313929465d_enat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_enat_simps(3)
% 0.35/0.69 thf(fact_9370_times__enat__simps_I4_J,axiom,
% 0.35/0.69 ! [M2: nat] :
% 0.35/0.69 ( ( ( M2 = zero_zero_nat )
% 0.35/0.69 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 0.35/0.69 = zero_z5237406670263579293d_enat ) )
% 0.35/0.69 & ( ( M2 != zero_zero_nat )
% 0.35/0.69 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 0.35/0.69 = extend5688581933313929465d_enat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_enat_simps(4)
% 0.35/0.69 thf(fact_9371_imult__is__infinity,axiom,
% 0.35/0.69 ! [A: extended_enat,B: extended_enat] :
% 0.35/0.69 ( ( ( times_7803423173614009249d_enat @ A @ B )
% 0.35/0.69 = extend5688581933313929465d_enat )
% 0.35/0.69 = ( ( ( A = extend5688581933313929465d_enat )
% 0.35/0.69 & ( B != zero_z5237406670263579293d_enat ) )
% 0.35/0.69 | ( ( B = extend5688581933313929465d_enat )
% 0.35/0.69 & ( A != zero_z5237406670263579293d_enat ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % imult_is_infinity
% 0.35/0.69 thf(fact_9372_VEBT__internal_Oelim__dead_Ocases,axiom,
% 0.35/0.69 ! [X: produc7272778201969148633d_enat] :
% 0.35/0.69 ( ! [A3: $o,B3: $o,Uu2: extended_enat] :
% 0.35/0.69 ( X
% 0.35/0.69 != ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B3 ) @ Uu2 ) )
% 0.35/0.69 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69 ( X
% 0.35/0.69 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ extend5688581933313929465d_enat ) )
% 0.35/0.69 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,L4: nat] :
% 0.35/0.69 ( X
% 0.35/0.69 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.elim_dead.cases
% 0.35/0.69 thf(fact_9373_imult__infinity,axiom,
% 0.35/0.69 ! [N: extended_enat] :
% 0.35/0.69 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.35/0.69 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 0.35/0.69 = extend5688581933313929465d_enat ) ) ).
% 0.35/0.69
% 0.35/0.69 % imult_infinity
% 0.35/0.69 thf(fact_9374_imult__infinity__right,axiom,
% 0.35/0.69 ! [N: extended_enat] :
% 0.35/0.69 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 0.35/0.69 => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 0.35/0.69 = extend5688581933313929465d_enat ) ) ).
% 0.35/0.69
% 0.35/0.69 % imult_infinity_right
% 0.35/0.69 thf(fact_9375_times__enat__def,axiom,
% 0.35/0.69 ( times_7803423173614009249d_enat
% 0.35/0.69 = ( ^ [M6: extended_enat,N4: extended_enat] :
% 0.35/0.69 ( extend3600170679010898289d_enat
% 0.35/0.69 @ ^ [O: nat] :
% 0.35/0.69 ( extend3600170679010898289d_enat
% 0.35/0.69 @ ^ [P5: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P5 ) )
% 0.35/0.69 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 0.35/0.69 @ N4 )
% 0.35/0.69 @ ( if_Extended_enat @ ( N4 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 0.35/0.69 @ M6 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_enat_def
% 0.35/0.69 thf(fact_9376_VEBT__internal_Oelim__dead_Opelims,axiom,
% 0.35/0.69 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 0.35/0.69 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 0.35/0.69 = Y )
% 0.35/0.69 => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X @ Xa2 ) )
% 0.35/0.69 => ( ! [A3: $o,B3: $o] :
% 0.35/0.69 ( ( X
% 0.35/0.69 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.69 => ( ( Y
% 0.35/0.69 = ( vEBT_Leaf @ A3 @ B3 ) )
% 0.35/0.69 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 0.35/0.69 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69 ( ( X
% 0.35/0.69 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.69 => ( ( Xa2 = extend5688581933313929465d_enat )
% 0.35/0.69 => ( ( Y
% 0.35/0.69 = ( vEBT_Node @ Info @ Deg2
% 0.35/0.69 @ ( map_VE8901447254227204932T_VEBT
% 0.35/0.69 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69 @ TreeList )
% 0.35/0.69 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 0.35/0.69 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 0.35/0.69 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 0.35/0.69 ( ( X
% 0.35/0.69 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 0.35/0.69 => ! [L4: nat] :
% 0.35/0.69 ( ( Xa2
% 0.35/0.69 = ( extended_enat2 @ L4 ) )
% 0.35/0.69 => ( ( Y
% 0.35/0.69 = ( vEBT_Node @ Info @ Deg2
% 0.35/0.69 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 0.35/0.69 @ ( map_VE8901447254227204932T_VEBT
% 0.35/0.69 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 0.35/0.69 @ TreeList ) )
% 0.35/0.69 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 0.35/0.69 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.elim_dead.pelims
% 0.35/0.69 thf(fact_9377_eSuc__def,axiom,
% 0.35/0.69 ( extended_eSuc
% 0.35/0.69 = ( extend3600170679010898289d_enat
% 0.35/0.69 @ ^ [N4: nat] : ( extended_enat2 @ ( suc @ N4 ) )
% 0.35/0.69 @ extend5688581933313929465d_enat ) ) ).
% 0.35/0.69
% 0.35/0.69 % eSuc_def
% 0.35/0.69 thf(fact_9378_binomial__def,axiom,
% 0.35/0.69 ( binomial
% 0.35/0.69 = ( ^ [N4: nat,K3: nat] :
% 0.35/0.69 ( finite_card_set_nat
% 0.35/0.69 @ ( collect_set_nat
% 0.35/0.69 @ ^ [K7: set_nat] :
% 0.35/0.69 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 0.35/0.69 & ( ( finite_card_nat @ K7 )
% 0.35/0.69 = K3 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % binomial_def
% 0.35/0.69 thf(fact_9379_enat__eSuc__iff,axiom,
% 0.35/0.69 ! [Y: nat,X: extended_enat] :
% 0.35/0.69 ( ( ( extended_enat2 @ Y )
% 0.35/0.69 = ( extended_eSuc @ X ) )
% 0.35/0.69 = ( ? [N4: nat] :
% 0.35/0.69 ( ( Y
% 0.35/0.69 = ( suc @ N4 ) )
% 0.35/0.69 & ( ( extended_enat2 @ N4 )
% 0.35/0.69 = X ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % enat_eSuc_iff
% 0.35/0.69 thf(fact_9380_eSuc__enat__iff,axiom,
% 0.35/0.69 ! [X: extended_enat,Y: nat] :
% 0.35/0.69 ( ( ( extended_eSuc @ X )
% 0.35/0.69 = ( extended_enat2 @ Y ) )
% 0.35/0.69 = ( ? [N4: nat] :
% 0.35/0.69 ( ( Y
% 0.35/0.69 = ( suc @ N4 ) )
% 0.35/0.69 & ( X
% 0.35/0.69 = ( extended_enat2 @ N4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % eSuc_enat_iff
% 0.35/0.69 thf(fact_9381_eSuc__enat,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 0.35/0.69 = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % eSuc_enat
% 0.35/0.69 thf(fact_9382_mult__eSuc__right,axiom,
% 0.35/0.69 ! [M2: extended_enat,N: extended_enat] :
% 0.35/0.69 ( ( times_7803423173614009249d_enat @ M2 @ ( extended_eSuc @ N ) )
% 0.35/0.69 = ( plus_p3455044024723400733d_enat @ M2 @ ( times_7803423173614009249d_enat @ M2 @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % mult_eSuc_right
% 0.35/0.69 thf(fact_9383_mult__eSuc,axiom,
% 0.35/0.69 ! [M2: extended_enat,N: extended_enat] :
% 0.35/0.69 ( ( times_7803423173614009249d_enat @ ( extended_eSuc @ M2 ) @ N )
% 0.35/0.69 = ( plus_p3455044024723400733d_enat @ N @ ( times_7803423173614009249d_enat @ M2 @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % mult_eSuc
% 0.35/0.69 thf(fact_9384_less__than__iff,axiom,
% 0.35/0.69 ! [X: nat,Y: nat] :
% 0.35/0.69 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 0.35/0.69 = ( ord_less_nat @ X @ Y ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_than_iff
% 0.35/0.69 thf(fact_9385_Real_Opositive_Orsp,axiom,
% 0.35/0.69 ( bNF_re728719798268516973at_o_o @ realrel
% 0.35/0.69 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.35/0.69 @ ^ [X7: nat > rat] :
% 0.35/0.69 ? [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 & ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 0.35/0.69 @ ^ [X7: nat > rat] :
% 0.35/0.69 ? [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 & ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Real.positive.rsp
% 0.35/0.69 thf(fact_9386_Gcd__nat__set__eq__fold,axiom,
% 0.35/0.69 ! [Xs2: list_nat] :
% 0.35/0.69 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs2 ) )
% 0.35/0.69 = ( fold_nat_nat @ gcd_gcd_nat @ Xs2 @ zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % Gcd_nat_set_eq_fold
% 0.35/0.69 thf(fact_9387_times__real_Orsp,axiom,
% 0.35/0.69 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 0.35/0.69 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) )
% 0.35/0.69 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_real.rsp
% 0.35/0.69 thf(fact_9388_Real_Opositive_Otransfer,axiom,
% 0.35/0.69 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 0.35/0.69 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 0.35/0.69 @ ^ [X7: nat > rat] :
% 0.35/0.69 ? [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 & ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 0.35/0.69 @ positive2 ) ).
% 0.35/0.69
% 0.35/0.69 % Real.positive.transfer
% 0.35/0.69 thf(fact_9389_Real_Opositive__mult,axiom,
% 0.35/0.69 ! [X: real,Y: real] :
% 0.35/0.69 ( ( positive2 @ X )
% 0.35/0.69 => ( ( positive2 @ Y )
% 0.35/0.69 => ( positive2 @ ( times_times_real @ X @ Y ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Real.positive_mult
% 0.35/0.69 thf(fact_9390_times__real_Otransfer,axiom,
% 0.35/0.69 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 0.35/0.69 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) )
% 0.35/0.69 @ times_times_real ) ).
% 0.35/0.69
% 0.35/0.69 % times_real.transfer
% 0.35/0.69 thf(fact_9391_Real_Opositive_Orep__eq,axiom,
% 0.35/0.69 ( positive2
% 0.35/0.69 = ( ^ [X4: real] :
% 0.35/0.69 ? [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 & ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ R @ ( rep_real @ X4 @ N4 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Real.positive.rep_eq
% 0.35/0.69 thf(fact_9392_Real_Opositive__def,axiom,
% 0.35/0.69 ( positive2
% 0.35/0.69 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 0.35/0.69 @ ^ [X7: nat > rat] :
% 0.35/0.69 ? [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 & ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Real.positive_def
% 0.35/0.69 thf(fact_9393_Real_Opositive_Oabs__eq,axiom,
% 0.35/0.69 ! [X: nat > rat] :
% 0.35/0.69 ( ( realrel @ X @ X )
% 0.35/0.69 => ( ( positive2 @ ( real2 @ X ) )
% 0.35/0.69 = ( ? [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 & ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ R @ ( X @ N4 ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Real.positive.abs_eq
% 0.35/0.69 thf(fact_9394_times__real_Oabs__eq,axiom,
% 0.35/0.69 ! [Xa2: nat > rat,X: nat > rat] :
% 0.35/0.69 ( ( realrel @ Xa2 @ Xa2 )
% 0.35/0.69 => ( ( realrel @ X @ X )
% 0.35/0.69 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 0.35/0.69 = ( real2
% 0.35/0.69 @ ^ [N4: nat] : ( times_times_rat @ ( Xa2 @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_real.abs_eq
% 0.35/0.69 thf(fact_9395_le__Real,axiom,
% 0.35/0.69 ! [X8: nat > rat,Y7: nat > rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ( cauchy @ Y7 )
% 0.35/0.69 => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 0.35/0.69 = ( ! [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 => ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ ( plus_plus_rat @ ( Y7 @ N4 ) @ R ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % le_Real
% 0.35/0.69 thf(fact_9396_not__positive__Real,axiom,
% 0.35/0.69 ! [X8: nat > rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 0.35/0.69 = ( ! [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 => ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ R ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % not_positive_Real
% 0.35/0.69 thf(fact_9397_cauchy__mult,axiom,
% 0.35/0.69 ! [X8: nat > rat,Y7: nat > rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ( cauchy @ Y7 )
% 0.35/0.69 => ( cauchy
% 0.35/0.69 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % cauchy_mult
% 0.35/0.69 thf(fact_9398_mult__Real,axiom,
% 0.35/0.69 ! [X8: nat > rat,Y7: nat > rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ( cauchy @ Y7 )
% 0.35/0.69 => ( ( times_times_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 0.35/0.69 = ( real2
% 0.35/0.69 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % mult_Real
% 0.35/0.69 thf(fact_9399_cauchyD,axiom,
% 0.35/0.69 ! [X8: nat > rat,R3: rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 0.35/0.69 => ? [K: nat] :
% 0.35/0.69 ! [M3: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K @ M3 )
% 0.35/0.69 => ! [N8: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K @ N8 )
% 0.35/0.69 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M3 ) @ ( X8 @ N8 ) ) ) @ R3 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % cauchyD
% 0.35/0.69 thf(fact_9400_cauchyI,axiom,
% 0.35/0.69 ! [X8: nat > rat] :
% 0.35/0.69 ( ! [R4: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 0.35/0.69 => ? [K4: nat] :
% 0.35/0.69 ! [M: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K4 @ M )
% 0.35/0.69 => ! [N3: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K4 @ N3 )
% 0.35/0.69 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M ) @ ( X8 @ N3 ) ) ) @ R4 ) ) ) )
% 0.35/0.69 => ( cauchy @ X8 ) ) ).
% 0.35/0.69
% 0.35/0.69 % cauchyI
% 0.35/0.69 thf(fact_9401_cauchy__def,axiom,
% 0.35/0.69 ( cauchy
% 0.35/0.69 = ( ^ [X7: nat > rat] :
% 0.35/0.69 ! [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 => ? [K3: nat] :
% 0.35/0.69 ! [M6: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ M6 )
% 0.35/0.69 => ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M6 ) @ ( X7 @ N4 ) ) ) @ R ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % cauchy_def
% 0.35/0.69 thf(fact_9402_positive__Real,axiom,
% 0.35/0.69 ! [X8: nat > rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ( positive2 @ ( real2 @ X8 ) )
% 0.35/0.69 = ( ? [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 & ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ R @ ( X8 @ N4 ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % positive_Real
% 0.35/0.69 thf(fact_9403_cauchy__not__vanishes__cases,axiom,
% 0.35/0.69 ! [X8: nat > rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ~ ( vanishes @ X8 )
% 0.35/0.69 => ? [B3: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 0.35/0.69 & ? [K: nat] :
% 0.35/0.69 ( ! [N8: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K @ N8 )
% 0.35/0.69 => ( ord_less_rat @ B3 @ ( uminus_uminus_rat @ ( X8 @ N8 ) ) ) )
% 0.35/0.69 | ! [N8: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K @ N8 )
% 0.35/0.69 => ( ord_less_rat @ B3 @ ( X8 @ N8 ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % cauchy_not_vanishes_cases
% 0.35/0.69 thf(fact_9404_cauchy__not__vanishes,axiom,
% 0.35/0.69 ! [X8: nat > rat] :
% 0.35/0.69 ( ( cauchy @ X8 )
% 0.35/0.69 => ( ~ ( vanishes @ X8 )
% 0.35/0.69 => ? [B3: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 0.35/0.69 & ? [K: nat] :
% 0.35/0.69 ! [N8: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K @ N8 )
% 0.35/0.69 => ( ord_less_rat @ B3 @ ( abs_abs_rat @ ( X8 @ N8 ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % cauchy_not_vanishes
% 0.35/0.69 thf(fact_9405_vanishesD,axiom,
% 0.35/0.69 ! [X8: nat > rat,R3: rat] :
% 0.35/0.69 ( ( vanishes @ X8 )
% 0.35/0.69 => ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 0.35/0.69 => ? [K: nat] :
% 0.35/0.69 ! [N8: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K @ N8 )
% 0.35/0.69 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N8 ) ) @ R3 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % vanishesD
% 0.35/0.69 thf(fact_9406_vanishesI,axiom,
% 0.35/0.69 ! [X8: nat > rat] :
% 0.35/0.69 ( ! [R4: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 0.35/0.69 => ? [K4: nat] :
% 0.35/0.69 ! [N3: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K4 @ N3 )
% 0.35/0.69 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R4 ) ) )
% 0.35/0.69 => ( vanishes @ X8 ) ) ).
% 0.35/0.69
% 0.35/0.69 % vanishesI
% 0.35/0.69 thf(fact_9407_vanishes__def,axiom,
% 0.35/0.69 ( vanishes
% 0.35/0.69 = ( ^ [X7: nat > rat] :
% 0.35/0.69 ! [R: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ R )
% 0.35/0.69 => ? [K3: nat] :
% 0.35/0.69 ! [N4: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ K3 @ N4 )
% 0.35/0.69 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N4 ) ) @ R ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % vanishes_def
% 0.35/0.69 thf(fact_9408_vanishes__mult__bounded,axiom,
% 0.35/0.69 ! [X8: nat > rat,Y7: nat > rat] :
% 0.35/0.69 ( ? [A6: rat] :
% 0.35/0.69 ( ( ord_less_rat @ zero_zero_rat @ A6 )
% 0.35/0.69 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ A6 ) )
% 0.35/0.69 => ( ( vanishes @ Y7 )
% 0.35/0.69 => ( vanishes
% 0.35/0.69 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % vanishes_mult_bounded
% 0.35/0.69 thf(fact_9409_surj__int__decode,axiom,
% 0.35/0.69 ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 0.35/0.69 = top_top_set_int ) ).
% 0.35/0.69
% 0.35/0.69 % surj_int_decode
% 0.35/0.69 thf(fact_9410_bij__int__decode,axiom,
% 0.35/0.69 bij_betw_nat_int @ nat_int_decode @ top_top_set_nat @ top_top_set_int ).
% 0.35/0.69
% 0.35/0.69 % bij_int_decode
% 0.35/0.69 thf(fact_9411_inj__int__decode,axiom,
% 0.35/0.69 ! [A4: set_nat] : ( inj_on_nat_int @ nat_int_decode @ A4 ) ).
% 0.35/0.69
% 0.35/0.69 % inj_int_decode
% 0.35/0.69 thf(fact_9412_int__decode__eq,axiom,
% 0.35/0.69 ! [X: nat,Y: nat] :
% 0.35/0.69 ( ( ( nat_int_decode @ X )
% 0.35/0.69 = ( nat_int_decode @ Y ) )
% 0.35/0.69 = ( X = Y ) ) ).
% 0.35/0.69
% 0.35/0.69 % int_decode_eq
% 0.35/0.69 thf(fact_9413_nat__to__rat__surj__def,axiom,
% 0.35/0.69 ( nat_to_rat_surj
% 0.35/0.69 = ( ^ [N4: nat] :
% 0.35/0.69 ( produc6207742614233964070at_rat
% 0.35/0.69 @ ^ [A5: nat,B4: nat] : ( fract @ ( nat_int_decode @ A5 ) @ ( nat_int_decode @ B4 ) )
% 0.35/0.69 @ ( nat_prod_decode @ N4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_to_rat_surj_def
% 0.35/0.69 thf(fact_9414_bij__int__encode,axiom,
% 0.35/0.69 bij_betw_int_nat @ nat_int_encode @ top_top_set_int @ top_top_set_nat ).
% 0.35/0.69
% 0.35/0.69 % bij_int_encode
% 0.35/0.69 thf(fact_9415_int__encode__inverse,axiom,
% 0.35/0.69 ! [X: int] :
% 0.35/0.69 ( ( nat_int_decode @ ( nat_int_encode @ X ) )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 % int_encode_inverse
% 0.35/0.69 thf(fact_9416_int__decode__inverse,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( ( nat_int_encode @ ( nat_int_decode @ N ) )
% 0.35/0.69 = N ) ).
% 0.35/0.69
% 0.35/0.69 % int_decode_inverse
% 0.35/0.69 thf(fact_9417_inj__int__encode,axiom,
% 0.35/0.69 ! [A4: set_int] : ( inj_on_int_nat @ nat_int_encode @ A4 ) ).
% 0.35/0.69
% 0.35/0.69 % inj_int_encode
% 0.35/0.69 thf(fact_9418_int__encode__eq,axiom,
% 0.35/0.69 ! [X: int,Y: int] :
% 0.35/0.69 ( ( ( nat_int_encode @ X )
% 0.35/0.69 = ( nat_int_encode @ Y ) )
% 0.35/0.69 = ( X = Y ) ) ).
% 0.35/0.69
% 0.35/0.69 % int_encode_eq
% 0.35/0.69 thf(fact_9419_surj__int__encode,axiom,
% 0.35/0.69 ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 0.35/0.69 = top_top_set_nat ) ).
% 0.35/0.69
% 0.35/0.69 % surj_int_encode
% 0.35/0.69 thf(fact_9420_linear__scale__real,axiom,
% 0.35/0.69 ! [F2: real > real,R3: real,B: real] :
% 0.35/0.69 ( ( real_V4572627801940501177l_real @ F2 )
% 0.35/0.69 => ( ( F2 @ ( times_times_real @ R3 @ B ) )
% 0.35/0.69 = ( times_times_real @ R3 @ ( F2 @ B ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % linear_scale_real
% 0.35/0.69 thf(fact_9421_real__linearD,axiom,
% 0.35/0.69 ! [F2: real > real] :
% 0.35/0.69 ( ( real_V4572627801940501177l_real @ F2 )
% 0.35/0.69 => ~ ! [C: real] :
% 0.35/0.69 ( F2
% 0.35/0.69 != ( times_times_real @ C ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % real_linearD
% 0.35/0.69 thf(fact_9422_natLeq__Partial__order,axiom,
% 0.35/0.69 order_5251275573222108571on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.69
% 0.35/0.69 % natLeq_Partial_order
% 0.35/0.69 thf(fact_9423_natLeq__Preorder,axiom,
% 0.35/0.69 order_4861654808422542329on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.69
% 0.35/0.69 % natLeq_Preorder
% 0.35/0.69 thf(fact_9424_less__eq__int__def,axiom,
% 0.35/0.69 ( ord_less_eq_int
% 0.35/0.69 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 0.35/0.69 @ ( produc8739625826339149834_nat_o
% 0.35/0.69 @ ^ [X4: nat,Y4: nat] :
% 0.35/0.69 ( produc6081775807080527818_nat_o
% 0.35/0.69 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_eq_int_def
% 0.35/0.69 thf(fact_9425_int__encode__def,axiom,
% 0.35/0.69 ( nat_int_encode
% 0.35/0.69 = ( ^ [I: int] : ( nat_sum_encode @ ( if_Sum_sum_nat_nat @ ( ord_less_eq_int @ zero_zero_int @ I ) @ ( sum_Inl_nat_nat @ ( nat2 @ I ) ) @ ( sum_Inr_nat_nat @ ( nat2 @ ( minus_minus_int @ ( uminus_uminus_int @ I ) @ one_one_int ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % int_encode_def
% 0.35/0.69 thf(fact_9426_surj__sum__encode,axiom,
% 0.35/0.69 ( ( image_1320371278474632150at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat )
% 0.35/0.69 = top_top_set_nat ) ).
% 0.35/0.69
% 0.35/0.69 % surj_sum_encode
% 0.35/0.69 thf(fact_9427_inj__sum__encode,axiom,
% 0.35/0.69 ! [A4: set_Sum_sum_nat_nat] : ( inj_on6343450744447823682at_nat @ nat_sum_encode @ A4 ) ).
% 0.35/0.69
% 0.35/0.69 % inj_sum_encode
% 0.35/0.69 thf(fact_9428_sum__encode__eq,axiom,
% 0.35/0.69 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 0.35/0.69 ( ( ( nat_sum_encode @ X )
% 0.35/0.69 = ( nat_sum_encode @ Y ) )
% 0.35/0.69 = ( X = Y ) ) ).
% 0.35/0.69
% 0.35/0.69 % sum_encode_eq
% 0.35/0.69 thf(fact_9429_bij__sum__encode,axiom,
% 0.35/0.69 bij_be5432664580149595207at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat @ top_top_set_nat ).
% 0.35/0.69
% 0.35/0.69 % bij_sum_encode
% 0.35/0.69 thf(fact_9430_le__sum__encode__Inl,axiom,
% 0.35/0.69 ! [X: nat,Y: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ X @ Y )
% 0.35/0.69 => ( ord_less_eq_nat @ X @ ( nat_sum_encode @ ( sum_Inl_nat_nat @ Y ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % le_sum_encode_Inl
% 0.35/0.69 thf(fact_9431_le__sum__encode__Inr,axiom,
% 0.35/0.69 ! [X: nat,Y: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ X @ Y )
% 0.35/0.69 => ( ord_less_eq_nat @ X @ ( nat_sum_encode @ ( sum_Inr_nat_nat @ Y ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % le_sum_encode_Inr
% 0.35/0.69 thf(fact_9432_sum__decode__def,axiom,
% 0.35/0.69 ( nat_sum_decode
% 0.35/0.69 = ( ^ [N4: nat] : ( if_Sum_sum_nat_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( sum_Inl_nat_nat @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( sum_Inr_nat_nat @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % sum_decode_def
% 0.35/0.69 thf(fact_9433_sum__encode__inverse,axiom,
% 0.35/0.69 ! [X: sum_sum_nat_nat] :
% 0.35/0.69 ( ( nat_sum_decode @ ( nat_sum_encode @ X ) )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 % sum_encode_inverse
% 0.35/0.69 thf(fact_9434_sum__decode__inverse,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( ( nat_sum_encode @ ( nat_sum_decode @ N ) )
% 0.35/0.69 = N ) ).
% 0.35/0.69
% 0.35/0.69 % sum_decode_inverse
% 0.35/0.69 thf(fact_9435_bij__sum__decode,axiom,
% 0.35/0.69 bij_be4790990086886966983at_nat @ nat_sum_decode @ top_top_set_nat @ top_to6661820994512907621at_nat ).
% 0.35/0.69
% 0.35/0.69 % bij_sum_decode
% 0.35/0.69 thf(fact_9436_sum__decode__eq,axiom,
% 0.35/0.69 ! [X: nat,Y: nat] :
% 0.35/0.69 ( ( ( nat_sum_decode @ X )
% 0.35/0.69 = ( nat_sum_decode @ Y ) )
% 0.35/0.69 = ( X = Y ) ) ).
% 0.35/0.69
% 0.35/0.69 % sum_decode_eq
% 0.35/0.69 thf(fact_9437_inj__sum__decode,axiom,
% 0.35/0.69 ! [A4: set_nat] : ( inj_on5701776251185195458at_nat @ nat_sum_decode @ A4 ) ).
% 0.35/0.69
% 0.35/0.69 % inj_sum_decode
% 0.35/0.69 thf(fact_9438_surj__sum__decode,axiom,
% 0.35/0.69 ( ( image_678696785212003926at_nat @ nat_sum_decode @ top_top_set_nat )
% 0.35/0.69 = top_to6661820994512907621at_nat ) ).
% 0.35/0.69
% 0.35/0.69 % surj_sum_decode
% 0.35/0.69 thf(fact_9439_nth__item_Opinduct,axiom,
% 0.35/0.69 ! [A0: nat,P2: nat > $o] :
% 0.35/0.69 ( ( accp_nat @ nth_item_rel @ A0 )
% 0.35/0.69 => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 0.35/0.69 => ( P2 @ zero_zero_nat ) )
% 0.35/0.69 => ( ! [N3: nat] :
% 0.35/0.69 ( ( accp_nat @ nth_item_rel @ ( suc @ N3 ) )
% 0.35/0.69 => ( ! [A6: nat,Aa: nat] :
% 0.35/0.69 ( ( ( nat_sum_decode @ N3 )
% 0.35/0.69 = ( sum_Inl_nat_nat @ A6 ) )
% 0.35/0.69 => ( ( ( nat_sum_decode @ A6 )
% 0.35/0.69 = ( sum_Inl_nat_nat @ Aa ) )
% 0.35/0.69 => ( P2 @ Aa ) ) )
% 0.35/0.69 => ( ! [A6: nat,B6: nat] :
% 0.35/0.69 ( ( ( nat_sum_decode @ N3 )
% 0.35/0.69 = ( sum_Inl_nat_nat @ A6 ) )
% 0.35/0.69 => ( ( ( nat_sum_decode @ A6 )
% 0.35/0.69 = ( sum_Inr_nat_nat @ B6 ) )
% 0.35/0.69 => ( P2 @ B6 ) ) )
% 0.35/0.69 => ( ! [B6: nat,Ba: nat,X5: nat,Y6: nat] :
% 0.35/0.69 ( ( ( nat_sum_decode @ N3 )
% 0.35/0.69 = ( sum_Inr_nat_nat @ B6 ) )
% 0.35/0.69 => ( ( ( nat_sum_decode @ B6 )
% 0.35/0.69 = ( sum_Inr_nat_nat @ Ba ) )
% 0.35/0.69 => ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 0.35/0.69 = ( nat_prod_decode @ Ba ) )
% 0.35/0.69 => ( P2 @ X5 ) ) ) )
% 0.35/0.69 => ( ! [B6: nat,Ba: nat,X5: nat,Y6: nat] :
% 0.35/0.69 ( ( ( nat_sum_decode @ N3 )
% 0.35/0.69 = ( sum_Inr_nat_nat @ B6 ) )
% 0.35/0.69 => ( ( ( nat_sum_decode @ B6 )
% 0.35/0.69 = ( sum_Inr_nat_nat @ Ba ) )
% 0.35/0.69 => ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 0.35/0.69 = ( nat_prod_decode @ Ba ) )
% 0.35/0.69 => ( P2 @ Y6 ) ) ) )
% 0.35/0.69 => ( P2 @ ( suc @ N3 ) ) ) ) ) ) )
% 0.35/0.69 => ( P2 @ A0 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nth_item.pinduct
% 0.35/0.69 thf(fact_9440_int__decode__def,axiom,
% 0.35/0.69 ( nat_int_decode
% 0.35/0.69 = ( ^ [N4: nat] :
% 0.35/0.69 ( sum_ca7763040182479039464nt_nat @ semiri1314217659103216013at_int
% 0.35/0.69 @ ^ [B4: nat] : ( minus_minus_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ B4 ) ) @ one_one_int )
% 0.35/0.69 @ ( nat_sum_decode @ N4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % int_decode_def
% 0.35/0.69 thf(fact_9441_sum__encode__def,axiom,
% 0.35/0.69 ( nat_sum_encode
% 0.35/0.69 = ( sum_ca6763686470577984908at_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 0.35/0.69 @ ^ [B4: nat] : ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % sum_encode_def
% 0.35/0.69 thf(fact_9442_enat__def,axiom,
% 0.35/0.69 ( extended_enat2
% 0.35/0.69 = ( ^ [N4: nat] : ( extended_Abs_enat @ ( some_nat @ N4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % enat_def
% 0.35/0.69 thf(fact_9443_Bseq__monoseq__convergent_H__dec,axiom,
% 0.35/0.69 ! [F2: nat > real,M5: nat] :
% 0.35/0.69 ( ( bfun_nat_real
% 0.35/0.69 @ ^ [N4: nat] : ( F2 @ ( plus_plus_nat @ N4 @ M5 ) )
% 0.35/0.69 @ at_top_nat )
% 0.35/0.69 => ( ! [M: nat,N3: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ M5 @ M )
% 0.35/0.69 => ( ( ord_less_eq_nat @ M @ N3 )
% 0.35/0.69 => ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ M ) ) ) )
% 0.35/0.69 => ( topolo7531315842566124627t_real @ F2 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Bseq_monoseq_convergent'_dec
% 0.35/0.69 thf(fact_9444_Bseq__monoseq__convergent_H__inc,axiom,
% 0.35/0.69 ! [F2: nat > real,M5: nat] :
% 0.35/0.69 ( ( bfun_nat_real
% 0.35/0.69 @ ^ [N4: nat] : ( F2 @ ( plus_plus_nat @ N4 @ M5 ) )
% 0.35/0.69 @ at_top_nat )
% 0.35/0.69 => ( ! [M: nat,N3: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ M5 @ M )
% 0.35/0.69 => ( ( ord_less_eq_nat @ M @ N3 )
% 0.35/0.69 => ( ord_less_eq_real @ ( F2 @ M ) @ ( F2 @ N3 ) ) ) )
% 0.35/0.69 => ( topolo7531315842566124627t_real @ F2 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Bseq_monoseq_convergent'_inc
% 0.35/0.69 thf(fact_9445_Bseq__mono__convergent,axiom,
% 0.35/0.69 ! [X8: nat > real] :
% 0.35/0.69 ( ( bfun_nat_real @ X8 @ at_top_nat )
% 0.35/0.69 => ( ! [M: nat,N3: nat] :
% 0.35/0.69 ( ( ord_less_eq_nat @ M @ N3 )
% 0.35/0.69 => ( ord_less_eq_real @ ( X8 @ M ) @ ( X8 @ N3 ) ) )
% 0.35/0.69 => ( topolo7531315842566124627t_real @ X8 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Bseq_mono_convergent
% 0.35/0.69 thf(fact_9446_lcm__altdef__int,axiom,
% 0.35/0.69 ( gcd_lcm_int
% 0.35/0.69 = ( ^ [A5: int,B4: int] : ( divide_divide_int @ ( times_times_int @ ( abs_abs_int @ A5 ) @ ( abs_abs_int @ B4 ) ) @ ( gcd_gcd_int @ A5 @ B4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % lcm_altdef_int
% 0.35/0.69 thf(fact_9447_prod__gcd__lcm__int,axiom,
% 0.35/0.69 ! [M2: int,N: int] :
% 0.35/0.69 ( ( times_times_int @ ( abs_abs_int @ M2 ) @ ( abs_abs_int @ N ) )
% 0.35/0.69 = ( times_times_int @ ( gcd_gcd_int @ M2 @ N ) @ ( gcd_lcm_int @ M2 @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % prod_gcd_lcm_int
% 0.35/0.69 thf(fact_9448_lcm__0__iff__nat,axiom,
% 0.35/0.69 ! [M2: nat,N: nat] :
% 0.35/0.69 ( ( ( gcd_lcm_nat @ M2 @ N )
% 0.35/0.69 = zero_zero_nat )
% 0.35/0.69 = ( ( M2 = zero_zero_nat )
% 0.35/0.69 | ( N = zero_zero_nat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % lcm_0_iff_nat
% 0.35/0.69 thf(fact_9449_lcm__1__iff__nat,axiom,
% 0.35/0.69 ! [M2: nat,N: nat] :
% 0.35/0.69 ( ( ( gcd_lcm_nat @ M2 @ N )
% 0.35/0.69 = ( suc @ zero_zero_nat ) )
% 0.35/0.69 = ( ( M2
% 0.35/0.69 = ( suc @ zero_zero_nat ) )
% 0.35/0.69 & ( N
% 0.35/0.69 = ( suc @ zero_zero_nat ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % lcm_1_iff_nat
% 0.35/0.69 thf(fact_9450_prod__gcd__lcm__nat,axiom,
% 0.35/0.69 ( times_times_nat
% 0.35/0.69 = ( ^ [M6: nat,N4: nat] : ( times_times_nat @ ( gcd_gcd_nat @ M6 @ N4 ) @ ( gcd_lcm_nat @ M6 @ N4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % prod_gcd_lcm_nat
% 0.35/0.69 thf(fact_9451_lcm__pos__nat,axiom,
% 0.35/0.69 ! [M2: nat,N: nat] :
% 0.35/0.69 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 0.35/0.69 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.69 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M2 @ N ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % lcm_pos_nat
% 0.35/0.69 thf(fact_9452_lcm__code__integer,axiom,
% 0.35/0.69 ( gcd_lcm_Code_integer
% 0.35/0.69 = ( ^ [A5: code_integer,B4: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A5 ) @ ( abs_abs_Code_integer @ B4 ) ) @ ( gcd_gcd_Code_integer @ A5 @ B4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % lcm_code_integer
% 0.35/0.69 thf(fact_9453_lcm__nat__def,axiom,
% 0.35/0.69 ( gcd_lcm_nat
% 0.35/0.69 = ( ^ [X4: nat,Y4: nat] : ( divide_divide_nat @ ( times_times_nat @ X4 @ Y4 ) @ ( gcd_gcd_nat @ X4 @ Y4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % lcm_nat_def
% 0.35/0.69 thf(fact_9454_Lcm__eq__Max__nat,axiom,
% 0.35/0.69 ! [M5: set_nat] :
% 0.35/0.69 ( ( finite_finite_nat @ M5 )
% 0.35/0.69 => ( ( M5 != bot_bot_set_nat )
% 0.35/0.69 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 0.35/0.69 => ( ! [M: nat,N3: nat] :
% 0.35/0.69 ( ( member_nat @ M @ M5 )
% 0.35/0.69 => ( ( member_nat @ N3 @ M5 )
% 0.35/0.69 => ( member_nat @ ( gcd_lcm_nat @ M @ N3 ) @ M5 ) ) )
% 0.35/0.69 => ( ( gcd_Lcm_nat @ M5 )
% 0.35/0.69 = ( lattic8265883725875713057ax_nat @ M5 ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Lcm_eq_Max_nat
% 0.35/0.69 thf(fact_9455_Lcm__eq__0__I__nat,axiom,
% 0.35/0.69 ! [A4: set_nat] :
% 0.35/0.69 ( ( member_nat @ zero_zero_nat @ A4 )
% 0.35/0.69 => ( ( gcd_Lcm_nat @ A4 )
% 0.35/0.69 = zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % Lcm_eq_0_I_nat
% 0.35/0.69 thf(fact_9456_Lcm__0__iff__nat,axiom,
% 0.35/0.69 ! [A4: set_nat] :
% 0.35/0.69 ( ( finite_finite_nat @ A4 )
% 0.35/0.69 => ( ( ( gcd_Lcm_nat @ A4 )
% 0.35/0.69 = zero_zero_nat )
% 0.35/0.69 = ( member_nat @ zero_zero_nat @ A4 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Lcm_0_iff_nat
% 0.35/0.69 thf(fact_9457_Lcm__nat__infinite,axiom,
% 0.35/0.69 ! [M5: set_nat] :
% 0.35/0.69 ( ~ ( finite_finite_nat @ M5 )
% 0.35/0.69 => ( ( gcd_Lcm_nat @ M5 )
% 0.35/0.69 = zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % Lcm_nat_infinite
% 0.35/0.69 thf(fact_9458_Lcm__nat__def,axiom,
% 0.35/0.69 ( gcd_Lcm_nat
% 0.35/0.69 = ( ^ [M9: set_nat] : ( if_nat @ ( finite_finite_nat @ M9 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M9 ) @ zero_zero_nat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Lcm_nat_def
% 0.35/0.69 thf(fact_9459_unit__factor__simps_I1_J,axiom,
% 0.35/0.69 ( ( unit_f2748546683901255202or_nat @ zero_zero_nat )
% 0.35/0.69 = zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % unit_factor_simps(1)
% 0.35/0.69 thf(fact_9460_unit__factor__simps_I2_J,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( ( unit_f2748546683901255202or_nat @ ( suc @ N ) )
% 0.35/0.69 = one_one_nat ) ).
% 0.35/0.69
% 0.35/0.69 % unit_factor_simps(2)
% 0.35/0.69 thf(fact_9461_unit__factor__nat__def,axiom,
% 0.35/0.69 ( unit_f2748546683901255202or_nat
% 0.35/0.69 = ( ^ [N4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % unit_factor_nat_def
% 0.35/0.69 thf(fact_9462_times__num__def,axiom,
% 0.35/0.69 ( times_times_num
% 0.35/0.69 = ( ^ [M6: num,N4: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_num_def
% 0.35/0.69 thf(fact_9463_nat__of__num__code_I2_J,axiom,
% 0.35/0.69 ! [N: num] :
% 0.35/0.69 ( ( nat_of_num @ ( bit0 @ N ) )
% 0.35/0.69 = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_code(2)
% 0.35/0.69 thf(fact_9464_less__eq__num__def,axiom,
% 0.35/0.69 ( ord_less_eq_num
% 0.35/0.69 = ( ^ [M6: num,N4: num] : ( ord_less_eq_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_eq_num_def
% 0.35/0.69 thf(fact_9465_less__num__def,axiom,
% 0.35/0.69 ( ord_less_num
% 0.35/0.69 = ( ^ [M6: num,N4: num] : ( ord_less_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_num_def
% 0.35/0.69 thf(fact_9466_nat__of__num__inc,axiom,
% 0.35/0.69 ! [X: num] :
% 0.35/0.69 ( ( nat_of_num @ ( inc @ X ) )
% 0.35/0.69 = ( suc @ ( nat_of_num @ X ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_inc
% 0.35/0.69 thf(fact_9467_nat__of__num__mult,axiom,
% 0.35/0.69 ! [X: num,Y: num] :
% 0.35/0.69 ( ( nat_of_num @ ( times_times_num @ X @ Y ) )
% 0.35/0.69 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_mult
% 0.35/0.69 thf(fact_9468_nat__of__num__numeral,axiom,
% 0.35/0.69 nat_of_num = numeral_numeral_nat ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_numeral
% 0.35/0.69 thf(fact_9469_num__eq__iff,axiom,
% 0.35/0.69 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 0.35/0.69 = ( ^ [X4: num,Y4: num] :
% 0.35/0.69 ( ( nat_of_num @ X4 )
% 0.35/0.69 = ( nat_of_num @ Y4 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % num_eq_iff
% 0.35/0.69 thf(fact_9470_nat__of__num__inverse,axiom,
% 0.35/0.69 ! [X: num] :
% 0.35/0.69 ( ( num_of_nat @ ( nat_of_num @ X ) )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_inverse
% 0.35/0.69 thf(fact_9471_nat__of__num_Osimps_I2_J,axiom,
% 0.35/0.69 ! [X: num] :
% 0.35/0.69 ( ( nat_of_num @ ( bit0 @ X ) )
% 0.35/0.69 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num.simps(2)
% 0.35/0.69 thf(fact_9472_nat__of__num__pos,axiom,
% 0.35/0.69 ! [X: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_pos
% 0.35/0.69 thf(fact_9473_nat__of__num__neq__0,axiom,
% 0.35/0.69 ! [X: num] :
% 0.35/0.69 ( ( nat_of_num @ X )
% 0.35/0.69 != zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_neq_0
% 0.35/0.69 thf(fact_9474_nat__of__num__code_I1_J,axiom,
% 0.35/0.69 ( ( nat_of_num @ one )
% 0.35/0.69 = one_one_nat ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_code(1)
% 0.35/0.69 thf(fact_9475_nat__of__num__add,axiom,
% 0.35/0.69 ! [X: num,Y: num] :
% 0.35/0.69 ( ( nat_of_num @ ( plus_plus_num @ X @ Y ) )
% 0.35/0.69 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_add
% 0.35/0.69 thf(fact_9476_nat__of__num__sqr,axiom,
% 0.35/0.69 ! [X: num] :
% 0.35/0.69 ( ( nat_of_num @ ( sqr @ X ) )
% 0.35/0.69 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_sqr
% 0.35/0.69 thf(fact_9477_nat__of__num_Osimps_I1_J,axiom,
% 0.35/0.69 ( ( nat_of_num @ one )
% 0.35/0.69 = ( suc @ zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num.simps(1)
% 0.35/0.69 thf(fact_9478_nat__of__num_Osimps_I3_J,axiom,
% 0.35/0.69 ! [X: num] :
% 0.35/0.69 ( ( nat_of_num @ ( bit1 @ X ) )
% 0.35/0.69 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num.simps(3)
% 0.35/0.69 thf(fact_9479_num__of__nat__inverse,axiom,
% 0.35/0.69 ! [N: nat] :
% 0.35/0.69 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.35/0.69 => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 0.35/0.69 = N ) ) ).
% 0.35/0.69
% 0.35/0.69 % num_of_nat_inverse
% 0.35/0.69 thf(fact_9480_nat__of__num__code_I3_J,axiom,
% 0.35/0.69 ! [N: num] :
% 0.35/0.69 ( ( nat_of_num @ ( bit1 @ N ) )
% 0.35/0.69 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % nat_of_num_code(3)
% 0.35/0.69 thf(fact_9481_plus__num__def,axiom,
% 0.35/0.69 ( plus_plus_num
% 0.35/0.69 = ( ^ [M6: num,N4: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % plus_num_def
% 0.35/0.69 thf(fact_9482_natLeq__trans,axiom,
% 0.35/0.69 trans_nat @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.69
% 0.35/0.69 % natLeq_trans
% 0.35/0.69 thf(fact_9483_natLeq__antisym,axiom,
% 0.35/0.69 antisym_nat @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.69
% 0.35/0.69 % natLeq_antisym
% 0.35/0.69 thf(fact_9484_VEBT__internal_Olesseq_Oelims_I3_J,axiom,
% 0.35/0.69 ! [X: option_nat,Xa2: option_nat] :
% 0.35/0.69 ( ~ ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 0.35/0.69 => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.lesseq.elims(3)
% 0.35/0.69 thf(fact_9485_VEBT__internal_Olesseq_Oelims_I2_J,axiom,
% 0.35/0.69 ! [X: option_nat,Xa2: option_nat] :
% 0.35/0.69 ( ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 0.35/0.69 => ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.lesseq.elims(2)
% 0.35/0.69 thf(fact_9486_VEBT__internal_Olesseq_Oelims_I1_J,axiom,
% 0.35/0.69 ! [X: option_nat,Xa2: option_nat,Y: $o] :
% 0.35/0.69 ( ( ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 0.35/0.69 = Y )
% 0.35/0.69 => ( Y
% 0.35/0.69 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.lesseq.elims(1)
% 0.35/0.69 thf(fact_9487_VEBT__internal_Olesseq_Osimps,axiom,
% 0.35/0.69 ( vEBT_VEBT_lesseq
% 0.35/0.69 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % VEBT_internal.lesseq.simps
% 0.35/0.69 thf(fact_9488_integer__of__nat__0,axiom,
% 0.35/0.69 ( ( code_integer_of_nat @ zero_zero_nat )
% 0.35/0.69 = zero_z3403309356797280102nteger ) ).
% 0.35/0.69
% 0.35/0.69 % integer_of_nat_0
% 0.35/0.69 thf(fact_9489_natural__decr,axiom,
% 0.35/0.69 ! [N: code_natural] :
% 0.35/0.69 ( ( N != zero_z2226904508553997617atural )
% 0.35/0.69 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % natural_decr
% 0.35/0.69 thf(fact_9490_times__natural_Orep__eq,axiom,
% 0.35/0.69 ! [X: code_natural,Xa2: code_natural] :
% 0.35/0.69 ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X @ Xa2 ) )
% 0.35/0.69 = ( times_times_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa2 ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_natural.rep_eq
% 0.35/0.69 thf(fact_9491_zero__natural_Orep__eq,axiom,
% 0.35/0.69 ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 0.35/0.69 = zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % zero_natural.rep_eq
% 0.35/0.69 thf(fact_9492_less__eq__natural_Orep__eq,axiom,
% 0.35/0.69 ( ord_le1926595141338095240atural
% 0.35/0.69 = ( ^ [X4: code_natural,Xa3: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X4 ) @ ( code_nat_of_natural @ Xa3 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_eq_natural.rep_eq
% 0.35/0.69 thf(fact_9493_next_Osimps,axiom,
% 0.35/0.69 ! [V2: code_natural,W2: code_natural] :
% 0.35/0.69 ( ( next @ ( produc3574140220909816553atural @ V2 @ W2 ) )
% 0.35/0.69 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % next.simps
% 0.35/0.69 thf(fact_9494_Random_Orange__def,axiom,
% 0.35/0.69 ( range
% 0.35/0.69 = ( ^ [K3: code_natural] :
% 0.35/0.69 ( produc5538323210962509403atural
% 0.35/0.69 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K3 )
% 0.35/0.69 @ ^ [L2: code_natural] :
% 0.35/0.69 ( produc5538323210962509403atural @ next
% 0.35/0.69 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V3 @ ( times_2397367101498566445atural @ L2 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 0.35/0.69 @ one_one_Code_natural )
% 0.35/0.69 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V3 @ K3 ) ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Random.range_def
% 0.35/0.69 thf(fact_9495_Suc_Orep__eq,axiom,
% 0.35/0.69 ! [X: code_natural] :
% 0.35/0.69 ( ( code_nat_of_natural @ ( code_Suc @ X ) )
% 0.35/0.69 = ( suc @ ( code_nat_of_natural @ X ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Suc.rep_eq
% 0.35/0.69 thf(fact_9496_Suc_Oabs__eq,axiom,
% 0.35/0.69 ! [X: nat] :
% 0.35/0.69 ( ( code_Suc @ ( code_natural_of_nat @ X ) )
% 0.35/0.69 = ( code_natural_of_nat @ ( suc @ X ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % Suc.abs_eq
% 0.35/0.69 thf(fact_9497_less__eq__natural_Oabs__eq,axiom,
% 0.35/0.69 ! [Xa2: nat,X: nat] :
% 0.35/0.69 ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa2 ) @ ( code_natural_of_nat @ X ) )
% 0.35/0.69 = ( ord_less_eq_nat @ Xa2 @ X ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_eq_natural.abs_eq
% 0.35/0.69 thf(fact_9498_times__natural_Oabs__eq,axiom,
% 0.35/0.69 ! [Xa2: nat,X: nat] :
% 0.35/0.69 ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa2 ) @ ( code_natural_of_nat @ X ) )
% 0.35/0.69 = ( code_natural_of_nat @ ( times_times_nat @ Xa2 @ X ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_natural.abs_eq
% 0.35/0.69 thf(fact_9499_less__nat__rel,axiom,
% 0.35/0.69 ( ord_less_nat
% 0.35/0.69 = ( transi2163837189807498211lp_nat
% 0.35/0.69 @ ^ [M6: nat,N4: nat] :
% 0.35/0.69 ( N4
% 0.35/0.69 = ( suc @ M6 ) ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % less_nat_rel
% 0.35/0.69 thf(fact_9500_zero__natural__def,axiom,
% 0.35/0.69 ( zero_z2226904508553997617atural
% 0.35/0.69 = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % zero_natural_def
% 0.35/0.69 thf(fact_9501_Code__Numeral_OSuc__def,axiom,
% 0.35/0.69 ( code_Suc
% 0.35/0.69 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 0.35/0.69
% 0.35/0.69 % Code_Numeral.Suc_def
% 0.35/0.69 thf(fact_9502_times__natural__def,axiom,
% 0.35/0.69 ( times_2397367101498566445atural
% 0.35/0.69 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 0.35/0.69
% 0.35/0.69 % times_natural_def
% 0.35/0.69 thf(fact_9503_typerep_Osize__neq,axiom,
% 0.35/0.69 ! [X: typerep] :
% 0.35/0.69 ( ( size_size_typerep @ X )
% 0.35/0.69 != zero_zero_nat ) ).
% 0.35/0.69
% 0.35/0.69 % typerep.size_neq
% 0.35/0.69 thf(fact_9504_typerep_Osize_I2_J,axiom,
% 0.35/0.69 ! [X1: literal,X2: list_typerep] :
% 0.35/0.69 ( ( size_size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 0.35/0.69 = ( plus_plus_nat @ ( size_list_typerep @ size_size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % typerep.size(2)
% 0.35/0.69 thf(fact_9505_typerep_Osize__gen,axiom,
% 0.35/0.69 ! [X1: literal,X2: list_typerep] :
% 0.35/0.69 ( ( size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 0.35/0.69 = ( plus_plus_nat @ ( size_list_typerep @ size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % typerep.size_gen
% 0.35/0.69 thf(fact_9506_max__nat_Osemilattice__neutr__axioms,axiom,
% 0.35/0.69 semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 0.35/0.69
% 0.35/0.69 % max_nat.semilattice_neutr_axioms
% 0.35/0.69 thf(fact_9507_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 0.35/0.69 semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.35/0.69
% 0.35/0.69 % gcd_nat.semilattice_neutr_axioms
% 0.35/0.69 thf(fact_9508_real__times__code,axiom,
% 0.35/0.69 ! [X: rat,Y: rat] :
% 0.35/0.69 ( ( times_times_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 0.35/0.69 = ( ratreal @ ( times_times_rat @ X @ Y ) ) ) ).
% 0.35/0.69
% 0.35/0.69 % real_times_code
% 0.35/0.69 thf(fact_9509_max__nat_Omonoid__axioms,axiom,
% 0.35/0.69 monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 0.35/0.69
% 0.35/0.69 % max_nat.monoid_axioms
% 0.35/0.69 thf(fact_9510_gcd__nat_Omonoid__axioms,axiom,
% 0.35/0.69 monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 0.35/0.69
% 0.35/0.69 % gcd_nat.monoid_axioms
% 0.35/0.69 thf(fact_9511_natLeq__Card__order,axiom,
% 0.35/0.69 bNF_Ca1281551314933786834on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 0.35/0.69
% 0.35/0.69 % natLeq_Card_order
% 0.35/0.69 thf(fact_9512_card__of__nat,axiom,
% 0.35/0.69 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 0.35/0.69
% 0.35/0.69 % card_of_nat
% 0.35/0.69 thf(fact_9513_card__of__Field__natLeq,axiom,
% 0.35/0.69 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 0.35/0.69
% 0.35/0.69 % card_of_Field_natLeq
% 0.35/0.69
% 0.35/0.69 % Helper facts (35)
% 0.35/0.69 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 0.35/0.69 ! [X: int,Y: int] :
% 0.35/0.69 ( ( if_int @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 0.35/0.69 ! [X: int,Y: int] :
% 0.35/0.69 ( ( if_int @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 0.35/0.69 ! [X: nat,Y: nat] :
% 0.35/0.69 ( ( if_nat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 0.35/0.69 ! [X: nat,Y: nat] :
% 0.35/0.69 ( ( if_nat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 0.35/0.69 ! [X: num,Y: num] :
% 0.35/0.69 ( ( if_num @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 0.35/0.69 ! [X: num,Y: num] :
% 0.35/0.69 ( ( if_num @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 0.35/0.69 ! [X: rat,Y: rat] :
% 0.35/0.69 ( ( if_rat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 0.35/0.69 ! [X: rat,Y: rat] :
% 0.35/0.69 ( ( if_rat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 0.35/0.69 ! [X: real,Y: real] :
% 0.35/0.69 ( ( if_real @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 0.35/0.69 ! [X: real,Y: real] :
% 0.35/0.69 ( ( if_real @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.35/0.69 ! [X: complex,Y: complex] :
% 0.35/0.69 ( ( if_complex @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 0.35/0.69 ! [X: complex,Y: complex] :
% 0.35/0.69 ( ( if_complex @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.35/0.69 ! [X: extended_enat,Y: extended_enat] :
% 0.35/0.69 ( ( if_Extended_enat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 0.35/0.69 ! [X: extended_enat,Y: extended_enat] :
% 0.35/0.69 ( ( if_Extended_enat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.35/0.69 ! [X: code_integer,Y: code_integer] :
% 0.35/0.69 ( ( if_Code_integer @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 0.35/0.69 ! [X: code_integer,Y: code_integer] :
% 0.35/0.69 ( ( if_Code_integer @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: set_nat,Y: set_nat] :
% 0.35/0.69 ( ( if_set_nat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: set_nat,Y: set_nat] :
% 0.35/0.69 ( ( if_set_nat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.35/0.69 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.35/0.69 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 0.35/0.69 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 0.35/0.69 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: list_nat,Y: list_nat] :
% 0.35/0.69 ( ( if_list_nat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: list_nat,Y: list_nat] :
% 0.35/0.69 ( ( if_list_nat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: option_nat,Y: option_nat] :
% 0.35/0.69 ( ( if_option_nat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: option_nat,Y: option_nat] :
% 0.35/0.69 ( ( if_option_nat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.35/0.69 ! [X: option_num,Y: option_num] :
% 0.35/0.69 ( ( if_option_num @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 0.35/0.69 ! [X: option_num,Y: option_num] :
% 0.35/0.69 ( ( if_option_num @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 0.35/0.69 ( ( if_Sum_sum_nat_nat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 0.35/0.69 ( ( if_Sum_sum_nat_nat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.35/0.69 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.35/0.69 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 0.35/0.69 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 0.35/0.69 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.35/0.69 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 0.35/0.69 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 0.35/0.69 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.35/0.69 ! [P2: $o] :
% 0.35/0.69 ( ( P2 = $true )
% 0.35/0.69 | ( P2 = $false ) ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.35/0.69 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.35/0.69 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 0.35/0.69 = Y ) ).
% 0.35/0.69
% 0.35/0.69 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 0.35/0.69 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 0.35/0.69 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 0.35/0.69 = X ) ).
% 0.35/0.69
% 0.35/0.69 % Conjectures (1)
% 0.35/0.69 thf(conj_0,conjecture,
% 0.35/0.69 ( info
% 0.35/0.69 = ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) ) ).
% 0.35/0.69
% 0.35/0.69 %------------------------------------------------------------------------------
% 0.35/0.69 ------------------------
% 6.05/2.49 ---- Embedded in THF ---
% 6.05/2.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 6.05/2.49 %%% Generated on Fri Feb 27 13:42:40 EST 2026
% 6.05/2.49 %%% using '$$dhol' embedding, version 1.3.0.
% 6.05/2.49 %%% Logic specification used:
% 6.05/2.49 %%% thf(spec, logic, $$dhol).
% 6.05/2.49
% 6.05/2.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2DTF14485.p
% See solution above
% 6.40/2.54 ------------------------
% 8.60/4.72 ---- Cleaned THF ---
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.60/4.72 produc5542196010084753463at_nat: $tType ).
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% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.60/4.72 produc5491161045314408544at_nat: $tType ).
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% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 8.60/4.72 set_Pr4333006031979791559at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.60/4.72 produc424102278133772007at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.60/4.72 set_Pr1542805901266377927at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.60/4.72 list_P5464809261938338413at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.60/4.72 set_Pr4329608150637261639at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_Mt__Num__Onum_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 8.60/4.72 produc1193250871479095198on_num: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 8.60/4.72 produc8306885398267862888on_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.72 produc6121120109295599847at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.72 produc4471711990508489141at_nat: $tType ).
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% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.72 produc6392793444374437607at_nat: $tType ).
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% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_I_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J_J,type,
% 8.60/4.72 produc7036089656553540234on_num: $tType ).
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% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_I_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_Mt__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J_J,type,
% 8.60/4.72 produc2233624965454879586on_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.72 produc3843707927480180839at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__List__Olist_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.72 list_P8469869581646625389at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.72 set_Pr8693737435421807431at_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
% 8.60/4.72 produc5835291356934675326atural: $tType ).
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% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J_J,type,
% 8.60/4.72 set_Pr1916528119006554503T_VEBT: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.72 produc859450856879609959at_nat: $tType ).
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% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Code____Numeral__Ointeger_J_Mt__List__Olist_It__Code____Numeral__Ointeger_J_J_J,type,
% 8.60/4.72 set_Pr7565137564259432987nteger: $tType ).
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% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.72 produc9211091688327510695T_VEBT: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__Nat__Onat_J_J_J,type,
% 8.60/4.72 set_Pr8894456036836396799st_nat: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__Int__Oint_J_J_J,type,
% 8.60/4.72 set_Pr4080907618048478043st_int: $tType ).
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% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J_J,type,
% 8.60/4.72 set_Pr1262583345697558789T_VEBT: $tType ).
% 8.60/4.72
% 8.60/4.72 thf(ty_n_t__Product____Type__Oprod_It__List__Olist_It__Code____Numeral__Ointeger_J_Mt__List__Olist_It__Code____Numeral__Ointeger_J_J,type,
% 8.60/4.72 produc862207588354017979nteger: $tType ).
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% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_I_Eo_J_J_J,type,
% 8.60/4.72 set_Pr7508168486584781291list_o: $tType ).
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% 8.60/4.72 thf(ty_n_t__Set__Oset_It__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J_J,type,
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% 8.60/4.72 bNF_Ca5547107478637473181er_num: set_Pr4811707699266497531nteger > ( code_integer > num ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Code____Numeral__Ointeger_001t__Rat__Orat,type,
% 8.60/4.72 bNF_Ca8354645632395198811er_rat: set_Pr4811707699266497531nteger > ( code_integer > rat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Nat__Onat,type,
% 8.60/4.72 bNF_Ca1968104039914474786nt_nat: set_Pr958786334691620121nt_int > ( int > nat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Num__Onum,type,
% 8.60/4.72 bNF_Ca7748807862925029228nt_num: set_Pr958786334691620121nt_int > ( int > num ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Int__Oint_001t__Rat__Orat,type,
% 8.60/4.72 bNF_Ca1332973979827979050nt_rat: set_Pr958786334691620121nt_int > ( int > rat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.72 bNF_Ca968750328013420230at_nat: set_Pr1261947904930325089at_nat > ( nat > nat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Nat__Onat_001t__Num__Onum,type,
% 8.60/4.72 bNF_Ca6749454151023974672at_num: set_Pr1261947904930325089at_nat > ( nat > num ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Cardinal__Order__Relation_OrelChain_001t__Nat__Onat_001t__Rat__Orat,type,
% 8.60/4.72 bNF_Ca333620267926924494at_rat: set_Pr1261947904930325089at_nat > ( nat > rat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J,type,
% 8.60/4.72 bNF_re1962705104956426057at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J,type,
% 8.60/4.72 bNF_re895249473297799549at_rat: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > $o ) > ( ( nat > rat ) > nat > rat ) > ( ( nat > rat ) > nat > rat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001_Eo_001_Eo,type,
% 8.60/4.72 bNF_re728719798268516973at_o_o: ( ( nat > rat ) > ( nat > rat ) > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( ( nat > rat ) > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_I_062_It__Nat__Onat_Mt__Rat__Orat_J_M_062_It__Nat__Onat_Mt__Rat__Orat_J_J_001_062_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 8.60/4.72 bNF_re4695409256820837752l_real: ( ( nat > rat ) > real > $o ) > ( ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ) > ( ( nat > rat ) > ( nat > rat ) > nat > rat ) > ( real > real > real ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal,type,
% 8.60/4.72 bNF_re3023117138289059399t_real: ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > real > $o ) > ( ( nat > rat ) > nat > rat ) > ( real > real ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001_062_It__Nat__Onat_Mt__Rat__Orat_J_001t__Real__Oreal_001_Eo_001_Eo,type,
% 8.60/4.72 bNF_re4297313714947099218al_o_o: ( ( nat > rat ) > real > $o ) > ( $o > $o > $o ) > ( ( nat > rat ) > $o ) > ( real > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.60/4.72 bNF_re711492959462206631nt_int: ( int > int > $o ) > ( ( int > int ) > ( int > int ) > $o ) > ( int > int > int ) > ( int > int > int ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 8.60/4.72 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Nat__Onat_M_Eo_J,type,
% 8.60/4.72 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 bNF_re1345281282404953727at_nat: ( nat > nat > $o ) > ( ( nat > nat ) > ( nat > nat ) > $o ) > ( nat > nat > nat ) > ( nat > nat > nat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 8.60/4.72 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.72 bNF_re5653821019739307937at_nat: ( nat > nat > $o ) > ( nat > nat > $o ) > ( nat > nat ) > ( nat > nat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.60/4.72 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 8.60/4.72 bNF_re5228765855967844073nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo_001_Eo,type,
% 8.60/4.72 bNF_re8699439704749558557nt_o_o: ( product_prod_int_int > product_prod_int_int > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.60/4.72 bNF_re7145576690424134365nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( product_prod_int_int > product_prod_int_int ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Rat__Orat_Mt__Rat__Orat_J,type,
% 8.60/4.72 bNF_re7627151682743391978at_rat: ( product_prod_int_int > rat > $o ) > ( ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ) > ( product_prod_int_int > product_prod_int_int > product_prod_int_int ) > ( rat > rat > rat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001_Eo_001_Eo,type,
% 8.60/4.72 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 8.60/4.72 bNF_re8279943556446156061nt_rat: ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > rat > $o ) > ( product_prod_int_int > product_prod_int_int ) > ( rat > rat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 8.60/4.72 bNF_re717283939379294677_int_o: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( int > int > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.60/4.72 bNF_re7408651293131936558nt_int: ( product_prod_nat_nat > int > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( int > int > int ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001_Eo_001_Eo,type,
% 8.60/4.72 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 8.60/4.72 bNF_re7400052026677387805at_int: ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( int > int ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 8.60/4.72 bNF_re4202695980764964119_nat_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.72 bNF_re3099431351363272937at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 8.60/4.72 bNF_re3666534408544137501at_o_o: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 bNF_re2241393799969408733at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( product_prod_nat_nat > product_prod_nat_nat ) > ( product_prod_nat_nat > product_prod_nat_nat ) > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Wellorder__Constructions_OordIso_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.72 bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_BNF__Wellorder__Relation_Owo__rel_001t__Nat__Onat,type,
% 8.60/4.72 bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Binomial_Obinomial,type,
% 8.60/4.72 binomial: nat > nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Binomial_Ogbinomial_001t__Code____Numeral__Ointeger,type,
% 8.60/4.72 gbinom8545251970709558553nteger: code_integer > nat > code_integer ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Binomial_Ogbinomial_001t__Complex__Ocomplex,type,
% 8.60/4.72 gbinomial_complex: complex > nat > complex ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Binomial_Ogbinomial_001t__Int__Oint,type,
% 8.60/4.72 gbinomial_int: int > nat > int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Binomial_Ogbinomial_001t__Nat__Onat,type,
% 8.60/4.72 gbinomial_nat: nat > nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Binomial_Ogbinomial_001t__Rat__Orat,type,
% 8.60/4.72 gbinomial_rat: rat > nat > rat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Binomial_Ogbinomial_001t__Real__Oreal,type,
% 8.60/4.72 gbinomial_real: real > nat > real ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Oand__int__rel,type,
% 8.60/4.72 bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Oconcat__bit,type,
% 8.60/4.72 bit_concat_bit: nat > int > int > int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Onot_001t__Int__Oint,type,
% 8.60/4.72 bit_ri7919022796975470100ot_int: int > int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Code____Numeral__Ointeger,type,
% 8.60/4.72 bit_ri6519982836138164636nteger: nat > code_integer > code_integer ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Oring__bit__operations__class_Osigned__take__bit_001t__Int__Oint,type,
% 8.60/4.72 bit_ri631733984087533419it_int: nat > int > int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Code____Numeral__Ointeger,type,
% 8.60/4.72 bit_se3949692690581998587nteger: code_integer > code_integer > code_integer ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Int__Oint,type,
% 8.60/4.72 bit_se725231765392027082nd_int: int > int > int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oand_001t__Nat__Onat,type,
% 8.60/4.72 bit_se727722235901077358nd_nat: nat > nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Int__Oint,type,
% 8.60/4.72 bit_se8568078237143864401it_int: nat > int > int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Odrop__bit_001t__Nat__Onat,type,
% 8.60/4.72 bit_se8570568707652914677it_nat: nat > nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Bit__Operations_Osemiring__bit__operations__class_Oflip__bit_001t__Code____Numeral__Ointeger,type,
% 8.60/4.72 bit_se1345352211410354436nteger: nat > code_integer > code_integer ).
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% 8.60/4.72 lattic4420706379359479199al_rat: ( real > rat ) > set_real > real ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Lattices__Big_Osemilattice__neutr__set_OF_001t__Nat__Onat,type,
% 8.60/4.72 lattic7826324295020591184_F_nat: ( nat > nat > nat ) > nat > set_nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 8.60/4.72 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 8.60/4.72 append_nat: list_nat > list_nat > list_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oconcat_001_Eo,type,
% 8.60/4.72 concat_o: list_list_o > list_o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oconcat_001t__Int__Oint,type,
% 8.60/4.72 concat_int: list_list_int > list_int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 8.60/4.72 concat_nat: list_list_nat > list_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oconcat_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.72 concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ocount__list_001_Eo,type,
% 8.60/4.72 count_list_o: list_o > $o > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ocount__list_001t__Complex__Ocomplex,type,
% 8.60/4.72 count_list_complex: list_complex > complex > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ocount__list_001t__Int__Oint,type,
% 8.60/4.72 count_list_int: list_int > int > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ocount__list_001t__Nat__Onat,type,
% 8.60/4.72 count_list_nat: list_nat > nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ocount__list_001t__Real__Oreal,type,
% 8.60/4.72 count_list_real: list_real > real > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ocount__list_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.72 count_list_set_nat: list_set_nat > set_nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ocount__list_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.72 count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001_Eo,type,
% 8.60/4.72 distinct_o: list_o > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__Complex__Ocomplex,type,
% 8.60/4.72 distinct_complex: list_complex > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 8.60/4.72 distinct_int: list_int > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__List__Olist_It__Nat__Onat_J,type,
% 8.60/4.72 distinct_list_nat: list_list_nat > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 8.60/4.72 distinct_nat: list_nat > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 distin6923225563576452346at_nat: list_P6011104703257516679at_nat > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__Real__Oreal,type,
% 8.60/4.72 distinct_real: list_real > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.72 distinct_set_nat: list_set_nat > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Odistinct_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.72 distinct_VEBT_VEBT: list_VEBT_VEBT > $o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oenumerate_001_Eo,type,
% 8.60/4.72 enumerate_o: nat > list_o > list_P7333126701944960589_nat_o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
% 8.60/4.72 enumerate_int: nat > list_int > list_P3521021558325789923at_int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
% 8.60/4.72 enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Oenumerate_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.72 enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ofind_001_Eo,type,
% 8.60/4.72 find_o: ( $o > $o ) > list_o > option_o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ofind_001t__Int__Oint,type,
% 8.60/4.72 find_int: ( int > $o ) > list_int > option_int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ofind_001t__Nat__Onat,type,
% 8.60/4.72 find_nat: ( nat > $o ) > list_nat > option_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ofind_001t__Num__Onum,type,
% 8.60/4.72 find_num: ( num > $o ) > list_num > option_num ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ofind_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 find_P8199882355184865565at_nat: ( product_prod_nat_nat > $o ) > list_P6011104703257516679at_nat > option4927543243414619207at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ofind_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.72 find_VEBT_VEBT: ( vEBT_VEBT > $o ) > list_VEBT_VEBT > option_VEBT_VEBT ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Ofold_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.72 fold_nat_nat: ( nat > nat > nat ) > list_nat > nat > nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olenlex_001_Eo,type,
% 8.60/4.72 lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olenlex_001t__Code____Numeral__Ointeger,type,
% 8.60/4.72 lenlex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olenlex_001t__Int__Oint,type,
% 8.60/4.72 lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olenlex_001t__Nat__Onat,type,
% 8.60/4.72 lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olenlex_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 lenlex325483962726685836at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olenlex_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.72 lenlex1357538814655152620at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olenlex_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.72 lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olex_001_Eo,type,
% 8.60/4.72 lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olex_001t__Code____Numeral__Ointeger,type,
% 8.60/4.72 lex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olex_001t__Int__Oint,type,
% 8.60/4.72 lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olex_001t__Nat__Onat,type,
% 8.60/4.72 lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olex_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 lex_Pr8571645452597969515at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olex_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.72 lex_se2245640040323279819at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olex_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.72 lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 8.60/4.72 linord2614967742042102400et_nat: set_nat > list_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001_062_It__Code____Numeral__Ointeger_Mt__Nat__Onat_J,type,
% 8.60/4.72 cons_C1897838848541180310er_nat: ( code_integer > nat ) > list_C4705013386053401436er_nat > list_C4705013386053401436er_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001_062_It__Int__Oint_Mt__Nat__Onat_J,type,
% 8.60/4.72 cons_int_nat: ( int > nat ) > list_int_nat > list_int_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 cons_nat_nat: ( nat > nat ) > list_nat_nat > list_nat_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Nat__Onat_J,type,
% 8.60/4.72 cons_P4861729644591583992at_nat: ( product_prod_nat_nat > nat ) > list_P9162950289778280392at_nat > list_P9162950289778280392at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Nat__Onat_J,type,
% 8.60/4.72 cons_s2538900923071588440at_nat: ( set_Pr1261947904930325089at_nat > nat ) > list_s9130966667114977576at_nat > list_s9130966667114977576at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001_Eo,type,
% 8.60/4.72 cons_o: $o > list_o > list_o ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Code____Numeral__Ointeger,type,
% 8.60/4.72 cons_Code_integer: code_integer > list_Code_integer > list_Code_integer ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Complex__Ocomplex,type,
% 8.60/4.72 cons_complex: complex > list_complex > list_complex ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 8.60/4.72 cons_int: int > list_int > list_int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 8.60/4.72 cons_nat: nat > list_nat > list_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Num__Onum,type,
% 8.60/4.72 cons_num: num > list_num > list_num ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.60/4.72 cons_P9044669534377732177nteger: produc8923325533196201883nteger > list_P5578671422887162913nteger > list_P5578671422887162913nteger ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 8.60/4.72 cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.72 cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.72 cons_P8732206157123786781at_nat: produc859450856879609959at_nat > list_P8469869581646625389at_nat > list_P8469869581646625389at_nat ).
% 8.60/4.72
% 8.60/4.72 thf(sy_c_List_Olist_OCons_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.73 cons_P3940603068885512221at_nat: produc3843707927480180839at_nat > list_P5464809261938338413at_nat > list_P5464809261938338413at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_OCons_001t__Real__Oreal,type,
% 8.60/4.73 cons_real: real > list_real > list_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 cons_set_nat: set_nat > list_set_nat > list_set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_OCons_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 cons_s6881495754146722583at_nat: set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_OCons_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 8.60/4.73 nil_nat: list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Omap_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 map_VE8901447254227204932T_VEBT: ( vEBT_VEBT > vEBT_VEBT ) > list_VEBT_VEBT > list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 8.60/4.73 set_o2: list_o > set_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 set_Code_integer2: list_Code_integer > set_Code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 8.60/4.73 set_complex2: list_complex > set_complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 8.60/4.73 set_int2: list_int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 8.60/4.73 set_list_o2: list_list_o > set_list_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 8.60/4.73 set_list_int2: list_list_int > set_list_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 8.60/4.73 set_list_nat2: list_list_nat > set_list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 8.60/4.73 set_nat2: list_nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__Complex__Ocomplex_J,type,
% 8.60/4.73 set_Pr1389080609085208608omplex: list_P3924974545808530565omplex > set_Pr5421754520313593387omplex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__Real__Oreal_J,type,
% 8.60/4.73 set_Pr2600826154070092190o_real: list_P5232166724548748803o_real > set_Pr6573716822653411497o_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 set_Pr655345902815428824T_VEBT: list_P7495141550334521929T_VEBT > set_Pr7543698050874017315T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 8.60/4.73 set_Pr920681315882439344nteger: list_P5578671422887162913nteger > set_Pr4811707699266497531nteger ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_M_Eo_J,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
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% 8.60/4.73 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Int__Oint_J,type,
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% 8.60/4.73
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 8.60/4.73 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J,type,
% 8.60/4.73 nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 8.60/4.73 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 8.60/4.73 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 8.60/4.73 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 8.60/4.73 nth_real: list_real > nat > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 nth_set_nat: list_set_nat > nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 8.60/4.73 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 8.60/4.73 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 8.60/4.73 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 8.60/4.73 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 8.60/4.73 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 8.60/4.73 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 8.60/4.73 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct__lists_001_Eo,type,
% 8.60/4.73 product_lists_o: list_list_o > list_list_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct__lists_001t__Int__Oint,type,
% 8.60/4.73 product_lists_int: list_list_int > list_list_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct__lists_001t__Nat__Onat,type,
% 8.60/4.73 product_lists_nat: list_list_nat > list_list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oproduct__lists_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 produc3021084454716106787T_VEBT: list_list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oreplicate_001_Eo,type,
% 8.60/4.73 replicate_o: nat > $o > list_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 8.60/4.73 replicate_complex: nat > complex > list_complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 8.60/4.73 replicate_int: nat > int > list_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 8.60/4.73 replicate_nat: nat > nat > list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 8.60/4.73 replicate_real: nat > real > list_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 replicate_set_nat: nat > set_nat > list_set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Orotate1_001_Eo,type,
% 8.60/4.73 rotate1_o: list_o > list_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Orotate1_001t__Int__Oint,type,
% 8.60/4.73 rotate1_int: list_int > list_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
% 8.60/4.73 rotate1_nat: list_nat > list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Orotate1_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 8.60/4.73 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 8.60/4.73 take_nat: nat > list_nat > list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Otake_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oupt,type,
% 8.60/4.73 upt: nat > nat > list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Oupto,type,
% 8.60/4.73 upto: int > int > list_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001_Eo_001_Eo,type,
% 8.60/4.73 zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001_Eo_001t__Complex__Ocomplex,type,
% 8.60/4.73 zip_o_complex: list_o > list_complex > list_P3924974545808530565omplex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001_Eo_001t__Int__Oint,type,
% 8.60/4.73 zip_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001_Eo_001t__Nat__Onat,type,
% 8.60/4.73 zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001_Eo_001t__Real__Oreal,type,
% 8.60/4.73 zip_o_real: list_o > list_real > list_P5232166724548748803o_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 zip_Co3543743374963494515nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001_Eo,type,
% 8.60/4.73 zip_complex_o: list_complex > list_o > list_P7942624414058669295plex_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 8.60/4.73 zip_complex_complex: list_complex > list_complex > list_P7664491975274850627omplex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Int__Oint,type,
% 8.60/4.73 zip_complex_int: list_complex > list_int > list_P2206113689347244737ex_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Nat__Onat,type,
% 8.60/4.73 zip_complex_nat: list_complex > list_nat > list_P4696196834278971493ex_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__Real__Oreal,type,
% 8.60/4.73 zip_complex_real: list_complex > list_real > list_P7647014805210017729x_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Complex__Ocomplex_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 zip_co9157518722488180109T_VEBT: list_complex > list_VEBT_VEBT > list_P7977503562704621835T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Complex__Ocomplex,type,
% 8.60/4.73 zip_int_complex: list_int > list_complex > list_P1797514011394873281omplex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Int__Oint,type,
% 8.60/4.73 zip_int_int: list_int > list_int > list_P5707943133018811711nt_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Int__Oint_001t__Real__Oreal,type,
% 8.60/4.73 zip_int_real: list_int > list_real > list_P6863124054624500543t_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 zip_nat_VEBT_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 zip_Pr4664179122662387191at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Real__Oreal_001_Eo,type,
% 8.60/4.73 zip_real_o: list_real > list_o > list_P3595434254542482545real_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Complex__Ocomplex,type,
% 8.60/4.73 zip_real_complex: list_real > list_complex > list_P3881527313128557121omplex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Int__Oint,type,
% 8.60/4.73 zip_real_int: list_real > list_int > list_P4344331454722006975al_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Nat__Onat,type,
% 8.60/4.73 zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.60/4.73 zip_real_real: list_real > list_real > list_P8689742595348180415l_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Real__Oreal_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 zip_se5600341670672612855at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > list_P5464809261938338413at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 8.60/4.73 zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Complex__Ocomplex,type,
% 8.60/4.73 zip_VE2794733401258833515omplex: list_VEBT_VEBT > list_complex > list_P4108580160459392801omplex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 8.60/4.73 zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 8.60/4.73 zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__Real__Oreal,type,
% 8.60/4.73 zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_List_Ozip_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_OSuc,type,
% 8.60/4.73 suc: nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 8.60/4.73 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 8.60/4.73 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Onat_Opred,type,
% 8.60/4.73 pred: nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 semiri4939895301339042750nteger: nat > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Onatural,type,
% 8.60/4.73 semiri3763490453095760265atural: nat > code_natural ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 8.60/4.73 semiri8010041392384452111omplex: nat > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 8.60/4.73 semiri4216267220026989637d_enat: nat > extended_enat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 8.60/4.73 semiri1314217659103216013at_int: nat > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 8.60/4.73 semiri1316708129612266289at_nat: nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 8.60/4.73 semiri681578069525770553at_rat: nat > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 8.60/4.73 semiri5074537144036343181t_real: nat > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 semiri4055485073559036834nteger: ( code_integer > code_integer ) > nat > code_integer > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 8.60/4.73 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
% 8.60/4.73 semiri8420488043553186161ux_int: ( int > int ) > nat > int > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 8.60/4.73 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 8.60/4.73 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 8.60/4.73 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 8.60/4.73 size_size_list_o: list_o > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
% 8.60/4.73 size_s3445333598471063425nteger: list_Code_integer > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 8.60/4.73 size_s3451745648224563538omplex: list_complex > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 8.60/4.73 size_size_list_int: list_int > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
% 8.60/4.73 size_s2710708370519433104list_o: list_list_o > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
% 8.60/4.73 size_s533118279054570080st_int: list_list_int > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
% 8.60/4.73 size_s3023201423986296836st_nat: list_list_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.73 size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 8.60/4.73 size_size_list_nat: list_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
% 8.60/4.73 size_size_list_num: list_num > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 8.60/4.73 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 8.60/4.73 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.73 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 8.60/4.73 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Int__Oint_J_J,type,
% 8.60/4.73 size_s2970893825323803983at_int: list_P3521021558325789923at_int > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.73 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 8.60/4.73 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 8.60/4.73 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.73 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 8.60/4.73 size_size_list_real: list_real > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 8.60/4.73 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.73 size_s8736152011456118867at_nat: list_s1210847774152347623at_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 8.60/4.73 size_size_num: num > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 8.60/4.73 size_size_option_nat: option_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 8.60/4.73 size_size_option_num: option_num > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 8.60/4.73 size_size_char: char > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__Typerep__Otyperep,type,
% 8.60/4.73 size_size_typerep: typerep > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oint__decode,type,
% 8.60/4.73 nat_int_decode: nat > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oint__encode,type,
% 8.60/4.73 nat_int_encode: int > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Olist__decode,type,
% 8.60/4.73 nat_list_decode: nat > list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Olist__decode__rel,type,
% 8.60/4.73 nat_list_decode_rel: nat > nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 8.60/4.73 nat_list_encode: list_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 8.60/4.73 nat_list_encode_rel: list_nat > list_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oprod__decode,type,
% 8.60/4.73 nat_prod_decode: nat > product_prod_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 8.60/4.73 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 8.60/4.73 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 8.60/4.73 nat_prod_encode: product_prod_nat_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 8.60/4.73 nat_set_decode: nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 8.60/4.73 nat_set_encode: set_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Osum__decode,type,
% 8.60/4.73 nat_sum_decode: nat > sum_sum_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Osum__encode,type,
% 8.60/4.73 nat_sum_encode: sum_sum_nat_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Nat__Bijection_Otriangle,type,
% 8.60/4.73 nat_triangle: nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_NthRoot_Oroot,type,
% 8.60/4.73 root: nat > real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_NthRoot_Osqrt,type,
% 8.60/4.73 sqrt: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_OBitM,type,
% 8.60/4.73 bitM: num > num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oinc,type,
% 8.60/4.73 inc: num > num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onat__of__num,type,
% 8.60/4.73 nat_of_num: num > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 8.60/4.73 neg_nu7009210354673126013omplex: complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 8.60/4.73 neg_numeral_dbl_int: int > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 8.60/4.73 neg_numeral_dbl_rat: rat > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 8.60/4.73 neg_numeral_dbl_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 8.60/4.73 neg_nu6511756317524482435omplex: complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 8.60/4.73 neg_nu3811975205180677377ec_int: int > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 8.60/4.73 neg_nu3179335615603231917ec_rat: rat > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 8.60/4.73 neg_nu6075765906172075777c_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 8.60/4.73 neg_nu8557863876264182079omplex: complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 8.60/4.73 neg_nu5851722552734809277nc_int: int > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 8.60/4.73 neg_nu5219082963157363817nc_rat: rat > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 8.60/4.73 neg_nu8295874005876285629c_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 8.60/4.73 neg_numeral_sub_int: num > num > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onum_OBit0,type,
% 8.60/4.73 bit0: num > num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onum_OBit1,type,
% 8.60/4.73 bit1: num > num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onum_OOne,type,
% 8.60/4.73 one: num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onum_Osize__num,type,
% 8.60/4.73 size_num: num > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onum__of__nat,type,
% 8.60/4.73 num_of_nat: nat > num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 numera6620942414471956472nteger: num > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Onatural,type,
% 8.60/4.73 numera5444537566228673987atural: num > code_natural ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 8.60/4.73 numera6690914467698888265omplex: num > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 8.60/4.73 numera1916890842035813515d_enat: num > extended_enat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 8.60/4.73 numeral_numeral_int: num > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 8.60/4.73 numeral_numeral_nat: num > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 8.60/4.73 numeral_numeral_rat: num > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 8.60/4.73 numeral_numeral_real: num > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Opow,type,
% 8.60/4.73 pow: num > num > num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Opred__numeral,type,
% 8.60/4.73 pred_numeral: num > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Num_Osqr,type,
% 8.60/4.73 sqr: num > num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 8.60/4.73 none_nat: option_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 8.60/4.73 none_num: option_num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_OSome_001_Eo,type,
% 8.60/4.73 some_o: $o > option_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_OSome_001t__Int__Oint,type,
% 8.60/4.73 some_int: int > option_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 8.60/4.73 some_nat: nat > option_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 8.60/4.73 some_num: num > option_num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_OSome_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 some_VEBT_VEBT: vEBT_VEBT > option_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 8.60/4.73 case_option_num_num: num > ( num > num ) > option_num > num ).
% 8.60/4.73
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% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 8.60/4.73 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 8.60/4.73 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 8.60/4.73 produc2761476792215241774st_nat: ( nat > nat > list_nat ) > product_prod_nat_nat > list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 8.60/4.73 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 8.60/4.73 product_snd_int_int: product_prod_int_int > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Product__Type_Oscomp_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Code____Numeral__Onatural_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_001t__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Product____Type__Oprod_It__Code____Numeral__Onatural_Mt__Code____Numeral__Onatural_J_J,type,
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% 8.60/4.73
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Random_Olog,type,
% 8.60/4.73 log: code_natural > code_natural > code_natural ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Random_Ominus__shift,type,
% 8.60/4.73 minus_shift: code_natural > code_natural > code_natural > code_natural ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Random_Onext,type,
% 8.60/4.73 next: produc7822875418678951345atural > produc5835291356934675326atural ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Random_Orange,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_OAbs__Rat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_OFract,type,
% 8.60/4.73 fract: int > int > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_ORep__Rat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_Ofield__char__0__class_ORats_001t__Real__Oreal,type,
% 8.60/4.73 field_5140801741446780682s_real: set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_Onormalize,type,
% 8.60/4.73 normalize: product_prod_int_int > product_prod_int_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_Opcr__rat,type,
% 8.60/4.73 pcr_rat: product_prod_int_int > rat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_Opositive,type,
% 8.60/4.73 positive: rat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_Oquotient__of,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rat_Oratrel,type,
% 8.60/4.73 ratrel: product_prod_int_int > product_prod_int_int > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_ORatreal,type,
% 8.60/4.73 ratreal: rat > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_OReal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_Ocauchy,type,
% 8.60/4.73 cauchy: ( nat > rat ) > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_Opcr__real,type,
% 8.60/4.73 pcr_real: ( nat > rat ) > real > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_Opositive,type,
% 8.60/4.73 positive2: real > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_Orealrel,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_Orep__real,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real_Ovanishes,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
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% 8.60/4.73 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real__Vector__Spaces_Olinear_001t__Real__Oreal_001t__Real__Oreal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Relation_OField_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Relation_OId_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Relation_Oantisym_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Relation_Orefl__on_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Relation_Ototal__on_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Relation_Otrans_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Int__Oint,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Oalgebraic__semidom__class_Ocoprime_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
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% 8.60/4.73 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Onatural,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Ounit__factor__class_Ounit__factor_001t__Nat__Onat,type,
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% 8.60/4.73 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Series_Osums_001t__Complex__Ocomplex,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Series_Osums_001t__Int__Oint,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Series_Osums_001t__Nat__Onat,type,
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% 8.60/4.73
% 8.60/4.73 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
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% 8.60/4.73
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% 8.60/4.73 image_int_int: ( int > int ) > set_int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Nat__Onat,type,
% 8.60/4.73 image_int_nat: ( int > nat ) > set_int > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__List__Olist_It__Nat__Onat_J_001t__Nat__Onat,type,
% 8.60/4.73 image_list_nat_nat: ( list_nat > nat ) > set_list_nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
% 8.60/4.73 image_nat_int: ( nat > int ) > set_nat > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__List__Olist_It__Nat__Onat_J,type,
% 8.60/4.73 image_nat_list_nat: ( nat > list_nat ) > set_nat > set_list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 image_5846123807819985514at_nat: ( nat > product_prod_nat_nat ) > set_nat > set_Pr1261947904930325089at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 image_nat_set_nat: ( nat > set_nat ) > set_nat > set_set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 8.60/4.73 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 image_678696785212003926at_nat: ( nat > sum_sum_nat_nat ) > set_nat > set_Sum_sum_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 8.60/4.73 image_2486076414777270412at_nat: ( product_prod_nat_nat > nat ) > set_Pr1261947904930325089at_nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.60/4.73 image_real_real: ( real > real ) > set_real > set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 8.60/4.73 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oimage_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat,type,
% 8.60/4.73 image_1320371278474632150at_nat: ( sum_sum_nat_nat > nat ) > set_Sum_sum_nat_nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001_Eo,type,
% 8.60/4.73 insert_o: $o > set_o > set_o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
% 8.60/4.73 insert_complex: complex > set_complex > set_complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 8.60/4.73 insert_int: int > set_int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__List__Olist_It__Nat__Onat_J,type,
% 8.60/4.73 insert_list_nat: list_nat > set_list_nat > set_list_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 8.60/4.73 insert_nat: nat > set_nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 8.60/4.73 insert_num: num > set_num > set_num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 8.60/4.73 insert_rat: rat > set_rat > set_rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 8.60/4.73 insert_real: real > set_real > set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 insert_set_nat: set_nat > set_set_nat > set_set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set_Ovimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 vimage_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Code____Numeral__Ointeger,type,
% 8.60/4.73 set_fo1084959871951514735nteger: ( nat > code_integer > code_integer ) > nat > nat > code_integer > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 8.60/4.73 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 8.60/4.73 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 8.60/4.73 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 8.60/4.73 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 8.60/4.73 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 8.60/4.73 set_or1266510415728281911st_int: int > int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 8.60/4.73 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 8.60/4.73 set_or7049704709247886629st_num: num > num > set_num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 8.60/4.73 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 8.60/4.73 set_or1222579329274155063t_real: real > real > set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 8.60/4.73 set_or4662586982721622107an_int: int > int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 8.60/4.73 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 8.60/4.73 set_ord_atLeast_nat: nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 8.60/4.73 set_ord_atMost_int: int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 8.60/4.73 set_ord_atMost_nat: nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 8.60/4.73 set_ord_atMost_num: num > set_num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 8.60/4.73 set_ord_atMost_rat: rat > set_rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 8.60/4.73 set_ord_atMost_real: real > set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 set_or4236626031148496127et_nat: set_nat > set_set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 8.60/4.73 set_or6656581121297822940st_int: int > int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 8.60/4.73 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 8.60/4.73 set_or5832277885323065728an_int: int > int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 8.60/4.73 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 8.60/4.73 set_or1633881224788618240n_real: real > real > set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 8.60/4.73 set_or1210151606488870762an_nat: nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 8.60/4.73 set_or5849166863359141190n_real: real > set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 8.60/4.73 set_ord_lessThan_int: int > set_int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 8.60/4.73 set_ord_lessThan_nat: nat > set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 8.60/4.73 set_ord_lessThan_num: num > set_num ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 8.60/4.73 set_ord_lessThan_rat: rat > set_rat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 8.60/4.73 set_or5984915006950818249n_real: real > set_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 set_or890127255671739683et_nat: set_nat > set_set_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_String_Ochar_OChar,type,
% 8.60/4.73 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_String_Ochar_Osize__char,type,
% 8.60/4.73 size_char: char > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 8.60/4.73 comm_s629917340098488124ar_nat: char > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_String_Ointeger__of__char,type,
% 8.60/4.73 integer_of_char: char > code_integer ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 8.60/4.73 unique3096191561947761185of_nat: nat > char ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Sum__Type_OInl_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 sum_Inl_nat_nat: nat > sum_sum_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Sum__Type_OInr_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 sum_Inr_nat_nat: nat > sum_sum_nat_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Sum__Type_Osum_Ocase__sum_001t__Nat__Onat_001t__Int__Oint_001t__Nat__Onat,type,
% 8.60/4.73 sum_ca7763040182479039464nt_nat: ( nat > int ) > ( nat > int ) > sum_sum_nat_nat > int ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Sum__Type_Osum_Ocase__sum_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 8.60/4.73 sum_ca6763686470577984908at_nat: ( nat > nat ) > ( nat > nat ) > sum_sum_nat_nat > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.60/4.73 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 8.60/4.73 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 8.60/4.73 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 8.60/4.73 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Topological__Spaces_Otopological__space__class_Oconvergent_001t__Real__Oreal,type,
% 8.60/4.73 topolo7531315842566124627t_real: ( nat > real ) > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 8.60/4.73 topolo2815343760600316023s_real: real > filter_real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 8.60/4.73 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oarccos,type,
% 8.60/4.73 arccos: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 8.60/4.73 arcosh_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oarctan,type,
% 8.60/4.73 arctan: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 8.60/4.73 arsinh_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 8.60/4.73 artanh_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 8.60/4.73 cos_complex: complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 8.60/4.73 cos_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Ocos__coeff,type,
% 8.60/4.73 cos_coeff: nat > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 8.60/4.73 cot_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 8.60/4.73 exp_complex: complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 8.60/4.73 exp_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 8.60/4.73 ln_ln_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Olog,type,
% 8.60/4.73 log2: real > real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Opi,type,
% 8.60/4.73 pi: real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 8.60/4.73 powr_real: real > real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 8.60/4.73 sin_complex: complex > complex ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 8.60/4.73 sin_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Osin__coeff,type,
% 8.60/4.73 sin_coeff: nat > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 8.60/4.73 tan_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 8.60/4.73 tanh_real: real > real ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 8.60/4.73 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 8.60/4.73 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Transitive__Closure_Otranclp_001t__Nat__Onat,type,
% 8.60/4.73 transi2163837189807498211lp_nat: ( nat > nat > $o ) > nat > nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Typerep_Otyperep_OTyperep,type,
% 8.60/4.73 typerep2: literal > list_typerep > typerep ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_Typerep_Otyperep_Osize__typerep,type,
% 8.60/4.73 size_typerep: typerep > nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 8.60/4.73 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
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% 8.60/4.73 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
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% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_I_Eo_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.73 member1087064965665443052T_VEBT: produc1922972420619397443T_VEBT > set_Pr5170412164475753123T_VEBT > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Code____Numeral__Ointeger_J_Mt__List__Olist_It__Code____Numeral__Ointeger_J_J,type,
% 8.60/4.73 member749217712838834276nteger: produc862207588354017979nteger > set_Pr7565137564259432987nteger > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Int__Oint_J_Mt__List__Olist_It__Int__Oint_J_J,type,
% 8.60/4.73 member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_I_Eo_J_J,type,
% 8.60/4.73 member6688923169008879818list_o: produc149729814636038835list_o > set_Pr1150278048023938153list_o > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 8.60/4.73 member7340969449405702474st_nat: produc1828647624359046049st_nat > set_Pr3451248702717554689st_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Nat__Onat_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.73 member5968030670617646438T_VEBT: produc872621073311890639T_VEBT > set_Pr1262583345697558789T_VEBT > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.73 member6693912407220327184at_nat: produc6392793444374437607at_nat > set_Pr1542805901266377927at_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_Mt__List__Olist_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 8.60/4.73 member4080735728053443344at_nat: produc424102278133772007at_nat > set_Pr4333006031979791559at_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_I_Eo_J_J,type,
% 8.60/4.73 member3126162362653435956list_o: produc3962069817607390347list_o > set_Pr7508168486584781291list_o > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__Int__Oint_J_J,type,
% 8.60/4.73 member3703241499402361532st_int: produc7831203938951381541st_int > set_Pr4080907618048478043st_int > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__Nat__Onat_J_J,type,
% 8.60/4.73 member6193324644334088288st_nat: produc1097915047028332489st_nat > set_Pr8894456036836396799st_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__List__Olist_It__VEBT____Definitions__OVEBT_J_Mt__List__Olist_It__VEBT____Definitions__OVEBT_J_J,type,
% 8.60/4.73 member4439316823752958928T_VEBT: produc9211091688327510695T_VEBT > set_Pr1916528119006554503T_VEBT > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 8.60/4.73 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 member8549952807677709168T_VEBT: produc8025551001238799321T_VEBT > set_Pr6167073792073659919T_VEBT > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_M_Eo_J,type,
% 8.60/4.73 member772602641336174712real_o: product_prod_real_o > set_Pr4936984352647145239real_o > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Complex__Ocomplex_J,type,
% 8.60/4.73 member7358116576843751780omplex: produc6979889472282505531omplex > set_Pr6591433984475009307omplex > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Int__Oint_J,type,
% 8.60/4.73 member1627681773268152802al_int: produc8786904178792722361al_int > set_Pr1019928272762051225al_int > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Nat__Onat_J,type,
% 8.60/4.73 member5805532792777349510al_nat: produc3741383161447143261al_nat > set_Pr3510011417693777981al_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 8.60/4.73 member7849222048561428706l_real: produc2422161461964618553l_real > set_Pr6218003697084177305l_real > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Real__Oreal_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 member7262085504369356948T_VEBT: produc3757001726724277373T_VEBT > set_Pr6019664923565264691T_VEBT > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 8.60/4.73 member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 8.60/4.73 member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 8.60/4.73 member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Complex__Ocomplex_J,type,
% 8.60/4.73 member3207599676835851048omplex: produc8380087813684007313omplex > set_Pr216944050393469383omplex > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 8.60/4.73 member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 8.60/4.73 member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Real__Oreal_J,type,
% 8.60/4.73 member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 8.60/4.73 member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Rat__Orat,type,
% 8.60/4.73 member_rat: rat > set_rat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Real__Oreal,type,
% 8.60/4.73 member_real: real > set_real > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 8.60/4.73 member_set_nat: set_nat > set_set_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 8.60/4.73 member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 8.60/4.73 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_a____,type,
% 8.60/4.73 a: $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_b____,type,
% 8.60/4.73 b: $o ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_deg____,type,
% 8.60/4.73 deg: nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_info____,type,
% 8.60/4.73 info: option4927543243414619207at_nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_m____,type,
% 8.60/4.73 m: nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_ma____,type,
% 8.60/4.73 ma: nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_mi____,type,
% 8.60/4.73 mi: nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_na____,type,
% 8.60/4.73 na: nat ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_sa____,type,
% 8.60/4.73 sa: vEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_summary_H____,type,
% 8.60/4.73 summary: vEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_summary____,type,
% 8.60/4.73 summary2: vEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_treeList_H____,type,
% 8.60/4.73 treeList: list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(sy_v_treeList____,type,
% 8.60/4.73 treeList2: list_VEBT_VEBT ).
% 8.60/4.73
% 8.60/4.73 thf(fact_0_case4_I9_J,axiom,
% 8.60/4.73 ord_less_eq_nat @ mi @ ma ).
% 8.60/4.73
% 8.60/4.73 thf(fact_1_option_Oinject,axiom,
% 8.60/4.73 ! [X2: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 8.60/4.73 ( ( ( some_P7363390416028606310at_nat @ X2 )
% 8.60/4.73 = ( some_P7363390416028606310at_nat @ Y2 ) )
% 8.60/4.73 = ( X2 = Y2 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_2_option_Oinject,axiom,
% 8.60/4.73 ! [X2: nat,Y2: nat] :
% 8.60/4.73 ( ( ( some_nat @ X2 )
% 8.60/4.73 = ( some_nat @ Y2 ) )
% 8.60/4.73 = ( X2 = Y2 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_3_option_Oinject,axiom,
% 8.60/4.73 ! [X2: num,Y2: num] :
% 8.60/4.73 ( ( ( some_num @ X2 )
% 8.60/4.73 = ( some_num @ Y2 ) )
% 8.60/4.73 = ( X2 = Y2 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_4_prod_Oinject,axiom,
% 8.60/4.73 ! [X1: code_integer,X2: code_integer,Y1: code_integer,Y2: code_integer] :
% 8.60/4.73 ( ( ( produc1086072967326762835nteger @ X1 @ X2 )
% 8.60/4.73 = ( produc1086072967326762835nteger @ Y1 @ Y2 ) )
% 8.60/4.73 = ( ( X1 = Y1 )
% 8.60/4.73 & ( X2 = Y2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_5_prod_Oinject,axiom,
% 8.60/4.73 ! [X1: product_prod_nat_nat,X2: product_prod_nat_nat,Y1: product_prod_nat_nat,Y2: product_prod_nat_nat] :
% 8.60/4.73 ( ( ( produc6161850002892822231at_nat @ X1 @ X2 )
% 8.60/4.73 = ( produc6161850002892822231at_nat @ Y1 @ Y2 ) )
% 8.60/4.73 = ( ( X1 = Y1 )
% 8.60/4.73 & ( X2 = Y2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_6_prod_Oinject,axiom,
% 8.60/4.73 ! [X1: set_Pr1261947904930325089at_nat,X2: set_Pr1261947904930325089at_nat,Y1: set_Pr1261947904930325089at_nat,Y2: set_Pr1261947904930325089at_nat] :
% 8.60/4.73 ( ( ( produc2922128104949294807at_nat @ X1 @ X2 )
% 8.60/4.73 = ( produc2922128104949294807at_nat @ Y1 @ Y2 ) )
% 8.60/4.73 = ( ( X1 = Y1 )
% 8.60/4.73 & ( X2 = Y2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_7_prod_Oinject,axiom,
% 8.60/4.73 ! [X1: nat,X2: nat,Y1: nat,Y2: nat] :
% 8.60/4.73 ( ( ( product_Pair_nat_nat @ X1 @ X2 )
% 8.60/4.73 = ( product_Pair_nat_nat @ Y1 @ Y2 ) )
% 8.60/4.73 = ( ( X1 = Y1 )
% 8.60/4.73 & ( X2 = Y2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_8_prod_Oinject,axiom,
% 8.60/4.73 ! [X1: int,X2: int,Y1: int,Y2: int] :
% 8.60/4.73 ( ( ( product_Pair_int_int @ X1 @ X2 )
% 8.60/4.73 = ( product_Pair_int_int @ Y1 @ Y2 ) )
% 8.60/4.73 = ( ( X1 = Y1 )
% 8.60/4.73 & ( X2 = Y2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_9_old_Oprod_Oinject,axiom,
% 8.60/4.73 ! [A: code_integer,B: code_integer,A2: code_integer,B2: code_integer] :
% 8.60/4.73 ( ( ( produc1086072967326762835nteger @ A @ B )
% 8.60/4.73 = ( produc1086072967326762835nteger @ A2 @ B2 ) )
% 8.60/4.73 = ( ( A = A2 )
% 8.60/4.73 & ( B = B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_10_old_Oprod_Oinject,axiom,
% 8.60/4.73 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 8.60/4.73 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 8.60/4.73 = ( produc6161850002892822231at_nat @ A2 @ B2 ) )
% 8.60/4.73 = ( ( A = A2 )
% 8.60/4.73 & ( B = B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_11_old_Oprod_Oinject,axiom,
% 8.60/4.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 8.60/4.73 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 8.60/4.73 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 8.60/4.73 = ( ( A = A2 )
% 8.60/4.73 & ( B = B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_12_old_Oprod_Oinject,axiom,
% 8.60/4.73 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 8.60/4.73 ( ( ( product_Pair_nat_nat @ A @ B )
% 8.60/4.73 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 8.60/4.73 = ( ( A = A2 )
% 8.60/4.73 & ( B = B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_13_old_Oprod_Oinject,axiom,
% 8.60/4.73 ! [A: int,B: int,A2: int,B2: int] :
% 8.60/4.73 ( ( ( product_Pair_int_int @ A @ B )
% 8.60/4.73 = ( product_Pair_int_int @ A2 @ B2 ) )
% 8.60/4.73 = ( ( A = A2 )
% 8.60/4.73 & ( B = B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_14_prod__decode__aux_Ocases,axiom,
% 8.60/4.73 ! [X: product_prod_nat_nat] :
% 8.60/4.73 ~ ! [K: nat,M: nat] :
% 8.60/4.73 ( X
% 8.60/4.73 != ( product_Pair_nat_nat @ K @ M ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_15_old_Oprod_Oexhaust,axiom,
% 8.60/4.73 ! [Y: produc8923325533196201883nteger] :
% 8.60/4.73 ~ ! [A3: code_integer,B3: code_integer] :
% 8.60/4.73 ( Y
% 8.60/4.73 != ( produc1086072967326762835nteger @ A3 @ B3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_16_old_Oprod_Oexhaust,axiom,
% 8.60/4.73 ! [Y: produc859450856879609959at_nat] :
% 8.60/4.73 ~ ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 8.60/4.73 ( Y
% 8.60/4.73 != ( produc6161850002892822231at_nat @ A3 @ B3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_17_old_Oprod_Oexhaust,axiom,
% 8.60/4.73 ! [Y: produc3843707927480180839at_nat] :
% 8.60/4.73 ~ ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 8.60/4.73 ( Y
% 8.60/4.73 != ( produc2922128104949294807at_nat @ A3 @ B3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_18_old_Oprod_Oexhaust,axiom,
% 8.60/4.73 ! [Y: product_prod_nat_nat] :
% 8.60/4.73 ~ ! [A3: nat,B3: nat] :
% 8.60/4.73 ( Y
% 8.60/4.73 != ( product_Pair_nat_nat @ A3 @ B3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_19_old_Oprod_Oexhaust,axiom,
% 8.60/4.73 ! [Y: product_prod_int_int] :
% 8.60/4.73 ~ ! [A3: int,B3: int] :
% 8.60/4.73 ( Y
% 8.60/4.73 != ( product_Pair_int_int @ A3 @ B3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_20_surj__pair,axiom,
% 8.60/4.73 ! [P: produc8923325533196201883nteger] :
% 8.60/4.73 ? [X3: code_integer,Y3: code_integer] :
% 8.60/4.73 ( P
% 8.60/4.73 = ( produc1086072967326762835nteger @ X3 @ Y3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_21_surj__pair,axiom,
% 8.60/4.73 ! [P: produc859450856879609959at_nat] :
% 8.60/4.73 ? [X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 8.60/4.73 ( P
% 8.60/4.73 = ( produc6161850002892822231at_nat @ X3 @ Y3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_22_surj__pair,axiom,
% 8.60/4.73 ! [P: produc3843707927480180839at_nat] :
% 8.60/4.73 ? [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] :
% 8.60/4.73 ( P
% 8.60/4.73 = ( produc2922128104949294807at_nat @ X3 @ Y3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_23_surj__pair,axiom,
% 8.60/4.73 ! [P: product_prod_nat_nat] :
% 8.60/4.73 ? [X3: nat,Y3: nat] :
% 8.60/4.73 ( P
% 8.60/4.73 = ( product_Pair_nat_nat @ X3 @ Y3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_24_surj__pair,axiom,
% 8.60/4.73 ! [P: product_prod_int_int] :
% 8.60/4.73 ? [X3: int,Y3: int] :
% 8.60/4.73 ( P
% 8.60/4.73 = ( product_Pair_int_int @ X3 @ Y3 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_25_prod__cases,axiom,
% 8.60/4.73 ! [P2: produc8923325533196201883nteger > $o,P: produc8923325533196201883nteger] :
% 8.60/4.73 ( ! [A3: code_integer,B3: code_integer] : ( P2 @ ( produc1086072967326762835nteger @ A3 @ B3 ) )
% 8.60/4.73 => ( P2 @ P ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_26_prod__cases,axiom,
% 8.60/4.73 ! [P2: produc859450856879609959at_nat > $o,P: produc859450856879609959at_nat] :
% 8.60/4.73 ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] : ( P2 @ ( produc6161850002892822231at_nat @ A3 @ B3 ) )
% 8.60/4.73 => ( P2 @ P ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_27_prod__cases,axiom,
% 8.60/4.73 ! [P2: produc3843707927480180839at_nat > $o,P: produc3843707927480180839at_nat] :
% 8.60/4.73 ( ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( P2 @ ( produc2922128104949294807at_nat @ A3 @ B3 ) )
% 8.60/4.73 => ( P2 @ P ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_28_prod__cases,axiom,
% 8.60/4.73 ! [P2: product_prod_nat_nat > $o,P: product_prod_nat_nat] :
% 8.60/4.73 ( ! [A3: nat,B3: nat] : ( P2 @ ( product_Pair_nat_nat @ A3 @ B3 ) )
% 8.60/4.73 => ( P2 @ P ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_29_prod__cases,axiom,
% 8.60/4.73 ! [P2: product_prod_int_int > $o,P: product_prod_int_int] :
% 8.60/4.73 ( ! [A3: int,B3: int] : ( P2 @ ( product_Pair_int_int @ A3 @ B3 ) )
% 8.60/4.73 => ( P2 @ P ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_30_Pair__inject,axiom,
% 8.60/4.73 ! [A: code_integer,B: code_integer,A2: code_integer,B2: code_integer] :
% 8.60/4.73 ( ( ( produc1086072967326762835nteger @ A @ B )
% 8.60/4.73 = ( produc1086072967326762835nteger @ A2 @ B2 ) )
% 8.60/4.73 => ~ ( ( A = A2 )
% 8.60/4.73 => ( B != B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_31_Pair__inject,axiom,
% 8.60/4.73 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,A2: product_prod_nat_nat,B2: product_prod_nat_nat] :
% 8.60/4.73 ( ( ( produc6161850002892822231at_nat @ A @ B )
% 8.60/4.73 = ( produc6161850002892822231at_nat @ A2 @ B2 ) )
% 8.60/4.73 => ~ ( ( A = A2 )
% 8.60/4.73 => ( B != B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_32_Pair__inject,axiom,
% 8.60/4.73 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 8.60/4.73 ( ( ( produc2922128104949294807at_nat @ A @ B )
% 8.60/4.73 = ( produc2922128104949294807at_nat @ A2 @ B2 ) )
% 8.60/4.73 => ~ ( ( A = A2 )
% 8.60/4.73 => ( B != B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_33_Pair__inject,axiom,
% 8.60/4.73 ! [A: nat,B: nat,A2: nat,B2: nat] :
% 8.60/4.73 ( ( ( product_Pair_nat_nat @ A @ B )
% 8.60/4.73 = ( product_Pair_nat_nat @ A2 @ B2 ) )
% 8.60/4.73 => ~ ( ( A = A2 )
% 8.60/4.73 => ( B != B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_34_Pair__inject,axiom,
% 8.60/4.73 ! [A: int,B: int,A2: int,B2: int] :
% 8.60/4.73 ( ( ( product_Pair_int_int @ A @ B )
% 8.60/4.73 = ( product_Pair_int_int @ A2 @ B2 ) )
% 8.60/4.73 => ~ ( ( A = A2 )
% 8.60/4.73 => ( B != B2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_35_prod__cases3,axiom,
% 8.60/4.73 ! [Y: produc859450856879609959at_nat] :
% 8.60/4.73 ~ ! [A3: product_prod_nat_nat,B3: nat,C: nat] :
% 8.60/4.73 ( Y
% 8.60/4.73 != ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ C ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_36_max__in__set__def,axiom,
% 8.60/4.73 ( vEBT_VEBT_max_in_set
% 8.60/4.73 = ( ^ [Xs: set_nat,X4: nat] :
% 8.60/4.73 ( ( member_nat @ X4 @ Xs )
% 8.60/4.73 & ! [Y4: nat] :
% 8.60/4.73 ( ( member_nat @ Y4 @ Xs )
% 8.60/4.73 => ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_37_min__in__set__def,axiom,
% 8.60/4.73 ( vEBT_VEBT_min_in_set
% 8.60/4.73 = ( ^ [Xs: set_nat,X4: nat] :
% 8.60/4.73 ( ( member_nat @ X4 @ Xs )
% 8.60/4.73 & ! [Y4: nat] :
% 8.60/4.73 ( ( member_nat @ Y4 @ Xs )
% 8.60/4.73 => ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_38_lesseq__shift,axiom,
% 8.60/4.73 ( ord_less_eq_nat
% 8.60/4.73 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_39_prod__induct3,axiom,
% 8.60/4.73 ! [P2: produc859450856879609959at_nat > $o,X: produc859450856879609959at_nat] :
% 8.60/4.73 ( ! [A3: product_prod_nat_nat,B3: nat,C: nat] : ( P2 @ ( produc6161850002892822231at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ C ) ) )
% 8.60/4.73 => ( P2 @ X ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_40_order__refl,axiom,
% 8.60/4.73 ! [X: set_nat] : ( ord_less_eq_set_nat @ X @ X ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_41_order__refl,axiom,
% 8.60/4.73 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_42_order__refl,axiom,
% 8.60/4.73 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_43_order__refl,axiom,
% 8.60/4.73 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_44_order__refl,axiom,
% 8.60/4.73 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_45_dual__order_Orefl,axiom,
% 8.60/4.73 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_46_dual__order_Orefl,axiom,
% 8.60/4.73 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_47_dual__order_Orefl,axiom,
% 8.60/4.73 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_48_dual__order_Orefl,axiom,
% 8.60/4.73 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_49_dual__order_Orefl,axiom,
% 8.60/4.73 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_50_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca8354645632395198811er_rat
% 8.60/4.73 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > rat] :
% 8.60/4.73 ! [I: code_integer,J: code_integer] :
% 8.60/4.73 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_51_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca333620267926924494at_rat
% 8.60/4.73 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > rat] :
% 8.60/4.73 ! [I: nat,J: nat] :
% 8.60/4.73 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_52_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca1332973979827979050nt_rat
% 8.60/4.73 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > rat] :
% 8.60/4.73 ! [I: int,J: int] :
% 8.60/4.73 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_rat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_53_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca5547107478637473181er_num
% 8.60/4.73 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > num] :
% 8.60/4.73 ! [I: code_integer,J: code_integer] :
% 8.60/4.73 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_54_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca6749454151023974672at_num
% 8.60/4.73 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > num] :
% 8.60/4.73 ! [I: nat,J: nat] :
% 8.60/4.73 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_55_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca7748807862925029228nt_num
% 8.60/4.73 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > num] :
% 8.60/4.73 ! [I: int,J: int] :
% 8.60/4.73 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_num @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_56_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca8989775692481694547er_nat
% 8.60/4.73 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > nat] :
% 8.60/4.73 ! [I: code_integer,J: code_integer] :
% 8.60/4.73 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_57_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca968750328013420230at_nat
% 8.60/4.73 = ( ^ [R: set_Pr1261947904930325089at_nat,As: nat > nat] :
% 8.60/4.73 ! [I: nat,J: nat] :
% 8.60/4.73 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_58_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca1968104039914474786nt_nat
% 8.60/4.73 = ( ^ [R: set_Pr958786334691620121nt_int,As: int > nat] :
% 8.60/4.73 ! [I: int,J: int] :
% 8.60/4.73 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_nat @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_59_relChain__def,axiom,
% 8.60/4.73 ( bNF_Ca8987285221972644271er_int
% 8.60/4.73 = ( ^ [R: set_Pr4811707699266497531nteger,As: code_integer > int] :
% 8.60/4.73 ! [I: code_integer,J: code_integer] :
% 8.60/4.73 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ I @ J ) @ R )
% 8.60/4.73 => ( ord_less_eq_int @ ( As @ I ) @ ( As @ J ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_60_fold__atLeastAtMost__nat_Ocases,axiom,
% 8.60/4.73 ! [X: produc4471711990508489141at_nat] :
% 8.60/4.73 ~ ! [F: nat > nat > nat,A3: nat,B3: nat,Acc: nat] :
% 8.60/4.73 ( X
% 8.60/4.73 != ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A3 @ ( product_Pair_nat_nat @ B3 @ Acc ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_61_le__prod__encode__1,axiom,
% 8.60/4.73 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_62_le__prod__encode__2,axiom,
% 8.60/4.73 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_63_lift__Suc__mono__le,axiom,
% 8.60/4.73 ! [F2: nat > set_nat,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_set_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_64_lift__Suc__mono__le,axiom,
% 8.60/4.73 ! [F2: nat > rat,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_rat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_65_lift__Suc__mono__le,axiom,
% 8.60/4.73 ! [F2: nat > num,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_num @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_66_lift__Suc__mono__le,axiom,
% 8.60/4.73 ! [F2: nat > nat,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_67_lift__Suc__mono__le,axiom,
% 8.60/4.73 ! [F2: nat > int,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_int @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_68_lift__Suc__antimono__le,axiom,
% 8.60/4.73 ! [F2: nat > set_nat,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_set_nat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_set_nat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_69_lift__Suc__antimono__le,axiom,
% 8.60/4.73 ! [F2: nat > rat,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_rat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_70_lift__Suc__antimono__le,axiom,
% 8.60/4.73 ! [F2: nat > num,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_num @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_num @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_71_lift__Suc__antimono__le,axiom,
% 8.60/4.73 ! [F2: nat > nat,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_nat @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_72_lift__Suc__antimono__le,axiom,
% 8.60/4.73 ! [F2: nat > int,N: nat,N2: nat] :
% 8.60/4.73 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ ( suc @ N3 ) ) @ ( F2 @ N3 ) )
% 8.60/4.73 => ( ( ord_less_eq_nat @ N @ N2 )
% 8.60/4.73 => ( ord_less_eq_int @ ( F2 @ N2 ) @ ( F2 @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_73_le__refl,axiom,
% 8.60/4.73 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_74_le__trans,axiom,
% 8.60/4.73 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.73 => ( ( ord_less_eq_nat @ J2 @ K2 )
% 8.60/4.73 => ( ord_less_eq_nat @ I2 @ K2 ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_75__C1_C_I2_J,axiom,
% 8.60/4.73 ( deg
% 8.60/4.73 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_76_old_Onat_Oinject,axiom,
% 8.60/4.73 ! [Nat: nat,Nat2: nat] :
% 8.60/4.73 ( ( ( suc @ Nat )
% 8.60/4.73 = ( suc @ Nat2 ) )
% 8.60/4.73 = ( Nat = Nat2 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_77_nat_Oinject,axiom,
% 8.60/4.73 ! [X2: nat,Y2: nat] :
% 8.60/4.73 ( ( ( suc @ X2 )
% 8.60/4.73 = ( suc @ Y2 ) )
% 8.60/4.73 = ( X2 = Y2 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_78_prod__encode__eq,axiom,
% 8.60/4.73 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.60/4.73 ( ( ( nat_prod_encode @ X )
% 8.60/4.73 = ( nat_prod_encode @ Y ) )
% 8.60/4.73 = ( X = Y ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_79_Suc__le__mono,axiom,
% 8.60/4.73 ! [N: nat,M2: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M2 ) )
% 8.60/4.73 = ( ord_less_eq_nat @ N @ M2 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_80_n__not__Suc__n,axiom,
% 8.60/4.73 ! [N: nat] :
% 8.60/4.73 ( N
% 8.60/4.73 != ( suc @ N ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_81_Suc__inject,axiom,
% 8.60/4.73 ! [X: nat,Y: nat] :
% 8.60/4.73 ( ( ( suc @ X )
% 8.60/4.73 = ( suc @ Y ) )
% 8.60/4.73 => ( X = Y ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_82_transitive__stepwise__le,axiom,
% 8.60/4.73 ! [M2: nat,N: nat,R2: nat > nat > $o] :
% 8.60/4.73 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.73 => ( ! [X3: nat] : ( R2 @ X3 @ X3 )
% 8.60/4.73 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 8.60/4.73 ( ( R2 @ X3 @ Y3 )
% 8.60/4.73 => ( ( R2 @ Y3 @ Z )
% 8.60/4.73 => ( R2 @ X3 @ Z ) ) )
% 8.60/4.73 => ( ! [N3: nat] : ( R2 @ N3 @ ( suc @ N3 ) )
% 8.60/4.73 => ( R2 @ M2 @ N ) ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_83_nat__induct__at__least,axiom,
% 8.60/4.73 ! [M2: nat,N: nat,P2: nat > $o] :
% 8.60/4.73 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.73 => ( ( P2 @ M2 )
% 8.60/4.73 => ( ! [N3: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ M2 @ N3 )
% 8.60/4.73 => ( ( P2 @ N3 )
% 8.60/4.73 => ( P2 @ ( suc @ N3 ) ) ) )
% 8.60/4.73 => ( P2 @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_84_mem__Collect__eq,axiom,
% 8.60/4.73 ! [A: int,P2: int > $o] :
% 8.60/4.73 ( ( member_int @ A @ ( collect_int @ P2 ) )
% 8.60/4.73 = ( P2 @ A ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_85_mem__Collect__eq,axiom,
% 8.60/4.73 ! [A: complex,P2: complex > $o] :
% 8.60/4.73 ( ( member_complex @ A @ ( collect_complex @ P2 ) )
% 8.60/4.73 = ( P2 @ A ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_86_mem__Collect__eq,axiom,
% 8.60/4.73 ! [A: real,P2: real > $o] :
% 8.60/4.73 ( ( member_real @ A @ ( collect_real @ P2 ) )
% 8.60/4.73 = ( P2 @ A ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_87_mem__Collect__eq,axiom,
% 8.60/4.73 ! [A: list_nat,P2: list_nat > $o] :
% 8.60/4.73 ( ( member_list_nat @ A @ ( collect_list_nat @ P2 ) )
% 8.60/4.73 = ( P2 @ A ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_88_mem__Collect__eq,axiom,
% 8.60/4.73 ! [A: set_nat,P2: set_nat > $o] :
% 8.60/4.73 ( ( member_set_nat @ A @ ( collect_set_nat @ P2 ) )
% 8.60/4.73 = ( P2 @ A ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_89_mem__Collect__eq,axiom,
% 8.60/4.73 ! [A: nat,P2: nat > $o] :
% 8.60/4.73 ( ( member_nat @ A @ ( collect_nat @ P2 ) )
% 8.60/4.73 = ( P2 @ A ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_90_Collect__mem__eq,axiom,
% 8.60/4.73 ! [A4: set_int] :
% 8.60/4.73 ( ( collect_int
% 8.60/4.73 @ ^ [X4: int] : ( member_int @ X4 @ A4 ) )
% 8.60/4.73 = A4 ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_91_Collect__mem__eq,axiom,
% 8.60/4.73 ! [A4: set_complex] :
% 8.60/4.73 ( ( collect_complex
% 8.60/4.73 @ ^ [X4: complex] : ( member_complex @ X4 @ A4 ) )
% 8.60/4.73 = A4 ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_92_Collect__mem__eq,axiom,
% 8.60/4.73 ! [A4: set_real] :
% 8.60/4.73 ( ( collect_real
% 8.60/4.73 @ ^ [X4: real] : ( member_real @ X4 @ A4 ) )
% 8.60/4.73 = A4 ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_93_Collect__mem__eq,axiom,
% 8.60/4.73 ! [A4: set_list_nat] :
% 8.60/4.73 ( ( collect_list_nat
% 8.60/4.73 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A4 ) )
% 8.60/4.73 = A4 ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_94_Collect__mem__eq,axiom,
% 8.60/4.73 ! [A4: set_set_nat] :
% 8.60/4.73 ( ( collect_set_nat
% 8.60/4.73 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A4 ) )
% 8.60/4.73 = A4 ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_95_Collect__mem__eq,axiom,
% 8.60/4.73 ! [A4: set_nat] :
% 8.60/4.73 ( ( collect_nat
% 8.60/4.73 @ ^ [X4: nat] : ( member_nat @ X4 @ A4 ) )
% 8.60/4.73 = A4 ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_96_Collect__cong,axiom,
% 8.60/4.73 ! [P2: complex > $o,Q: complex > $o] :
% 8.60/4.73 ( ! [X3: complex] :
% 8.60/4.73 ( ( P2 @ X3 )
% 8.60/4.73 = ( Q @ X3 ) )
% 8.60/4.73 => ( ( collect_complex @ P2 )
% 8.60/4.73 = ( collect_complex @ Q ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_97_Collect__cong,axiom,
% 8.60/4.73 ! [P2: real > $o,Q: real > $o] :
% 8.60/4.73 ( ! [X3: real] :
% 8.60/4.73 ( ( P2 @ X3 )
% 8.60/4.73 = ( Q @ X3 ) )
% 8.60/4.73 => ( ( collect_real @ P2 )
% 8.60/4.73 = ( collect_real @ Q ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_98_Collect__cong,axiom,
% 8.60/4.73 ! [P2: list_nat > $o,Q: list_nat > $o] :
% 8.60/4.73 ( ! [X3: list_nat] :
% 8.60/4.73 ( ( P2 @ X3 )
% 8.60/4.73 = ( Q @ X3 ) )
% 8.60/4.73 => ( ( collect_list_nat @ P2 )
% 8.60/4.73 = ( collect_list_nat @ Q ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_99_Collect__cong,axiom,
% 8.60/4.73 ! [P2: set_nat > $o,Q: set_nat > $o] :
% 8.60/4.73 ( ! [X3: set_nat] :
% 8.60/4.73 ( ( P2 @ X3 )
% 8.60/4.73 = ( Q @ X3 ) )
% 8.60/4.73 => ( ( collect_set_nat @ P2 )
% 8.60/4.73 = ( collect_set_nat @ Q ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_100_Collect__cong,axiom,
% 8.60/4.73 ! [P2: nat > $o,Q: nat > $o] :
% 8.60/4.73 ( ! [X3: nat] :
% 8.60/4.73 ( ( P2 @ X3 )
% 8.60/4.73 = ( Q @ X3 ) )
% 8.60/4.73 => ( ( collect_nat @ P2 )
% 8.60/4.73 = ( collect_nat @ Q ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_101_full__nat__induct,axiom,
% 8.60/4.73 ! [P2: nat > $o,N: nat] :
% 8.60/4.73 ( ! [N3: nat] :
% 8.60/4.73 ( ! [M3: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ ( suc @ M3 ) @ N3 )
% 8.60/4.73 => ( P2 @ M3 ) )
% 8.60/4.73 => ( P2 @ N3 ) )
% 8.60/4.73 => ( P2 @ N ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_102_not__less__eq__eq,axiom,
% 8.60/4.73 ! [M2: nat,N: nat] :
% 8.60/4.73 ( ( ~ ( ord_less_eq_nat @ M2 @ N ) )
% 8.60/4.73 = ( ord_less_eq_nat @ ( suc @ N ) @ M2 ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_103_Suc__n__not__le__n,axiom,
% 8.60/4.73 ! [N: nat] :
% 8.60/4.73 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_104_le__Suc__eq,axiom,
% 8.60/4.73 ! [M2: nat,N: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.60/4.73 = ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.73 | ( M2
% 8.60/4.73 = ( suc @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_105_Suc__le__D,axiom,
% 8.60/4.73 ! [N: nat,M4: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ ( suc @ N ) @ M4 )
% 8.60/4.73 => ? [M: nat] :
% 8.60/4.73 ( M4
% 8.60/4.73 = ( suc @ M ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_106_le__SucI,axiom,
% 8.60/4.73 ! [M2: nat,N: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.73 => ( ord_less_eq_nat @ M2 @ ( suc @ N ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_107_le__SucE,axiom,
% 8.60/4.73 ! [M2: nat,N: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.60/4.73 => ( ~ ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.73 => ( M2
% 8.60/4.73 = ( suc @ N ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_108_Suc__leD,axiom,
% 8.60/4.73 ! [M2: nat,N: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 8.60/4.73 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_109_order__antisym__conv,axiom,
% 8.60/4.73 ! [Y: set_nat,X: set_nat] :
% 8.60/4.73 ( ( ord_less_eq_set_nat @ Y @ X )
% 8.60/4.73 => ( ( ord_less_eq_set_nat @ X @ Y )
% 8.60/4.73 = ( X = Y ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_110_order__antisym__conv,axiom,
% 8.60/4.73 ! [Y: rat,X: rat] :
% 8.60/4.73 ( ( ord_less_eq_rat @ Y @ X )
% 8.60/4.73 => ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.73 = ( X = Y ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_111_order__antisym__conv,axiom,
% 8.60/4.73 ! [Y: num,X: num] :
% 8.60/4.73 ( ( ord_less_eq_num @ Y @ X )
% 8.60/4.73 => ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.73 = ( X = Y ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_112_order__antisym__conv,axiom,
% 8.60/4.73 ! [Y: nat,X: nat] :
% 8.60/4.73 ( ( ord_less_eq_nat @ Y @ X )
% 8.60/4.73 => ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.73 = ( X = Y ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_113_order__antisym__conv,axiom,
% 8.60/4.73 ! [Y: int,X: int] :
% 8.60/4.73 ( ( ord_less_eq_int @ Y @ X )
% 8.60/4.73 => ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.73 = ( X = Y ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_114_linorder__le__cases,axiom,
% 8.60/4.73 ! [X: rat,Y: rat] :
% 8.60/4.73 ( ~ ( ord_less_eq_rat @ X @ Y )
% 8.60/4.73 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_115_linorder__le__cases,axiom,
% 8.60/4.73 ! [X: num,Y: num] :
% 8.60/4.73 ( ~ ( ord_less_eq_num @ X @ Y )
% 8.60/4.73 => ( ord_less_eq_num @ Y @ X ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_116_linorder__le__cases,axiom,
% 8.60/4.73 ! [X: nat,Y: nat] :
% 8.60/4.73 ( ~ ( ord_less_eq_nat @ X @ Y )
% 8.60/4.73 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_117_linorder__le__cases,axiom,
% 8.60/4.73 ! [X: int,Y: int] :
% 8.60/4.73 ( ~ ( ord_less_eq_int @ X @ Y )
% 8.60/4.73 => ( ord_less_eq_int @ Y @ X ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_118_ord__le__eq__subst,axiom,
% 8.60/4.73 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 8.60/4.73 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.73 => ( ( ( F2 @ B )
% 8.60/4.73 = C2 )
% 8.60/4.73 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.73 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.73 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.73 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_119_ord__le__eq__subst,axiom,
% 8.60/4.73 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 8.60/4.73 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.73 => ( ( ( F2 @ B )
% 8.60/4.73 = C2 )
% 8.60/4.73 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.73 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.73 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.73 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_120_ord__le__eq__subst,axiom,
% 8.60/4.73 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 8.60/4.73 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.73 => ( ( ( F2 @ B )
% 8.60/4.73 = C2 )
% 8.60/4.73 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.73 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.73 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.73 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.73
% 8.60/4.73 thf(fact_121_ord__le__eq__subst,axiom,
% 8.60/4.73 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 8.60/4.73 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.73 => ( ( ( F2 @ B )
% 8.60/4.73 = C2 )
% 8.60/4.73 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.73 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.73 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.73 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_122_ord__le__eq__subst,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ( F2 @ B )
% 8.60/4.74 = C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_123_ord__le__eq__subst,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ( F2 @ B )
% 8.60/4.74 = C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_124_ord__le__eq__subst,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ( F2 @ B )
% 8.60/4.74 = C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_125_ord__le__eq__subst,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ( F2 @ B )
% 8.60/4.74 = C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_126_ord__le__eq__subst,axiom,
% 8.60/4.74 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ( F2 @ B )
% 8.60/4.74 = C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_127_ord__le__eq__subst,axiom,
% 8.60/4.74 ! [A: nat,B: nat,F2: nat > num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ( F2 @ B )
% 8.60/4.74 = C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_128_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_129_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_130_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_131_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_132_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_133_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: num,F2: num > num,B: num,C2: num] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_134_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_135_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: int,F2: num > int,B: num,C2: num] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_136_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_137_ord__eq__le__subst,axiom,
% 8.60/4.74 ! [A: num,F2: nat > num,B: nat,C2: nat] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_138_linorder__linear,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.74 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_139_linorder__linear,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.74 | ( ord_less_eq_num @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_140_linorder__linear,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.74 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_141_linorder__linear,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.74 | ( ord_less_eq_int @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_142_order__eq__refl,axiom,
% 8.60/4.74 ! [X: set_nat,Y: set_nat] :
% 8.60/4.74 ( ( X = Y )
% 8.60/4.74 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_143_order__eq__refl,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( X = Y )
% 8.60/4.74 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_144_order__eq__refl,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( X = Y )
% 8.60/4.74 => ( ord_less_eq_num @ X @ Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_145_order__eq__refl,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( X = Y )
% 8.60/4.74 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_146_order__eq__refl,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( X = Y )
% 8.60/4.74 => ( ord_less_eq_int @ X @ Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_147_order__subst2,axiom,
% 8.60/4.74 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_148_order__subst2,axiom,
% 8.60/4.74 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_149_order__subst2,axiom,
% 8.60/4.74 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_150_order__subst2,axiom,
% 8.60/4.74 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_151_order__subst2,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_152_order__subst2,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_153_order__subst2,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_154_order__subst2,axiom,
% 8.60/4.74 ! [A: num,B: num,F2: num > int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_155_order__subst2,axiom,
% 8.60/4.74 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_156_order__subst2,axiom,
% 8.60/4.74 ! [A: nat,B: nat,F2: nat > num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_num @ ( F2 @ B ) @ C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_157_order__subst1,axiom,
% 8.60/4.74 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_158_order__subst1,axiom,
% 8.60/4.74 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_159_order__subst1,axiom,
% 8.60/4.74 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_160_order__subst1,axiom,
% 8.60/4.74 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ C2 )
% 8.60/4.74 => ( ! [X3: int,Y3: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_161_order__subst1,axiom,
% 8.60/4.74 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_162_order__subst1,axiom,
% 8.60/4.74 ! [A: num,F2: num > num,B: num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_163_order__subst1,axiom,
% 8.60/4.74 ! [A: num,F2: nat > num,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_164_order__subst1,axiom,
% 8.60/4.74 ! [A: num,F2: int > num,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ C2 )
% 8.60/4.74 => ( ! [X3: int,Y3: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_165_order__subst1,axiom,
% 8.60/4.74 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_166_order__subst1,axiom,
% 8.60/4.74 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ! [X3: num,Y3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_167_Orderings_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 8.60/4.74 & ( ord_less_eq_set_nat @ B4 @ A5 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_168_Orderings_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: rat,B4: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A5 @ B4 )
% 8.60/4.74 & ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_169_Orderings_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: num,B4: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A5 @ B4 )
% 8.60/4.74 & ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_170_Orderings_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: nat,B4: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A5 @ B4 )
% 8.60/4.74 & ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_171_Orderings_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: int,B4: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A5 @ B4 )
% 8.60/4.74 & ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_172_antisym,axiom,
% 8.60/4.74 ! [A: set_nat,B: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_set_nat @ B @ A )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_173_antisym,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_174_antisym,axiom,
% 8.60/4.74 ! [A: num,B: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ A )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_175_antisym,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_176_antisym,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ A )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_177_dual__order_Otrans,axiom,
% 8.60/4.74 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 8.60/4.74 => ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_178_dual__order_Otrans,axiom,
% 8.60/4.74 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ C2 @ B )
% 8.60/4.74 => ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_179_dual__order_Otrans,axiom,
% 8.60/4.74 ! [B: num,A: num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_num @ C2 @ B )
% 8.60/4.74 => ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_180_dual__order_Otrans,axiom,
% 8.60/4.74 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_nat @ C2 @ B )
% 8.60/4.74 => ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_181_dual__order_Otrans,axiom,
% 8.60/4.74 ! [B: int,A: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ C2 @ B )
% 8.60/4.74 => ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_182_dual__order_Oantisym,axiom,
% 8.60/4.74 ! [B: set_nat,A: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_183_dual__order_Oantisym,axiom,
% 8.60/4.74 ! [B: rat,A: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_184_dual__order_Oantisym,axiom,
% 8.60/4.74 ! [B: num,A: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_185_dual__order_Oantisym,axiom,
% 8.60/4.74 ! [B: nat,A: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_186_dual__order_Oantisym,axiom,
% 8.60/4.74 ! [B: int,A: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_187_dual__order_Oeq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 8.60/4.74 & ( ord_less_eq_set_nat @ A5 @ B4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_188_dual__order_Oeq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: rat,B4: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ B4 @ A5 )
% 8.60/4.74 & ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_189_dual__order_Oeq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: num,B4: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ B4 @ A5 )
% 8.60/4.74 & ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_190_dual__order_Oeq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: nat,B4: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ B4 @ A5 )
% 8.60/4.74 & ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_191_dual__order_Oeq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [A5: int,B4: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ B4 @ A5 )
% 8.60/4.74 & ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_192_linorder__wlog,axiom,
% 8.60/4.74 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 8.60/4.74 ( ! [A3: rat,B3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: rat,B3: rat] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_193_linorder__wlog,axiom,
% 8.60/4.74 ! [P2: num > num > $o,A: num,B: num] :
% 8.60/4.74 ( ! [A3: num,B3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: num,B3: num] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_194_linorder__wlog,axiom,
% 8.60/4.74 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 8.60/4.74 ( ! [A3: nat,B3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: nat,B3: nat] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_195_linorder__wlog,axiom,
% 8.60/4.74 ! [P2: int > int > $o,A: int,B: int] :
% 8.60/4.74 ( ! [A3: int,B3: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: int,B3: int] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_196_order__trans,axiom,
% 8.60/4.74 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_197_order__trans,axiom,
% 8.60/4.74 ! [X: rat,Y: rat,Z3: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_198_order__trans,axiom,
% 8.60/4.74 ! [X: num,Y: num,Z3: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_num @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_eq_num @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_199_order__trans,axiom,
% 8.60/4.74 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_200_order__trans,axiom,
% 8.60/4.74 ! [X: int,Y: int,Z3: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_int @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_201_order_Otrans,axiom,
% 8.60/4.74 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_202_order_Otrans,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_203_order_Otrans,axiom,
% 8.60/4.74 ! [A: num,B: num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_204_order_Otrans,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_205_order_Otrans,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_206_order__antisym,axiom,
% 8.60/4.74 ! [X: set_nat,Y: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_set_nat @ Y @ X )
% 8.60/4.74 => ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_207_order__antisym,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_rat @ Y @ X )
% 8.60/4.74 => ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_208_order__antisym,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_num @ Y @ X )
% 8.60/4.74 => ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_209_order__antisym,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_nat @ Y @ X )
% 8.60/4.74 => ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_210_order__antisym,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.74 => ( ( ord_less_eq_int @ Y @ X )
% 8.60/4.74 => ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_211_ord__le__eq__trans,axiom,
% 8.60/4.74 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_212_ord__le__eq__trans,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_213_ord__le__eq__trans,axiom,
% 8.60/4.74 ! [A: num,B: num,C2: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_214_ord__le__eq__trans,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_215_ord__le__eq__trans,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_216_ord__eq__le__trans,axiom,
% 8.60/4.74 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_217_ord__eq__le__trans,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_218_ord__eq__le__trans,axiom,
% 8.60/4.74 ! [A: num,B: num,C2: num] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_num @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_219_ord__eq__le__trans,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_220_ord__eq__le__trans,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ C2 )
% 8.60/4.74 => ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_221_order__class_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: set_nat,Z2: set_nat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [X4: set_nat,Y4: set_nat] :
% 8.60/4.74 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 8.60/4.74 & ( ord_less_eq_set_nat @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_222_order__class_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [X4: rat,Y4: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 8.60/4.74 & ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_223_order__class_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [X4: num,Y4: num] :
% 8.60/4.74 ( ( ord_less_eq_num @ X4 @ Y4 )
% 8.60/4.74 & ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_224_order__class_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [X4: nat,Y4: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 8.60/4.74 & ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_225_order__class_Oorder__eq__iff,axiom,
% 8.60/4.74 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 8.60/4.74 = ( ^ [X4: int,Y4: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ X4 @ Y4 )
% 8.60/4.74 & ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_226_le__cases3,axiom,
% 8.60/4.74 ! [X: rat,Y: rat,Z3: rat] :
% 8.60/4.74 ( ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_rat @ Y @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_rat @ Y @ X )
% 8.60/4.74 => ~ ( ord_less_eq_rat @ X @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_rat @ X @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_rat @ Z3 @ Y ) )
% 8.60/4.74 => ( ( ( ord_less_eq_rat @ Z3 @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 8.60/4.74 => ( ( ( ord_less_eq_rat @ Y @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_rat @ Z3 @ X ) )
% 8.60/4.74 => ~ ( ( ord_less_eq_rat @ Z3 @ X )
% 8.60/4.74 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_227_le__cases3,axiom,
% 8.60/4.74 ! [X: num,Y: num,Z3: num] :
% 8.60/4.74 ( ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_num @ Y @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_num @ Y @ X )
% 8.60/4.74 => ~ ( ord_less_eq_num @ X @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_num @ X @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_num @ Z3 @ Y ) )
% 8.60/4.74 => ( ( ( ord_less_eq_num @ Z3 @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_num @ Y @ X ) )
% 8.60/4.74 => ( ( ( ord_less_eq_num @ Y @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_num @ Z3 @ X ) )
% 8.60/4.74 => ~ ( ( ord_less_eq_num @ Z3 @ X )
% 8.60/4.74 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_228_le__cases3,axiom,
% 8.60/4.74 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.74 ( ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_nat @ Y @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_nat @ Y @ X )
% 8.60/4.74 => ~ ( ord_less_eq_nat @ X @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_nat @ X @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_nat @ Z3 @ Y ) )
% 8.60/4.74 => ( ( ( ord_less_eq_nat @ Z3 @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 8.60/4.74 => ( ( ( ord_less_eq_nat @ Y @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_nat @ Z3 @ X ) )
% 8.60/4.74 => ~ ( ( ord_less_eq_nat @ Z3 @ X )
% 8.60/4.74 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_229_le__cases3,axiom,
% 8.60/4.74 ! [X: int,Y: int,Z3: int] :
% 8.60/4.74 ( ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_int @ Y @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_int @ Y @ X )
% 8.60/4.74 => ~ ( ord_less_eq_int @ X @ Z3 ) )
% 8.60/4.74 => ( ( ( ord_less_eq_int @ X @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_int @ Z3 @ Y ) )
% 8.60/4.74 => ( ( ( ord_less_eq_int @ Z3 @ Y )
% 8.60/4.74 => ~ ( ord_less_eq_int @ Y @ X ) )
% 8.60/4.74 => ( ( ( ord_less_eq_int @ Y @ Z3 )
% 8.60/4.74 => ~ ( ord_less_eq_int @ Z3 @ X ) )
% 8.60/4.74 => ~ ( ( ord_less_eq_int @ Z3 @ X )
% 8.60/4.74 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_230_nle__le,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 8.60/4.74 = ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.74 & ( B != A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_231_nle__le,axiom,
% 8.60/4.74 ! [A: num,B: num] :
% 8.60/4.74 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 8.60/4.74 = ( ( ord_less_eq_num @ B @ A )
% 8.60/4.74 & ( B != A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_232_nle__le,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 8.60/4.74 = ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.74 & ( B != A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_233_nle__le,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 8.60/4.74 = ( ( ord_less_eq_int @ B @ A )
% 8.60/4.74 & ( B != A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_234_bounded__Max__nat,axiom,
% 8.60/4.74 ! [P2: nat > $o,X: nat,M5: nat] :
% 8.60/4.74 ( ( P2 @ X )
% 8.60/4.74 => ( ! [X3: nat] :
% 8.60/4.74 ( ( P2 @ X3 )
% 8.60/4.74 => ( ord_less_eq_nat @ X3 @ M5 ) )
% 8.60/4.74 => ~ ! [M: nat] :
% 8.60/4.74 ( ( P2 @ M )
% 8.60/4.74 => ~ ! [X5: nat] :
% 8.60/4.74 ( ( P2 @ X5 )
% 8.60/4.74 => ( ord_less_eq_nat @ X5 @ M ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_235_Nat_Oex__has__greatest__nat,axiom,
% 8.60/4.74 ! [P2: nat > $o,K2: nat,B: nat] :
% 8.60/4.74 ( ( P2 @ K2 )
% 8.60/4.74 => ( ! [Y3: nat] :
% 8.60/4.74 ( ( P2 @ Y3 )
% 8.60/4.74 => ( ord_less_eq_nat @ Y3 @ B ) )
% 8.60/4.74 => ? [X3: nat] :
% 8.60/4.74 ( ( P2 @ X3 )
% 8.60/4.74 & ! [Y6: nat] :
% 8.60/4.74 ( ( P2 @ Y6 )
% 8.60/4.74 => ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_236_nat__le__linear,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.74 | ( ord_less_eq_nat @ N @ M2 ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_237_le__antisym,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.74 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.60/4.74 => ( M2 = N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_238_eq__imp__le,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( M2 = N )
% 8.60/4.74 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_239_le0,axiom,
% 8.60/4.74 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_240_bot__nat__0_Oextremum,axiom,
% 8.60/4.74 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_241_le__0__eq,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 8.60/4.74 = ( N = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_242_bot__nat__0_Oextremum__uniqueI,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.60/4.74 => ( A = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_243_bot__nat__0_Oextremum__unique,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.60/4.74 = ( A = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_244_less__eq__nat_Osimps_I1_J,axiom,
% 8.60/4.74 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_245_not0__implies__Suc,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( N != zero_zero_nat )
% 8.60/4.74 => ? [M: nat] :
% 8.60/4.74 ( N
% 8.60/4.74 = ( suc @ M ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_246_Zero__not__Suc,axiom,
% 8.60/4.74 ! [M2: nat] :
% 8.60/4.74 ( zero_zero_nat
% 8.60/4.74 != ( suc @ M2 ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_247_Zero__neq__Suc,axiom,
% 8.60/4.74 ! [M2: nat] :
% 8.60/4.74 ( zero_zero_nat
% 8.60/4.74 != ( suc @ M2 ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_248_Suc__neq__Zero,axiom,
% 8.60/4.74 ! [M2: nat] :
% 8.60/4.74 ( ( suc @ M2 )
% 8.60/4.74 != zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_249_zero__induct,axiom,
% 8.60/4.74 ! [P2: nat > $o,K2: nat] :
% 8.60/4.74 ( ( P2 @ K2 )
% 8.60/4.74 => ( ! [N3: nat] :
% 8.60/4.74 ( ( P2 @ ( suc @ N3 ) )
% 8.60/4.74 => ( P2 @ N3 ) )
% 8.60/4.74 => ( P2 @ zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_250_diff__induct,axiom,
% 8.60/4.74 ! [P2: nat > nat > $o,M2: nat,N: nat] :
% 8.60/4.74 ( ! [X3: nat] : ( P2 @ X3 @ zero_zero_nat )
% 8.60/4.74 => ( ! [Y3: nat] : ( P2 @ zero_zero_nat @ ( suc @ Y3 ) )
% 8.60/4.74 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.74 ( ( P2 @ X3 @ Y3 )
% 8.60/4.74 => ( P2 @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 8.60/4.74 => ( P2 @ M2 @ N ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_251_list__decode_Ocases,axiom,
% 8.60/4.74 ! [X: nat] :
% 8.60/4.74 ( ( X != zero_zero_nat )
% 8.60/4.74 => ~ ! [N3: nat] :
% 8.60/4.74 ( X
% 8.60/4.74 != ( suc @ N3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_252_nat_Odistinct_I1_J,axiom,
% 8.60/4.74 ! [X2: nat] :
% 8.60/4.74 ( zero_zero_nat
% 8.60/4.74 != ( suc @ X2 ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_253_old_Onat_Odistinct_I2_J,axiom,
% 8.60/4.74 ! [Nat2: nat] :
% 8.60/4.74 ( ( suc @ Nat2 )
% 8.60/4.74 != zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_254_old_Onat_Odistinct_I1_J,axiom,
% 8.60/4.74 ! [Nat2: nat] :
% 8.60/4.74 ( zero_zero_nat
% 8.60/4.74 != ( suc @ Nat2 ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_255_nat_OdiscI,axiom,
% 8.60/4.74 ! [Nat: nat,X2: nat] :
% 8.60/4.74 ( ( Nat
% 8.60/4.74 = ( suc @ X2 ) )
% 8.60/4.74 => ( Nat != zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_256_old_Onat_Oexhaust,axiom,
% 8.60/4.74 ! [Y: nat] :
% 8.60/4.74 ( ( Y != zero_zero_nat )
% 8.60/4.74 => ~ ! [Nat3: nat] :
% 8.60/4.74 ( Y
% 8.60/4.74 != ( suc @ Nat3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_257_nat__induct,axiom,
% 8.60/4.74 ! [P2: nat > $o,N: nat] :
% 8.60/4.74 ( ( P2 @ zero_zero_nat )
% 8.60/4.74 => ( ! [N3: nat] :
% 8.60/4.74 ( ( P2 @ N3 )
% 8.60/4.74 => ( P2 @ ( suc @ N3 ) ) )
% 8.60/4.74 => ( P2 @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_258_case4_I12_J,axiom,
% 8.60/4.74 vEBT_invar_vebt @ sa @ deg ).
% 8.60/4.74
% 8.60/4.74 thf(fact_259_le__zero__eq,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 8.60/4.74 = ( N = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_260_option_Osize_I4_J,axiom,
% 8.60/4.74 ! [X2: product_prod_nat_nat] :
% 8.60/4.74 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 8.60/4.74 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_261_option_Osize_I4_J,axiom,
% 8.60/4.74 ! [X2: nat] :
% 8.60/4.74 ( ( size_size_option_nat @ ( some_nat @ X2 ) )
% 8.60/4.74 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_262_option_Osize_I4_J,axiom,
% 8.60/4.74 ! [X2: num] :
% 8.60/4.74 ( ( size_size_option_num @ ( some_num @ X2 ) )
% 8.60/4.74 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_263_vebt__buildup_Ocases,axiom,
% 8.60/4.74 ! [X: nat] :
% 8.60/4.74 ( ( X != zero_zero_nat )
% 8.60/4.74 => ( ( X
% 8.60/4.74 != ( suc @ zero_zero_nat ) )
% 8.60/4.74 => ~ ! [Va: nat] :
% 8.60/4.74 ( X
% 8.60/4.74 != ( suc @ ( suc @ Va ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_264_exists__least__lemma,axiom,
% 8.60/4.74 ! [P2: nat > $o] :
% 8.60/4.74 ( ~ ( P2 @ zero_zero_nat )
% 8.60/4.74 => ( ? [X_1: nat] : ( P2 @ X_1 )
% 8.60/4.74 => ? [N3: nat] :
% 8.60/4.74 ( ~ ( P2 @ N3 )
% 8.60/4.74 & ( P2 @ ( suc @ N3 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_265_le__numeral__extra_I3_J,axiom,
% 8.60/4.74 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 8.60/4.74
% 8.60/4.74 thf(fact_266_le__numeral__extra_I3_J,axiom,
% 8.60/4.74 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 8.60/4.74
% 8.60/4.74 thf(fact_267_le__numeral__extra_I3_J,axiom,
% 8.60/4.74 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 8.60/4.74
% 8.60/4.74 thf(fact_268_le__numeral__extra_I3_J,axiom,
% 8.60/4.74 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 8.60/4.74
% 8.60/4.74 thf(fact_269_zero__le,axiom,
% 8.60/4.74 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_270_divides__aux__eq,axiom,
% 8.60/4.74 ! [Q2: code_integer,R3: code_integer] :
% 8.60/4.74 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 8.60/4.74 = ( R3 = zero_z3403309356797280102nteger ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_271_divides__aux__eq,axiom,
% 8.60/4.74 ! [Q2: nat,R3: nat] :
% 8.60/4.74 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 8.60/4.74 = ( R3 = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_272_divides__aux__eq,axiom,
% 8.60/4.74 ! [Q2: int,R3: int] :
% 8.60/4.74 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.60/4.74 = ( R3 = zero_zero_int ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_273_one__le__mult__iff,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) )
% 8.60/4.74 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 8.60/4.74 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_274__C1_C_I1_J,axiom,
% 8.60/4.74 ( sa
% 8.60/4.74 = ( vEBT_Leaf @ a @ b ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_275_valid__tree__deg__neq__0,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT] :
% 8.60/4.74 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_276_valid__0__not,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT] :
% 8.60/4.74 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_277_Leaf__0__not,axiom,
% 8.60/4.74 ! [A: $o,B: $o] :
% 8.60/4.74 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_278_prod__decode__eq,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( ( nat_prod_decode @ X )
% 8.60/4.74 = ( nat_prod_decode @ Y ) )
% 8.60/4.74 = ( X = Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_279_insert_H__pres__valid,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.74 => ( vEBT_invar_vebt @ ( vEBT_VEBT_insert @ T @ X ) @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_280_mult__is__0,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ M2 @ N )
% 8.60/4.74 = zero_zero_nat )
% 8.60/4.74 = ( ( M2 = zero_zero_nat )
% 8.60/4.74 | ( N = zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_281_mult__0__right,axiom,
% 8.60/4.74 ! [M2: nat] :
% 8.60/4.74 ( ( times_times_nat @ M2 @ zero_zero_nat )
% 8.60/4.74 = zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_282_mult__cancel1,axiom,
% 8.60/4.74 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ K2 @ M2 )
% 8.60/4.74 = ( times_times_nat @ K2 @ N ) )
% 8.60/4.74 = ( ( M2 = N )
% 8.60/4.74 | ( K2 = zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_283_mult__cancel2,axiom,
% 8.60/4.74 ! [M2: nat,K2: nat,N: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ M2 @ K2 )
% 8.60/4.74 = ( times_times_nat @ N @ K2 ) )
% 8.60/4.74 = ( ( M2 = N )
% 8.60/4.74 | ( K2 = zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_284_prod__decode__inverse,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( nat_prod_encode @ ( nat_prod_decode @ N ) )
% 8.60/4.74 = N ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_285_prod__encode__inverse,axiom,
% 8.60/4.74 ! [X: product_prod_nat_nat] :
% 8.60/4.74 ( ( nat_prod_decode @ ( nat_prod_encode @ X ) )
% 8.60/4.74 = X ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_286_one__eq__mult__iff,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ( suc @ zero_zero_nat )
% 8.60/4.74 = ( times_times_nat @ M2 @ N ) )
% 8.60/4.74 = ( ( M2
% 8.60/4.74 = ( suc @ zero_zero_nat ) )
% 8.60/4.74 & ( N
% 8.60/4.74 = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_287_mult__eq__1__iff,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ M2 @ N )
% 8.60/4.74 = ( suc @ zero_zero_nat ) )
% 8.60/4.74 = ( ( M2
% 8.60/4.74 = ( suc @ zero_zero_nat ) )
% 8.60/4.74 & ( N
% 8.60/4.74 = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_288_mult_Oleft__commute,axiom,
% 8.60/4.74 ! [B: real,A: real,C2: real] :
% 8.60/4.74 ( ( times_times_real @ B @ ( times_times_real @ A @ C2 ) )
% 8.60/4.74 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_289_mult_Oleft__commute,axiom,
% 8.60/4.74 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.74 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C2 ) )
% 8.60/4.74 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_290_mult_Oleft__commute,axiom,
% 8.60/4.74 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.74 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C2 ) )
% 8.60/4.74 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_291_mult_Oleft__commute,axiom,
% 8.60/4.74 ! [B: int,A: int,C2: int] :
% 8.60/4.74 ( ( times_times_int @ B @ ( times_times_int @ A @ C2 ) )
% 8.60/4.74 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_292_mult_Ocommute,axiom,
% 8.60/4.74 ( times_times_real
% 8.60/4.74 = ( ^ [A5: real,B4: real] : ( times_times_real @ B4 @ A5 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_293_mult_Ocommute,axiom,
% 8.60/4.74 ( times_times_rat
% 8.60/4.74 = ( ^ [A5: rat,B4: rat] : ( times_times_rat @ B4 @ A5 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_294_mult_Ocommute,axiom,
% 8.60/4.74 ( times_times_nat
% 8.60/4.74 = ( ^ [A5: nat,B4: nat] : ( times_times_nat @ B4 @ A5 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_295_mult_Ocommute,axiom,
% 8.60/4.74 ( times_times_int
% 8.60/4.74 = ( ^ [A5: int,B4: int] : ( times_times_int @ B4 @ A5 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_296_mult_Oassoc,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_297_mult_Oassoc,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_298_mult_Oassoc,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_299_mult_Oassoc,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_300_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_301_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_302_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_303_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.60/4.74 = ( times_times_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_304_size__neq__size__imp__neq,axiom,
% 8.60/4.74 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 8.60/4.74 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 8.60/4.74 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_305_size__neq__size__imp__neq,axiom,
% 8.60/4.74 ! [X: list_o,Y: list_o] :
% 8.60/4.74 ( ( ( size_size_list_o @ X )
% 8.60/4.74 != ( size_size_list_o @ Y ) )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_306_size__neq__size__imp__neq,axiom,
% 8.60/4.74 ! [X: list_nat,Y: list_nat] :
% 8.60/4.74 ( ( ( size_size_list_nat @ X )
% 8.60/4.74 != ( size_size_list_nat @ Y ) )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_307_size__neq__size__imp__neq,axiom,
% 8.60/4.74 ! [X: list_int,Y: list_int] :
% 8.60/4.74 ( ( ( size_size_list_int @ X )
% 8.60/4.74 != ( size_size_list_int @ Y ) )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_308_size__neq__size__imp__neq,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( ( size_size_num @ X )
% 8.60/4.74 != ( size_size_num @ Y ) )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_309_Suc__mult__cancel1,axiom,
% 8.60/4.74 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ ( suc @ K2 ) @ M2 )
% 8.60/4.74 = ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 8.60/4.74 = ( M2 = N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_310_mult__0,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( times_times_nat @ zero_zero_nat @ N )
% 8.60/4.74 = zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_311_mult__le__mono2,axiom,
% 8.60/4.74 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_312_mult__le__mono1,axiom,
% 8.60/4.74 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_313_mult__le__mono,axiom,
% 8.60/4.74 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.74 => ( ( ord_less_eq_nat @ K2 @ L )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ L ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_314_le__square,axiom,
% 8.60/4.74 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_315_le__cube,axiom,
% 8.60/4.74 ! [M2: nat] : ( ord_less_eq_nat @ M2 @ ( times_times_nat @ M2 @ ( times_times_nat @ M2 @ M2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_316_Suc__mult__le__cancel1,axiom,
% 8.60/4.74 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K2 ) @ M2 ) @ ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 8.60/4.74 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_317_zero__reorient,axiom,
% 8.60/4.74 ! [X: complex] :
% 8.60/4.74 ( ( zero_zero_complex = X )
% 8.60/4.74 = ( X = zero_zero_complex ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_318_zero__reorient,axiom,
% 8.60/4.74 ! [X: real] :
% 8.60/4.74 ( ( zero_zero_real = X )
% 8.60/4.74 = ( X = zero_zero_real ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_319_zero__reorient,axiom,
% 8.60/4.74 ! [X: rat] :
% 8.60/4.74 ( ( zero_zero_rat = X )
% 8.60/4.74 = ( X = zero_zero_rat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_320_zero__reorient,axiom,
% 8.60/4.74 ! [X: nat] :
% 8.60/4.74 ( ( zero_zero_nat = X )
% 8.60/4.74 = ( X = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_321_zero__reorient,axiom,
% 8.60/4.74 ! [X: int] :
% 8.60/4.74 ( ( zero_zero_int = X )
% 8.60/4.74 = ( X = zero_zero_int ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_322_mult__cancel__right,axiom,
% 8.60/4.74 ! [A: complex,C2: complex,B: complex] :
% 8.60/4.74 ( ( ( times_times_complex @ A @ C2 )
% 8.60/4.74 = ( times_times_complex @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_complex )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_323_mult__cancel__right,axiom,
% 8.60/4.74 ! [A: real,C2: real,B: real] :
% 8.60/4.74 ( ( ( times_times_real @ A @ C2 )
% 8.60/4.74 = ( times_times_real @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_real )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_324_mult__cancel__right,axiom,
% 8.60/4.74 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.74 ( ( ( times_times_rat @ A @ C2 )
% 8.60/4.74 = ( times_times_rat @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_rat )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_325_mult__cancel__right,axiom,
% 8.60/4.74 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ A @ C2 )
% 8.60/4.74 = ( times_times_nat @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_nat )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_326_mult__cancel__right,axiom,
% 8.60/4.74 ! [A: int,C2: int,B: int] :
% 8.60/4.74 ( ( ( times_times_int @ A @ C2 )
% 8.60/4.74 = ( times_times_int @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_int )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_327_mult__cancel__left,axiom,
% 8.60/4.74 ! [C2: complex,A: complex,B: complex] :
% 8.60/4.74 ( ( ( times_times_complex @ C2 @ A )
% 8.60/4.74 = ( times_times_complex @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_complex )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_328_mult__cancel__left,axiom,
% 8.60/4.74 ! [C2: real,A: real,B: real] :
% 8.60/4.74 ( ( ( times_times_real @ C2 @ A )
% 8.60/4.74 = ( times_times_real @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_real )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_329_mult__cancel__left,axiom,
% 8.60/4.74 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.74 ( ( ( times_times_rat @ C2 @ A )
% 8.60/4.74 = ( times_times_rat @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_rat )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_330_mult__cancel__left,axiom,
% 8.60/4.74 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ C2 @ A )
% 8.60/4.74 = ( times_times_nat @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_nat )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_331_mult__cancel__left,axiom,
% 8.60/4.74 ! [C2: int,A: int,B: int] :
% 8.60/4.74 ( ( ( times_times_int @ C2 @ A )
% 8.60/4.74 = ( times_times_int @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_int )
% 8.60/4.74 | ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_332_mult__eq__0__iff,axiom,
% 8.60/4.74 ! [A: complex,B: complex] :
% 8.60/4.74 ( ( ( times_times_complex @ A @ B )
% 8.60/4.74 = zero_zero_complex )
% 8.60/4.74 = ( ( A = zero_zero_complex )
% 8.60/4.74 | ( B = zero_zero_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_333_mult__eq__0__iff,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ( times_times_real @ A @ B )
% 8.60/4.74 = zero_zero_real )
% 8.60/4.74 = ( ( A = zero_zero_real )
% 8.60/4.74 | ( B = zero_zero_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_334_mult__eq__0__iff,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ( times_times_rat @ A @ B )
% 8.60/4.74 = zero_zero_rat )
% 8.60/4.74 = ( ( A = zero_zero_rat )
% 8.60/4.74 | ( B = zero_zero_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_335_mult__eq__0__iff,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ A @ B )
% 8.60/4.74 = zero_zero_nat )
% 8.60/4.74 = ( ( A = zero_zero_nat )
% 8.60/4.74 | ( B = zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_336_mult__eq__0__iff,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ( times_times_int @ A @ B )
% 8.60/4.74 = zero_zero_int )
% 8.60/4.74 = ( ( A = zero_zero_int )
% 8.60/4.74 | ( B = zero_zero_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_337_mult__zero__right,axiom,
% 8.60/4.74 ! [A: complex] :
% 8.60/4.74 ( ( times_times_complex @ A @ zero_zero_complex )
% 8.60/4.74 = zero_zero_complex ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_338_mult__zero__right,axiom,
% 8.60/4.74 ! [A: real] :
% 8.60/4.74 ( ( times_times_real @ A @ zero_zero_real )
% 8.60/4.74 = zero_zero_real ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_339_mult__zero__right,axiom,
% 8.60/4.74 ! [A: rat] :
% 8.60/4.74 ( ( times_times_rat @ A @ zero_zero_rat )
% 8.60/4.74 = zero_zero_rat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_340_mult__zero__right,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ( ( times_times_nat @ A @ zero_zero_nat )
% 8.60/4.74 = zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_341_mult__zero__right,axiom,
% 8.60/4.74 ! [A: int] :
% 8.60/4.74 ( ( times_times_int @ A @ zero_zero_int )
% 8.60/4.74 = zero_zero_int ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_342_mult__zero__left,axiom,
% 8.60/4.74 ! [A: complex] :
% 8.60/4.74 ( ( times_times_complex @ zero_zero_complex @ A )
% 8.60/4.74 = zero_zero_complex ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_343_mult__zero__left,axiom,
% 8.60/4.74 ! [A: real] :
% 8.60/4.74 ( ( times_times_real @ zero_zero_real @ A )
% 8.60/4.74 = zero_zero_real ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_344_mult__zero__left,axiom,
% 8.60/4.74 ! [A: rat] :
% 8.60/4.74 ( ( times_times_rat @ zero_zero_rat @ A )
% 8.60/4.74 = zero_zero_rat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_345_mult__zero__left,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ( ( times_times_nat @ zero_zero_nat @ A )
% 8.60/4.74 = zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_346_mult__zero__left,axiom,
% 8.60/4.74 ! [A: int] :
% 8.60/4.74 ( ( times_times_int @ zero_zero_int @ A )
% 8.60/4.74 = zero_zero_int ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_347_mul__shift,axiom,
% 8.60/4.74 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ X @ Y )
% 8.60/4.74 = Z3 )
% 8.60/4.74 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 8.60/4.74 = ( some_nat @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_348_invar__vebt_Ointros_I1_J,axiom,
% 8.60/4.74 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_349_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_350_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_351_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_352_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_353_zero__le__mult__iff,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.60/4.74 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 8.60/4.74 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.74 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_354_zero__le__mult__iff,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.60/4.74 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.60/4.74 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.74 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_355_zero__le__mult__iff,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.60/4.74 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 8.60/4.74 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.74 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_356_mult__nonneg__nonpos2,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_357_mult__nonneg__nonpos2,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_358_mult__nonneg__nonpos2,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_359_mult__nonneg__nonpos2,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_360_mult__nonpos__nonneg,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_361_mult__nonpos__nonneg,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_362_mult__nonpos__nonneg,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_363_mult__nonpos__nonneg,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_364_mult__nonneg__nonpos,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_365_mult__nonneg__nonpos,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_366_mult__nonneg__nonpos,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.74 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_367_mult__nonneg__nonpos,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_368_VEBT_Oinject_I2_J,axiom,
% 8.60/4.74 ! [X21: $o,X22: $o,Y21: $o,Y22: $o] :
% 8.60/4.74 ( ( ( vEBT_Leaf @ X21 @ X22 )
% 8.60/4.74 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 8.60/4.74 = ( ( X21 = Y21 )
% 8.60/4.74 & ( X22 = Y22 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_369_mul__def,axiom,
% 8.60/4.74 ( vEBT_VEBT_mul
% 8.60/4.74 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_370_VEBT_Osize_I4_J,axiom,
% 8.60/4.74 ! [X21: $o,X22: $o] :
% 8.60/4.74 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 8.60/4.74 = zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_371_mult__not__zero,axiom,
% 8.60/4.74 ! [A: complex,B: complex] :
% 8.60/4.74 ( ( ( times_times_complex @ A @ B )
% 8.60/4.74 != zero_zero_complex )
% 8.60/4.74 => ( ( A != zero_zero_complex )
% 8.60/4.74 & ( B != zero_zero_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_372_mult__not__zero,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ( times_times_real @ A @ B )
% 8.60/4.74 != zero_zero_real )
% 8.60/4.74 => ( ( A != zero_zero_real )
% 8.60/4.74 & ( B != zero_zero_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_373_mult__not__zero,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ( times_times_rat @ A @ B )
% 8.60/4.74 != zero_zero_rat )
% 8.60/4.74 => ( ( A != zero_zero_rat )
% 8.60/4.74 & ( B != zero_zero_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_374_mult__not__zero,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ A @ B )
% 8.60/4.74 != zero_zero_nat )
% 8.60/4.74 => ( ( A != zero_zero_nat )
% 8.60/4.74 & ( B != zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_375_mult__not__zero,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ( times_times_int @ A @ B )
% 8.60/4.74 != zero_zero_int )
% 8.60/4.74 => ( ( A != zero_zero_int )
% 8.60/4.74 & ( B != zero_zero_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_376_divisors__zero,axiom,
% 8.60/4.74 ! [A: complex,B: complex] :
% 8.60/4.74 ( ( ( times_times_complex @ A @ B )
% 8.60/4.74 = zero_zero_complex )
% 8.60/4.74 => ( ( A = zero_zero_complex )
% 8.60/4.74 | ( B = zero_zero_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_377_divisors__zero,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ( times_times_real @ A @ B )
% 8.60/4.74 = zero_zero_real )
% 8.60/4.74 => ( ( A = zero_zero_real )
% 8.60/4.74 | ( B = zero_zero_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_378_divisors__zero,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ( times_times_rat @ A @ B )
% 8.60/4.74 = zero_zero_rat )
% 8.60/4.74 => ( ( A = zero_zero_rat )
% 8.60/4.74 | ( B = zero_zero_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_379_divisors__zero,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ A @ B )
% 8.60/4.74 = zero_zero_nat )
% 8.60/4.74 => ( ( A = zero_zero_nat )
% 8.60/4.74 | ( B = zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_380_divisors__zero,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ( times_times_int @ A @ B )
% 8.60/4.74 = zero_zero_int )
% 8.60/4.74 => ( ( A = zero_zero_int )
% 8.60/4.74 | ( B = zero_zero_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_381_no__zero__divisors,axiom,
% 8.60/4.74 ! [A: complex,B: complex] :
% 8.60/4.74 ( ( A != zero_zero_complex )
% 8.60/4.74 => ( ( B != zero_zero_complex )
% 8.60/4.74 => ( ( times_times_complex @ A @ B )
% 8.60/4.74 != zero_zero_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_382_no__zero__divisors,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( A != zero_zero_real )
% 8.60/4.74 => ( ( B != zero_zero_real )
% 8.60/4.74 => ( ( times_times_real @ A @ B )
% 8.60/4.74 != zero_zero_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_383_no__zero__divisors,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( A != zero_zero_rat )
% 8.60/4.74 => ( ( B != zero_zero_rat )
% 8.60/4.74 => ( ( times_times_rat @ A @ B )
% 8.60/4.74 != zero_zero_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_384_no__zero__divisors,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( A != zero_zero_nat )
% 8.60/4.74 => ( ( B != zero_zero_nat )
% 8.60/4.74 => ( ( times_times_nat @ A @ B )
% 8.60/4.74 != zero_zero_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_385_no__zero__divisors,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( A != zero_zero_int )
% 8.60/4.74 => ( ( B != zero_zero_int )
% 8.60/4.74 => ( ( times_times_int @ A @ B )
% 8.60/4.74 != zero_zero_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_386_mult__left__cancel,axiom,
% 8.60/4.74 ! [C2: complex,A: complex,B: complex] :
% 8.60/4.74 ( ( C2 != zero_zero_complex )
% 8.60/4.74 => ( ( ( times_times_complex @ C2 @ A )
% 8.60/4.74 = ( times_times_complex @ C2 @ B ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_387_mult__left__cancel,axiom,
% 8.60/4.74 ! [C2: real,A: real,B: real] :
% 8.60/4.74 ( ( C2 != zero_zero_real )
% 8.60/4.74 => ( ( ( times_times_real @ C2 @ A )
% 8.60/4.74 = ( times_times_real @ C2 @ B ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_388_mult__left__cancel,axiom,
% 8.60/4.74 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.74 ( ( C2 != zero_zero_rat )
% 8.60/4.74 => ( ( ( times_times_rat @ C2 @ A )
% 8.60/4.74 = ( times_times_rat @ C2 @ B ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_389_mult__left__cancel,axiom,
% 8.60/4.74 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.74 ( ( C2 != zero_zero_nat )
% 8.60/4.74 => ( ( ( times_times_nat @ C2 @ A )
% 8.60/4.74 = ( times_times_nat @ C2 @ B ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_390_mult__left__cancel,axiom,
% 8.60/4.74 ! [C2: int,A: int,B: int] :
% 8.60/4.74 ( ( C2 != zero_zero_int )
% 8.60/4.74 => ( ( ( times_times_int @ C2 @ A )
% 8.60/4.74 = ( times_times_int @ C2 @ B ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_391_mult__right__cancel,axiom,
% 8.60/4.74 ! [C2: complex,A: complex,B: complex] :
% 8.60/4.74 ( ( C2 != zero_zero_complex )
% 8.60/4.74 => ( ( ( times_times_complex @ A @ C2 )
% 8.60/4.74 = ( times_times_complex @ B @ C2 ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_392_mult__right__cancel,axiom,
% 8.60/4.74 ! [C2: real,A: real,B: real] :
% 8.60/4.74 ( ( C2 != zero_zero_real )
% 8.60/4.74 => ( ( ( times_times_real @ A @ C2 )
% 8.60/4.74 = ( times_times_real @ B @ C2 ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_393_mult__right__cancel,axiom,
% 8.60/4.74 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.74 ( ( C2 != zero_zero_rat )
% 8.60/4.74 => ( ( ( times_times_rat @ A @ C2 )
% 8.60/4.74 = ( times_times_rat @ B @ C2 ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_394_mult__right__cancel,axiom,
% 8.60/4.74 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.74 ( ( C2 != zero_zero_nat )
% 8.60/4.74 => ( ( ( times_times_nat @ A @ C2 )
% 8.60/4.74 = ( times_times_nat @ B @ C2 ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_395_mult__right__cancel,axiom,
% 8.60/4.74 ! [C2: int,A: int,B: int] :
% 8.60/4.74 ( ( C2 != zero_zero_int )
% 8.60/4.74 => ( ( ( times_times_int @ A @ C2 )
% 8.60/4.74 = ( times_times_int @ B @ C2 ) )
% 8.60/4.74 = ( A = B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_396_mult__mono,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_real @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_397_mult__mono,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_398_mult__mono,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_399_mult__mono,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_400_mult__mono_H,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_real @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_401_mult__mono_H,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_402_mult__mono_H,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_403_mult__mono_H,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ C2 @ D )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_404_zero__le__square,axiom,
% 8.60/4.74 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_405_zero__le__square,axiom,
% 8.60/4.74 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_406_zero__le__square,axiom,
% 8.60/4.74 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_407_split__mult__pos__le,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 8.60/4.74 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.74 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 8.60/4.74 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_408_split__mult__pos__le,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.60/4.74 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.74 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_409_split__mult__pos__le,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 8.60/4.74 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.74 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 8.60/4.74 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_410_mult__left__mono__neg,axiom,
% 8.60/4.74 ! [B: real,A: real,C2: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_411_mult__left__mono__neg,axiom,
% 8.60/4.74 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_412_mult__left__mono__neg,axiom,
% 8.60/4.74 ! [B: int,A: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_413_mult__nonpos__nonpos,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.74 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.60/4.74 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_414_mult__nonpos__nonpos,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.74 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.60/4.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_415_mult__nonpos__nonpos,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.74 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.60/4.74 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_416_mult__left__mono,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_417_mult__left__mono,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_418_mult__left__mono,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_419_mult__left__mono,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_420_mult__right__mono__neg,axiom,
% 8.60/4.74 ! [B: real,A: real,C2: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_421_mult__right__mono__neg,axiom,
% 8.60/4.74 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_422_mult__right__mono__neg,axiom,
% 8.60/4.74 ! [B: int,A: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_423_mult__right__mono,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_424_mult__right__mono,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_425_mult__right__mono,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_426_mult__right__mono,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_427_mult__le__0__iff,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 8.60/4.74 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 8.60/4.74 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.74 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_428_mult__le__0__iff,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 8.60/4.74 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.60/4.74 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.74 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_429_mult__le__0__iff,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 8.60/4.74 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 8.60/4.74 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.74 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_430_split__mult__neg__le,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 8.60/4.74 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.74 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 8.60/4.74 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_431_split__mult__neg__le,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.60/4.74 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.74 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 8.60/4.74 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_432_split__mult__neg__le,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.74 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 8.60/4.74 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.60/4.74 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 8.60/4.74 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_433_split__mult__neg__le,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 8.60/4.74 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.74 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 8.60/4.74 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_434_mult__nonneg__nonneg,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.74 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.74 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_435_mult__nonneg__nonneg,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_436_mult__nonneg__nonneg,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_437_mult__nonneg__nonneg,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.74 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_438_valid__eq,axiom,
% 8.60/4.74 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 8.60/4.74
% 8.60/4.74 thf(fact_439_valid__eq1,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT,D: nat] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ T @ D )
% 8.60/4.74 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_440_valid__eq2,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT,D: nat] :
% 8.60/4.74 ( ( vEBT_VEBT_valid @ T @ D )
% 8.60/4.74 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_441_deg1Leaf,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 8.60/4.74 = ( ? [A5: $o,B4: $o] :
% 8.60/4.74 ( T
% 8.60/4.74 = ( vEBT_Leaf @ A5 @ B4 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_442_deg__1__Leaf,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 8.60/4.74 => ? [A3: $o,B3: $o] :
% 8.60/4.74 ( T
% 8.60/4.74 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_443_deg__1__Leafy,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT,N: nat] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.74 => ( ( N = one_one_nat )
% 8.60/4.74 => ? [A3: $o,B3: $o] :
% 8.60/4.74 ( T
% 8.60/4.74 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_444_nat__mult__eq__cancel__disj,axiom,
% 8.60/4.74 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ K2 @ M2 )
% 8.60/4.74 = ( times_times_nat @ K2 @ N ) )
% 8.60/4.74 = ( ( K2 = zero_zero_nat )
% 8.60/4.74 | ( M2 = N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_445_deg__not__0,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT,N: nat] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.74 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_446_VEBT_Osize__gen_I2_J,axiom,
% 8.60/4.74 ! [X21: $o,X22: $o] :
% 8.60/4.74 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X22 ) )
% 8.60/4.74 = zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_447_deg__SUcn__Node,axiom,
% 8.60/4.74 ! [Tree: vEBT_VEBT,N: nat] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 8.60/4.74 => ? [Info: option4927543243414619207at_nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.60/4.74 ( Tree
% 8.60/4.74 = ( vEBT_Node @ Info @ ( suc @ ( suc @ N ) ) @ TreeList @ S ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_448_case4_I13_J,axiom,
% 8.60/4.74 ( ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) )
% 8.60/4.74 = ( vEBT_VEBT_set_vebt @ sa ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_449_deg__deg__n,axiom,
% 8.60/4.74 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 8.60/4.74 => ( Deg = N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_450_VEBT_Oinject_I1_J,axiom,
% 8.60/4.74 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 8.60/4.74 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 8.60/4.74 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 8.60/4.74 = ( ( X11 = Y11 )
% 8.60/4.74 & ( X12 = Y12 )
% 8.60/4.74 & ( X13 = Y13 )
% 8.60/4.74 & ( X14 = Y14 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_451_not__gr__zero,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 8.60/4.74 = ( N = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_452_mult__1,axiom,
% 8.60/4.74 ! [A: code_integer] :
% 8.60/4.74 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_453_mult__1,axiom,
% 8.60/4.74 ! [A: complex] :
% 8.60/4.74 ( ( times_times_complex @ one_one_complex @ A )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_454_mult__1,axiom,
% 8.60/4.74 ! [A: real] :
% 8.60/4.74 ( ( times_times_real @ one_one_real @ A )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_455_mult__1,axiom,
% 8.60/4.74 ! [A: rat] :
% 8.60/4.74 ( ( times_times_rat @ one_one_rat @ A )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_456_mult__1,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ( ( times_times_nat @ one_one_nat @ A )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_457_mult__1,axiom,
% 8.60/4.74 ! [A: int] :
% 8.60/4.74 ( ( times_times_int @ one_one_int @ A )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_458_mult_Oright__neutral,axiom,
% 8.60/4.74 ! [A: code_integer] :
% 8.60/4.74 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_459_mult_Oright__neutral,axiom,
% 8.60/4.74 ! [A: complex] :
% 8.60/4.74 ( ( times_times_complex @ A @ one_one_complex )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_460_mult_Oright__neutral,axiom,
% 8.60/4.74 ! [A: real] :
% 8.60/4.74 ( ( times_times_real @ A @ one_one_real )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_461_mult_Oright__neutral,axiom,
% 8.60/4.74 ! [A: rat] :
% 8.60/4.74 ( ( times_times_rat @ A @ one_one_rat )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_462_mult_Oright__neutral,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ( ( times_times_nat @ A @ one_one_nat )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_463_mult_Oright__neutral,axiom,
% 8.60/4.74 ! [A: int] :
% 8.60/4.74 ( ( times_times_int @ A @ one_one_int )
% 8.60/4.74 = A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_464_Suc__less__eq,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 8.60/4.74 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_465_Suc__mono,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.74 => ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_466_lessI,axiom,
% 8.60/4.74 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_467_bot__nat__0_Onot__eq__extremum,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ( ( A != zero_zero_nat )
% 8.60/4.74 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_468_neq0__conv,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( N != zero_zero_nat )
% 8.60/4.74 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_469_less__nat__zero__code,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_470_nat__1__eq__mult__iff,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( one_one_nat
% 8.60/4.74 = ( times_times_nat @ M2 @ N ) )
% 8.60/4.74 = ( ( M2 = one_one_nat )
% 8.60/4.74 & ( N = one_one_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_471_nat__mult__eq__1__iff,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ( times_times_nat @ M2 @ N )
% 8.60/4.74 = one_one_nat )
% 8.60/4.74 = ( ( M2 = one_one_nat )
% 8.60/4.74 & ( N = one_one_nat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_472_case4_I3_J,axiom,
% 8.60/4.74 vEBT_invar_vebt @ summary2 @ m ).
% 8.60/4.74
% 8.60/4.74 thf(fact_473_mult__cancel__left1,axiom,
% 8.60/4.74 ! [C2: code_integer,B: code_integer] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_3573771949741848930nteger @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_z3403309356797280102nteger )
% 8.60/4.74 | ( B = one_one_Code_integer ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_474_mult__cancel__left1,axiom,
% 8.60/4.74 ! [C2: complex,B: complex] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_complex @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_complex )
% 8.60/4.74 | ( B = one_one_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_475_mult__cancel__left1,axiom,
% 8.60/4.74 ! [C2: real,B: real] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_real @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_real )
% 8.60/4.74 | ( B = one_one_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_476_mult__cancel__left1,axiom,
% 8.60/4.74 ! [C2: rat,B: rat] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_rat @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_rat )
% 8.60/4.74 | ( B = one_one_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_477_mult__cancel__left1,axiom,
% 8.60/4.74 ! [C2: int,B: int] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_int @ C2 @ B ) )
% 8.60/4.74 = ( ( C2 = zero_zero_int )
% 8.60/4.74 | ( B = one_one_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_478_mult__cancel__left2,axiom,
% 8.60/4.74 ! [C2: code_integer,A: code_integer] :
% 8.60/4.74 ( ( ( times_3573771949741848930nteger @ C2 @ A )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_z3403309356797280102nteger )
% 8.60/4.74 | ( A = one_one_Code_integer ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_479_mult__cancel__left2,axiom,
% 8.60/4.74 ! [C2: complex,A: complex] :
% 8.60/4.74 ( ( ( times_times_complex @ C2 @ A )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_complex )
% 8.60/4.74 | ( A = one_one_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_480_mult__cancel__left2,axiom,
% 8.60/4.74 ! [C2: real,A: real] :
% 8.60/4.74 ( ( ( times_times_real @ C2 @ A )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_real )
% 8.60/4.74 | ( A = one_one_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_481_mult__cancel__left2,axiom,
% 8.60/4.74 ! [C2: rat,A: rat] :
% 8.60/4.74 ( ( ( times_times_rat @ C2 @ A )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_rat )
% 8.60/4.74 | ( A = one_one_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_482_mult__cancel__left2,axiom,
% 8.60/4.74 ! [C2: int,A: int] :
% 8.60/4.74 ( ( ( times_times_int @ C2 @ A )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_int )
% 8.60/4.74 | ( A = one_one_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_483_mult__cancel__right1,axiom,
% 8.60/4.74 ! [C2: code_integer,B: code_integer] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_3573771949741848930nteger @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_z3403309356797280102nteger )
% 8.60/4.74 | ( B = one_one_Code_integer ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_484_mult__cancel__right1,axiom,
% 8.60/4.74 ! [C2: complex,B: complex] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_complex @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_complex )
% 8.60/4.74 | ( B = one_one_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_485_mult__cancel__right1,axiom,
% 8.60/4.74 ! [C2: real,B: real] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_real @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_real )
% 8.60/4.74 | ( B = one_one_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_486_mult__cancel__right1,axiom,
% 8.60/4.74 ! [C2: rat,B: rat] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_rat @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_rat )
% 8.60/4.74 | ( B = one_one_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_487_mult__cancel__right1,axiom,
% 8.60/4.74 ! [C2: int,B: int] :
% 8.60/4.74 ( ( C2
% 8.60/4.74 = ( times_times_int @ B @ C2 ) )
% 8.60/4.74 = ( ( C2 = zero_zero_int )
% 8.60/4.74 | ( B = one_one_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_488_mult__cancel__right2,axiom,
% 8.60/4.74 ! [A: code_integer,C2: code_integer] :
% 8.60/4.74 ( ( ( times_3573771949741848930nteger @ A @ C2 )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_z3403309356797280102nteger )
% 8.60/4.74 | ( A = one_one_Code_integer ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_489_mult__cancel__right2,axiom,
% 8.60/4.74 ! [A: complex,C2: complex] :
% 8.60/4.74 ( ( ( times_times_complex @ A @ C2 )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_complex )
% 8.60/4.74 | ( A = one_one_complex ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_490_mult__cancel__right2,axiom,
% 8.60/4.74 ! [A: real,C2: real] :
% 8.60/4.74 ( ( ( times_times_real @ A @ C2 )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_real )
% 8.60/4.74 | ( A = one_one_real ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_491_mult__cancel__right2,axiom,
% 8.60/4.74 ! [A: rat,C2: rat] :
% 8.60/4.74 ( ( ( times_times_rat @ A @ C2 )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_rat )
% 8.60/4.74 | ( A = one_one_rat ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_492_mult__cancel__right2,axiom,
% 8.60/4.74 ! [A: int,C2: int] :
% 8.60/4.74 ( ( ( times_times_int @ A @ C2 )
% 8.60/4.74 = C2 )
% 8.60/4.74 = ( ( C2 = zero_zero_int )
% 8.60/4.74 | ( A = one_one_int ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_493_zero__less__Suc,axiom,
% 8.60/4.74 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_494_less__Suc0,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.60/4.74 = ( N = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_495_nat__mult__less__cancel__disj,axiom,
% 8.60/4.74 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.60/4.74 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.74 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_496_mult__less__cancel2,axiom,
% 8.60/4.74 ! [M2: nat,K2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) )
% 8.60/4.74 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.74 & ( ord_less_nat @ M2 @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_497_nat__0__less__mult__iff,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M2 @ N ) )
% 8.60/4.74 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.60/4.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_498_less__one,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ( ( ord_less_nat @ N @ one_one_nat )
% 8.60/4.74 = ( N = zero_zero_nat ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_499_nat__mult__le__cancel__disj,axiom,
% 8.60/4.74 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.60/4.74 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.74 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_500_mult__le__cancel2,axiom,
% 8.60/4.74 ! [M2: nat,K2: nat,N: nat] :
% 8.60/4.74 ( ( ord_less_eq_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) )
% 8.60/4.74 = ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.74 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_501_set__vebt__set__vebt_H__valid,axiom,
% 8.60/4.74 ! [T: vEBT_VEBT,N: nat] :
% 8.60/4.74 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.74 => ( ( vEBT_set_vebt @ T )
% 8.60/4.74 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_502_linorder__neqE__linordered__idom,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_real @ X @ Y )
% 8.60/4.74 => ( ord_less_real @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_503_linorder__neqE__linordered__idom,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_rat @ X @ Y )
% 8.60/4.74 => ( ord_less_rat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_504_linorder__neqE__linordered__idom,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_int @ X @ Y )
% 8.60/4.74 => ( ord_less_int @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_505_lt__ex,axiom,
% 8.60/4.74 ! [X: real] :
% 8.60/4.74 ? [Y3: real] : ( ord_less_real @ Y3 @ X ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_506_lt__ex,axiom,
% 8.60/4.74 ! [X: rat] :
% 8.60/4.74 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_507_lt__ex,axiom,
% 8.60/4.74 ! [X: int] :
% 8.60/4.74 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_508_gt__ex,axiom,
% 8.60/4.74 ! [X: real] :
% 8.60/4.74 ? [X_12: real] : ( ord_less_real @ X @ X_12 ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_509_gt__ex,axiom,
% 8.60/4.74 ! [X: rat] :
% 8.60/4.74 ? [X_12: rat] : ( ord_less_rat @ X @ X_12 ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_510_gt__ex,axiom,
% 8.60/4.74 ! [X: nat] :
% 8.60/4.74 ? [X_12: nat] : ( ord_less_nat @ X @ X_12 ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_511_gt__ex,axiom,
% 8.60/4.74 ! [X: int] :
% 8.60/4.74 ? [X_12: int] : ( ord_less_int @ X @ X_12 ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_512_dense,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ( ord_less_real @ X @ Y )
% 8.60/4.74 => ? [Z: real] :
% 8.60/4.74 ( ( ord_less_real @ X @ Z )
% 8.60/4.74 & ( ord_less_real @ Z @ Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_513_dense,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( ord_less_rat @ X @ Y )
% 8.60/4.74 => ? [Z: rat] :
% 8.60/4.74 ( ( ord_less_rat @ X @ Z )
% 8.60/4.74 & ( ord_less_rat @ Z @ Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_514_less__imp__neq,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ( ord_less_real @ X @ Y )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_515_less__imp__neq,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( ord_less_rat @ X @ Y )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_516_less__imp__neq,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( ord_less_num @ X @ Y )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_517_less__imp__neq,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( ord_less_nat @ X @ Y )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_518_less__imp__neq,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( ord_less_int @ X @ Y )
% 8.60/4.74 => ( X != Y ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_519_order_Oasym,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_real @ A @ B )
% 8.60/4.74 => ~ ( ord_less_real @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_520_order_Oasym,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_rat @ A @ B )
% 8.60/4.74 => ~ ( ord_less_rat @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_521_order_Oasym,axiom,
% 8.60/4.74 ! [A: num,B: num] :
% 8.60/4.74 ( ( ord_less_num @ A @ B )
% 8.60/4.74 => ~ ( ord_less_num @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_522_order_Oasym,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_nat @ A @ B )
% 8.60/4.74 => ~ ( ord_less_nat @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_523_order_Oasym,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_int @ A @ B )
% 8.60/4.74 => ~ ( ord_less_int @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_524_ord__eq__less__trans,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.74 => ( ord_less_real @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_525_ord__eq__less__trans,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.74 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_526_ord__eq__less__trans,axiom,
% 8.60/4.74 ! [A: num,B: num,C2: num] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_num @ B @ C2 )
% 8.60/4.74 => ( ord_less_num @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_527_ord__eq__less__trans,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.74 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_528_ord__eq__less__trans,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( A = B )
% 8.60/4.74 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.74 => ( ord_less_int @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_529_ord__less__eq__trans,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( ord_less_real @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_real @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_530_ord__less__eq__trans,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_rat @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_531_ord__less__eq__trans,axiom,
% 8.60/4.74 ! [A: num,B: num,C2: num] :
% 8.60/4.74 ( ( ord_less_num @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_num @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_532_ord__less__eq__trans,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_nat @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_533_ord__less__eq__trans,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_int @ A @ B )
% 8.60/4.74 => ( ( B = C2 )
% 8.60/4.74 => ( ord_less_int @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_534_less__induct,axiom,
% 8.60/4.74 ! [P2: nat > $o,A: nat] :
% 8.60/4.74 ( ! [X3: nat] :
% 8.60/4.74 ( ! [Y6: nat] :
% 8.60/4.74 ( ( ord_less_nat @ Y6 @ X3 )
% 8.60/4.74 => ( P2 @ Y6 ) )
% 8.60/4.74 => ( P2 @ X3 ) )
% 8.60/4.74 => ( P2 @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_535_antisym__conv3,axiom,
% 8.60/4.74 ! [Y: real,X: real] :
% 8.60/4.74 ( ~ ( ord_less_real @ Y @ X )
% 8.60/4.74 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.60/4.74 = ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_536_antisym__conv3,axiom,
% 8.60/4.74 ! [Y: rat,X: rat] :
% 8.60/4.74 ( ~ ( ord_less_rat @ Y @ X )
% 8.60/4.74 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.60/4.74 = ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_537_antisym__conv3,axiom,
% 8.60/4.74 ! [Y: num,X: num] :
% 8.60/4.74 ( ~ ( ord_less_num @ Y @ X )
% 8.60/4.74 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.60/4.74 = ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_538_antisym__conv3,axiom,
% 8.60/4.74 ! [Y: nat,X: nat] :
% 8.60/4.74 ( ~ ( ord_less_nat @ Y @ X )
% 8.60/4.74 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.60/4.74 = ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_539_antisym__conv3,axiom,
% 8.60/4.74 ! [Y: int,X: int] :
% 8.60/4.74 ( ~ ( ord_less_int @ Y @ X )
% 8.60/4.74 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.60/4.74 = ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_540_linorder__cases,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ~ ( ord_less_real @ X @ Y )
% 8.60/4.74 => ( ( X != Y )
% 8.60/4.74 => ( ord_less_real @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_541_linorder__cases,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ~ ( ord_less_rat @ X @ Y )
% 8.60/4.74 => ( ( X != Y )
% 8.60/4.74 => ( ord_less_rat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_542_linorder__cases,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ~ ( ord_less_num @ X @ Y )
% 8.60/4.74 => ( ( X != Y )
% 8.60/4.74 => ( ord_less_num @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_543_linorder__cases,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ~ ( ord_less_nat @ X @ Y )
% 8.60/4.74 => ( ( X != Y )
% 8.60/4.74 => ( ord_less_nat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_544_linorder__cases,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ~ ( ord_less_int @ X @ Y )
% 8.60/4.74 => ( ( X != Y )
% 8.60/4.74 => ( ord_less_int @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_545_dual__order_Oasym,axiom,
% 8.60/4.74 ! [B: real,A: real] :
% 8.60/4.74 ( ( ord_less_real @ B @ A )
% 8.60/4.74 => ~ ( ord_less_real @ A @ B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_546_dual__order_Oasym,axiom,
% 8.60/4.74 ! [B: rat,A: rat] :
% 8.60/4.74 ( ( ord_less_rat @ B @ A )
% 8.60/4.74 => ~ ( ord_less_rat @ A @ B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_547_dual__order_Oasym,axiom,
% 8.60/4.74 ! [B: num,A: num] :
% 8.60/4.74 ( ( ord_less_num @ B @ A )
% 8.60/4.74 => ~ ( ord_less_num @ A @ B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_548_dual__order_Oasym,axiom,
% 8.60/4.74 ! [B: nat,A: nat] :
% 8.60/4.74 ( ( ord_less_nat @ B @ A )
% 8.60/4.74 => ~ ( ord_less_nat @ A @ B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_549_dual__order_Oasym,axiom,
% 8.60/4.74 ! [B: int,A: int] :
% 8.60/4.74 ( ( ord_less_int @ B @ A )
% 8.60/4.74 => ~ ( ord_less_int @ A @ B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_550_dual__order_Oirrefl,axiom,
% 8.60/4.74 ! [A: real] :
% 8.60/4.74 ~ ( ord_less_real @ A @ A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_551_dual__order_Oirrefl,axiom,
% 8.60/4.74 ! [A: rat] :
% 8.60/4.74 ~ ( ord_less_rat @ A @ A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_552_dual__order_Oirrefl,axiom,
% 8.60/4.74 ! [A: num] :
% 8.60/4.74 ~ ( ord_less_num @ A @ A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_553_dual__order_Oirrefl,axiom,
% 8.60/4.74 ! [A: nat] :
% 8.60/4.74 ~ ( ord_less_nat @ A @ A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_554_dual__order_Oirrefl,axiom,
% 8.60/4.74 ! [A: int] :
% 8.60/4.74 ~ ( ord_less_int @ A @ A ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_555_exists__least__iff,axiom,
% 8.60/4.74 ( ( ^ [P3: nat > $o] :
% 8.60/4.74 ? [X6: nat] : ( P3 @ X6 ) )
% 8.60/4.74 = ( ^ [P4: nat > $o] :
% 8.60/4.74 ? [N4: nat] :
% 8.60/4.74 ( ( P4 @ N4 )
% 8.60/4.74 & ! [M6: nat] :
% 8.60/4.74 ( ( ord_less_nat @ M6 @ N4 )
% 8.60/4.74 => ~ ( P4 @ M6 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_556_linorder__less__wlog,axiom,
% 8.60/4.74 ! [P2: real > real > $o,A: real,B: real] :
% 8.60/4.74 ( ! [A3: real,B3: real] :
% 8.60/4.74 ( ( ord_less_real @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: real] : ( P2 @ A3 @ A3 )
% 8.60/4.74 => ( ! [A3: real,B3: real] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_557_linorder__less__wlog,axiom,
% 8.60/4.74 ! [P2: rat > rat > $o,A: rat,B: rat] :
% 8.60/4.74 ( ! [A3: rat,B3: rat] :
% 8.60/4.74 ( ( ord_less_rat @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: rat] : ( P2 @ A3 @ A3 )
% 8.60/4.74 => ( ! [A3: rat,B3: rat] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_558_linorder__less__wlog,axiom,
% 8.60/4.74 ! [P2: num > num > $o,A: num,B: num] :
% 8.60/4.74 ( ! [A3: num,B3: num] :
% 8.60/4.74 ( ( ord_less_num @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: num] : ( P2 @ A3 @ A3 )
% 8.60/4.74 => ( ! [A3: num,B3: num] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_559_linorder__less__wlog,axiom,
% 8.60/4.74 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 8.60/4.74 ( ! [A3: nat,B3: nat] :
% 8.60/4.74 ( ( ord_less_nat @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: nat] : ( P2 @ A3 @ A3 )
% 8.60/4.74 => ( ! [A3: nat,B3: nat] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_560_linorder__less__wlog,axiom,
% 8.60/4.74 ! [P2: int > int > $o,A: int,B: int] :
% 8.60/4.74 ( ! [A3: int,B3: int] :
% 8.60/4.74 ( ( ord_less_int @ A3 @ B3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( ! [A3: int] : ( P2 @ A3 @ A3 )
% 8.60/4.74 => ( ! [A3: int,B3: int] :
% 8.60/4.74 ( ( P2 @ B3 @ A3 )
% 8.60/4.74 => ( P2 @ A3 @ B3 ) )
% 8.60/4.74 => ( P2 @ A @ B ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_561_order_Ostrict__trans,axiom,
% 8.60/4.74 ! [A: real,B: real,C2: real] :
% 8.60/4.74 ( ( ord_less_real @ A @ B )
% 8.60/4.74 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.74 => ( ord_less_real @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_562_order_Ostrict__trans,axiom,
% 8.60/4.74 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_rat @ A @ B )
% 8.60/4.74 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.74 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_563_order_Ostrict__trans,axiom,
% 8.60/4.74 ! [A: num,B: num,C2: num] :
% 8.60/4.74 ( ( ord_less_num @ A @ B )
% 8.60/4.74 => ( ( ord_less_num @ B @ C2 )
% 8.60/4.74 => ( ord_less_num @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_564_order_Ostrict__trans,axiom,
% 8.60/4.74 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_nat @ A @ B )
% 8.60/4.74 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.74 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_565_order_Ostrict__trans,axiom,
% 8.60/4.74 ! [A: int,B: int,C2: int] :
% 8.60/4.74 ( ( ord_less_int @ A @ B )
% 8.60/4.74 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.74 => ( ord_less_int @ A @ C2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_566_not__less__iff__gr__or__eq,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.60/4.74 = ( ( ord_less_real @ Y @ X )
% 8.60/4.74 | ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_567_not__less__iff__gr__or__eq,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.60/4.74 = ( ( ord_less_rat @ Y @ X )
% 8.60/4.74 | ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_568_not__less__iff__gr__or__eq,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.60/4.74 = ( ( ord_less_num @ Y @ X )
% 8.60/4.74 | ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_569_not__less__iff__gr__or__eq,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.60/4.74 = ( ( ord_less_nat @ Y @ X )
% 8.60/4.74 | ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_570_not__less__iff__gr__or__eq,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.60/4.74 = ( ( ord_less_int @ Y @ X )
% 8.60/4.74 | ( X = Y ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_571_dual__order_Ostrict__trans,axiom,
% 8.60/4.74 ! [B: real,A: real,C2: real] :
% 8.60/4.74 ( ( ord_less_real @ B @ A )
% 8.60/4.74 => ( ( ord_less_real @ C2 @ B )
% 8.60/4.74 => ( ord_less_real @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_572_dual__order_Ostrict__trans,axiom,
% 8.60/4.74 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.74 ( ( ord_less_rat @ B @ A )
% 8.60/4.74 => ( ( ord_less_rat @ C2 @ B )
% 8.60/4.74 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_573_dual__order_Ostrict__trans,axiom,
% 8.60/4.74 ! [B: num,A: num,C2: num] :
% 8.60/4.74 ( ( ord_less_num @ B @ A )
% 8.60/4.74 => ( ( ord_less_num @ C2 @ B )
% 8.60/4.74 => ( ord_less_num @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_574_dual__order_Ostrict__trans,axiom,
% 8.60/4.74 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.74 ( ( ord_less_nat @ B @ A )
% 8.60/4.74 => ( ( ord_less_nat @ C2 @ B )
% 8.60/4.74 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_575_dual__order_Ostrict__trans,axiom,
% 8.60/4.74 ! [B: int,A: int,C2: int] :
% 8.60/4.74 ( ( ord_less_int @ B @ A )
% 8.60/4.74 => ( ( ord_less_int @ C2 @ B )
% 8.60/4.74 => ( ord_less_int @ C2 @ A ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_576_order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_real @ A @ B )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_577_order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_rat @ A @ B )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_578_order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [A: num,B: num] :
% 8.60/4.74 ( ( ord_less_num @ A @ B )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_579_order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_nat @ A @ B )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_580_order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_int @ A @ B )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_581_dual__order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [B: real,A: real] :
% 8.60/4.74 ( ( ord_less_real @ B @ A )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_582_dual__order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [B: rat,A: rat] :
% 8.60/4.74 ( ( ord_less_rat @ B @ A )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_583_dual__order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [B: num,A: num] :
% 8.60/4.74 ( ( ord_less_num @ B @ A )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_584_dual__order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [B: nat,A: nat] :
% 8.60/4.74 ( ( ord_less_nat @ B @ A )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_585_dual__order_Ostrict__implies__not__eq,axiom,
% 8.60/4.74 ! [B: int,A: int] :
% 8.60/4.74 ( ( ord_less_int @ B @ A )
% 8.60/4.74 => ( A != B ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_586_nat__neq__iff,axiom,
% 8.60/4.74 ! [M2: nat,N: nat] :
% 8.60/4.74 ( ( M2 != N )
% 8.60/4.74 = ( ( ord_less_nat @ M2 @ N )
% 8.60/4.74 | ( ord_less_nat @ N @ M2 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_587_less__not__refl,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ~ ( ord_less_nat @ N @ N ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_588_less__not__refl2,axiom,
% 8.60/4.74 ! [N: nat,M2: nat] :
% 8.60/4.74 ( ( ord_less_nat @ N @ M2 )
% 8.60/4.74 => ( M2 != N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_589_less__not__refl3,axiom,
% 8.60/4.74 ! [S2: nat,T: nat] :
% 8.60/4.74 ( ( ord_less_nat @ S2 @ T )
% 8.60/4.74 => ( S2 != T ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_590_less__irrefl__nat,axiom,
% 8.60/4.74 ! [N: nat] :
% 8.60/4.74 ~ ( ord_less_nat @ N @ N ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_591_nat__less__induct,axiom,
% 8.60/4.74 ! [P2: nat > $o,N: nat] :
% 8.60/4.74 ( ! [N3: nat] :
% 8.60/4.74 ( ! [M3: nat] :
% 8.60/4.74 ( ( ord_less_nat @ M3 @ N3 )
% 8.60/4.74 => ( P2 @ M3 ) )
% 8.60/4.74 => ( P2 @ N3 ) )
% 8.60/4.74 => ( P2 @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_592_infinite__descent,axiom,
% 8.60/4.74 ! [P2: nat > $o,N: nat] :
% 8.60/4.74 ( ! [N3: nat] :
% 8.60/4.74 ( ~ ( P2 @ N3 )
% 8.60/4.74 => ? [M3: nat] :
% 8.60/4.74 ( ( ord_less_nat @ M3 @ N3 )
% 8.60/4.74 & ~ ( P2 @ M3 ) ) )
% 8.60/4.74 => ( P2 @ N ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_593_linorder__neqE__nat,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_nat @ X @ Y )
% 8.60/4.74 => ( ord_less_nat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_594_linorder__neqE,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_real @ X @ Y )
% 8.60/4.74 => ( ord_less_real @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_595_linorder__neqE,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_rat @ X @ Y )
% 8.60/4.74 => ( ord_less_rat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_596_linorder__neqE,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_num @ X @ Y )
% 8.60/4.74 => ( ord_less_num @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_597_linorder__neqE,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_nat @ X @ Y )
% 8.60/4.74 => ( ord_less_nat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_598_linorder__neqE,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 => ( ~ ( ord_less_int @ X @ Y )
% 8.60/4.74 => ( ord_less_int @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_599_order__less__asym,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ( ord_less_real @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_real @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_600_order__less__asym,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( ord_less_rat @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_601_order__less__asym,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( ord_less_num @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_num @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_602_order__less__asym,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( ord_less_nat @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_603_order__less__asym,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( ord_less_int @ X @ Y )
% 8.60/4.74 => ~ ( ord_less_int @ Y @ X ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_604_linorder__neq__iff,axiom,
% 8.60/4.74 ! [X: real,Y: real] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 = ( ( ord_less_real @ X @ Y )
% 8.60/4.74 | ( ord_less_real @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_605_linorder__neq__iff,axiom,
% 8.60/4.74 ! [X: rat,Y: rat] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 = ( ( ord_less_rat @ X @ Y )
% 8.60/4.74 | ( ord_less_rat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_606_linorder__neq__iff,axiom,
% 8.60/4.74 ! [X: num,Y: num] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 = ( ( ord_less_num @ X @ Y )
% 8.60/4.74 | ( ord_less_num @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_607_linorder__neq__iff,axiom,
% 8.60/4.74 ! [X: nat,Y: nat] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 = ( ( ord_less_nat @ X @ Y )
% 8.60/4.74 | ( ord_less_nat @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_608_linorder__neq__iff,axiom,
% 8.60/4.74 ! [X: int,Y: int] :
% 8.60/4.74 ( ( X != Y )
% 8.60/4.74 = ( ( ord_less_int @ X @ Y )
% 8.60/4.74 | ( ord_less_int @ Y @ X ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_609_order__less__asym_H,axiom,
% 8.60/4.74 ! [A: real,B: real] :
% 8.60/4.74 ( ( ord_less_real @ A @ B )
% 8.60/4.74 => ~ ( ord_less_real @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_610_order__less__asym_H,axiom,
% 8.60/4.74 ! [A: rat,B: rat] :
% 8.60/4.74 ( ( ord_less_rat @ A @ B )
% 8.60/4.74 => ~ ( ord_less_rat @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_611_order__less__asym_H,axiom,
% 8.60/4.74 ! [A: num,B: num] :
% 8.60/4.74 ( ( ord_less_num @ A @ B )
% 8.60/4.74 => ~ ( ord_less_num @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_612_order__less__asym_H,axiom,
% 8.60/4.74 ! [A: nat,B: nat] :
% 8.60/4.74 ( ( ord_less_nat @ A @ B )
% 8.60/4.74 => ~ ( ord_less_nat @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_613_order__less__asym_H,axiom,
% 8.60/4.74 ! [A: int,B: int] :
% 8.60/4.74 ( ( ord_less_int @ A @ B )
% 8.60/4.74 => ~ ( ord_less_int @ B @ A ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_614_order__less__trans,axiom,
% 8.60/4.74 ! [X: real,Y: real,Z3: real] :
% 8.60/4.74 ( ( ord_less_real @ X @ Y )
% 8.60/4.74 => ( ( ord_less_real @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_615_order__less__trans,axiom,
% 8.60/4.74 ! [X: rat,Y: rat,Z3: rat] :
% 8.60/4.74 ( ( ord_less_rat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_rat @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_616_order__less__trans,axiom,
% 8.60/4.74 ! [X: num,Y: num,Z3: num] :
% 8.60/4.74 ( ( ord_less_num @ X @ Y )
% 8.60/4.74 => ( ( ord_less_num @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_617_order__less__trans,axiom,
% 8.60/4.74 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.74 ( ( ord_less_nat @ X @ Y )
% 8.60/4.74 => ( ( ord_less_nat @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_618_order__less__trans,axiom,
% 8.60/4.74 ! [X: int,Y: int,Z3: int] :
% 8.60/4.74 ( ( ord_less_int @ X @ Y )
% 8.60/4.74 => ( ( ord_less_int @ Y @ Z3 )
% 8.60/4.74 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_619_ord__eq__less__subst,axiom,
% 8.60/4.74 ! [A: real,F2: real > real,B: real,C2: real] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.74 => ( ! [X3: real,Y3: real] :
% 8.60/4.74 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_620_ord__eq__less__subst,axiom,
% 8.60/4.74 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.74 => ( ! [X3: real,Y3: real] :
% 8.60/4.74 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_621_ord__eq__less__subst,axiom,
% 8.60/4.74 ! [A: num,F2: real > num,B: real,C2: real] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.74 => ( ! [X3: real,Y3: real] :
% 8.60/4.74 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_622_ord__eq__less__subst,axiom,
% 8.60/4.74 ! [A: nat,F2: real > nat,B: real,C2: real] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.74 => ( ! [X3: real,Y3: real] :
% 8.60/4.74 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.74 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.74
% 8.60/4.74 thf(fact_623_ord__eq__less__subst,axiom,
% 8.60/4.74 ! [A: int,F2: real > int,B: real,C2: real] :
% 8.60/4.74 ( ( A
% 8.60/4.74 = ( F2 @ B ) )
% 8.60/4.74 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.74 => ( ! [X3: real,Y3: real] :
% 8.60/4.74 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.74 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_624_ord__eq__less__subst,axiom,
% 8.60/4.75 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 8.60/4.75 ( ( A
% 8.60/4.75 = ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_625_ord__eq__less__subst,axiom,
% 8.60/4.75 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( A
% 8.60/4.75 = ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_626_ord__eq__less__subst,axiom,
% 8.60/4.75 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 8.60/4.75 ( ( A
% 8.60/4.75 = ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_627_ord__eq__less__subst,axiom,
% 8.60/4.75 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 8.60/4.75 ( ( A
% 8.60/4.75 = ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_628_ord__eq__less__subst,axiom,
% 8.60/4.75 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 8.60/4.75 ( ( A
% 8.60/4.75 = ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_629_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_630_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_631_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > num,C2: num] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_632_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_633_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > int,C2: int] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_634_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_635_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_636_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_637_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_638_ord__less__eq__subst,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ( F2 @ B )
% 8.60/4.75 = C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_639_order__less__irrefl,axiom,
% 8.60/4.75 ! [X: real] :
% 8.60/4.75 ~ ( ord_less_real @ X @ X ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_640_order__less__irrefl,axiom,
% 8.60/4.75 ! [X: rat] :
% 8.60/4.75 ~ ( ord_less_rat @ X @ X ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_641_order__less__irrefl,axiom,
% 8.60/4.75 ! [X: num] :
% 8.60/4.75 ~ ( ord_less_num @ X @ X ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_642_order__less__irrefl,axiom,
% 8.60/4.75 ! [X: nat] :
% 8.60/4.75 ~ ( ord_less_nat @ X @ X ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_643_order__less__irrefl,axiom,
% 8.60/4.75 ! [X: int] :
% 8.60/4.75 ~ ( ord_less_int @ X @ X ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_644_order__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: real > real,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_645_order__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_646_order__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: num > real,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_647_order__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: nat > real,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_648_order__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: int > real,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.75 => ( ! [X3: int,Y3: int] :
% 8.60/4.75 ( ( ord_less_int @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_649_order__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_650_order__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_651_order__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_652_order__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_653_order__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.75 => ( ! [X3: int,Y3: int] :
% 8.60/4.75 ( ( ord_less_int @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_654_order__less__subst2,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_655_order__less__subst2,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_656_order__less__subst2,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > num,C2: num] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_657_order__less__subst2,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_658_order__less__subst2,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > int,C2: int] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_659_order__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_660_order__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_661_order__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_662_order__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_663_order__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_664_order__less__not__sym,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_real @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_665_order__less__not__sym,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_666_order__less__not__sym,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_num @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_667_order__less__not__sym,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_668_order__less__not__sym,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_int @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_669_order__less__imp__triv,axiom,
% 8.60/4.75 ! [X: real,Y: real,P2: $o] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( ( ord_less_real @ Y @ X )
% 8.60/4.75 => P2 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_670_order__less__imp__triv,axiom,
% 8.60/4.75 ! [X: rat,Y: rat,P2: $o] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_rat @ Y @ X )
% 8.60/4.75 => P2 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_671_order__less__imp__triv,axiom,
% 8.60/4.75 ! [X: num,Y: num,P2: $o] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 => ( ( ord_less_num @ Y @ X )
% 8.60/4.75 => P2 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_672_order__less__imp__triv,axiom,
% 8.60/4.75 ! [X: nat,Y: nat,P2: $o] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_nat @ Y @ X )
% 8.60/4.75 => P2 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_673_order__less__imp__triv,axiom,
% 8.60/4.75 ! [X: int,Y: int,P2: $o] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 => ( ( ord_less_int @ Y @ X )
% 8.60/4.75 => P2 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_674_linorder__less__linear,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 | ( X = Y )
% 8.60/4.75 | ( ord_less_real @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_675_linorder__less__linear,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 | ( X = Y )
% 8.60/4.75 | ( ord_less_rat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_676_linorder__less__linear,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 | ( X = Y )
% 8.60/4.75 | ( ord_less_num @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_677_linorder__less__linear,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 | ( X = Y )
% 8.60/4.75 | ( ord_less_nat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_678_linorder__less__linear,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 | ( X = Y )
% 8.60/4.75 | ( ord_less_int @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_679_order__less__imp__not__eq,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( X != Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_680_order__less__imp__not__eq,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( X != Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_681_order__less__imp__not__eq,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 => ( X != Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_682_order__less__imp__not__eq,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ( X != Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_683_order__less__imp__not__eq,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 => ( X != Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_684_order__less__imp__not__eq2,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( Y != X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_685_order__less__imp__not__eq2,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( Y != X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_686_order__less__imp__not__eq2,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 => ( Y != X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_687_order__less__imp__not__eq2,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ( Y != X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_688_order__less__imp__not__eq2,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 => ( Y != X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_689_order__less__imp__not__less,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_real @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_690_order__less__imp__not__less,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_691_order__less__imp__not__less,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_num @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_692_order__less__imp__not__less,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_693_order__less__imp__not__less,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 => ~ ( ord_less_int @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_694_less__numeral__extra_I4_J,axiom,
% 8.60/4.75 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_695_less__numeral__extra_I4_J,axiom,
% 8.60/4.75 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_696_less__numeral__extra_I4_J,axiom,
% 8.60/4.75 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_697_less__numeral__extra_I4_J,axiom,
% 8.60/4.75 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_698_less__numeral__extra_I4_J,axiom,
% 8.60/4.75 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_699_one__reorient,axiom,
% 8.60/4.75 ! [X: code_integer] :
% 8.60/4.75 ( ( one_one_Code_integer = X )
% 8.60/4.75 = ( X = one_one_Code_integer ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_700_one__reorient,axiom,
% 8.60/4.75 ! [X: complex] :
% 8.60/4.75 ( ( one_one_complex = X )
% 8.60/4.75 = ( X = one_one_complex ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_701_one__reorient,axiom,
% 8.60/4.75 ! [X: real] :
% 8.60/4.75 ( ( one_one_real = X )
% 8.60/4.75 = ( X = one_one_real ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_702_one__reorient,axiom,
% 8.60/4.75 ! [X: nat] :
% 8.60/4.75 ( ( one_one_nat = X )
% 8.60/4.75 = ( X = one_one_nat ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_703_one__reorient,axiom,
% 8.60/4.75 ! [X: int] :
% 8.60/4.75 ( ( one_one_int = X )
% 8.60/4.75 = ( X = one_one_int ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_704_less__numeral__extra_I1_J,axiom,
% 8.60/4.75 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.60/4.75
% 8.60/4.75 thf(fact_705_less__numeral__extra_I1_J,axiom,
% 8.60/4.75 ord_less_real @ zero_zero_real @ one_one_real ).
% 8.60/4.75
% 8.60/4.75 thf(fact_706_less__numeral__extra_I1_J,axiom,
% 8.60/4.75 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_707_less__numeral__extra_I1_J,axiom,
% 8.60/4.75 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_708_less__numeral__extra_I1_J,axiom,
% 8.60/4.75 ord_less_int @ zero_zero_int @ one_one_int ).
% 8.60/4.75
% 8.60/4.75 thf(fact_709_not__one__less__zero,axiom,
% 8.60/4.75 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_710_not__one__less__zero,axiom,
% 8.60/4.75 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_711_not__one__less__zero,axiom,
% 8.60/4.75 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_712_not__one__less__zero,axiom,
% 8.60/4.75 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_713_not__one__less__zero,axiom,
% 8.60/4.75 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_714_zero__less__one,axiom,
% 8.60/4.75 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.60/4.75
% 8.60/4.75 thf(fact_715_zero__less__one,axiom,
% 8.60/4.75 ord_less_real @ zero_zero_real @ one_one_real ).
% 8.60/4.75
% 8.60/4.75 thf(fact_716_zero__less__one,axiom,
% 8.60/4.75 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_717_zero__less__one,axiom,
% 8.60/4.75 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_718_zero__less__one,axiom,
% 8.60/4.75 ord_less_int @ zero_zero_int @ one_one_int ).
% 8.60/4.75
% 8.60/4.75 thf(fact_719_lift__Suc__mono__less__iff,axiom,
% 8.60/4.75 ! [F2: nat > real,N: nat,M2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_real @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 8.60/4.75 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_720_lift__Suc__mono__less__iff,axiom,
% 8.60/4.75 ! [F2: nat > rat,N: nat,M2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_rat @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 8.60/4.75 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_721_lift__Suc__mono__less__iff,axiom,
% 8.60/4.75 ! [F2: nat > num,N: nat,M2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_num @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 8.60/4.75 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_722_lift__Suc__mono__less__iff,axiom,
% 8.60/4.75 ! [F2: nat > nat,N: nat,M2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 8.60/4.75 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_723_lift__Suc__mono__less__iff,axiom,
% 8.60/4.75 ! [F2: nat > int,N: nat,M2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_int @ ( F2 @ N ) @ ( F2 @ M2 ) )
% 8.60/4.75 = ( ord_less_nat @ N @ M2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_724_lift__Suc__mono__less,axiom,
% 8.60/4.75 ! [F2: nat > real,N: nat,N2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_nat @ N @ N2 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_725_lift__Suc__mono__less,axiom,
% 8.60/4.75 ! [F2: nat > rat,N: nat,N2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_rat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_nat @ N @ N2 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_726_lift__Suc__mono__less,axiom,
% 8.60/4.75 ! [F2: nat > num,N: nat,N2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_num @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_nat @ N @ N2 )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_727_lift__Suc__mono__less,axiom,
% 8.60/4.75 ! [F2: nat > nat,N: nat,N2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_nat @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_nat @ N @ N2 )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_728_lift__Suc__mono__less,axiom,
% 8.60/4.75 ! [F2: nat > int,N: nat,N2: nat] :
% 8.60/4.75 ( ! [N3: nat] : ( ord_less_int @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.60/4.75 => ( ( ord_less_nat @ N @ N2 )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ N ) @ ( F2 @ N2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_729_less__1__mult,axiom,
% 8.60/4.75 ! [M2: code_integer,N: code_integer] :
% 8.60/4.75 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M2 )
% 8.60/4.75 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M2 @ N ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_730_less__1__mult,axiom,
% 8.60/4.75 ! [M2: real,N: real] :
% 8.60/4.75 ( ( ord_less_real @ one_one_real @ M2 )
% 8.60/4.75 => ( ( ord_less_real @ one_one_real @ N )
% 8.60/4.75 => ( ord_less_real @ one_one_real @ ( times_times_real @ M2 @ N ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_731_less__1__mult,axiom,
% 8.60/4.75 ! [M2: rat,N: rat] :
% 8.60/4.75 ( ( ord_less_rat @ one_one_rat @ M2 )
% 8.60/4.75 => ( ( ord_less_rat @ one_one_rat @ N )
% 8.60/4.75 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M2 @ N ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_732_less__1__mult,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ one_one_nat @ M2 )
% 8.60/4.75 => ( ( ord_less_nat @ one_one_nat @ N )
% 8.60/4.75 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_733_less__1__mult,axiom,
% 8.60/4.75 ! [M2: int,N: int] :
% 8.60/4.75 ( ( ord_less_int @ one_one_int @ M2 )
% 8.60/4.75 => ( ( ord_less_int @ one_one_int @ N )
% 8.60/4.75 => ( ord_less_int @ one_one_int @ ( times_times_int @ M2 @ N ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_734_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 8.60/4.75 ! [Uu: $o,Uv: $o,D: nat] :
% 8.60/4.75 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 8.60/4.75 = ( D = one_one_nat ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_735_nat__induct__non__zero,axiom,
% 8.60/4.75 ! [N: nat,P2: nat > $o] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.75 => ( ( P2 @ one_one_nat )
% 8.60/4.75 => ( ! [N3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.60/4.75 => ( ( P2 @ N3 )
% 8.60/4.75 => ( P2 @ ( suc @ N3 ) ) ) )
% 8.60/4.75 => ( P2 @ N ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_736_order__le__imp__less__or__eq,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ X @ Y )
% 8.60/4.75 => ( ( ord_less_real @ X @ Y )
% 8.60/4.75 | ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_737_order__le__imp__less__or__eq,axiom,
% 8.60/4.75 ! [X: set_nat,Y: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_set_nat @ X @ Y )
% 8.60/4.75 | ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_738_order__le__imp__less__or__eq,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 | ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_739_order__le__imp__less__or__eq,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.75 => ( ( ord_less_num @ X @ Y )
% 8.60/4.75 | ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_740_order__le__imp__less__or__eq,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 | ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_741_order__le__imp__less__or__eq,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.75 => ( ( ord_less_int @ X @ Y )
% 8.60/4.75 | ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_742_linorder__le__less__linear,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ X @ Y )
% 8.60/4.75 | ( ord_less_real @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_743_linorder__le__less__linear,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.75 | ( ord_less_rat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_744_linorder__le__less__linear,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.75 | ( ord_less_num @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_745_linorder__le__less__linear,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.75 | ( ord_less_nat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_746_linorder__le__less__linear,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.75 | ( ord_less_int @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_747_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_748_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_749_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: num,B: num,F2: num > real,C2: real] :
% 8.60/4.75 ( ( ord_less_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_750_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: nat,B: nat,F2: nat > real,C2: real] :
% 8.60/4.75 ( ( ord_less_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_751_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: int,B: int,F2: int > real,C2: real] :
% 8.60/4.75 ( ( ord_less_int @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: int,Y3: int] :
% 8.60/4.75 ( ( ord_less_int @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_752_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: real,B: real,F2: real > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_753_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_754_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_755_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: nat,B: nat,F2: nat > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_756_order__less__le__subst2,axiom,
% 8.60/4.75 ! [A: int,B: int,F2: int > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_int @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: int,Y3: int] :
% 8.60/4.75 ( ( ord_less_int @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_757_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_758_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_759_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: num,F2: rat > num,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_num @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_760_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: nat,F2: rat > nat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_761_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: int,F2: rat > int,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_int @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_762_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: num > real,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_763_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_764_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: num,F2: num > num,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_num @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_765_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: nat,F2: num > nat,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_nat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_766_order__less__le__subst1,axiom,
% 8.60/4.75 ! [A: int,F2: num > int,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_int @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_767_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > real,C2: real] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_768_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_769_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > num,C2: num] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_770_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_771_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,F2: rat > int,C2: int] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_772_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: num,B: num,F2: num > real,C2: real] :
% 8.60/4.75 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_773_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: num,B: num,F2: num > rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_774_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: num,B: num,F2: num > num,C2: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_num @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_num @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_num @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_775_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: num,B: num,F2: num > nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_776_order__le__less__subst2,axiom,
% 8.60/4.75 ! [A: num,B: num,F2: num > int,C2: int] :
% 8.60/4.75 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ ( F2 @ B ) @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_int @ ( F2 @ A ) @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_777_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: real > real,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_778_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: rat > real,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_779_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: num > real,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_780_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: nat > real,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_781_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: real,F2: int > real,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_eq_real @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.75 => ( ! [X3: int,Y3: int] :
% 8.60/4.75 ( ( ord_less_int @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_real @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_real @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_782_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: real > rat,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.75 => ( ! [X3: real,Y3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_783_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: rat > rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: rat,Y3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_784_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: num > rat,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_num @ B @ C2 )
% 8.60/4.75 => ( ! [X3: num,Y3: num] :
% 8.60/4.75 ( ( ord_less_num @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_785_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: nat > rat,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.75 => ( ! [X3: nat,Y3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_786_order__le__less__subst1,axiom,
% 8.60/4.75 ! [A: rat,F2: int > rat,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ ( F2 @ B ) )
% 8.60/4.75 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.75 => ( ! [X3: int,Y3: int] :
% 8.60/4.75 ( ( ord_less_int @ X3 @ Y3 )
% 8.60/4.75 => ( ord_less_rat @ ( F2 @ X3 ) @ ( F2 @ Y3 ) ) )
% 8.60/4.75 => ( ord_less_rat @ A @ ( F2 @ C2 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_787_order__less__le__trans,axiom,
% 8.60/4.75 ! [X: real,Y: real,Z3: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_real @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_788_order__less__le__trans,axiom,
% 8.60/4.75 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_set_nat @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_789_order__less__le__trans,axiom,
% 8.60/4.75 ! [X: rat,Y: rat,Z3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_rat @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_790_order__less__le__trans,axiom,
% 8.60/4.75 ! [X: num,Y: num,Z3: num] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_num @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_791_order__less__le__trans,axiom,
% 8.60/4.75 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_nat @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_792_order__less__le__trans,axiom,
% 8.60/4.75 ! [X: int,Y: int,Z3: int] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_int @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_793_order__le__less__trans,axiom,
% 8.60/4.75 ! [X: real,Y: real,Z3: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ X @ Y )
% 8.60/4.75 => ( ( ord_less_real @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_real @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_794_order__le__less__trans,axiom,
% 8.60/4.75 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_set_nat @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_set_nat @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_795_order__le__less__trans,axiom,
% 8.60/4.75 ! [X: rat,Y: rat,Z3: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_rat @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_rat @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_796_order__le__less__trans,axiom,
% 8.60/4.75 ! [X: num,Y: num,Z3: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.75 => ( ( ord_less_num @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_num @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_797_order__le__less__trans,axiom,
% 8.60/4.75 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_nat @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_nat @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_798_order__le__less__trans,axiom,
% 8.60/4.75 ! [X: int,Y: int,Z3: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.75 => ( ( ord_less_int @ Y @ Z3 )
% 8.60/4.75 => ( ord_less_int @ X @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_799_order__neq__le__trans,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( A != B )
% 8.60/4.75 => ( ( ord_less_eq_real @ A @ B )
% 8.60/4.75 => ( ord_less_real @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_800_order__neq__le__trans,axiom,
% 8.60/4.75 ! [A: set_nat,B: set_nat] :
% 8.60/4.75 ( ( A != B )
% 8.60/4.75 => ( ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.75 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_801_order__neq__le__trans,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( A != B )
% 8.60/4.75 => ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ord_less_rat @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_802_order__neq__le__trans,axiom,
% 8.60/4.75 ! [A: num,B: num] :
% 8.60/4.75 ( ( A != B )
% 8.60/4.75 => ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ord_less_num @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_803_order__neq__le__trans,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( A != B )
% 8.60/4.75 => ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.75 => ( ord_less_nat @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_804_order__neq__le__trans,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( A != B )
% 8.60/4.75 => ( ( ord_less_eq_int @ A @ B )
% 8.60/4.75 => ( ord_less_int @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_805_order__le__neq__trans,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.75 => ( ( A != B )
% 8.60/4.75 => ( ord_less_real @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_806_order__le__neq__trans,axiom,
% 8.60/4.75 ! [A: set_nat,B: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.75 => ( ( A != B )
% 8.60/4.75 => ( ord_less_set_nat @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_807_order__le__neq__trans,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ( A != B )
% 8.60/4.75 => ( ord_less_rat @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_808_order__le__neq__trans,axiom,
% 8.60/4.75 ! [A: num,B: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ( A != B )
% 8.60/4.75 => ( ord_less_num @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_809_order__le__neq__trans,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.75 => ( ( A != B )
% 8.60/4.75 => ( ord_less_nat @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_810_order__le__neq__trans,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.75 => ( ( A != B )
% 8.60/4.75 => ( ord_less_int @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_811_order__less__imp__le,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_real @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_812_order__less__imp__le,axiom,
% 8.60/4.75 ! [X: set_nat,Y: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_813_order__less__imp__le,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_814_order__less__imp__le,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_num @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_num @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_815_order__less__imp__le,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_816_order__less__imp__le,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_int @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_int @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_817_linorder__not__less,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.60/4.75 = ( ord_less_eq_real @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_818_linorder__not__less,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.60/4.75 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_819_linorder__not__less,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.60/4.75 = ( ord_less_eq_num @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_820_linorder__not__less,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.60/4.75 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_821_linorder__not__less,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.60/4.75 = ( ord_less_eq_int @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_822_linorder__not__le,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 8.60/4.75 = ( ord_less_real @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_823_linorder__not__le,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 8.60/4.75 = ( ord_less_rat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_824_linorder__not__le,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 8.60/4.75 = ( ord_less_num @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_825_linorder__not__le,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 8.60/4.75 = ( ord_less_nat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_826_linorder__not__le,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 8.60/4.75 = ( ord_less_int @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_827_order__less__le,axiom,
% 8.60/4.75 ( ord_less_real
% 8.60/4.75 = ( ^ [X4: real,Y4: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ X4 @ Y4 )
% 8.60/4.75 & ( X4 != Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_828_order__less__le,axiom,
% 8.60/4.75 ( ord_less_set_nat
% 8.60/4.75 = ( ^ [X4: set_nat,Y4: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 8.60/4.75 & ( X4 != Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_829_order__less__le,axiom,
% 8.60/4.75 ( ord_less_rat
% 8.60/4.75 = ( ^ [X4: rat,Y4: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 8.60/4.75 & ( X4 != Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_830_order__less__le,axiom,
% 8.60/4.75 ( ord_less_num
% 8.60/4.75 = ( ^ [X4: num,Y4: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X4 @ Y4 )
% 8.60/4.75 & ( X4 != Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_831_order__less__le,axiom,
% 8.60/4.75 ( ord_less_nat
% 8.60/4.75 = ( ^ [X4: nat,Y4: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 8.60/4.75 & ( X4 != Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_832_order__less__le,axiom,
% 8.60/4.75 ( ord_less_int
% 8.60/4.75 = ( ^ [X4: int,Y4: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ X4 @ Y4 )
% 8.60/4.75 & ( X4 != Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_833_order__le__less,axiom,
% 8.60/4.75 ( ord_less_eq_real
% 8.60/4.75 = ( ^ [X4: real,Y4: real] :
% 8.60/4.75 ( ( ord_less_real @ X4 @ Y4 )
% 8.60/4.75 | ( X4 = Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_834_order__le__less,axiom,
% 8.60/4.75 ( ord_less_eq_set_nat
% 8.60/4.75 = ( ^ [X4: set_nat,Y4: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ X4 @ Y4 )
% 8.60/4.75 | ( X4 = Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_835_order__le__less,axiom,
% 8.60/4.75 ( ord_less_eq_rat
% 8.60/4.75 = ( ^ [X4: rat,Y4: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X4 @ Y4 )
% 8.60/4.75 | ( X4 = Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_836_order__le__less,axiom,
% 8.60/4.75 ( ord_less_eq_num
% 8.60/4.75 = ( ^ [X4: num,Y4: num] :
% 8.60/4.75 ( ( ord_less_num @ X4 @ Y4 )
% 8.60/4.75 | ( X4 = Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_837_order__le__less,axiom,
% 8.60/4.75 ( ord_less_eq_nat
% 8.60/4.75 = ( ^ [X4: nat,Y4: nat] :
% 8.60/4.75 ( ( ord_less_nat @ X4 @ Y4 )
% 8.60/4.75 | ( X4 = Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_838_order__le__less,axiom,
% 8.60/4.75 ( ord_less_eq_int
% 8.60/4.75 = ( ^ [X4: int,Y4: int] :
% 8.60/4.75 ( ( ord_less_int @ X4 @ Y4 )
% 8.60/4.75 | ( X4 = Y4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_839_dual__order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [B: real,A: real] :
% 8.60/4.75 ( ( ord_less_real @ B @ A )
% 8.60/4.75 => ( ord_less_eq_real @ B @ A ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_840_dual__order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [B: set_nat,A: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ B @ A )
% 8.60/4.75 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_841_dual__order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [B: rat,A: rat] :
% 8.60/4.75 ( ( ord_less_rat @ B @ A )
% 8.60/4.75 => ( ord_less_eq_rat @ B @ A ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_842_dual__order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [B: num,A: num] :
% 8.60/4.75 ( ( ord_less_num @ B @ A )
% 8.60/4.75 => ( ord_less_eq_num @ B @ A ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_843_dual__order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [B: nat,A: nat] :
% 8.60/4.75 ( ( ord_less_nat @ B @ A )
% 8.60/4.75 => ( ord_less_eq_nat @ B @ A ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_844_dual__order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [B: int,A: int] :
% 8.60/4.75 ( ( ord_less_int @ B @ A )
% 8.60/4.75 => ( ord_less_eq_int @ B @ A ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_845_order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ord_less_eq_real @ A @ B ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_846_order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [A: set_nat,B: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ A @ B )
% 8.60/4.75 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_847_order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_848_order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [A: num,B: num] :
% 8.60/4.75 ( ( ord_less_num @ A @ B )
% 8.60/4.75 => ( ord_less_eq_num @ A @ B ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_849_order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ B )
% 8.60/4.75 => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_850_order_Ostrict__implies__order,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ A @ B )
% 8.60/4.75 => ( ord_less_eq_int @ A @ B ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_851_dual__order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_real
% 8.60/4.75 = ( ^ [B4: real,A5: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ B4 @ A5 )
% 8.60/4.75 & ~ ( ord_less_eq_real @ A5 @ B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_852_dual__order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_set_nat
% 8.60/4.75 = ( ^ [B4: set_nat,A5: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 8.60/4.75 & ~ ( ord_less_eq_set_nat @ A5 @ B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_853_dual__order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_rat
% 8.60/4.75 = ( ^ [B4: rat,A5: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ B4 @ A5 )
% 8.60/4.75 & ~ ( ord_less_eq_rat @ A5 @ B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_854_dual__order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_num
% 8.60/4.75 = ( ^ [B4: num,A5: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ B4 @ A5 )
% 8.60/4.75 & ~ ( ord_less_eq_num @ A5 @ B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_855_dual__order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_nat
% 8.60/4.75 = ( ^ [B4: nat,A5: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ B4 @ A5 )
% 8.60/4.75 & ~ ( ord_less_eq_nat @ A5 @ B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_856_dual__order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_int
% 8.60/4.75 = ( ^ [B4: int,A5: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ B4 @ A5 )
% 8.60/4.75 & ~ ( ord_less_eq_int @ A5 @ B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_857_dual__order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [B: real,A: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ B @ A )
% 8.60/4.75 => ( ( ord_less_eq_real @ C2 @ B )
% 8.60/4.75 => ( ord_less_real @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_858_dual__order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ B @ A )
% 8.60/4.75 => ( ( ord_less_eq_set_nat @ C2 @ B )
% 8.60/4.75 => ( ord_less_set_nat @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_859_dual__order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ B @ A )
% 8.60/4.75 => ( ( ord_less_eq_rat @ C2 @ B )
% 8.60/4.75 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_860_dual__order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [B: num,A: num,C2: num] :
% 8.60/4.75 ( ( ord_less_num @ B @ A )
% 8.60/4.75 => ( ( ord_less_eq_num @ C2 @ B )
% 8.60/4.75 => ( ord_less_num @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_861_dual__order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ B @ A )
% 8.60/4.75 => ( ( ord_less_eq_nat @ C2 @ B )
% 8.60/4.75 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_862_dual__order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [B: int,A: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ B @ A )
% 8.60/4.75 => ( ( ord_less_eq_int @ C2 @ B )
% 8.60/4.75 => ( ord_less_int @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_863_dual__order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [B: real,A: real,C2: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ B @ A )
% 8.60/4.75 => ( ( ord_less_real @ C2 @ B )
% 8.60/4.75 => ( ord_less_real @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_864_dual__order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ B @ A )
% 8.60/4.75 => ( ( ord_less_set_nat @ C2 @ B )
% 8.60/4.75 => ( ord_less_set_nat @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_865_dual__order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.75 => ( ( ord_less_rat @ C2 @ B )
% 8.60/4.75 => ( ord_less_rat @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_866_dual__order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [B: num,A: num,C2: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ B @ A )
% 8.60/4.75 => ( ( ord_less_num @ C2 @ B )
% 8.60/4.75 => ( ord_less_num @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_867_dual__order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.75 => ( ( ord_less_nat @ C2 @ B )
% 8.60/4.75 => ( ord_less_nat @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_868_dual__order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [B: int,A: int,C2: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.75 => ( ( ord_less_int @ C2 @ B )
% 8.60/4.75 => ( ord_less_int @ C2 @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_869_dual__order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_real
% 8.60/4.75 = ( ^ [B4: real,A5: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ B4 @ A5 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_870_dual__order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_set_nat
% 8.60/4.75 = ( ^ [B4: set_nat,A5: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ B4 @ A5 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_871_dual__order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_rat
% 8.60/4.75 = ( ^ [B4: rat,A5: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ B4 @ A5 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_872_dual__order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_num
% 8.60/4.75 = ( ^ [B4: num,A5: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ B4 @ A5 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_873_dual__order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_nat
% 8.60/4.75 = ( ^ [B4: nat,A5: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ B4 @ A5 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_874_dual__order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_int
% 8.60/4.75 = ( ^ [B4: int,A5: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ B4 @ A5 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_875_dual__order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_real
% 8.60/4.75 = ( ^ [B4: real,A5: real] :
% 8.60/4.75 ( ( ord_less_real @ B4 @ A5 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_876_dual__order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_set_nat
% 8.60/4.75 = ( ^ [B4: set_nat,A5: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ B4 @ A5 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_877_dual__order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_rat
% 8.60/4.75 = ( ^ [B4: rat,A5: rat] :
% 8.60/4.75 ( ( ord_less_rat @ B4 @ A5 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_878_dual__order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_num
% 8.60/4.75 = ( ^ [B4: num,A5: num] :
% 8.60/4.75 ( ( ord_less_num @ B4 @ A5 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_879_dual__order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_nat
% 8.60/4.75 = ( ^ [B4: nat,A5: nat] :
% 8.60/4.75 ( ( ord_less_nat @ B4 @ A5 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_880_dual__order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_int
% 8.60/4.75 = ( ^ [B4: int,A5: int] :
% 8.60/4.75 ( ( ord_less_int @ B4 @ A5 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_881_dense__le__bounded,axiom,
% 8.60/4.75 ! [X: real,Y: real,Z3: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( ! [W: real] :
% 8.60/4.75 ( ( ord_less_real @ X @ W )
% 8.60/4.75 => ( ( ord_less_real @ W @ Y )
% 8.60/4.75 => ( ord_less_eq_real @ W @ Z3 ) ) )
% 8.60/4.75 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_882_dense__le__bounded,axiom,
% 8.60/4.75 ! [X: rat,Y: rat,Z3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( ! [W: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X @ W )
% 8.60/4.75 => ( ( ord_less_rat @ W @ Y )
% 8.60/4.75 => ( ord_less_eq_rat @ W @ Z3 ) ) )
% 8.60/4.75 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_883_dense__ge__bounded,axiom,
% 8.60/4.75 ! [Z3: real,X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_real @ Z3 @ X )
% 8.60/4.75 => ( ! [W: real] :
% 8.60/4.75 ( ( ord_less_real @ Z3 @ W )
% 8.60/4.75 => ( ( ord_less_real @ W @ X )
% 8.60/4.75 => ( ord_less_eq_real @ Y @ W ) ) )
% 8.60/4.75 => ( ord_less_eq_real @ Y @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_884_dense__ge__bounded,axiom,
% 8.60/4.75 ! [Z3: rat,X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_rat @ Z3 @ X )
% 8.60/4.75 => ( ! [W: rat] :
% 8.60/4.75 ( ( ord_less_rat @ Z3 @ W )
% 8.60/4.75 => ( ( ord_less_rat @ W @ X )
% 8.60/4.75 => ( ord_less_eq_rat @ Y @ W ) ) )
% 8.60/4.75 => ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_885_order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_real
% 8.60/4.75 = ( ^ [A5: real,B4: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ A5 @ B4 )
% 8.60/4.75 & ~ ( ord_less_eq_real @ B4 @ A5 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_886_order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_set_nat
% 8.60/4.75 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 8.60/4.75 & ~ ( ord_less_eq_set_nat @ B4 @ A5 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_887_order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_rat
% 8.60/4.75 = ( ^ [A5: rat,B4: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A5 @ B4 )
% 8.60/4.75 & ~ ( ord_less_eq_rat @ B4 @ A5 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_888_order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_num
% 8.60/4.75 = ( ^ [A5: num,B4: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ A5 @ B4 )
% 8.60/4.75 & ~ ( ord_less_eq_num @ B4 @ A5 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_889_order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_nat
% 8.60/4.75 = ( ^ [A5: nat,B4: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ A5 @ B4 )
% 8.60/4.75 & ~ ( ord_less_eq_nat @ B4 @ A5 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_890_order_Ostrict__iff__not,axiom,
% 8.60/4.75 ( ord_less_int
% 8.60/4.75 = ( ^ [A5: int,B4: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ A5 @ B4 )
% 8.60/4.75 & ~ ( ord_less_eq_int @ B4 @ A5 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_891_order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [A: real,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_real @ B @ C2 )
% 8.60/4.75 => ( ord_less_real @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_892_order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_set_nat @ B @ C2 )
% 8.60/4.75 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_893_order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.75 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_894_order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [A: num,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_num @ B @ C2 )
% 8.60/4.75 => ( ord_less_num @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_895_order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.75 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_896_order_Ostrict__trans2,axiom,
% 8.60/4.75 ! [A: int,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ A @ B )
% 8.60/4.75 => ( ( ord_less_eq_int @ B @ C2 )
% 8.60/4.75 => ( ord_less_int @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_897_order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [A: real,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.75 => ( ord_less_real @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_898_order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_set_nat @ B @ C2 )
% 8.60/4.75 => ( ord_less_set_nat @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_899_order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.75 => ( ord_less_rat @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_900_order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [A: num,B: num,C2: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ A @ B )
% 8.60/4.75 => ( ( ord_less_num @ B @ C2 )
% 8.60/4.75 => ( ord_less_num @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_901_order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.75 => ( ord_less_nat @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_902_order_Ostrict__trans1,axiom,
% 8.60/4.75 ! [A: int,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.75 => ( ord_less_int @ A @ C2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_903_order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_real
% 8.60/4.75 = ( ^ [A5: real,B4: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ A5 @ B4 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_904_order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_set_nat
% 8.60/4.75 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ A5 @ B4 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_905_order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_rat
% 8.60/4.75 = ( ^ [A5: rat,B4: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ A5 @ B4 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_906_order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_num
% 8.60/4.75 = ( ^ [A5: num,B4: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ A5 @ B4 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_907_order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_nat
% 8.60/4.75 = ( ^ [A5: nat,B4: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ A5 @ B4 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_908_order_Ostrict__iff__order,axiom,
% 8.60/4.75 ( ord_less_int
% 8.60/4.75 = ( ^ [A5: int,B4: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ A5 @ B4 )
% 8.60/4.75 & ( A5 != B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_909_order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_real
% 8.60/4.75 = ( ^ [A5: real,B4: real] :
% 8.60/4.75 ( ( ord_less_real @ A5 @ B4 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_910_order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_set_nat
% 8.60/4.75 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.60/4.75 ( ( ord_less_set_nat @ A5 @ B4 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_911_order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_rat
% 8.60/4.75 = ( ^ [A5: rat,B4: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A5 @ B4 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_912_order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_num
% 8.60/4.75 = ( ^ [A5: num,B4: num] :
% 8.60/4.75 ( ( ord_less_num @ A5 @ B4 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_913_order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_nat
% 8.60/4.75 = ( ^ [A5: nat,B4: nat] :
% 8.60/4.75 ( ( ord_less_nat @ A5 @ B4 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_914_order_Oorder__iff__strict,axiom,
% 8.60/4.75 ( ord_less_eq_int
% 8.60/4.75 = ( ^ [A5: int,B4: int] :
% 8.60/4.75 ( ( ord_less_int @ A5 @ B4 )
% 8.60/4.75 | ( A5 = B4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_915_not__le__imp__less,axiom,
% 8.60/4.75 ! [Y: real,X: real] :
% 8.60/4.75 ( ~ ( ord_less_eq_real @ Y @ X )
% 8.60/4.75 => ( ord_less_real @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_916_not__le__imp__less,axiom,
% 8.60/4.75 ! [Y: rat,X: rat] :
% 8.60/4.75 ( ~ ( ord_less_eq_rat @ Y @ X )
% 8.60/4.75 => ( ord_less_rat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_917_not__le__imp__less,axiom,
% 8.60/4.75 ! [Y: num,X: num] :
% 8.60/4.75 ( ~ ( ord_less_eq_num @ Y @ X )
% 8.60/4.75 => ( ord_less_num @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_918_not__le__imp__less,axiom,
% 8.60/4.75 ! [Y: nat,X: nat] :
% 8.60/4.75 ( ~ ( ord_less_eq_nat @ Y @ X )
% 8.60/4.75 => ( ord_less_nat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_919_not__le__imp__less,axiom,
% 8.60/4.75 ! [Y: int,X: int] :
% 8.60/4.75 ( ~ ( ord_less_eq_int @ Y @ X )
% 8.60/4.75 => ( ord_less_int @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_920_less__le__not__le,axiom,
% 8.60/4.75 ( ord_less_real
% 8.60/4.75 = ( ^ [X4: real,Y4: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ X4 @ Y4 )
% 8.60/4.75 & ~ ( ord_less_eq_real @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_921_less__le__not__le,axiom,
% 8.60/4.75 ( ord_less_set_nat
% 8.60/4.75 = ( ^ [X4: set_nat,Y4: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ X4 @ Y4 )
% 8.60/4.75 & ~ ( ord_less_eq_set_nat @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_922_less__le__not__le,axiom,
% 8.60/4.75 ( ord_less_rat
% 8.60/4.75 = ( ^ [X4: rat,Y4: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 8.60/4.75 & ~ ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_923_less__le__not__le,axiom,
% 8.60/4.75 ( ord_less_num
% 8.60/4.75 = ( ^ [X4: num,Y4: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X4 @ Y4 )
% 8.60/4.75 & ~ ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_924_less__le__not__le,axiom,
% 8.60/4.75 ( ord_less_nat
% 8.60/4.75 = ( ^ [X4: nat,Y4: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 8.60/4.75 & ~ ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_925_less__le__not__le,axiom,
% 8.60/4.75 ( ord_less_int
% 8.60/4.75 = ( ^ [X4: int,Y4: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ X4 @ Y4 )
% 8.60/4.75 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_926_dense__le,axiom,
% 8.60/4.75 ! [Y: real,Z3: real] :
% 8.60/4.75 ( ! [X3: real] :
% 8.60/4.75 ( ( ord_less_real @ X3 @ Y )
% 8.60/4.75 => ( ord_less_eq_real @ X3 @ Z3 ) )
% 8.60/4.75 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_927_dense__le,axiom,
% 8.60/4.75 ! [Y: rat,Z3: rat] :
% 8.60/4.75 ( ! [X3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ X3 @ Y )
% 8.60/4.75 => ( ord_less_eq_rat @ X3 @ Z3 ) )
% 8.60/4.75 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_928_dense__ge,axiom,
% 8.60/4.75 ! [Z3: real,Y: real] :
% 8.60/4.75 ( ! [X3: real] :
% 8.60/4.75 ( ( ord_less_real @ Z3 @ X3 )
% 8.60/4.75 => ( ord_less_eq_real @ Y @ X3 ) )
% 8.60/4.75 => ( ord_less_eq_real @ Y @ Z3 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_929_dense__ge,axiom,
% 8.60/4.75 ! [Z3: rat,Y: rat] :
% 8.60/4.75 ( ! [X3: rat] :
% 8.60/4.75 ( ( ord_less_rat @ Z3 @ X3 )
% 8.60/4.75 => ( ord_less_eq_rat @ Y @ X3 ) )
% 8.60/4.75 => ( ord_less_eq_rat @ Y @ Z3 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_930_antisym__conv2,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ X @ Y )
% 8.60/4.75 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_931_antisym__conv2,axiom,
% 8.60/4.75 ! [X: set_nat,Y: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.60/4.75 => ( ( ~ ( ord_less_set_nat @ X @ Y ) )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_932_antisym__conv2,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.75 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_933_antisym__conv2,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.75 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_934_antisym__conv2,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.75 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_935_antisym__conv2,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.75 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_936_antisym__conv1,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ~ ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_real @ X @ Y )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_937_antisym__conv1,axiom,
% 8.60/4.75 ! [X: set_nat,Y: set_nat] :
% 8.60/4.75 ( ~ ( ord_less_set_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_set_nat @ X @ Y )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_938_antisym__conv1,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ~ ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_rat @ X @ Y )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_939_antisym__conv1,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ~ ( ord_less_num @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_num @ X @ Y )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_940_antisym__conv1,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ~ ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_nat @ X @ Y )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_941_antisym__conv1,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ~ ( ord_less_int @ X @ Y )
% 8.60/4.75 => ( ( ord_less_eq_int @ X @ Y )
% 8.60/4.75 = ( X = Y ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_942_nless__le,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ~ ( ord_less_real @ A @ B ) )
% 8.60/4.75 = ( ~ ( ord_less_eq_real @ A @ B )
% 8.60/4.75 | ( A = B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_943_nless__le,axiom,
% 8.60/4.75 ! [A: set_nat,B: set_nat] :
% 8.60/4.75 ( ( ~ ( ord_less_set_nat @ A @ B ) )
% 8.60/4.75 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 8.60/4.75 | ( A = B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_944_nless__le,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ~ ( ord_less_rat @ A @ B ) )
% 8.60/4.75 = ( ~ ( ord_less_eq_rat @ A @ B )
% 8.60/4.75 | ( A = B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_945_nless__le,axiom,
% 8.60/4.75 ! [A: num,B: num] :
% 8.60/4.75 ( ( ~ ( ord_less_num @ A @ B ) )
% 8.60/4.75 = ( ~ ( ord_less_eq_num @ A @ B )
% 8.60/4.75 | ( A = B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_946_nless__le,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ~ ( ord_less_nat @ A @ B ) )
% 8.60/4.75 = ( ~ ( ord_less_eq_nat @ A @ B )
% 8.60/4.75 | ( A = B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_947_nless__le,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ~ ( ord_less_int @ A @ B ) )
% 8.60/4.75 = ( ~ ( ord_less_eq_int @ A @ B )
% 8.60/4.75 | ( A = B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_948_leI,axiom,
% 8.60/4.75 ! [X: real,Y: real] :
% 8.60/4.75 ( ~ ( ord_less_real @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_real @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_949_leI,axiom,
% 8.60/4.75 ! [X: rat,Y: rat] :
% 8.60/4.75 ( ~ ( ord_less_rat @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_950_leI,axiom,
% 8.60/4.75 ! [X: num,Y: num] :
% 8.60/4.75 ( ~ ( ord_less_num @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_num @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_951_leI,axiom,
% 8.60/4.75 ! [X: nat,Y: nat] :
% 8.60/4.75 ( ~ ( ord_less_nat @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_952_leI,axiom,
% 8.60/4.75 ! [X: int,Y: int] :
% 8.60/4.75 ( ~ ( ord_less_int @ X @ Y )
% 8.60/4.75 => ( ord_less_eq_int @ Y @ X ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_953_leD,axiom,
% 8.60/4.75 ! [Y: real,X: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ Y @ X )
% 8.60/4.75 => ~ ( ord_less_real @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_954_leD,axiom,
% 8.60/4.75 ! [Y: set_nat,X: set_nat] :
% 8.60/4.75 ( ( ord_less_eq_set_nat @ Y @ X )
% 8.60/4.75 => ~ ( ord_less_set_nat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_955_leD,axiom,
% 8.60/4.75 ! [Y: rat,X: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ Y @ X )
% 8.60/4.75 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_956_leD,axiom,
% 8.60/4.75 ! [Y: num,X: num] :
% 8.60/4.75 ( ( ord_less_eq_num @ Y @ X )
% 8.60/4.75 => ~ ( ord_less_num @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_957_leD,axiom,
% 8.60/4.75 ! [Y: nat,X: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ Y @ X )
% 8.60/4.75 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_958_leD,axiom,
% 8.60/4.75 ! [Y: int,X: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ Y @ X )
% 8.60/4.75 => ~ ( ord_less_int @ X @ Y ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_959_zero__less__iff__neq__zero,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.75 = ( N != zero_zero_nat ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_960_gr__implies__not__zero,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.75 => ( N != zero_zero_nat ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_961_not__less__zero,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_962_gr__zeroI,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ( ( N != zero_zero_nat )
% 8.60/4.75 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_963_less__numeral__extra_I3_J,axiom,
% 8.60/4.75 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_964_less__numeral__extra_I3_J,axiom,
% 8.60/4.75 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_965_less__numeral__extra_I3_J,axiom,
% 8.60/4.75 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_966_less__numeral__extra_I3_J,axiom,
% 8.60/4.75 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_967_not__less__less__Suc__eq,axiom,
% 8.60/4.75 ! [N: nat,M2: nat] :
% 8.60/4.75 ( ~ ( ord_less_nat @ N @ M2 )
% 8.60/4.75 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 8.60/4.75 = ( N = M2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_968_strict__inc__induct,axiom,
% 8.60/4.75 ! [I2: nat,J2: nat,P2: nat > $o] :
% 8.60/4.75 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.75 => ( ! [I3: nat] :
% 8.60/4.75 ( ( J2
% 8.60/4.75 = ( suc @ I3 ) )
% 8.60/4.75 => ( P2 @ I3 ) )
% 8.60/4.75 => ( ! [I3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I3 @ J2 )
% 8.60/4.75 => ( ( P2 @ ( suc @ I3 ) )
% 8.60/4.75 => ( P2 @ I3 ) ) )
% 8.60/4.75 => ( P2 @ I2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_969_less__Suc__induct,axiom,
% 8.60/4.75 ! [I2: nat,J2: nat,P2: nat > nat > $o] :
% 8.60/4.75 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.75 => ( ! [I3: nat] : ( P2 @ I3 @ ( suc @ I3 ) )
% 8.60/4.75 => ( ! [I3: nat,J3: nat,K: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I3 @ J3 )
% 8.60/4.75 => ( ( ord_less_nat @ J3 @ K )
% 8.60/4.75 => ( ( P2 @ I3 @ J3 )
% 8.60/4.75 => ( ( P2 @ J3 @ K )
% 8.60/4.75 => ( P2 @ I3 @ K ) ) ) ) )
% 8.60/4.75 => ( P2 @ I2 @ J2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_970_less__trans__Suc,axiom,
% 8.60/4.75 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.75 => ( ( ord_less_nat @ J2 @ K2 )
% 8.60/4.75 => ( ord_less_nat @ ( suc @ I2 ) @ K2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_971_Suc__less__SucD,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 8.60/4.75 => ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_972_less__antisym,axiom,
% 8.60/4.75 ! [N: nat,M2: nat] :
% 8.60/4.75 ( ~ ( ord_less_nat @ N @ M2 )
% 8.60/4.75 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 8.60/4.75 => ( M2 = N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_973_Suc__less__eq2,axiom,
% 8.60/4.75 ! [N: nat,M2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.60/4.75 = ( ? [M7: nat] :
% 8.60/4.75 ( ( M2
% 8.60/4.75 = ( suc @ M7 ) )
% 8.60/4.75 & ( ord_less_nat @ N @ M7 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_974_All__less__Suc,axiom,
% 8.60/4.75 ! [N: nat,P2: nat > $o] :
% 8.60/4.75 ( ( ! [I: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 8.60/4.75 => ( P2 @ I ) ) )
% 8.60/4.75 = ( ( P2 @ N )
% 8.60/4.75 & ! [I: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I @ N )
% 8.60/4.75 => ( P2 @ I ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_975_not__less__eq,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ~ ( ord_less_nat @ M2 @ N ) )
% 8.60/4.75 = ( ord_less_nat @ N @ ( suc @ M2 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_976_less__Suc__eq,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 8.60/4.75 = ( ( ord_less_nat @ M2 @ N )
% 8.60/4.75 | ( M2 = N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_977_Ex__less__Suc,axiom,
% 8.60/4.75 ! [N: nat,P2: nat > $o] :
% 8.60/4.75 ( ( ? [I: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 8.60/4.75 & ( P2 @ I ) ) )
% 8.60/4.75 = ( ( P2 @ N )
% 8.60/4.75 | ? [I: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I @ N )
% 8.60/4.75 & ( P2 @ I ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_978_less__SucI,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.75 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_979_less__SucE,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 8.60/4.75 => ( ~ ( ord_less_nat @ M2 @ N )
% 8.60/4.75 => ( M2 = N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_980_Suc__lessI,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.75 => ( ( ( suc @ M2 )
% 8.60/4.75 != N )
% 8.60/4.75 => ( ord_less_nat @ ( suc @ M2 ) @ N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_981_Suc__lessE,axiom,
% 8.60/4.75 ! [I2: nat,K2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ ( suc @ I2 ) @ K2 )
% 8.60/4.75 => ~ ! [J3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I2 @ J3 )
% 8.60/4.75 => ( K2
% 8.60/4.75 != ( suc @ J3 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_982_Suc__lessD,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ ( suc @ M2 ) @ N )
% 8.60/4.75 => ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_983_Nat_OlessE,axiom,
% 8.60/4.75 ! [I2: nat,K2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I2 @ K2 )
% 8.60/4.75 => ( ( K2
% 8.60/4.75 != ( suc @ I2 ) )
% 8.60/4.75 => ~ ! [J3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I2 @ J3 )
% 8.60/4.75 => ( K2
% 8.60/4.75 != ( suc @ J3 ) ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_984_VEBT_Odistinct_I1_J,axiom,
% 8.60/4.75 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X22: $o] :
% 8.60/4.75 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 8.60/4.75 != ( vEBT_Leaf @ X21 @ X22 ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_985_VEBT_Oexhaust,axiom,
% 8.60/4.75 ! [Y: vEBT_VEBT] :
% 8.60/4.75 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 8.60/4.75 ( Y
% 8.60/4.75 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 8.60/4.75 => ~ ! [X212: $o,X222: $o] :
% 8.60/4.75 ( Y
% 8.60/4.75 != ( vEBT_Leaf @ X212 @ X222 ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_986_le__numeral__extra_I4_J,axiom,
% 8.60/4.75 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 8.60/4.75
% 8.60/4.75 thf(fact_987_le__numeral__extra_I4_J,axiom,
% 8.60/4.75 ord_less_eq_real @ one_one_real @ one_one_real ).
% 8.60/4.75
% 8.60/4.75 thf(fact_988_le__numeral__extra_I4_J,axiom,
% 8.60/4.75 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_989_le__numeral__extra_I4_J,axiom,
% 8.60/4.75 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_990_le__numeral__extra_I4_J,axiom,
% 8.60/4.75 ord_less_eq_int @ one_one_int @ one_one_int ).
% 8.60/4.75
% 8.60/4.75 thf(fact_991_zero__neq__one,axiom,
% 8.60/4.75 zero_z3403309356797280102nteger != one_one_Code_integer ).
% 8.60/4.75
% 8.60/4.75 thf(fact_992_zero__neq__one,axiom,
% 8.60/4.75 zero_zero_complex != one_one_complex ).
% 8.60/4.75
% 8.60/4.75 thf(fact_993_zero__neq__one,axiom,
% 8.60/4.75 zero_zero_real != one_one_real ).
% 8.60/4.75
% 8.60/4.75 thf(fact_994_zero__neq__one,axiom,
% 8.60/4.75 zero_zero_rat != one_one_rat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_995_zero__neq__one,axiom,
% 8.60/4.75 zero_zero_nat != one_one_nat ).
% 8.60/4.75
% 8.60/4.75 thf(fact_996_zero__neq__one,axiom,
% 8.60/4.75 zero_zero_int != one_one_int ).
% 8.60/4.75
% 8.60/4.75 thf(fact_997_bot__nat__0_Oextremum__strict,axiom,
% 8.60/4.75 ! [A: nat] :
% 8.60/4.75 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_998_gr0I,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ( ( N != zero_zero_nat )
% 8.60/4.75 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_999_not__gr0,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 8.60/4.75 = ( N = zero_zero_nat ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1000_not__less0,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1001_less__zeroE,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1002_gr__implies__not0,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.75 => ( N != zero_zero_nat ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1003_infinite__descent0,axiom,
% 8.60/4.75 ! [P2: nat > $o,N: nat] :
% 8.60/4.75 ( ( P2 @ zero_zero_nat )
% 8.60/4.75 => ( ! [N3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.60/4.75 => ( ~ ( P2 @ N3 )
% 8.60/4.75 => ? [M3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M3 @ N3 )
% 8.60/4.75 & ~ ( P2 @ M3 ) ) ) )
% 8.60/4.75 => ( P2 @ N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1004_mult_Ocomm__neutral,axiom,
% 8.60/4.75 ! [A: code_integer] :
% 8.60/4.75 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1005_mult_Ocomm__neutral,axiom,
% 8.60/4.75 ! [A: complex] :
% 8.60/4.75 ( ( times_times_complex @ A @ one_one_complex )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1006_mult_Ocomm__neutral,axiom,
% 8.60/4.75 ! [A: real] :
% 8.60/4.75 ( ( times_times_real @ A @ one_one_real )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1007_mult_Ocomm__neutral,axiom,
% 8.60/4.75 ! [A: rat] :
% 8.60/4.75 ( ( times_times_rat @ A @ one_one_rat )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1008_mult_Ocomm__neutral,axiom,
% 8.60/4.75 ! [A: nat] :
% 8.60/4.75 ( ( times_times_nat @ A @ one_one_nat )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1009_mult_Ocomm__neutral,axiom,
% 8.60/4.75 ! [A: int] :
% 8.60/4.75 ( ( times_times_int @ A @ one_one_int )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1010_comm__monoid__mult__class_Omult__1,axiom,
% 8.60/4.75 ! [A: code_integer] :
% 8.60/4.75 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1011_comm__monoid__mult__class_Omult__1,axiom,
% 8.60/4.75 ! [A: complex] :
% 8.60/4.75 ( ( times_times_complex @ one_one_complex @ A )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1012_comm__monoid__mult__class_Omult__1,axiom,
% 8.60/4.75 ! [A: real] :
% 8.60/4.75 ( ( times_times_real @ one_one_real @ A )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1013_comm__monoid__mult__class_Omult__1,axiom,
% 8.60/4.75 ! [A: rat] :
% 8.60/4.75 ( ( times_times_rat @ one_one_rat @ A )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1014_comm__monoid__mult__class_Omult__1,axiom,
% 8.60/4.75 ! [A: nat] :
% 8.60/4.75 ( ( times_times_nat @ one_one_nat @ A )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1015_comm__monoid__mult__class_Omult__1,axiom,
% 8.60/4.75 ! [A: int] :
% 8.60/4.75 ( ( times_times_int @ one_one_int @ A )
% 8.60/4.75 = A ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1016_less__mono__imp__le__mono,axiom,
% 8.60/4.75 ! [F2: nat > nat,I2: nat,J2: nat] :
% 8.60/4.75 ( ! [I3: nat,J3: nat] :
% 8.60/4.75 ( ( ord_less_nat @ I3 @ J3 )
% 8.60/4.75 => ( ord_less_nat @ ( F2 @ I3 ) @ ( F2 @ J3 ) ) )
% 8.60/4.75 => ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.75 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( F2 @ J2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1017_le__neq__implies__less,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.75 => ( ( M2 != N )
% 8.60/4.75 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1018_less__or__eq__imp__le,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ( ord_less_nat @ M2 @ N )
% 8.60/4.75 | ( M2 = N ) )
% 8.60/4.75 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1019_le__eq__less__or__eq,axiom,
% 8.60/4.75 ( ord_less_eq_nat
% 8.60/4.75 = ( ^ [M6: nat,N4: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M6 @ N4 )
% 8.60/4.75 | ( M6 = N4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1020_less__imp__le__nat,axiom,
% 8.60/4.75 ! [M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.75 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1021_nat__less__le,axiom,
% 8.60/4.75 ( ord_less_nat
% 8.60/4.75 = ( ^ [M6: nat,N4: nat] :
% 8.60/4.75 ( ( ord_less_eq_nat @ M6 @ N4 )
% 8.60/4.75 & ( M6 != N4 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1022_nat__mult__1,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ( ( times_times_nat @ one_one_nat @ N )
% 8.60/4.75 = N ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1023_nat__mult__1__right,axiom,
% 8.60/4.75 ! [N: nat] :
% 8.60/4.75 ( ( times_times_nat @ N @ one_one_nat )
% 8.60/4.75 = N ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1024_nat__mult__eq__cancel1,axiom,
% 8.60/4.75 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.75 => ( ( ( times_times_nat @ K2 @ M2 )
% 8.60/4.75 = ( times_times_nat @ K2 @ N ) )
% 8.60/4.75 = ( M2 = N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1025_nat__mult__less__cancel1,axiom,
% 8.60/4.75 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.75 => ( ( ord_less_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.60/4.75 = ( ord_less_nat @ M2 @ N ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1026_mult__less__cancel__right2,axiom,
% 8.60/4.75 ! [A: code_integer,C2: code_integer] :
% 8.60/4.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 8.60/4.75 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1027_mult__less__cancel__right2,axiom,
% 8.60/4.75 ! [A: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_real @ A @ one_one_real ) )
% 8.60/4.75 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1028_mult__less__cancel__right2,axiom,
% 8.60/4.75 ! [A: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_rat @ A @ one_one_rat ) )
% 8.60/4.75 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1029_mult__less__cancel__right2,axiom,
% 8.60/4.75 ! [A: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_int @ A @ one_one_int ) )
% 8.60/4.75 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1030_mult__less__cancel__right1,axiom,
% 8.60/4.75 ! [C2: code_integer,B: code_integer] :
% 8.60/4.75 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 8.60/4.75 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1031_mult__less__cancel__right1,axiom,
% 8.60/4.75 ! [C2: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_real @ one_one_real @ B ) )
% 8.60/4.75 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1032_mult__less__cancel__right1,axiom,
% 8.60/4.75 ! [C2: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_rat @ one_one_rat @ B ) )
% 8.60/4.75 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1033_mult__less__cancel__right1,axiom,
% 8.60/4.75 ! [C2: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_int @ one_one_int @ B ) )
% 8.60/4.75 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1034_mult__less__cancel__left2,axiom,
% 8.60/4.75 ! [C2: code_integer,A: code_integer] :
% 8.60/4.75 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 8.60/4.75 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1035_mult__less__cancel__left2,axiom,
% 8.60/4.75 ! [C2: real,A: real] :
% 8.60/4.75 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_real @ A @ one_one_real ) )
% 8.60/4.75 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1036_mult__less__cancel__left2,axiom,
% 8.60/4.75 ! [C2: rat,A: rat] :
% 8.60/4.75 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_rat @ A @ one_one_rat ) )
% 8.60/4.75 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1037_mult__less__cancel__left2,axiom,
% 8.60/4.75 ! [C2: int,A: int] :
% 8.60/4.75 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_int @ A @ one_one_int ) )
% 8.60/4.75 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1038_mult__less__cancel__left1,axiom,
% 8.60/4.75 ! [C2: code_integer,B: code_integer] :
% 8.60/4.75 ( ( ord_le6747313008572928689nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 8.60/4.75 & ( ( ord_le3102999989581377725nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1039_mult__less__cancel__left1,axiom,
% 8.60/4.75 ! [C2: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_real @ one_one_real @ B ) )
% 8.60/4.75 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1040_mult__less__cancel__left1,axiom,
% 8.60/4.75 ! [C2: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_rat @ one_one_rat @ B ) )
% 8.60/4.75 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1041_mult__less__cancel__left1,axiom,
% 8.60/4.75 ! [C2: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_int @ one_one_int @ B ) )
% 8.60/4.75 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1042_mult__le__cancel__right2,axiom,
% 8.60/4.75 ! [A: code_integer,C2: code_integer] :
% 8.60/4.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 8.60/4.75 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1043_mult__le__cancel__right2,axiom,
% 8.60/4.75 ! [A: real,C2: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_eq_real @ A @ one_one_real ) )
% 8.60/4.75 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1044_mult__le__cancel__right2,axiom,
% 8.60/4.75 ! [A: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 8.60/4.75 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1045_mult__le__cancel__right2,axiom,
% 8.60/4.75 ! [A: int,C2: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_eq_int @ A @ one_one_int ) )
% 8.60/4.75 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1046_mult__le__cancel__right1,axiom,
% 8.60/4.75 ! [C2: code_integer,B: code_integer] :
% 8.60/4.75 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 8.60/4.75 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1047_mult__le__cancel__right1,axiom,
% 8.60/4.75 ! [C2: real,B: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_eq_real @ one_one_real @ B ) )
% 8.60/4.75 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1048_mult__le__cancel__right1,axiom,
% 8.60/4.75 ! [C2: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 8.60/4.75 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1049_mult__le__cancel__right1,axiom,
% 8.60/4.75 ! [C2: int,B: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_eq_int @ one_one_int @ B ) )
% 8.60/4.75 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1050_mult__le__cancel__left2,axiom,
% 8.60/4.75 ! [C2: code_integer,A: code_integer] :
% 8.60/4.75 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 8.60/4.75 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1051_mult__le__cancel__left2,axiom,
% 8.60/4.75 ! [C2: real,A: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_eq_real @ A @ one_one_real ) )
% 8.60/4.75 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1052_mult__le__cancel__left2,axiom,
% 8.60/4.75 ! [C2: rat,A: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 8.60/4.75 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1053_mult__le__cancel__left2,axiom,
% 8.60/4.75 ! [C2: int,A: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ C2 )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_eq_int @ A @ one_one_int ) )
% 8.60/4.75 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1054_mult__le__cancel__left1,axiom,
% 8.60/4.75 ! [C2: code_integer,B: code_integer] :
% 8.60/4.75 ( ( ord_le3102999989581377725nteger @ C2 @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C2 )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 8.60/4.75 & ( ( ord_le6747313008572928689nteger @ C2 @ zero_z3403309356797280102nteger )
% 8.60/4.75 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1055_mult__le__cancel__left1,axiom,
% 8.60/4.75 ! [C2: real,B: real] :
% 8.60/4.75 ( ( ord_less_eq_real @ C2 @ ( times_times_real @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_eq_real @ one_one_real @ B ) )
% 8.60/4.75 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1056_mult__le__cancel__left1,axiom,
% 8.60/4.75 ! [C2: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_eq_rat @ C2 @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 8.60/4.75 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1057_mult__le__cancel__left1,axiom,
% 8.60/4.75 ! [C2: int,B: int] :
% 8.60/4.75 ( ( ord_less_eq_int @ C2 @ ( times_times_int @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_eq_int @ one_one_int @ B ) )
% 8.60/4.75 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1058_mult__neg__neg,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ zero_zero_real )
% 8.60/4.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1059_mult__neg__neg,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.60/4.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1060_mult__neg__neg,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ A @ zero_zero_int )
% 8.60/4.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1061_not__square__less__zero,axiom,
% 8.60/4.75 ! [A: real] :
% 8.60/4.75 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1062_not__square__less__zero,axiom,
% 8.60/4.75 ! [A: rat] :
% 8.60/4.75 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1063_not__square__less__zero,axiom,
% 8.60/4.75 ! [A: int] :
% 8.60/4.75 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1064_mult__less__0__iff,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.75 & ( ord_less_real @ B @ zero_zero_real ) )
% 8.60/4.75 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.60/4.75 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1065_mult__less__0__iff,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.75 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 8.60/4.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.60/4.75 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1066_mult__less__0__iff,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.75 & ( ord_less_int @ B @ zero_zero_int ) )
% 8.60/4.75 | ( ( ord_less_int @ A @ zero_zero_int )
% 8.60/4.75 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1067_mult__neg__pos,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ zero_zero_real )
% 8.60/4.75 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1068_mult__neg__pos,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.60/4.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1069_mult__neg__pos,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.60/4.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.60/4.75 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1070_mult__neg__pos,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ A @ zero_zero_int )
% 8.60/4.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1071_mult__pos__neg,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1072_mult__pos__neg,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1073_mult__pos__neg,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.60/4.75 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1074_mult__pos__neg,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1075_mult__pos__pos,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.75 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.60/4.75 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1076_mult__pos__pos,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.75 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.60/4.75 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1077_mult__pos__pos,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.75 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.60/4.75 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1078_mult__pos__pos,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.75 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.75 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1079_mult__pos__neg2,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.75 => ( ( ord_less_real @ B @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1080_mult__pos__neg2,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.75 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1081_mult__pos__neg2,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.75 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.60/4.75 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1082_mult__pos__neg2,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.75 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1083_zero__less__mult__iff,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.75 & ( ord_less_real @ zero_zero_real @ B ) )
% 8.60/4.75 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.60/4.75 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1084_zero__less__mult__iff,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.75 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 8.60/4.75 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.60/4.75 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1085_zero__less__mult__iff,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.75 & ( ord_less_int @ zero_zero_int @ B ) )
% 8.60/4.75 | ( ( ord_less_int @ A @ zero_zero_int )
% 8.60/4.75 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1086_zero__less__mult__pos,axiom,
% 8.60/4.75 ! [A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.60/4.75 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.75 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1087_zero__less__mult__pos,axiom,
% 8.60/4.75 ! [A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.60/4.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.75 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1088_zero__less__mult__pos,axiom,
% 8.60/4.75 ! [A: nat,B: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 8.60/4.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.75 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1089_zero__less__mult__pos,axiom,
% 8.60/4.75 ! [A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 8.60/4.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.75 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1090_zero__less__mult__pos2,axiom,
% 8.60/4.75 ! [B: real,A: real] :
% 8.60/4.75 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 8.60/4.75 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.75 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1091_zero__less__mult__pos2,axiom,
% 8.60/4.75 ! [B: rat,A: rat] :
% 8.60/4.75 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 8.60/4.75 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.75 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1092_zero__less__mult__pos2,axiom,
% 8.60/4.75 ! [B: nat,A: nat] :
% 8.60/4.75 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 8.60/4.75 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.75 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1093_zero__less__mult__pos2,axiom,
% 8.60/4.75 ! [B: int,A: int] :
% 8.60/4.75 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 8.60/4.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.75 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1094_mult__less__cancel__left__neg,axiom,
% 8.60/4.75 ! [C2: real,A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.75 = ( ord_less_real @ B @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1095_mult__less__cancel__left__neg,axiom,
% 8.60/4.75 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.75 = ( ord_less_rat @ B @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1096_mult__less__cancel__left__neg,axiom,
% 8.60/4.75 ! [C2: int,A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.75 = ( ord_less_int @ B @ A ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1097_mult__less__cancel__left__pos,axiom,
% 8.60/4.75 ! [C2: real,A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.75 = ( ord_less_real @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1098_mult__less__cancel__left__pos,axiom,
% 8.60/4.75 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.75 = ( ord_less_rat @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1099_mult__less__cancel__left__pos,axiom,
% 8.60/4.75 ! [C2: int,A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.75 = ( ord_less_int @ A @ B ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1100_mult__strict__left__mono__neg,axiom,
% 8.60/4.75 ! [B: real,A: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ B @ A )
% 8.60/4.75 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1101_mult__strict__left__mono__neg,axiom,
% 8.60/4.75 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ B @ A )
% 8.60/4.75 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1102_mult__strict__left__mono__neg,axiom,
% 8.60/4.75 ! [B: int,A: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ B @ A )
% 8.60/4.75 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1103_mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: real,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1104_mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1105_mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.60/4.75 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1106_mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: int,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1107_mult__less__cancel__left__disj,axiom,
% 8.60/4.75 ! [C2: real,A: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 & ( ord_less_real @ A @ B ) )
% 8.60/4.75 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 & ( ord_less_real @ B @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1108_mult__less__cancel__left__disj,axiom,
% 8.60/4.75 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 & ( ord_less_rat @ A @ B ) )
% 8.60/4.75 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1109_mult__less__cancel__left__disj,axiom,
% 8.60/4.75 ! [C2: int,A: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 & ( ord_less_int @ A @ B ) )
% 8.60/4.75 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 & ( ord_less_int @ B @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1110_mult__strict__right__mono__neg,axiom,
% 8.60/4.75 ! [B: real,A: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ B @ A )
% 8.60/4.75 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1111_mult__strict__right__mono__neg,axiom,
% 8.60/4.75 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ B @ A )
% 8.60/4.75 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1112_mult__strict__right__mono__neg,axiom,
% 8.60/4.75 ! [B: int,A: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ B @ A )
% 8.60/4.75 => ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1113_mult__strict__right__mono,axiom,
% 8.60/4.75 ! [A: real,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1114_mult__strict__right__mono,axiom,
% 8.60/4.75 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1115_mult__strict__right__mono,axiom,
% 8.60/4.75 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.60/4.75 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1116_mult__strict__right__mono,axiom,
% 8.60/4.75 ! [A: int,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1117_mult__less__cancel__right__disj,axiom,
% 8.60/4.75 ! [A: real,C2: real,B: real] :
% 8.60/4.75 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 & ( ord_less_real @ A @ B ) )
% 8.60/4.75 | ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.75 & ( ord_less_real @ B @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1118_mult__less__cancel__right__disj,axiom,
% 8.60/4.75 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.75 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 & ( ord_less_rat @ A @ B ) )
% 8.60/4.75 | ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.75 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1119_mult__less__cancel__right__disj,axiom,
% 8.60/4.75 ! [A: int,C2: int,B: int] :
% 8.60/4.75 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.60/4.75 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 & ( ord_less_int @ A @ B ) )
% 8.60/4.75 | ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.75 & ( ord_less_int @ B @ A ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1120_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: real,B: real,C2: real] :
% 8.60/4.75 ( ( ord_less_real @ A @ B )
% 8.60/4.75 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.75 => ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1121_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.75 ( ( ord_less_rat @ A @ B )
% 8.60/4.75 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.75 => ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1122_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.75 ( ( ord_less_nat @ A @ B )
% 8.60/4.75 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.60/4.75 => ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1123_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 8.60/4.75 ! [A: int,B: int,C2: int] :
% 8.60/4.75 ( ( ord_less_int @ A @ B )
% 8.60/4.75 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.75 => ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ) ).
% 8.60/4.75
% 8.60/4.75 thf(fact_1124_not__one__le__zero,axiom,
% 8.60/4.75 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1125_not__one__le__zero,axiom,
% 8.60/4.76 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1126_not__one__le__zero,axiom,
% 8.60/4.76 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1127_not__one__le__zero,axiom,
% 8.60/4.76 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1128_not__one__le__zero,axiom,
% 8.60/4.76 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1129_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1130_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1131_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1132_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1133_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1134_zero__less__one__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1135_zero__less__one__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1136_zero__less__one__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1137_zero__less__one__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1138_zero__less__one__class_Ozero__le__one,axiom,
% 8.60/4.76 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1139_nat__mult__le__cancel1,axiom,
% 8.60/4.76 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.76 => ( ( ord_less_eq_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.60/4.76 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1140_less__Suc__eq__0__disj,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 8.60/4.76 = ( ( M2 = zero_zero_nat )
% 8.60/4.76 | ? [J: nat] :
% 8.60/4.76 ( ( M2
% 8.60/4.76 = ( suc @ J ) )
% 8.60/4.76 & ( ord_less_nat @ J @ N ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1141_gr0__implies__Suc,axiom,
% 8.60/4.76 ! [N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.76 => ? [M: nat] :
% 8.60/4.76 ( N
% 8.60/4.76 = ( suc @ M ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1142_All__less__Suc2,axiom,
% 8.60/4.76 ! [N: nat,P2: nat > $o] :
% 8.60/4.76 ( ( ! [I: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 8.60/4.76 => ( P2 @ I ) ) )
% 8.60/4.76 = ( ( P2 @ zero_zero_nat )
% 8.60/4.76 & ! [I: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I @ N )
% 8.60/4.76 => ( P2 @ ( suc @ I ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1143_gr0__conv__Suc,axiom,
% 8.60/4.76 ! [N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.76 = ( ? [M6: nat] :
% 8.60/4.76 ( N
% 8.60/4.76 = ( suc @ M6 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1144_Ex__less__Suc2,axiom,
% 8.60/4.76 ! [N: nat,P2: nat > $o] :
% 8.60/4.76 ( ( ? [I: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I @ ( suc @ N ) )
% 8.60/4.76 & ( P2 @ I ) ) )
% 8.60/4.76 = ( ( P2 @ zero_zero_nat )
% 8.60/4.76 | ? [I: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I @ N )
% 8.60/4.76 & ( P2 @ ( suc @ I ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1145_le__imp__less__Suc,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.76 => ( ord_less_nat @ M2 @ ( suc @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1146_less__eq__Suc__le,axiom,
% 8.60/4.76 ( ord_less_nat
% 8.60/4.76 = ( ^ [N4: nat] : ( ord_less_eq_nat @ ( suc @ N4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1147_less__Suc__eq__le,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ M2 @ ( suc @ N ) )
% 8.60/4.76 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1148_le__less__Suc__eq,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.76 => ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 8.60/4.76 = ( N = M2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1149_Suc__le__lessD,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 8.60/4.76 => ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1150_inc__induct,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,P2: nat > $o] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 => ( ( P2 @ J2 )
% 8.60/4.76 => ( ! [N3: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ N3 )
% 8.60/4.76 => ( ( ord_less_nat @ N3 @ J2 )
% 8.60/4.76 => ( ( P2 @ ( suc @ N3 ) )
% 8.60/4.76 => ( P2 @ N3 ) ) ) )
% 8.60/4.76 => ( P2 @ I2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1151_dec__induct,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,P2: nat > $o] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 => ( ( P2 @ I2 )
% 8.60/4.76 => ( ! [N3: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ N3 )
% 8.60/4.76 => ( ( ord_less_nat @ N3 @ J2 )
% 8.60/4.76 => ( ( P2 @ N3 )
% 8.60/4.76 => ( P2 @ ( suc @ N3 ) ) ) ) )
% 8.60/4.76 => ( P2 @ J2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1152_Suc__le__eq,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 8.60/4.76 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1153_Suc__leI,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.76 => ( ord_less_eq_nat @ ( suc @ M2 ) @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1154_ex__least__nat__le,axiom,
% 8.60/4.76 ! [P2: nat > $o,N: nat] :
% 8.60/4.76 ( ( P2 @ N )
% 8.60/4.76 => ( ~ ( P2 @ zero_zero_nat )
% 8.60/4.76 => ? [K: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ K @ N )
% 8.60/4.76 & ! [I4: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I4 @ K )
% 8.60/4.76 => ~ ( P2 @ I4 ) )
% 8.60/4.76 & ( P2 @ K ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1155_Suc__mult__less__cancel1,axiom,
% 8.60/4.76 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K2 ) @ M2 ) @ ( times_times_nat @ ( suc @ K2 ) @ N ) )
% 8.60/4.76 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1156_mult__less__mono1,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.76 => ( ord_less_nat @ ( times_times_nat @ I2 @ K2 ) @ ( times_times_nat @ J2 @ K2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1157_mult__less__mono2,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.60/4.76 => ( ord_less_nat @ ( times_times_nat @ K2 @ I2 ) @ ( times_times_nat @ K2 @ J2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1158_One__nat__def,axiom,
% 8.60/4.76 ( one_one_nat
% 8.60/4.76 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1159_mult__eq__self__implies__10,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( M2
% 8.60/4.76 = ( times_times_nat @ M2 @ N ) )
% 8.60/4.76 => ( ( N = one_one_nat )
% 8.60/4.76 | ( M2 = zero_zero_nat ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1160_mult__less__le__imp__less,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_real @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.76 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1161_mult__less__le__imp__less,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_rat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.76 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1162_mult__less__le__imp__less,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_nat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.76 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1163_mult__less__le__imp__less,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_int @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.76 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1164_mult__le__less__imp__less,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.76 => ( ( ord_less_real @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1165_mult__le__less__imp__less,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.76 => ( ( ord_less_rat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1166_mult__le__less__imp__less,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.76 => ( ( ord_less_nat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1167_mult__le__less__imp__less,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.76 => ( ( ord_less_int @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1168_mult__right__le__imp__le,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1169_mult__right__le__imp__le,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1170_mult__right__le__imp__le,axiom,
% 8.60/4.76 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1171_mult__right__le__imp__le,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1172_mult__left__le__imp__le,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1173_mult__left__le__imp__le,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1174_mult__left__le__imp__le,axiom,
% 8.60/4.76 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1175_mult__left__le__imp__le,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1176_mult__le__cancel__left__pos,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1177_mult__le__cancel__left__pos,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1178_mult__le__cancel__left__pos,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1179_mult__le__cancel__left__neg,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.76 => ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1180_mult__le__cancel__left__neg,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.76 => ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1181_mult__le__cancel__left__neg,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.76 => ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1182_mult__less__cancel__right,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 8.60/4.76 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.76 => ( ord_less_real @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1183_mult__less__cancel__right,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 8.60/4.76 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.76 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1184_mult__less__cancel__right,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.60/4.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.76 => ( ord_less_int @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1185_mult__strict__mono_H,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ B )
% 8.60/4.76 => ( ( ord_less_real @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1186_mult__strict__mono_H,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ B )
% 8.60/4.76 => ( ( ord_less_rat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1187_mult__strict__mono_H,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ B )
% 8.60/4.76 => ( ( ord_less_nat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1188_mult__strict__mono_H,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ B )
% 8.60/4.76 => ( ( ord_less_int @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1189_mult__right__less__imp__less,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1190_mult__right__less__imp__less,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1191_mult__right__less__imp__less,axiom,
% 8.60/4.76 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_nat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1192_mult__right__less__imp__less,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1193_mult__less__cancel__left,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.76 = ( ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.76 => ( ord_less_real @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1194_mult__less__cancel__left,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.76 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.76 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1195_mult__less__cancel__left,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.76 => ( ord_less_int @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1196_mult__strict__mono,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ B )
% 8.60/4.76 => ( ( ord_less_real @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1197_mult__strict__mono,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ B )
% 8.60/4.76 => ( ( ord_less_rat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1198_mult__strict__mono,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ B )
% 8.60/4.76 => ( ( ord_less_nat @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1199_mult__strict__mono,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ B )
% 8.60/4.76 => ( ( ord_less_int @ C2 @ D )
% 8.60/4.76 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1200_mult__left__less__imp__less,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_real @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1201_mult__left__less__imp__less,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_rat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1202_mult__left__less__imp__less,axiom,
% 8.60/4.76 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.76 => ( ord_less_nat @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1203_mult__left__less__imp__less,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_int @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1204_mult__le__cancel__right,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 8.60/4.76 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_eq_real @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.76 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1205_mult__le__cancel__right,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 8.60/4.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_eq_rat @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.76 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1206_mult__le__cancel__right,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.60/4.76 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_eq_int @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.76 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1207_mult__le__cancel__left,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.60/4.76 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.60/4.76 => ( ord_less_eq_real @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.60/4.76 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1208_mult__le__cancel__left,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.60/4.76 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.60/4.76 => ( ord_less_eq_rat @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.60/4.76 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1209_mult__le__cancel__left,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.60/4.76 = ( ( ( ord_less_int @ zero_zero_int @ C2 )
% 8.60/4.76 => ( ord_less_eq_int @ A @ B ) )
% 8.60/4.76 & ( ( ord_less_int @ C2 @ zero_zero_int )
% 8.60/4.76 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1210_VEBT__internal_Onaive__member_Ocases,axiom,
% 8.60/4.76 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.76 ( ! [A3: $o,B3: $o,X3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 8.60/4.76 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Ux ) )
% 8.60/4.76 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ X3 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1211_mult__left__le,axiom,
% 8.60/4.76 ! [C2: code_integer,A: code_integer] :
% 8.60/4.76 ( ( ord_le3102999989581377725nteger @ C2 @ one_one_Code_integer )
% 8.60/4.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.60/4.76 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1212_mult__left__le,axiom,
% 8.60/4.76 ! [C2: real,A: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ C2 @ one_one_real )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.76 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1213_mult__left__le,axiom,
% 8.60/4.76 ! [C2: rat,A: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ C2 @ one_one_rat )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.76 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1214_mult__left__le,axiom,
% 8.60/4.76 ! [C2: nat,A: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ C2 @ one_one_nat )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.76 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C2 ) @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1215_mult__left__le,axiom,
% 8.60/4.76 ! [C2: int,A: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ C2 @ one_one_int )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.76 => ( ord_less_eq_int @ ( times_times_int @ A @ C2 ) @ A ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1216_mult__le__one,axiom,
% 8.60/4.76 ! [A: code_integer,B: code_integer] :
% 8.60/4.76 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.60/4.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.60/4.76 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 8.60/4.76 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1217_mult__le__one,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ one_one_real )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.76 => ( ( ord_less_eq_real @ B @ one_one_real )
% 8.60/4.76 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1218_mult__le__one,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.76 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 8.60/4.76 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1219_mult__le__one,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.60/4.76 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.76 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 8.60/4.76 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1220_mult__le__one,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ one_one_int )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.76 => ( ( ord_less_eq_int @ B @ one_one_int )
% 8.60/4.76 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1221_mult__right__le__one__le,axiom,
% 8.60/4.76 ! [X: code_integer,Y: code_integer] :
% 8.60/4.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 8.60/4.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.60/4.76 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 8.60/4.76 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1222_mult__right__le__one__le,axiom,
% 8.60/4.76 ! [X: real,Y: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.60/4.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.60/4.76 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1223_mult__right__le__one__le,axiom,
% 8.60/4.76 ! [X: rat,Y: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.60/4.76 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 8.60/4.76 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1224_mult__right__le__one__le,axiom,
% 8.60/4.76 ! [X: int,Y: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.60/4.76 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 8.60/4.76 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1225_mult__left__le__one__le,axiom,
% 8.60/4.76 ! [X: code_integer,Y: code_integer] :
% 8.60/4.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 8.60/4.76 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.60/4.76 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 8.60/4.76 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1226_mult__left__le__one__le,axiom,
% 8.60/4.76 ! [X: real,Y: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.60/4.76 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.60/4.76 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 8.60/4.76 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1227_mult__left__le__one__le,axiom,
% 8.60/4.76 ! [X: rat,Y: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.60/4.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.60/4.76 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 8.60/4.76 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1228_mult__left__le__one__le,axiom,
% 8.60/4.76 ! [X: int,Y: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.60/4.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.60/4.76 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 8.60/4.76 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1229_ex__least__nat__less,axiom,
% 8.60/4.76 ! [P2: nat > $o,N: nat] :
% 8.60/4.76 ( ( P2 @ N )
% 8.60/4.76 => ( ~ ( P2 @ zero_zero_nat )
% 8.60/4.76 => ? [K: nat] :
% 8.60/4.76 ( ( ord_less_nat @ K @ N )
% 8.60/4.76 & ! [I4: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I4 @ K )
% 8.60/4.76 => ~ ( P2 @ I4 ) )
% 8.60/4.76 & ( P2 @ ( suc @ K ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1230_n__less__n__mult__m,axiom,
% 8.60/4.76 ! [N: nat,M2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.76 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 8.60/4.76 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1231_n__less__m__mult__n,axiom,
% 8.60/4.76 ! [N: nat,M2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.76 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 8.60/4.76 => ( ord_less_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1232_one__less__mult,axiom,
% 8.60/4.76 ! [N: nat,M2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.60/4.76 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 8.60/4.76 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M2 @ N ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1233_greater__shift,axiom,
% 8.60/4.76 ( ord_less_nat
% 8.60/4.76 = ( ^ [Y4: nat,X4: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1234_less__shift,axiom,
% 8.60/4.76 ( ord_less_nat
% 8.60/4.76 = ( ^ [X4: nat,Y4: nat] : ( vEBT_VEBT_less @ ( some_nat @ X4 ) @ ( some_nat @ Y4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1235_buildup__gives__valid,axiom,
% 8.60/4.76 ! [N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.76 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1236_field__le__mult__one__interval,axiom,
% 8.60/4.76 ! [X: real,Y: real] :
% 8.60/4.76 ( ! [Z: real] :
% 8.60/4.76 ( ( ord_less_real @ zero_zero_real @ Z )
% 8.60/4.76 => ( ( ord_less_real @ Z @ one_one_real )
% 8.60/4.76 => ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ Y ) ) )
% 8.60/4.76 => ( ord_less_eq_real @ X @ Y ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1237_field__le__mult__one__interval,axiom,
% 8.60/4.76 ! [X: rat,Y: rat] :
% 8.60/4.76 ( ! [Z: rat] :
% 8.60/4.76 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 8.60/4.76 => ( ( ord_less_rat @ Z @ one_one_rat )
% 8.60/4.76 => ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ Y ) ) )
% 8.60/4.76 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1238_case4_I2_J,axiom,
% 8.60/4.76 ! [S2: vEBT_VEBT] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ S2 @ m )
% 8.60/4.76 => ( ( ( vEBT_VEBT_set_vebt @ summary2 )
% 8.60/4.76 = ( vEBT_VEBT_set_vebt @ S2 ) )
% 8.60/4.76 => ( S2 = summary2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1239_maxt__corr,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_maxt @ T )
% 8.60/4.76 = ( some_nat @ X ) )
% 8.60/4.76 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1240_maxt__sound,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 8.60/4.76 => ( ( vEBT_vebt_maxt @ T )
% 8.60/4.76 = ( some_nat @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1241_mint__corr,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_mint @ T )
% 8.60/4.76 = ( some_nat @ X ) )
% 8.60/4.76 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1242_mint__sound,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 8.60/4.76 => ( ( vEBT_vebt_mint @ T )
% 8.60/4.76 = ( some_nat @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1243_mult__le__cancel__iff2,axiom,
% 8.60/4.76 ! [Z3: real,X: real,Y: real] :
% 8.60/4.76 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 8.60/4.76 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ X ) @ ( times_times_real @ Z3 @ Y ) )
% 8.60/4.76 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1244_mult__le__cancel__iff2,axiom,
% 8.60/4.76 ! [Z3: rat,X: rat,Y: rat] :
% 8.60/4.76 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 8.60/4.76 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ X ) @ ( times_times_rat @ Z3 @ Y ) )
% 8.60/4.76 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1245_mult__le__cancel__iff2,axiom,
% 8.60/4.76 ! [Z3: int,X: int,Y: int] :
% 8.60/4.76 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 8.60/4.76 => ( ( ord_less_eq_int @ ( times_times_int @ Z3 @ X ) @ ( times_times_int @ Z3 @ Y ) )
% 8.60/4.76 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1246_mult__le__cancel__iff1,axiom,
% 8.60/4.76 ! [Z3: real,X: real,Y: real] :
% 8.60/4.76 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 8.60/4.76 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 8.60/4.76 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1247_mult__le__cancel__iff1,axiom,
% 8.60/4.76 ! [Z3: rat,X: rat,Y: rat] :
% 8.60/4.76 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 8.60/4.76 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 8.60/4.76 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1248_mult__le__cancel__iff1,axiom,
% 8.60/4.76 ! [Z3: int,X: int,Y: int] :
% 8.60/4.76 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 8.60/4.76 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 8.60/4.76 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1249_ac,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,H: nat,K2: vEBT_VEBT] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ H )
% 8.60/4.76 => ( ( vEBT_invar_vebt @ K2 @ H )
% 8.60/4.76 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 8.60/4.76 = ( vEBT_VEBT_set_vebt @ K2 ) )
% 8.60/4.76 => ( ( vEBT_vebt_mint @ T )
% 8.60/4.76 = ( vEBT_vebt_mint @ K2 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1250_ad,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,H: nat,K2: vEBT_VEBT] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ H )
% 8.60/4.76 => ( ( vEBT_invar_vebt @ K2 @ H )
% 8.60/4.76 => ( ( ( vEBT_VEBT_set_vebt @ T )
% 8.60/4.76 = ( vEBT_VEBT_set_vebt @ K2 ) )
% 8.60/4.76 => ( ( vEBT_vebt_maxt @ T )
% 8.60/4.76 = ( vEBT_vebt_maxt @ K2 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1251_case4_I5_J,axiom,
% 8.60/4.76 m = na ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1252_vebt__buildup_Osimps_I1_J,axiom,
% 8.60/4.76 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 8.60/4.76 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1253_vebt__buildup_Osimps_I2_J,axiom,
% 8.60/4.76 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 8.60/4.76 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1254_mult__less__iff1,axiom,
% 8.60/4.76 ! [Z3: real,X: real,Y: real] :
% 8.60/4.76 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 8.60/4.76 => ( ( ord_less_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ Z3 ) )
% 8.60/4.76 = ( ord_less_real @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1255_mult__less__iff1,axiom,
% 8.60/4.76 ! [Z3: rat,X: rat,Y: rat] :
% 8.60/4.76 ( ( ord_less_rat @ zero_zero_rat @ Z3 )
% 8.60/4.76 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ Z3 ) )
% 8.60/4.76 = ( ord_less_rat @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1256_mult__less__iff1,axiom,
% 8.60/4.76 ! [Z3: int,X: int,Y: int] :
% 8.60/4.76 ( ( ord_less_int @ zero_zero_int @ Z3 )
% 8.60/4.76 => ( ( ord_less_int @ ( times_times_int @ X @ Z3 ) @ ( times_times_int @ Y @ Z3 ) )
% 8.60/4.76 = ( ord_less_int @ X @ Y ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1257_vebt__maxt_Osimps_I3_J,axiom,
% 8.60/4.76 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 8.60/4.76 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 8.60/4.76 = ( some_nat @ Ma ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1258_vebt__mint_Osimps_I3_J,axiom,
% 8.60/4.76 ! [Mi: nat,Ma: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 8.60/4.76 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux2 @ Uy2 @ Uz ) )
% 8.60/4.76 = ( some_nat @ Mi ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1259_maxt__corr__help,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_maxt @ T )
% 8.60/4.76 = ( some_nat @ Maxi ) )
% 8.60/4.76 => ( ( vEBT_vebt_member @ T @ X )
% 8.60/4.76 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1260_mint__corr__help,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_mint @ T )
% 8.60/4.76 = ( some_nat @ Mini ) )
% 8.60/4.76 => ( ( vEBT_vebt_member @ T @ X )
% 8.60/4.76 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1261_buildup__nothing__in__leaf,axiom,
% 8.60/4.76 ! [N: nat,X: nat] :
% 8.60/4.76 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1262_maxt__member,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_maxt @ T )
% 8.60/4.76 = ( some_nat @ Maxi ) )
% 8.60/4.76 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1263_mint__member,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_mint @ T )
% 8.60/4.76 = ( some_nat @ Maxi ) )
% 8.60/4.76 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1264_aa,axiom,
% 8.60/4.76 ord_less_eq_set_nat @ ( insert_nat @ mi @ ( insert_nat @ ma @ bot_bot_set_nat ) ) @ ( vEBT_VEBT_set_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList2 @ summary2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1265_VEBT__internal_Oinsert_H_Ocases,axiom,
% 8.60/4.76 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.76 ( ! [A3: $o,B3: $o,X3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 8.60/4.76 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ X3 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1266_member__correct,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( vEBT_vebt_member @ T @ X )
% 8.60/4.76 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1267_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 8.60/4.76 ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 8.60/4.76 ( ( vEBT_V1502963449132264192at_nat @ F2 @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ ( F2 @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1268_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 8.60/4.76 ! [F2: num > num > num,A: num,B: num] :
% 8.60/4.76 ( ( vEBT_V819420779217536731ft_num @ F2 @ ( some_num @ A ) @ ( some_num @ B ) )
% 8.60/4.76 = ( some_num @ ( F2 @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1269_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 8.60/4.76 ! [F2: nat > nat > nat,A: nat,B: nat] :
% 8.60/4.76 ( ( vEBT_V4262088993061758097ft_nat @ F2 @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 8.60/4.76 = ( some_nat @ ( F2 @ A @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1270_buildup__gives__empty,axiom,
% 8.60/4.76 ! [N: nat] :
% 8.60/4.76 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 8.60/4.76 = bot_bot_set_nat ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1271_pred__member,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 8.60/4.76 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 8.60/4.76 = ( ( vEBT_vebt_member @ T @ Y )
% 8.60/4.76 & ( ord_less_nat @ Y @ X )
% 8.60/4.76 & ! [Z4: nat] :
% 8.60/4.76 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 8.60/4.76 & ( ord_less_nat @ Z4 @ X ) )
% 8.60/4.76 => ( ord_less_eq_nat @ Z4 @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1272_succ__member,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 8.60/4.76 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 8.60/4.76 = ( ( vEBT_vebt_member @ T @ Y )
% 8.60/4.76 & ( ord_less_nat @ X @ Y )
% 8.60/4.76 & ! [Z4: nat] :
% 8.60/4.76 ( ( ( vEBT_vebt_member @ T @ Z4 )
% 8.60/4.76 & ( ord_less_nat @ X @ Z4 ) )
% 8.60/4.76 => ( ord_less_eq_nat @ Y @ Z4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1273_case4_I6_J,axiom,
% 8.60/4.76 ( deg
% 8.60/4.76 = ( plus_plus_nat @ na @ m ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1274_case4_I1_J,axiom,
% 8.60/4.76 ! [X5: vEBT_VEBT] :
% 8.60/4.76 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 8.60/4.76 => ( ( vEBT_invar_vebt @ X5 @ na )
% 8.60/4.76 & ! [Xa: vEBT_VEBT] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ Xa @ na )
% 8.60/4.76 => ( ( ( vEBT_VEBT_set_vebt @ X5 )
% 8.60/4.76 = ( vEBT_VEBT_set_vebt @ Xa ) )
% 8.60/4.76 => ( Xa = X5 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1275_bot_Oextremum__uniqueI,axiom,
% 8.60/4.76 ! [A: set_int] :
% 8.60/4.76 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 8.60/4.76 => ( A = bot_bot_set_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1276_bot_Oextremum__uniqueI,axiom,
% 8.60/4.76 ! [A: set_real] :
% 8.60/4.76 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 8.60/4.76 => ( A = bot_bot_set_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1277_bot_Oextremum__uniqueI,axiom,
% 8.60/4.76 ! [A: set_nat] :
% 8.60/4.76 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 8.60/4.76 => ( A = bot_bot_set_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1278_bot_Oextremum__uniqueI,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 8.60/4.76 => ( A = bot_bot_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1279_bot_Oextremum__unique,axiom,
% 8.60/4.76 ! [A: set_int] :
% 8.60/4.76 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 8.60/4.76 = ( A = bot_bot_set_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1280_bot_Oextremum__unique,axiom,
% 8.60/4.76 ! [A: set_real] :
% 8.60/4.76 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 8.60/4.76 = ( A = bot_bot_set_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1281_bot_Oextremum__unique,axiom,
% 8.60/4.76 ! [A: set_nat] :
% 8.60/4.76 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 8.60/4.76 = ( A = bot_bot_set_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1282_bot_Oextremum__unique,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 8.60/4.76 = ( A = bot_bot_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1283_bot_Oextremum,axiom,
% 8.60/4.76 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1284_bot_Oextremum,axiom,
% 8.60/4.76 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1285_bot_Oextremum,axiom,
% 8.60/4.76 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1286_bot_Oextremum,axiom,
% 8.60/4.76 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1287_bot_Oextremum__strict,axiom,
% 8.60/4.76 ! [A: set_nat] :
% 8.60/4.76 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1288_bot_Oextremum__strict,axiom,
% 8.60/4.76 ! [A: set_int] :
% 8.60/4.76 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1289_bot_Oextremum__strict,axiom,
% 8.60/4.76 ! [A: set_real] :
% 8.60/4.76 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1290_bot_Oextremum__strict,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1291_bot_Onot__eq__extremum,axiom,
% 8.60/4.76 ! [A: set_nat] :
% 8.60/4.76 ( ( A != bot_bot_set_nat )
% 8.60/4.76 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1292_bot_Onot__eq__extremum,axiom,
% 8.60/4.76 ! [A: set_int] :
% 8.60/4.76 ( ( A != bot_bot_set_int )
% 8.60/4.76 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1293_bot_Onot__eq__extremum,axiom,
% 8.60/4.76 ! [A: set_real] :
% 8.60/4.76 ( ( A != bot_bot_set_real )
% 8.60/4.76 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1294_bot_Onot__eq__extremum,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ( ( A != bot_bot_nat )
% 8.60/4.76 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1295_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 8.60/4.76 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 8.60/4.76 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw2 ) @ Ux2 ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1296_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 8.60/4.76 ! [A: $o,B: $o,X: nat] :
% 8.60/4.76 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.60/4.76 = ( ( ( X = zero_zero_nat )
% 8.60/4.76 => A )
% 8.60/4.76 & ( ( X != zero_zero_nat )
% 8.60/4.76 => ( ( ( X = one_one_nat )
% 8.60/4.76 => B )
% 8.60/4.76 & ( X = one_one_nat ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1297_member__valid__both__member__options,axiom,
% 8.60/4.76 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ Tree @ N )
% 8.60/4.76 => ( ( vEBT_vebt_member @ Tree @ X )
% 8.60/4.76 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 8.60/4.76 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1298_vebt__member_Osimps_I4_J,axiom,
% 8.60/4.76 ! [V2: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 8.60/4.76 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1299_vebt__member_Osimps_I1_J,axiom,
% 8.60/4.76 ! [A: $o,B: $o,X: nat] :
% 8.60/4.76 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.60/4.76 = ( ( ( X = zero_zero_nat )
% 8.60/4.76 => A )
% 8.60/4.76 & ( ( X != zero_zero_nat )
% 8.60/4.76 => ( ( ( X = one_one_nat )
% 8.60/4.76 => B )
% 8.60/4.76 & ( X = one_one_nat ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1300_vebt__member_Osimps_I3_J,axiom,
% 8.60/4.76 ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 8.60/4.76 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz ) @ X ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1301_maxt__corr__help__empty,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_maxt @ T )
% 8.60/4.76 = none_nat )
% 8.60/4.76 => ( ( vEBT_VEBT_set_vebt @ T )
% 8.60/4.76 = bot_bot_set_nat ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1302_mint__corr__help__empty,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( ( vEBT_vebt_mint @ T )
% 8.60/4.76 = none_nat )
% 8.60/4.76 => ( ( vEBT_VEBT_set_vebt @ T )
% 8.60/4.76 = bot_bot_set_nat ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1303_buildup__nothing__in__min__max,axiom,
% 8.60/4.76 ! [N: nat,X: nat] :
% 8.60/4.76 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1304_dele__member__cont__corr,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( vEBT_vebt_member @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 8.60/4.76 = ( ( X != Y )
% 8.60/4.76 & ( vEBT_vebt_member @ T @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1305_VEBT__internal_Omembermima_Ocases,axiom,
% 8.60/4.76 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.76 ( ! [Uu2: $o,Uv2: $o,Uw: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw ) )
% 8.60/4.76 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz2: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz2 ) )
% 8.60/4.76 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT,X3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ X3 ) )
% 8.60/4.76 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ X3 ) )
% 8.60/4.76 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT,X3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ X3 ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1306_case4_I8_J,axiom,
% 8.60/4.76 ( ( mi = ma )
% 8.60/4.76 => ! [X5: vEBT_VEBT] :
% 8.60/4.76 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList2 ) )
% 8.60/4.76 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1307_even__odd__cases,axiom,
% 8.60/4.76 ! [X: nat] :
% 8.60/4.76 ( ! [N3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( plus_plus_nat @ N3 @ N3 ) )
% 8.60/4.76 => ~ ! [N3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1308_delete__pres__valid,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ T @ X ) @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1309_maxbmo,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,X: nat] :
% 8.60/4.76 ( ( ( vEBT_vebt_maxt @ T )
% 8.60/4.76 = ( some_nat @ X ) )
% 8.60/4.76 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1310_dele__bmo__cont__corr,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 8.60/4.76 = ( ( X != Y )
% 8.60/4.76 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1311_both__member__options__equiv__member,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 8.60/4.76 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1312_valid__member__both__member__options,axiom,
% 8.60/4.76 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.76 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 8.60/4.76 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1313_both__member__options__def,axiom,
% 8.60/4.76 ( vEBT_V8194947554948674370ptions
% 8.60/4.76 = ( ^ [T2: vEBT_VEBT,X4: nat] :
% 8.60/4.76 ( ( vEBT_V5719532721284313246member @ T2 @ X4 )
% 8.60/4.76 | ( vEBT_VEBT_membermima @ T2 @ X4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1314_add__right__cancel,axiom,
% 8.60/4.76 ! [B: real,A: real,C2: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ B @ A )
% 8.60/4.76 = ( plus_plus_real @ C2 @ A ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1315_add__right__cancel,axiom,
% 8.60/4.76 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ B @ A )
% 8.60/4.76 = ( plus_plus_rat @ C2 @ A ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1316_add__right__cancel,axiom,
% 8.60/4.76 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ B @ A )
% 8.60/4.76 = ( plus_plus_nat @ C2 @ A ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1317_add__right__cancel,axiom,
% 8.60/4.76 ! [B: int,A: int,C2: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ B @ A )
% 8.60/4.76 = ( plus_plus_int @ C2 @ A ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1318_add__left__cancel,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ A @ B )
% 8.60/4.76 = ( plus_plus_real @ A @ C2 ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1319_add__left__cancel,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ A @ B )
% 8.60/4.76 = ( plus_plus_rat @ A @ C2 ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1320_add__left__cancel,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ A @ B )
% 8.60/4.76 = ( plus_plus_nat @ A @ C2 ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1321_add__left__cancel,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ A @ B )
% 8.60/4.76 = ( plus_plus_int @ A @ C2 ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1322_mi__eq__ma__no__ch,axiom,
% 8.60/4.76 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.60/4.76 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 8.60/4.76 => ( ( Mi = Ma )
% 8.60/4.76 => ( ! [X5: vEBT_VEBT] :
% 8.60/4.76 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.60/4.76 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) )
% 8.60/4.76 & ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1323_add__le__cancel__left,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1324_add__le__cancel__left,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1325_add__le__cancel__left,axiom,
% 8.60/4.76 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1326_add__le__cancel__left,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_eq_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1327_add__le__cancel__right,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_eq_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1328_add__le__cancel__right,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1329_add__le__cancel__right,axiom,
% 8.60/4.76 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_eq_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1330_add__le__cancel__right,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_eq_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1331_add_Oright__neutral,axiom,
% 8.60/4.76 ! [A: complex] :
% 8.60/4.76 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1332_add_Oright__neutral,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( plus_plus_real @ A @ zero_zero_real )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1333_add_Oright__neutral,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1334_add_Oright__neutral,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1335_add_Oright__neutral,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( plus_plus_int @ A @ zero_zero_int )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1336_double__zero__sym,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( zero_zero_real
% 8.60/4.76 = ( plus_plus_real @ A @ A ) )
% 8.60/4.76 = ( A = zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1337_double__zero__sym,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( zero_zero_rat
% 8.60/4.76 = ( plus_plus_rat @ A @ A ) )
% 8.60/4.76 = ( A = zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1338_double__zero__sym,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( zero_zero_int
% 8.60/4.76 = ( plus_plus_int @ A @ A ) )
% 8.60/4.76 = ( A = zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1339_add__cancel__left__left,axiom,
% 8.60/4.76 ! [B: complex,A: complex] :
% 8.60/4.76 ( ( ( plus_plus_complex @ B @ A )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_complex ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1340_add__cancel__left__left,axiom,
% 8.60/4.76 ! [B: real,A: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ B @ A )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1341_add__cancel__left__left,axiom,
% 8.60/4.76 ! [B: rat,A: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ B @ A )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1342_add__cancel__left__left,axiom,
% 8.60/4.76 ! [B: nat,A: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ B @ A )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1343_add__cancel__left__left,axiom,
% 8.60/4.76 ! [B: int,A: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ B @ A )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1344_add__cancel__left__right,axiom,
% 8.60/4.76 ! [A: complex,B: complex] :
% 8.60/4.76 ( ( ( plus_plus_complex @ A @ B )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_complex ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1345_add__cancel__left__right,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ A @ B )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1346_add__cancel__left__right,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ A @ B )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1347_add__cancel__left__right,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ A @ B )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1348_add__cancel__left__right,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ A @ B )
% 8.60/4.76 = A )
% 8.60/4.76 = ( B = zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1349_add__cancel__right__left,axiom,
% 8.60/4.76 ! [A: complex,B: complex] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_complex @ B @ A ) )
% 8.60/4.76 = ( B = zero_zero_complex ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1350_add__cancel__right__left,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_real @ B @ A ) )
% 8.60/4.76 = ( B = zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1351_add__cancel__right__left,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_rat @ B @ A ) )
% 8.60/4.76 = ( B = zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1352_add__cancel__right__left,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_nat @ B @ A ) )
% 8.60/4.76 = ( B = zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1353_add__cancel__right__left,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_int @ B @ A ) )
% 8.60/4.76 = ( B = zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1354_add__cancel__right__right,axiom,
% 8.60/4.76 ! [A: complex,B: complex] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_complex @ A @ B ) )
% 8.60/4.76 = ( B = zero_zero_complex ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1355_add__cancel__right__right,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_real @ A @ B ) )
% 8.60/4.76 = ( B = zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1356_add__cancel__right__right,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_rat @ A @ B ) )
% 8.60/4.76 = ( B = zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1357_add__cancel__right__right,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_nat @ A @ B ) )
% 8.60/4.76 = ( B = zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1358_add__cancel__right__right,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( A
% 8.60/4.76 = ( plus_plus_int @ A @ B ) )
% 8.60/4.76 = ( B = zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1359_add__eq__0__iff__both__eq__0,axiom,
% 8.60/4.76 ! [X: nat,Y: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ X @ Y )
% 8.60/4.76 = zero_zero_nat )
% 8.60/4.76 = ( ( X = zero_zero_nat )
% 8.60/4.76 & ( Y = zero_zero_nat ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1360_zero__eq__add__iff__both__eq__0,axiom,
% 8.60/4.76 ! [X: nat,Y: nat] :
% 8.60/4.76 ( ( zero_zero_nat
% 8.60/4.76 = ( plus_plus_nat @ X @ Y ) )
% 8.60/4.76 = ( ( X = zero_zero_nat )
% 8.60/4.76 & ( Y = zero_zero_nat ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1361_add__0,axiom,
% 8.60/4.76 ! [A: complex] :
% 8.60/4.76 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1362_add__0,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( plus_plus_real @ zero_zero_real @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1363_add__0,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1364_add__0,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1365_add__0,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( plus_plus_int @ zero_zero_int @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1366_add__less__cancel__right,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1367_add__less__cancel__right,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1368_add__less__cancel__right,axiom,
% 8.60/4.76 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1369_add__less__cancel__right,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.76 = ( ord_less_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1370_add__less__cancel__left,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1371_add__less__cancel__left,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1372_add__less__cancel__left,axiom,
% 8.60/4.76 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1373_add__less__cancel__left,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 8.60/4.76 = ( ord_less_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1374_add__Suc__right,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ M2 @ ( suc @ N ) )
% 8.60/4.76 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1375_Nat_Oadd__0__right,axiom,
% 8.60/4.76 ! [M2: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ M2 @ zero_zero_nat )
% 8.60/4.76 = M2 ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1376_add__is__0,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ M2 @ N )
% 8.60/4.76 = zero_zero_nat )
% 8.60/4.76 = ( ( M2 = zero_zero_nat )
% 8.60/4.76 & ( N = zero_zero_nat ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1377_nat__add__left__cancel__less,axiom,
% 8.60/4.76 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 8.60/4.76 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1378_nat__add__left__cancel__le,axiom,
% 8.60/4.76 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 8.60/4.76 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1379_not__Some__eq,axiom,
% 8.60/4.76 ! [X: option4927543243414619207at_nat] :
% 8.60/4.76 ( ( ! [Y4: product_prod_nat_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( some_P7363390416028606310at_nat @ Y4 ) ) )
% 8.60/4.76 = ( X = none_P5556105721700978146at_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1380_not__Some__eq,axiom,
% 8.60/4.76 ! [X: option_nat] :
% 8.60/4.76 ( ( ! [Y4: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( some_nat @ Y4 ) ) )
% 8.60/4.76 = ( X = none_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1381_not__Some__eq,axiom,
% 8.60/4.76 ! [X: option_num] :
% 8.60/4.76 ( ( ! [Y4: num] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( some_num @ Y4 ) ) )
% 8.60/4.76 = ( X = none_num ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1382_not__None__eq,axiom,
% 8.60/4.76 ! [X: option4927543243414619207at_nat] :
% 8.60/4.76 ( ( X != none_P5556105721700978146at_nat )
% 8.60/4.76 = ( ? [Y4: product_prod_nat_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ Y4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1383_not__None__eq,axiom,
% 8.60/4.76 ! [X: option_nat] :
% 8.60/4.76 ( ( X != none_nat )
% 8.60/4.76 = ( ? [Y4: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 = ( some_nat @ Y4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1384_not__None__eq,axiom,
% 8.60/4.76 ! [X: option_num] :
% 8.60/4.76 ( ( X != none_num )
% 8.60/4.76 = ( ? [Y4: num] :
% 8.60/4.76 ( X
% 8.60/4.76 = ( some_num @ Y4 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1385_add__le__same__cancel1,axiom,
% 8.60/4.76 ! [B: real,A: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1386_add__le__same__cancel1,axiom,
% 8.60/4.76 ! [B: rat,A: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1387_add__le__same__cancel1,axiom,
% 8.60/4.76 ! [B: nat,A: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1388_add__le__same__cancel1,axiom,
% 8.60/4.76 ! [B: int,A: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1389_add__le__same__cancel2,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1390_add__le__same__cancel2,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1391_add__le__same__cancel2,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1392_add__le__same__cancel2,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1393_le__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.60/4.76 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1394_le__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.60/4.76 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1395_le__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.60/4.76 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1396_le__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.60/4.76 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1397_le__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 8.60/4.76 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1398_le__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.60/4.76 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1399_le__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.60/4.76 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1400_le__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.60/4.76 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1401_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 8.60/4.76 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1402_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 8.60/4.76 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1403_double__add__le__zero__iff__single__add__le__zero,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 8.60/4.76 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1404_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 8.60/4.76 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1405_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 8.60/4.76 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1406_zero__le__double__add__iff__zero__le__single__add,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 8.60/4.76 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1407_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 8.60/4.76 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1408_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 8.60/4.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1409_zero__less__double__add__iff__zero__less__single__add,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 8.60/4.76 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1410_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 8.60/4.76 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1411_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 8.60/4.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1412_double__add__less__zero__iff__single__add__less__zero,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 8.60/4.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1413_less__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 8.60/4.76 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1414_less__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.60/4.76 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1415_less__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.60/4.76 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1416_less__add__same__cancel2,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.60/4.76 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1417_less__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.60/4.76 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1418_less__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.60/4.76 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1419_less__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.60/4.76 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1420_less__add__same__cancel1,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.60/4.76 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1421_add__less__same__cancel2,axiom,
% 8.60/4.76 ! [A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1422_add__less__same__cancel2,axiom,
% 8.60/4.76 ! [A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1423_add__less__same__cancel2,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1424_add__less__same__cancel2,axiom,
% 8.60/4.76 ! [A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.60/4.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1425_add__less__same__cancel1,axiom,
% 8.60/4.76 ! [B: real,A: real] :
% 8.60/4.76 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1426_add__less__same__cancel1,axiom,
% 8.60/4.76 ! [B: rat,A: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1427_add__less__same__cancel1,axiom,
% 8.60/4.76 ! [B: nat,A: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1428_add__less__same__cancel1,axiom,
% 8.60/4.76 ! [B: int,A: int] :
% 8.60/4.76 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.60/4.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1429_add__gr__0,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.76 = ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.60/4.76 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1430_mult__Suc__right,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( times_times_nat @ M2 @ ( suc @ N ) )
% 8.60/4.76 = ( plus_plus_nat @ M2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1431_add__right__imp__eq,axiom,
% 8.60/4.76 ! [B: real,A: real,C2: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ B @ A )
% 8.60/4.76 = ( plus_plus_real @ C2 @ A ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1432_add__right__imp__eq,axiom,
% 8.60/4.76 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ B @ A )
% 8.60/4.76 = ( plus_plus_rat @ C2 @ A ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1433_add__right__imp__eq,axiom,
% 8.60/4.76 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ B @ A )
% 8.60/4.76 = ( plus_plus_nat @ C2 @ A ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1434_add__right__imp__eq,axiom,
% 8.60/4.76 ! [B: int,A: int,C2: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ B @ A )
% 8.60/4.76 = ( plus_plus_int @ C2 @ A ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1435_add__left__imp__eq,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ A @ B )
% 8.60/4.76 = ( plus_plus_real @ A @ C2 ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1436_add__left__imp__eq,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ A @ B )
% 8.60/4.76 = ( plus_plus_rat @ A @ C2 ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1437_add__left__imp__eq,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ A @ B )
% 8.60/4.76 = ( plus_plus_nat @ A @ C2 ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1438_add__left__imp__eq,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ A @ B )
% 8.60/4.76 = ( plus_plus_int @ A @ C2 ) )
% 8.60/4.76 => ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1439_add_Oleft__commute,axiom,
% 8.60/4.76 ! [B: real,A: real,C2: real] :
% 8.60/4.76 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C2 ) )
% 8.60/4.76 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1440_add_Oleft__commute,axiom,
% 8.60/4.76 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C2 ) )
% 8.60/4.76 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1441_add_Oleft__commute,axiom,
% 8.60/4.76 ! [B: nat,A: nat,C2: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C2 ) )
% 8.60/4.76 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1442_add_Oleft__commute,axiom,
% 8.60/4.76 ! [B: int,A: int,C2: int] :
% 8.60/4.76 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C2 ) )
% 8.60/4.76 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1443_add_Ocommute,axiom,
% 8.60/4.76 ( plus_plus_real
% 8.60/4.76 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ B4 @ A5 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1444_add_Ocommute,axiom,
% 8.60/4.76 ( plus_plus_rat
% 8.60/4.76 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ B4 @ A5 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1445_add_Ocommute,axiom,
% 8.60/4.76 ( plus_plus_nat
% 8.60/4.76 = ( ^ [A5: nat,B4: nat] : ( plus_plus_nat @ B4 @ A5 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1446_add_Ocommute,axiom,
% 8.60/4.76 ( plus_plus_int
% 8.60/4.76 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ B4 @ A5 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1447_add_Oright__cancel,axiom,
% 8.60/4.76 ! [B: real,A: real,C2: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ B @ A )
% 8.60/4.76 = ( plus_plus_real @ C2 @ A ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1448_add_Oright__cancel,axiom,
% 8.60/4.76 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ B @ A )
% 8.60/4.76 = ( plus_plus_rat @ C2 @ A ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1449_add_Oright__cancel,axiom,
% 8.60/4.76 ! [B: int,A: int,C2: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ B @ A )
% 8.60/4.76 = ( plus_plus_int @ C2 @ A ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1450_add_Oleft__cancel,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ( plus_plus_real @ A @ B )
% 8.60/4.76 = ( plus_plus_real @ A @ C2 ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1451_add_Oleft__cancel,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ( plus_plus_rat @ A @ B )
% 8.60/4.76 = ( plus_plus_rat @ A @ C2 ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1452_add_Oleft__cancel,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ( plus_plus_int @ A @ B )
% 8.60/4.76 = ( plus_plus_int @ A @ C2 ) )
% 8.60/4.76 = ( B = C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1453_add_Oassoc,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1454_add_Oassoc,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1455_add_Oassoc,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1456_add_Oassoc,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1457_group__cancel_Oadd2,axiom,
% 8.60/4.76 ! [B5: real,K2: real,B: real,A: real] :
% 8.60/4.76 ( ( B5
% 8.60/4.76 = ( plus_plus_real @ K2 @ B ) )
% 8.60/4.76 => ( ( plus_plus_real @ A @ B5 )
% 8.60/4.76 = ( plus_plus_real @ K2 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1458_group__cancel_Oadd2,axiom,
% 8.60/4.76 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 8.60/4.76 ( ( B5
% 8.60/4.76 = ( plus_plus_rat @ K2 @ B ) )
% 8.60/4.76 => ( ( plus_plus_rat @ A @ B5 )
% 8.60/4.76 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1459_group__cancel_Oadd2,axiom,
% 8.60/4.76 ! [B5: nat,K2: nat,B: nat,A: nat] :
% 8.60/4.76 ( ( B5
% 8.60/4.76 = ( plus_plus_nat @ K2 @ B ) )
% 8.60/4.76 => ( ( plus_plus_nat @ A @ B5 )
% 8.60/4.76 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1460_group__cancel_Oadd2,axiom,
% 8.60/4.76 ! [B5: int,K2: int,B: int,A: int] :
% 8.60/4.76 ( ( B5
% 8.60/4.76 = ( plus_plus_int @ K2 @ B ) )
% 8.60/4.76 => ( ( plus_plus_int @ A @ B5 )
% 8.60/4.76 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1461_group__cancel_Oadd1,axiom,
% 8.60/4.76 ! [A4: real,K2: real,A: real,B: real] :
% 8.60/4.76 ( ( A4
% 8.60/4.76 = ( plus_plus_real @ K2 @ A ) )
% 8.60/4.76 => ( ( plus_plus_real @ A4 @ B )
% 8.60/4.76 = ( plus_plus_real @ K2 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1462_group__cancel_Oadd1,axiom,
% 8.60/4.76 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( A4
% 8.60/4.76 = ( plus_plus_rat @ K2 @ A ) )
% 8.60/4.76 => ( ( plus_plus_rat @ A4 @ B )
% 8.60/4.76 = ( plus_plus_rat @ K2 @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1463_group__cancel_Oadd1,axiom,
% 8.60/4.76 ! [A4: nat,K2: nat,A: nat,B: nat] :
% 8.60/4.76 ( ( A4
% 8.60/4.76 = ( plus_plus_nat @ K2 @ A ) )
% 8.60/4.76 => ( ( plus_plus_nat @ A4 @ B )
% 8.60/4.76 = ( plus_plus_nat @ K2 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1464_group__cancel_Oadd1,axiom,
% 8.60/4.76 ! [A4: int,K2: int,A: int,B: int] :
% 8.60/4.76 ( ( A4
% 8.60/4.76 = ( plus_plus_int @ K2 @ A ) )
% 8.60/4.76 => ( ( plus_plus_int @ A4 @ B )
% 8.60/4.76 = ( plus_plus_int @ K2 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1465_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.60/4.76 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ( plus_plus_real @ I2 @ K2 )
% 8.60/4.76 = ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1466_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.60/4.76 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ( plus_plus_rat @ I2 @ K2 )
% 8.60/4.76 = ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1467_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ( plus_plus_nat @ I2 @ K2 )
% 8.60/4.76 = ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1468_add__mono__thms__linordered__semiring_I4_J,axiom,
% 8.60/4.76 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ( plus_plus_int @ I2 @ K2 )
% 8.60/4.76 = ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1469_is__num__normalize_I1_J,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1470_is__num__normalize_I1_J,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1471_is__num__normalize_I1_J,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1472_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1473_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1474_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1475_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1476_bot__nat__def,axiom,
% 8.60/4.76 bot_bot_nat = zero_zero_nat ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1477_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 8.60/4.76 ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz: nat] :
% 8.60/4.76 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1478_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.60/4.76 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.76 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1479_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.60/4.76 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.76 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1480_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1481_add__mono__thms__linordered__semiring_I3_J,axiom,
% 8.60/4.76 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.76 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1482_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.60/4.76 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_eq_real @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1483_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.60/4.76 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_eq_rat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1484_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_eq_nat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1485_add__mono__thms__linordered__semiring_I2_J,axiom,
% 8.60/4.76 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_eq_int @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1486_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.60/4.76 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.76 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_eq_real @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1487_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.60/4.76 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.76 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_eq_rat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1488_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_eq_nat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1489_add__mono__thms__linordered__semiring_I1_J,axiom,
% 8.60/4.76 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.76 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_eq_int @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1490_add__mono,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_real @ C2 @ D )
% 8.60/4.76 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1491_add__mono,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_rat @ C2 @ D )
% 8.60/4.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1492_add__mono,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_nat @ C2 @ D )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1493_add__mono,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.76 => ( ( ord_less_eq_int @ C2 @ D )
% 8.60/4.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1494_add__left__mono,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.76 => ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1495_add__left__mono,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1496_add__left__mono,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1497_add__left__mono,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.76 => ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1498_less__eqE,axiom,
% 8.60/4.76 ! [A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.76 => ~ ! [C: nat] :
% 8.60/4.76 ( B
% 8.60/4.76 != ( plus_plus_nat @ A @ C ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1499_add__right__mono,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.76 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1500_add__right__mono,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1501_add__right__mono,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1502_add__right__mono,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1503_le__iff__add,axiom,
% 8.60/4.76 ( ord_less_eq_nat
% 8.60/4.76 = ( ^ [A5: nat,B4: nat] :
% 8.60/4.76 ? [C3: nat] :
% 8.60/4.76 ( B4
% 8.60/4.76 = ( plus_plus_nat @ A5 @ C3 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1504_add__le__imp__le__left,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_eq_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1505_add__le__imp__le__left,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1506_add__le__imp__le__left,axiom,
% 8.60/4.76 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1507_add__le__imp__le__left,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_eq_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1508_add__le__imp__le__right,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_eq_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1509_add__le__imp__le__right,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1510_add__le__imp__le__right,axiom,
% 8.60/4.76 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1511_add__le__imp__le__right,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_eq_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1512_comm__monoid__add__class_Oadd__0,axiom,
% 8.60/4.76 ! [A: complex] :
% 8.60/4.76 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1513_comm__monoid__add__class_Oadd__0,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( plus_plus_real @ zero_zero_real @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1514_comm__monoid__add__class_Oadd__0,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1515_comm__monoid__add__class_Oadd__0,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1516_comm__monoid__add__class_Oadd__0,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( plus_plus_int @ zero_zero_int @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1517_add_Ocomm__neutral,axiom,
% 8.60/4.76 ! [A: complex] :
% 8.60/4.76 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1518_add_Ocomm__neutral,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( plus_plus_real @ A @ zero_zero_real )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1519_add_Ocomm__neutral,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1520_add_Ocomm__neutral,axiom,
% 8.60/4.76 ! [A: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1521_add_Ocomm__neutral,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( plus_plus_int @ A @ zero_zero_int )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1522_add_Ogroup__left__neutral,axiom,
% 8.60/4.76 ! [A: complex] :
% 8.60/4.76 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1523_add_Ogroup__left__neutral,axiom,
% 8.60/4.76 ! [A: real] :
% 8.60/4.76 ( ( plus_plus_real @ zero_zero_real @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1524_add_Ogroup__left__neutral,axiom,
% 8.60/4.76 ! [A: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1525_add_Ogroup__left__neutral,axiom,
% 8.60/4.76 ! [A: int] :
% 8.60/4.76 ( ( plus_plus_int @ zero_zero_int @ A )
% 8.60/4.76 = A ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1526_add__less__imp__less__right,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1527_add__less__imp__less__right,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1528_add__less__imp__less__right,axiom,
% 8.60/4.76 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1529_add__less__imp__less__right,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.76 => ( ord_less_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1530_add__less__imp__less__left,axiom,
% 8.60/4.76 ! [C2: real,A: real,B: real] :
% 8.60/4.76 ( ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_real @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1531_add__less__imp__less__left,axiom,
% 8.60/4.76 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_rat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1532_add__less__imp__less__left,axiom,
% 8.60/4.76 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_nat @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1533_add__less__imp__less__left,axiom,
% 8.60/4.76 ! [C2: int,A: int,B: int] :
% 8.60/4.76 ( ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 8.60/4.76 => ( ord_less_int @ A @ B ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1534_add__strict__right__mono,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ B )
% 8.60/4.76 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1535_add__strict__right__mono,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ B )
% 8.60/4.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1536_add__strict__right__mono,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ B )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1537_add__strict__right__mono,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ B )
% 8.60/4.76 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1538_add__strict__left__mono,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ B )
% 8.60/4.76 => ( ord_less_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1539_add__strict__left__mono,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ B )
% 8.60/4.76 => ( ord_less_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1540_add__strict__left__mono,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ B )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1541_add__strict__left__mono,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ B )
% 8.60/4.76 => ( ord_less_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1542_add__strict__mono,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.76 ( ( ord_less_real @ A @ B )
% 8.60/4.76 => ( ( ord_less_real @ C2 @ D )
% 8.60/4.76 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1543_add__strict__mono,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.76 ( ( ord_less_rat @ A @ B )
% 8.60/4.76 => ( ( ord_less_rat @ C2 @ D )
% 8.60/4.76 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1544_add__strict__mono,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.76 ( ( ord_less_nat @ A @ B )
% 8.60/4.76 => ( ( ord_less_nat @ C2 @ D )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1545_add__strict__mono,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.76 ( ( ord_less_int @ A @ B )
% 8.60/4.76 => ( ( ord_less_int @ C2 @ D )
% 8.60/4.76 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1546_add__mono__thms__linordered__field_I1_J,axiom,
% 8.60/4.76 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.76 ( ( ( ord_less_real @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1547_add__mono__thms__linordered__field_I1_J,axiom,
% 8.60/4.76 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.76 ( ( ( ord_less_rat @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1548_add__mono__thms__linordered__field_I1_J,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1549_add__mono__thms__linordered__field_I1_J,axiom,
% 8.60/4.76 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.76 ( ( ( ord_less_int @ I2 @ J2 )
% 8.60/4.76 & ( K2 = L ) )
% 8.60/4.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1550_add__mono__thms__linordered__field_I2_J,axiom,
% 8.60/4.76 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_real @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1551_add__mono__thms__linordered__field_I2_J,axiom,
% 8.60/4.76 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_rat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1552_add__mono__thms__linordered__field_I2_J,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_nat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1553_add__mono__thms__linordered__field_I2_J,axiom,
% 8.60/4.76 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.76 ( ( ( I2 = J2 )
% 8.60/4.76 & ( ord_less_int @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1554_add__mono__thms__linordered__field_I5_J,axiom,
% 8.60/4.76 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.76 ( ( ( ord_less_real @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_real @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1555_add__mono__thms__linordered__field_I5_J,axiom,
% 8.60/4.76 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.76 ( ( ( ord_less_rat @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_rat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1556_add__mono__thms__linordered__field_I5_J,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_nat @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1557_add__mono__thms__linordered__field_I5_J,axiom,
% 8.60/4.76 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.76 ( ( ( ord_less_int @ I2 @ J2 )
% 8.60/4.76 & ( ord_less_int @ K2 @ L ) )
% 8.60/4.76 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1558_ring__class_Oring__distribs_I2_J,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1559_ring__class_Oring__distribs_I2_J,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1560_ring__class_Oring__distribs_I2_J,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1561_ring__class_Oring__distribs_I1_J,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.76 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1562_ring__class_Oring__distribs_I1_J,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.76 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1563_ring__class_Oring__distribs_I1_J,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.76 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1564_comm__semiring__class_Odistrib,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1565_comm__semiring__class_Odistrib,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1566_comm__semiring__class_Odistrib,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1567_comm__semiring__class_Odistrib,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1568_distrib__left,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.76 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1569_distrib__left,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.76 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1570_distrib__left,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 8.60/4.76 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1571_distrib__left,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.76 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1572_distrib__right,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1573_distrib__right,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1574_distrib__right,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1575_distrib__right,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 8.60/4.76 = ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1576_combine__common__factor,axiom,
% 8.60/4.76 ! [A: real,E: real,B: real,C2: real] :
% 8.60/4.76 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C2 ) )
% 8.60/4.76 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1577_combine__common__factor,axiom,
% 8.60/4.76 ! [A: rat,E: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C2 ) )
% 8.60/4.76 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1578_combine__common__factor,axiom,
% 8.60/4.76 ! [A: nat,E: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C2 ) )
% 8.60/4.76 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1579_combine__common__factor,axiom,
% 8.60/4.76 ! [A: int,E: int,B: int,C2: int] :
% 8.60/4.76 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C2 ) )
% 8.60/4.76 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1580_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 8.60/4.76 ( ( ( X = none_P5556105721700978146at_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_P5556105721700978146at_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1581_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 8.60/4.76 ( ( ( X = none_P5556105721700978146at_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: product_prod_nat_nat,B3: nat] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_nat @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1582_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option4927543243414619207at_nat,P2: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 8.60/4.76 ( ( ( X = none_P5556105721700978146at_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_num )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: product_prod_nat_nat,B3: num] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_num @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1583_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option_nat,P2: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 8.60/4.76 ( ( ( X = none_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_P5556105721700978146at_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: nat,B3: product_prod_nat_nat] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_nat @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1584_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option_nat,P2: option_nat > option_nat > $o,Y: option_nat] :
% 8.60/4.76 ( ( ( X = none_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: nat,B3: nat] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_nat @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_nat @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1585_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option_nat,P2: option_nat > option_num > $o,Y: option_num] :
% 8.60/4.76 ( ( ( X = none_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_num )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: nat,B3: num] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_nat @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_num @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1586_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option_num,P2: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 8.60/4.76 ( ( ( X = none_num )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_P5556105721700978146at_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: num,B3: product_prod_nat_nat] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_num @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1587_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option_num,P2: option_num > option_nat > $o,Y: option_nat] :
% 8.60/4.76 ( ( ( X = none_num )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_nat )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: num,B3: nat] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_num @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_nat @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1588_combine__options__cases,axiom,
% 8.60/4.76 ! [X: option_num,P2: option_num > option_num > $o,Y: option_num] :
% 8.60/4.76 ( ( ( X = none_num )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ( ( Y = none_num )
% 8.60/4.76 => ( P2 @ X @ Y ) )
% 8.60/4.76 => ( ! [A3: num,B3: num] :
% 8.60/4.76 ( ( X
% 8.60/4.76 = ( some_num @ A3 ) )
% 8.60/4.76 => ( ( Y
% 8.60/4.76 = ( some_num @ B3 ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) )
% 8.60/4.76 => ( P2 @ X @ Y ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1589_split__option__all,axiom,
% 8.60/4.76 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 8.60/4.76 ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 8.60/4.76 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 8.60/4.76 ( ( P4 @ none_P5556105721700978146at_nat )
% 8.60/4.76 & ! [X4: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X4 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1590_split__option__all,axiom,
% 8.60/4.76 ( ( ^ [P3: option_nat > $o] :
% 8.60/4.76 ! [X6: option_nat] : ( P3 @ X6 ) )
% 8.60/4.76 = ( ^ [P4: option_nat > $o] :
% 8.60/4.76 ( ( P4 @ none_nat )
% 8.60/4.76 & ! [X4: nat] : ( P4 @ ( some_nat @ X4 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1591_split__option__all,axiom,
% 8.60/4.76 ( ( ^ [P3: option_num > $o] :
% 8.60/4.76 ! [X6: option_num] : ( P3 @ X6 ) )
% 8.60/4.76 = ( ^ [P4: option_num > $o] :
% 8.60/4.76 ( ( P4 @ none_num )
% 8.60/4.76 & ! [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1592_split__option__ex,axiom,
% 8.60/4.76 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 8.60/4.76 ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 8.60/4.76 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 8.60/4.76 ( ( P4 @ none_P5556105721700978146at_nat )
% 8.60/4.76 | ? [X4: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X4 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1593_split__option__ex,axiom,
% 8.60/4.76 ( ( ^ [P3: option_nat > $o] :
% 8.60/4.76 ? [X6: option_nat] : ( P3 @ X6 ) )
% 8.60/4.76 = ( ^ [P4: option_nat > $o] :
% 8.60/4.76 ( ( P4 @ none_nat )
% 8.60/4.76 | ? [X4: nat] : ( P4 @ ( some_nat @ X4 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1594_split__option__ex,axiom,
% 8.60/4.76 ( ( ^ [P3: option_num > $o] :
% 8.60/4.76 ? [X6: option_num] : ( P3 @ X6 ) )
% 8.60/4.76 = ( ^ [P4: option_num > $o] :
% 8.60/4.76 ( ( P4 @ none_num )
% 8.60/4.76 | ? [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1595_option_Oexhaust,axiom,
% 8.60/4.76 ! [Y: option4927543243414619207at_nat] :
% 8.60/4.76 ( ( Y != none_P5556105721700978146at_nat )
% 8.60/4.76 => ~ ! [X23: product_prod_nat_nat] :
% 8.60/4.76 ( Y
% 8.60/4.76 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1596_option_Oexhaust,axiom,
% 8.60/4.76 ! [Y: option_nat] :
% 8.60/4.76 ( ( Y != none_nat )
% 8.60/4.76 => ~ ! [X23: nat] :
% 8.60/4.76 ( Y
% 8.60/4.76 != ( some_nat @ X23 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1597_option_Oexhaust,axiom,
% 8.60/4.76 ! [Y: option_num] :
% 8.60/4.76 ( ( Y != none_num )
% 8.60/4.76 => ~ ! [X23: num] :
% 8.60/4.76 ( Y
% 8.60/4.76 != ( some_num @ X23 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1598_option_OdiscI,axiom,
% 8.60/4.76 ! [Option: option4927543243414619207at_nat,X2: product_prod_nat_nat] :
% 8.60/4.76 ( ( Option
% 8.60/4.76 = ( some_P7363390416028606310at_nat @ X2 ) )
% 8.60/4.76 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1599_option_OdiscI,axiom,
% 8.60/4.76 ! [Option: option_nat,X2: nat] :
% 8.60/4.76 ( ( Option
% 8.60/4.76 = ( some_nat @ X2 ) )
% 8.60/4.76 => ( Option != none_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1600_option_OdiscI,axiom,
% 8.60/4.76 ! [Option: option_num,X2: num] :
% 8.60/4.76 ( ( Option
% 8.60/4.76 = ( some_num @ X2 ) )
% 8.60/4.76 => ( Option != none_num ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1601_option_Odistinct_I1_J,axiom,
% 8.60/4.76 ! [X2: product_prod_nat_nat] :
% 8.60/4.76 ( none_P5556105721700978146at_nat
% 8.60/4.76 != ( some_P7363390416028606310at_nat @ X2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1602_option_Odistinct_I1_J,axiom,
% 8.60/4.76 ! [X2: nat] :
% 8.60/4.76 ( none_nat
% 8.60/4.76 != ( some_nat @ X2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1603_option_Odistinct_I1_J,axiom,
% 8.60/4.76 ! [X2: num] :
% 8.60/4.76 ( none_num
% 8.60/4.76 != ( some_num @ X2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1604_VEBT__internal_Ooption__shift_Ocases,axiom,
% 8.60/4.76 ! [X: produc5542196010084753463at_nat] :
% 8.60/4.76 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 8.60/4.76 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc2899441246263362727at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat ) ) )
% 8.60/4.76 => ~ ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A3: product_prod_nat_nat,B3: product_prod_nat_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc2899441246263362727at_nat @ F @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A3 ) @ ( some_P7363390416028606310at_nat @ B3 ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1605_VEBT__internal_Ooption__shift_Ocases,axiom,
% 8.60/4.76 ! [X: produc8306885398267862888on_nat] :
% 8.60/4.76 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 8.60/4.76 => ( ! [Uw: nat > nat > nat,V: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc8929957630744042906on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V ) @ none_nat ) ) )
% 8.60/4.76 => ~ ! [F: nat > nat > nat,A3: nat,B3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc8929957630744042906on_nat @ F @ ( produc5098337634421038937on_nat @ ( some_nat @ A3 ) @ ( some_nat @ B3 ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1606_VEBT__internal_Ooption__shift_Ocases,axiom,
% 8.60/4.76 ! [X: produc1193250871479095198on_num] :
% 8.60/4.76 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 8.60/4.76 => ( ! [Uw: num > num > num,V: num] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc5778274026573060048on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V ) @ none_num ) ) )
% 8.60/4.76 => ~ ! [F: num > num > num,A3: num,B3: num] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc5778274026573060048on_num @ F @ ( produc8585076106096196333on_num @ ( some_num @ A3 ) @ ( some_num @ B3 ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1607_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 8.60/4.76 ! [X: produc5491161045314408544at_nat] :
% 8.60/4.76 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 8.60/4.76 => ( ! [Uw: product_prod_nat_nat > product_prod_nat_nat > $o,V: product_prod_nat_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc3994169339658061776at_nat @ Uw @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat ) ) )
% 8.60/4.76 => ~ ! [F: product_prod_nat_nat > product_prod_nat_nat > $o,X3: product_prod_nat_nat,Y3: product_prod_nat_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc3994169339658061776at_nat @ F @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X3 ) @ ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1608_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 8.60/4.76 ! [X: produc2233624965454879586on_nat] :
% 8.60/4.76 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 8.60/4.76 => ( ! [Uw: nat > nat > $o,V: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc4035269172776083154on_nat @ Uw @ ( produc5098337634421038937on_nat @ ( some_nat @ V ) @ none_nat ) ) )
% 8.60/4.76 => ~ ! [F: nat > nat > $o,X3: nat,Y3: nat] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc4035269172776083154on_nat @ F @ ( produc5098337634421038937on_nat @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1609_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 8.60/4.76 ! [X: produc7036089656553540234on_num] :
% 8.60/4.76 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 8.60/4.76 => ( ! [Uw: num > num > $o,V: num] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc3576312749637752826on_num @ Uw @ ( produc8585076106096196333on_num @ ( some_num @ V ) @ none_num ) ) )
% 8.60/4.76 => ~ ! [F: num > num > $o,X3: num,Y3: num] :
% 8.60/4.76 ( X
% 8.60/4.76 != ( produc3576312749637752826on_num @ F @ ( produc8585076106096196333on_num @ ( some_num @ X3 ) @ ( some_num @ Y3 ) ) ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1610_nat__arith_Osuc1,axiom,
% 8.60/4.76 ! [A4: nat,K2: nat,A: nat] :
% 8.60/4.76 ( ( A4
% 8.60/4.76 = ( plus_plus_nat @ K2 @ A ) )
% 8.60/4.76 => ( ( suc @ A4 )
% 8.60/4.76 = ( plus_plus_nat @ K2 @ ( suc @ A ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1611_add__Suc,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 8.60/4.76 = ( suc @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1612_add__Suc__shift,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ ( suc @ M2 ) @ N )
% 8.60/4.76 = ( plus_plus_nat @ M2 @ ( suc @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1613_add__eq__self__zero,axiom,
% 8.60/4.76 ! [M2: nat,N: nat] :
% 8.60/4.76 ( ( ( plus_plus_nat @ M2 @ N )
% 8.60/4.76 = M2 )
% 8.60/4.76 => ( N = zero_zero_nat ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1614_plus__nat_Oadd__0,axiom,
% 8.60/4.76 ! [N: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 8.60/4.76 = N ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1615_less__add__eq__less,axiom,
% 8.60/4.76 ! [K2: nat,L: nat,M2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_nat @ K2 @ L )
% 8.60/4.76 => ( ( ( plus_plus_nat @ M2 @ L )
% 8.60/4.76 = ( plus_plus_nat @ K2 @ N ) )
% 8.60/4.76 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1616_trans__less__add2,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,M2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1617_trans__less__add1,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,M2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1618_add__less__mono1,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1619_not__add__less2,axiom,
% 8.60/4.76 ! [J2: nat,I2: nat] :
% 8.60/4.76 ~ ( ord_less_nat @ ( plus_plus_nat @ J2 @ I2 ) @ I2 ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1620_not__add__less1,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat] :
% 8.60/4.76 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ I2 ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1621_add__less__mono,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.76 => ( ( ord_less_nat @ K2 @ L )
% 8.60/4.76 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1622_add__lessD1,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.76 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 8.60/4.76 => ( ord_less_nat @ I2 @ K2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1623_add__leE,axiom,
% 8.60/4.76 ! [M2: nat,K2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 8.60/4.76 => ~ ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.76 => ~ ( ord_less_eq_nat @ K2 @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1624_le__add1,axiom,
% 8.60/4.76 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1625_le__add2,axiom,
% 8.60/4.76 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1626_add__leD1,axiom,
% 8.60/4.76 ! [M2: nat,K2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 8.60/4.76 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1627_add__leD2,axiom,
% 8.60/4.76 ! [M2: nat,K2: nat,N: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M2 @ K2 ) @ N )
% 8.60/4.76 => ( ord_less_eq_nat @ K2 @ N ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1628_le__Suc__ex,axiom,
% 8.60/4.76 ! [K2: nat,L: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ K2 @ L )
% 8.60/4.76 => ? [N3: nat] :
% 8.60/4.76 ( L
% 8.60/4.76 = ( plus_plus_nat @ K2 @ N3 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1629_add__le__mono,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 => ( ( ord_less_eq_nat @ K2 @ L )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1630_add__le__mono1,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1631_trans__le__add1,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,M2: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J2 @ M2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1632_trans__le__add2,axiom,
% 8.60/4.76 ! [I2: nat,J2: nat,M2: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.76 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M2 @ J2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1633_nat__le__iff__add,axiom,
% 8.60/4.76 ( ord_less_eq_nat
% 8.60/4.76 = ( ^ [M6: nat,N4: nat] :
% 8.60/4.76 ? [K3: nat] :
% 8.60/4.76 ( N4
% 8.60/4.76 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1634_add__mult__distrib2,axiom,
% 8.60/4.76 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.76 ( ( times_times_nat @ K2 @ ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.76 = ( plus_plus_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1635_add__mult__distrib,axiom,
% 8.60/4.76 ! [M2: nat,N: nat,K2: nat] :
% 8.60/4.76 ( ( times_times_nat @ ( plus_plus_nat @ M2 @ N ) @ K2 )
% 8.60/4.76 = ( plus_plus_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1636_left__add__mult__distrib,axiom,
% 8.60/4.76 ! [I2: nat,U: nat,J2: nat,K2: nat] :
% 8.60/4.76 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ K2 ) )
% 8.60/4.76 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J2 ) @ U ) @ K2 ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1637_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 8.60/4.76 ! [Uu: $o,Uv: $o,Uw2: nat] :
% 8.60/4.76 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw2 ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1638_add__decreasing,axiom,
% 8.60/4.76 ! [A: real,C2: real,B: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.76 => ( ( ord_less_eq_real @ C2 @ B )
% 8.60/4.76 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1639_add__decreasing,axiom,
% 8.60/4.76 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.76 => ( ( ord_less_eq_rat @ C2 @ B )
% 8.60/4.76 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1640_add__decreasing,axiom,
% 8.60/4.76 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.60/4.76 => ( ( ord_less_eq_nat @ C2 @ B )
% 8.60/4.76 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1641_add__decreasing,axiom,
% 8.60/4.76 ! [A: int,C2: int,B: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.76 => ( ( ord_less_eq_int @ C2 @ B )
% 8.60/4.76 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1642_add__increasing,axiom,
% 8.60/4.76 ! [A: real,B: real,C2: real] :
% 8.60/4.76 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.76 => ( ( ord_less_eq_real @ B @ C2 )
% 8.60/4.76 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1643_add__increasing,axiom,
% 8.60/4.76 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.76 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.76 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1644_add__increasing,axiom,
% 8.60/4.76 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.76 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.76 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.76 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 8.60/4.76
% 8.60/4.76 thf(fact_1645_add__increasing,axiom,
% 8.60/4.76 ! [A: int,B: int,C2: int] :
% 8.60/4.76 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.76 => ( ( ord_less_eq_int @ B @ C2 )
% 8.60/4.77 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1646_add__decreasing2,axiom,
% 8.60/4.77 ! [C2: real,A: real,B: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.60/4.77 => ( ( ord_less_eq_real @ A @ B )
% 8.60/4.77 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1647_add__decreasing2,axiom,
% 8.60/4.77 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.60/4.77 => ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.77 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1648_add__decreasing2,axiom,
% 8.60/4.77 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ C2 @ zero_zero_nat )
% 8.60/4.77 => ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1649_add__decreasing2,axiom,
% 8.60/4.77 ! [C2: int,A: int,B: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ C2 @ zero_zero_int )
% 8.60/4.77 => ( ( ord_less_eq_int @ A @ B )
% 8.60/4.77 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1650_add__increasing2,axiom,
% 8.60/4.77 ! [C2: real,B: real,A: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.60/4.77 => ( ( ord_less_eq_real @ B @ A )
% 8.60/4.77 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1651_add__increasing2,axiom,
% 8.60/4.77 ! [C2: rat,B: rat,A: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.60/4.77 => ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.77 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1652_add__increasing2,axiom,
% 8.60/4.77 ! [C2: nat,B: nat,A: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.60/4.77 => ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.77 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1653_add__increasing2,axiom,
% 8.60/4.77 ! [C2: int,B: int,A: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.60/4.77 => ( ( ord_less_eq_int @ B @ A )
% 8.60/4.77 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1654_add__nonneg__nonneg,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.77 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.77 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1655_add__nonneg__nonneg,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1656_add__nonneg__nonneg,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.77 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1657_add__nonneg__nonneg,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.77 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.77 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1658_add__nonpos__nonpos,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.77 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.60/4.77 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1659_add__nonpos__nonpos,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.77 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.60/4.77 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1660_add__nonpos__nonpos,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.60/4.77 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.60/4.77 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1661_add__nonpos__nonpos,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.77 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.60/4.77 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1662_add__nonneg__eq__0__iff,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.60/4.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.60/4.77 => ( ( ( plus_plus_real @ X @ Y )
% 8.60/4.77 = zero_zero_real )
% 8.60/4.77 = ( ( X = zero_zero_real )
% 8.60/4.77 & ( Y = zero_zero_real ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1663_add__nonneg__eq__0__iff,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.60/4.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.60/4.77 => ( ( ( plus_plus_rat @ X @ Y )
% 8.60/4.77 = zero_zero_rat )
% 8.60/4.77 = ( ( X = zero_zero_rat )
% 8.60/4.77 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1664_add__nonneg__eq__0__iff,axiom,
% 8.60/4.77 ! [X: nat,Y: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.60/4.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.60/4.77 => ( ( ( plus_plus_nat @ X @ Y )
% 8.60/4.77 = zero_zero_nat )
% 8.60/4.77 = ( ( X = zero_zero_nat )
% 8.60/4.77 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1665_add__nonneg__eq__0__iff,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.60/4.77 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.60/4.77 => ( ( ( plus_plus_int @ X @ Y )
% 8.60/4.77 = zero_zero_int )
% 8.60/4.77 = ( ( X = zero_zero_int )
% 8.60/4.77 & ( Y = zero_zero_int ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1666_add__nonpos__eq__0__iff,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.60/4.77 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.60/4.77 => ( ( ( plus_plus_real @ X @ Y )
% 8.60/4.77 = zero_zero_real )
% 8.60/4.77 = ( ( X = zero_zero_real )
% 8.60/4.77 & ( Y = zero_zero_real ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1667_add__nonpos__eq__0__iff,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.60/4.77 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.60/4.77 => ( ( ( plus_plus_rat @ X @ Y )
% 8.60/4.77 = zero_zero_rat )
% 8.60/4.77 = ( ( X = zero_zero_rat )
% 8.60/4.77 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1668_add__nonpos__eq__0__iff,axiom,
% 8.60/4.77 ! [X: nat,Y: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 8.60/4.77 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 8.60/4.77 => ( ( ( plus_plus_nat @ X @ Y )
% 8.60/4.77 = zero_zero_nat )
% 8.60/4.77 = ( ( X = zero_zero_nat )
% 8.60/4.77 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1669_add__nonpos__eq__0__iff,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 8.60/4.77 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 8.60/4.77 => ( ( ( plus_plus_int @ X @ Y )
% 8.60/4.77 = zero_zero_int )
% 8.60/4.77 = ( ( X = zero_zero_int )
% 8.60/4.77 & ( Y = zero_zero_int ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1670_add__less__le__mono,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.77 ( ( ord_less_real @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_real @ C2 @ D )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1671_add__less__le__mono,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.77 ( ( ord_less_rat @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_rat @ C2 @ D )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1672_add__less__le__mono,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.77 ( ( ord_less_nat @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_nat @ C2 @ D )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1673_add__less__le__mono,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.77 ( ( ord_less_int @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_int @ C2 @ D )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1674_add__le__less__mono,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.77 => ( ( ord_less_real @ C2 @ D )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1675_add__le__less__mono,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.77 => ( ( ord_less_rat @ C2 @ D )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1676_add__le__less__mono,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( ord_less_nat @ C2 @ D )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1677_add__le__less__mono,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.77 => ( ( ord_less_int @ C2 @ D )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1678_add__mono__thms__linordered__field_I3_J,axiom,
% 8.60/4.77 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.77 ( ( ( ord_less_real @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_eq_real @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1679_add__mono__thms__linordered__field_I3_J,axiom,
% 8.60/4.77 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.77 ( ( ( ord_less_rat @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_eq_rat @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1680_add__mono__thms__linordered__field_I3_J,axiom,
% 8.60/4.77 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.77 ( ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_eq_nat @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1681_add__mono__thms__linordered__field_I3_J,axiom,
% 8.60/4.77 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.77 ( ( ( ord_less_int @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_eq_int @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1682_add__mono__thms__linordered__field_I4_J,axiom,
% 8.60/4.77 ! [I2: real,J2: real,K2: real,L: real] :
% 8.60/4.77 ( ( ( ord_less_eq_real @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_real @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ I2 @ K2 ) @ ( plus_plus_real @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1683_add__mono__thms__linordered__field_I4_J,axiom,
% 8.60/4.77 ! [I2: rat,J2: rat,K2: rat,L: rat] :
% 8.60/4.77 ( ( ( ord_less_eq_rat @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_rat @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K2 ) @ ( plus_plus_rat @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1684_add__mono__thms__linordered__field_I4_J,axiom,
% 8.60/4.77 ! [I2: nat,J2: nat,K2: nat,L: nat] :
% 8.60/4.77 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_nat @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( plus_plus_nat @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1685_add__mono__thms__linordered__field_I4_J,axiom,
% 8.60/4.77 ! [I2: int,J2: int,K2: int,L: int] :
% 8.60/4.77 ( ( ( ord_less_eq_int @ I2 @ J2 )
% 8.60/4.77 & ( ord_less_int @ K2 @ L ) )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ I2 @ K2 ) @ ( plus_plus_int @ J2 @ L ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1686_add__less__zeroD,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 8.60/4.77 => ( ( ord_less_real @ X @ zero_zero_real )
% 8.60/4.77 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1687_add__less__zeroD,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 8.60/4.77 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 8.60/4.77 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1688_add__less__zeroD,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 8.60/4.77 => ( ( ord_less_int @ X @ zero_zero_int )
% 8.60/4.77 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1689_pos__add__strict,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.77 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.77 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1690_pos__add__strict,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.77 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.77 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1691_pos__add__strict,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.77 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.77 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1692_pos__add__strict,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.77 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.77 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1693_canonically__ordered__monoid__add__class_OlessE,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_nat @ A @ B )
% 8.60/4.77 => ~ ! [C: nat] :
% 8.60/4.77 ( ( B
% 8.60/4.77 = ( plus_plus_nat @ A @ C ) )
% 8.60/4.77 => ( C = zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1694_add__pos__pos,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.77 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.60/4.77 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1695_add__pos__pos,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.77 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.60/4.77 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1696_add__pos__pos,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.77 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1697_add__pos__pos,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.77 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1698_add__neg__neg,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_real @ A @ zero_zero_real )
% 8.60/4.77 => ( ( ord_less_real @ B @ zero_zero_real )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1699_add__neg__neg,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.60/4.77 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1700_add__neg__neg,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.60/4.77 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1701_add__neg__neg,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_int @ A @ zero_zero_int )
% 8.60/4.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1702_add__mono1,axiom,
% 8.60/4.77 ! [A: code_integer,B: code_integer] :
% 8.60/4.77 ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.60/4.77 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1703_add__mono1,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_real @ A @ B )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1704_add__mono1,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_rat @ A @ B )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1705_add__mono1,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_nat @ A @ B )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1706_add__mono1,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_int @ A @ B )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1707_less__add__one,axiom,
% 8.60/4.77 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1708_less__add__one,axiom,
% 8.60/4.77 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1709_less__add__one,axiom,
% 8.60/4.77 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1710_less__add__one,axiom,
% 8.60/4.77 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1711_less__add__one,axiom,
% 8.60/4.77 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1712_add__is__1,axiom,
% 8.60/4.77 ! [M2: nat,N: nat] :
% 8.60/4.77 ( ( ( plus_plus_nat @ M2 @ N )
% 8.60/4.77 = ( suc @ zero_zero_nat ) )
% 8.60/4.77 = ( ( ( M2
% 8.60/4.77 = ( suc @ zero_zero_nat ) )
% 8.60/4.77 & ( N = zero_zero_nat ) )
% 8.60/4.77 | ( ( M2 = zero_zero_nat )
% 8.60/4.77 & ( N
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1713_one__is__add,axiom,
% 8.60/4.77 ! [M2: nat,N: nat] :
% 8.60/4.77 ( ( ( suc @ zero_zero_nat )
% 8.60/4.77 = ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.77 = ( ( ( M2
% 8.60/4.77 = ( suc @ zero_zero_nat ) )
% 8.60/4.77 & ( N = zero_zero_nat ) )
% 8.60/4.77 | ( ( M2 = zero_zero_nat )
% 8.60/4.77 & ( N
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1714_less__natE,axiom,
% 8.60/4.77 ! [M2: nat,N: nat] :
% 8.60/4.77 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.77 => ~ ! [Q3: nat] :
% 8.60/4.77 ( N
% 8.60/4.77 != ( suc @ ( plus_plus_nat @ M2 @ Q3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1715_less__add__Suc1,axiom,
% 8.60/4.77 ! [I2: nat,M2: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1716_less__add__Suc2,axiom,
% 8.60/4.77 ! [I2: nat,M2: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M2 @ I2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1717_less__iff__Suc__add,axiom,
% 8.60/4.77 ( ord_less_nat
% 8.60/4.77 = ( ^ [M6: nat,N4: nat] :
% 8.60/4.77 ? [K3: nat] :
% 8.60/4.77 ( N4
% 8.60/4.77 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1718_less__imp__Suc__add,axiom,
% 8.60/4.77 ! [M2: nat,N: nat] :
% 8.60/4.77 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.77 => ? [K: nat] :
% 8.60/4.77 ( N
% 8.60/4.77 = ( suc @ ( plus_plus_nat @ M2 @ K ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1719_less__imp__add__positive,axiom,
% 8.60/4.77 ! [I2: nat,J2: nat] :
% 8.60/4.77 ( ( ord_less_nat @ I2 @ J2 )
% 8.60/4.77 => ? [K: nat] :
% 8.60/4.77 ( ( ord_less_nat @ zero_zero_nat @ K )
% 8.60/4.77 & ( ( plus_plus_nat @ I2 @ K )
% 8.60/4.77 = J2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1720_mono__nat__linear__lb,axiom,
% 8.60/4.77 ! [F2: nat > nat,M2: nat,K2: nat] :
% 8.60/4.77 ( ! [M: nat,N3: nat] :
% 8.60/4.77 ( ( ord_less_nat @ M @ N3 )
% 8.60/4.77 => ( ord_less_nat @ ( F2 @ M ) @ ( F2 @ N3 ) ) )
% 8.60/4.77 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F2 @ M2 ) @ K2 ) @ ( F2 @ ( plus_plus_nat @ M2 @ K2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1721_mult__Suc,axiom,
% 8.60/4.77 ! [M2: nat,N: nat] :
% 8.60/4.77 ( ( times_times_nat @ ( suc @ M2 ) @ N )
% 8.60/4.77 = ( plus_plus_nat @ N @ ( times_times_nat @ M2 @ N ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1722_Suc__eq__plus1,axiom,
% 8.60/4.77 ( suc
% 8.60/4.77 = ( ^ [N4: nat] : ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1723_plus__1__eq__Suc,axiom,
% 8.60/4.77 ( ( plus_plus_nat @ one_one_nat )
% 8.60/4.77 = suc ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1724_Suc__eq__plus1__left,axiom,
% 8.60/4.77 ( suc
% 8.60/4.77 = ( plus_plus_nat @ one_one_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1725_VEBT__internal_OminNull_Ocases,axiom,
% 8.60/4.77 ! [X: vEBT_VEBT] :
% 8.60/4.77 ( ( X
% 8.60/4.77 != ( vEBT_Leaf @ $false @ $false ) )
% 8.60/4.77 => ( ! [Uv2: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.60/4.77 => ( ! [Uu2: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.60/4.77 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 8.60/4.77 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1726_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 8.60/4.77 ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 8.60/4.77 ( ( vEBT_V1502963449132264192at_nat @ Uw2 @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat )
% 8.60/4.77 = none_P5556105721700978146at_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1727_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 8.60/4.77 ! [Uw2: num > num > num,V2: num] :
% 8.60/4.77 ( ( vEBT_V819420779217536731ft_num @ Uw2 @ ( some_num @ V2 ) @ none_num )
% 8.60/4.77 = none_num ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1728_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 8.60/4.77 ! [Uw2: nat > nat > nat,V2: nat] :
% 8.60/4.77 ( ( vEBT_V4262088993061758097ft_nat @ Uw2 @ ( some_nat @ V2 ) @ none_nat )
% 8.60/4.77 = none_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1729_VEBT__internal_Ooption__shift_Oelims,axiom,
% 8.60/4.77 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 8.60/4.77 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb )
% 8.60/4.77 = Y )
% 8.60/4.77 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 8.60/4.77 => ( Y != none_P5556105721700978146at_nat ) )
% 8.60/4.77 => ( ( ? [V: product_prod_nat_nat] :
% 8.60/4.77 ( Xa2
% 8.60/4.77 = ( some_P7363390416028606310at_nat @ V ) )
% 8.60/4.77 => ( ( Xb = none_P5556105721700978146at_nat )
% 8.60/4.77 => ( Y != none_P5556105721700978146at_nat ) ) )
% 8.60/4.77 => ~ ! [A3: product_prod_nat_nat] :
% 8.60/4.77 ( ( Xa2
% 8.60/4.77 = ( some_P7363390416028606310at_nat @ A3 ) )
% 8.60/4.77 => ! [B3: product_prod_nat_nat] :
% 8.60/4.77 ( ( Xb
% 8.60/4.77 = ( some_P7363390416028606310at_nat @ B3 ) )
% 8.60/4.77 => ( Y
% 8.60/4.77 != ( some_P7363390416028606310at_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1730_VEBT__internal_Ooption__shift_Oelims,axiom,
% 8.60/4.77 ! [X: num > num > num,Xa2: option_num,Xb: option_num,Y: option_num] :
% 8.60/4.77 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb )
% 8.60/4.77 = Y )
% 8.60/4.77 => ( ( ( Xa2 = none_num )
% 8.60/4.77 => ( Y != none_num ) )
% 8.60/4.77 => ( ( ? [V: num] :
% 8.60/4.77 ( Xa2
% 8.60/4.77 = ( some_num @ V ) )
% 8.60/4.77 => ( ( Xb = none_num )
% 8.60/4.77 => ( Y != none_num ) ) )
% 8.60/4.77 => ~ ! [A3: num] :
% 8.60/4.77 ( ( Xa2
% 8.60/4.77 = ( some_num @ A3 ) )
% 8.60/4.77 => ! [B3: num] :
% 8.60/4.77 ( ( Xb
% 8.60/4.77 = ( some_num @ B3 ) )
% 8.60/4.77 => ( Y
% 8.60/4.77 != ( some_num @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1731_VEBT__internal_Ooption__shift_Oelims,axiom,
% 8.60/4.77 ! [X: nat > nat > nat,Xa2: option_nat,Xb: option_nat,Y: option_nat] :
% 8.60/4.77 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb )
% 8.60/4.77 = Y )
% 8.60/4.77 => ( ( ( Xa2 = none_nat )
% 8.60/4.77 => ( Y != none_nat ) )
% 8.60/4.77 => ( ( ? [V: nat] :
% 8.60/4.77 ( Xa2
% 8.60/4.77 = ( some_nat @ V ) )
% 8.60/4.77 => ( ( Xb = none_nat )
% 8.60/4.77 => ( Y != none_nat ) ) )
% 8.60/4.77 => ~ ! [A3: nat] :
% 8.60/4.77 ( ( Xa2
% 8.60/4.77 = ( some_nat @ A3 ) )
% 8.60/4.77 => ! [B3: nat] :
% 8.60/4.77 ( ( Xb
% 8.60/4.77 = ( some_nat @ B3 ) )
% 8.60/4.77 => ( Y
% 8.60/4.77 != ( some_nat @ ( X @ A3 @ B3 ) ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1732_field__le__epsilon,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ! [E2: real] :
% 8.60/4.77 ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.60/4.77 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 8.60/4.77 => ( ord_less_eq_real @ X @ Y ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1733_field__le__epsilon,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ! [E2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 8.60/4.77 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 8.60/4.77 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1734_add__neg__nonpos,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_real @ A @ zero_zero_real )
% 8.60/4.77 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1735_add__neg__nonpos,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.60/4.77 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1736_add__neg__nonpos,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_nat @ A @ zero_zero_nat )
% 8.60/4.77 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1737_add__neg__nonpos,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_int @ A @ zero_zero_int )
% 8.60/4.77 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1738_add__nonneg__pos,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.77 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.60/4.77 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1739_add__nonneg__pos,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.77 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.60/4.77 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1740_add__nonneg__pos,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.77 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1741_add__nonneg__pos,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.77 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.77 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1742_add__nonpos__neg,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.60/4.77 => ( ( ord_less_real @ B @ zero_zero_real )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1743_add__nonpos__neg,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.60/4.77 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1744_add__nonpos__neg,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 8.60/4.77 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 8.60/4.77 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1745_add__nonpos__neg,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.60/4.77 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1746_add__pos__nonneg,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.77 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.77 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1747_add__pos__nonneg,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.77 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1748_add__pos__nonneg,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1749_add__pos__nonneg,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.77 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.77 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1750_add__strict__increasing,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.77 => ( ( ord_less_eq_real @ B @ C2 )
% 8.60/4.77 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1751_add__strict__increasing,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.77 => ( ( ord_less_eq_rat @ B @ C2 )
% 8.60/4.77 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1752_add__strict__increasing,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.77 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.77 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1753_add__strict__increasing,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.77 => ( ( ord_less_eq_int @ B @ C2 )
% 8.60/4.77 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1754_add__strict__increasing2,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.77 => ( ( ord_less_real @ B @ C2 )
% 8.60/4.77 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1755_add__strict__increasing2,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.77 => ( ( ord_less_rat @ B @ C2 )
% 8.60/4.77 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1756_add__strict__increasing2,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.77 => ( ( ord_less_nat @ B @ C2 )
% 8.60/4.77 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1757_add__strict__increasing2,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.77 => ( ( ord_less_int @ B @ C2 )
% 8.60/4.77 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1758_sum__squares__ge__zero,axiom,
% 8.60/4.77 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1759_sum__squares__ge__zero,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1760_sum__squares__ge__zero,axiom,
% 8.60/4.77 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1761_not__sum__squares__lt__zero,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1762_not__sum__squares__lt__zero,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1763_not__sum__squares__lt__zero,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1764_discrete,axiom,
% 8.60/4.77 ( ord_le6747313008572928689nteger
% 8.60/4.77 = ( ^ [A5: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1765_discrete,axiom,
% 8.60/4.77 ( ord_less_nat
% 8.60/4.77 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1766_discrete,axiom,
% 8.60/4.77 ( ord_less_int
% 8.60/4.77 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1767_zero__less__two,axiom,
% 8.60/4.77 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1768_zero__less__two,axiom,
% 8.60/4.77 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1769_zero__less__two,axiom,
% 8.60/4.77 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1770_zero__less__two,axiom,
% 8.60/4.77 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1771_zero__less__two,axiom,
% 8.60/4.77 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1772_option_Osize_I3_J,axiom,
% 8.60/4.77 ( ( size_size_option_nat @ none_nat )
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1773_option_Osize_I3_J,axiom,
% 8.60/4.77 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1774_option_Osize_I3_J,axiom,
% 8.60/4.77 ( ( size_size_option_num @ none_num )
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1775_convex__bound__le,axiom,
% 8.60/4.77 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 8.60/4.77 ( ( ord_le3102999989581377725nteger @ X @ A )
% 8.60/4.77 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 8.60/4.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 8.60/4.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 8.60/4.77 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 8.60/4.77 = one_one_Code_integer )
% 8.60/4.77 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1776_convex__bound__le,axiom,
% 8.60/4.77 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ X @ A )
% 8.60/4.77 => ( ( ord_less_eq_real @ Y @ A )
% 8.60/4.77 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 8.60/4.77 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 8.60/4.77 => ( ( ( plus_plus_real @ U @ V2 )
% 8.60/4.77 = one_one_real )
% 8.60/4.77 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1777_convex__bound__le,axiom,
% 8.60/4.77 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ X @ A )
% 8.60/4.77 => ( ( ord_less_eq_rat @ Y @ A )
% 8.60/4.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 8.60/4.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 8.60/4.77 => ( ( ( plus_plus_rat @ U @ V2 )
% 8.60/4.77 = one_one_rat )
% 8.60/4.77 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1778_convex__bound__le,axiom,
% 8.60/4.77 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ X @ A )
% 8.60/4.77 => ( ( ord_less_eq_int @ Y @ A )
% 8.60/4.77 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.60/4.77 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 8.60/4.77 => ( ( ( plus_plus_int @ U @ V2 )
% 8.60/4.77 = one_one_int )
% 8.60/4.77 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1779_vebt__mint_Oelims,axiom,
% 8.60/4.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 8.60/4.77 ( ( ( vEBT_vebt_mint @ X )
% 8.60/4.77 = Y )
% 8.60/4.77 => ( ! [A3: $o,B3: $o] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.60/4.77 => ~ ( ( A3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A3
% 8.60/4.77 => ( ( B3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B3
% 8.60/4.77 => ( Y = none_nat ) ) ) ) ) )
% 8.60/4.77 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.60/4.77 => ( Y != none_nat ) )
% 8.60/4.77 => ~ ! [Mi2: nat] :
% 8.60/4.77 ( ? [Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 8.60/4.77 => ( Y
% 8.60/4.77 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1780_vebt__maxt_Oelims,axiom,
% 8.60/4.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 8.60/4.77 ( ( ( vEBT_vebt_maxt @ X )
% 8.60/4.77 = Y )
% 8.60/4.77 => ( ! [A3: $o,B3: $o] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.60/4.77 => ~ ( ( B3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B3
% 8.60/4.77 => ( ( A3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A3
% 8.60/4.77 => ( Y = none_nat ) ) ) ) ) )
% 8.60/4.77 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.60/4.77 => ( Y != none_nat ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat] :
% 8.60/4.77 ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 8.60/4.77 => ( Y
% 8.60/4.77 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1781_vebt__mint_Ocases,axiom,
% 8.60/4.77 ! [X: vEBT_VEBT] :
% 8.60/4.77 ( ! [A3: $o,B3: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( vEBT_Leaf @ A3 @ B3 ) )
% 8.60/4.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1782_convex__bound__lt,axiom,
% 8.60/4.77 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V2: code_integer] :
% 8.60/4.77 ( ( ord_le6747313008572928689nteger @ X @ A )
% 8.60/4.77 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 8.60/4.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 8.60/4.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V2 )
% 8.60/4.77 => ( ( ( plus_p5714425477246183910nteger @ U @ V2 )
% 8.60/4.77 = one_one_Code_integer )
% 8.60/4.77 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1783_convex__bound__lt,axiom,
% 8.60/4.77 ! [X: real,A: real,Y: real,U: real,V2: real] :
% 8.60/4.77 ( ( ord_less_real @ X @ A )
% 8.60/4.77 => ( ( ord_less_real @ Y @ A )
% 8.60/4.77 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 8.60/4.77 => ( ( ord_less_eq_real @ zero_zero_real @ V2 )
% 8.60/4.77 => ( ( ( plus_plus_real @ U @ V2 )
% 8.60/4.77 = one_one_real )
% 8.60/4.77 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1784_convex__bound__lt,axiom,
% 8.60/4.77 ! [X: rat,A: rat,Y: rat,U: rat,V2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ X @ A )
% 8.60/4.77 => ( ( ord_less_rat @ Y @ A )
% 8.60/4.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 8.60/4.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ V2 )
% 8.60/4.77 => ( ( ( plus_plus_rat @ U @ V2 )
% 8.60/4.77 = one_one_rat )
% 8.60/4.77 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1785_convex__bound__lt,axiom,
% 8.60/4.77 ! [X: int,A: int,Y: int,U: int,V2: int] :
% 8.60/4.77 ( ( ord_less_int @ X @ A )
% 8.60/4.77 => ( ( ord_less_int @ Y @ A )
% 8.60/4.77 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.60/4.77 => ( ( ord_less_eq_int @ zero_zero_int @ V2 )
% 8.60/4.77 => ( ( ( plus_plus_int @ U @ V2 )
% 8.60/4.77 = one_one_int )
% 8.60/4.77 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V2 @ Y ) ) @ A ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1786_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 8.60/4.77 ! [Mi: nat,Ma: nat,Va3: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 8.60/4.77 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va3 @ Vb ) @ X )
% 8.60/4.77 = ( ( X = Mi )
% 8.60/4.77 | ( X = Ma ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1787_vebt__member_Ocases,axiom,
% 8.60/4.77 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.77 ( ! [A3: $o,B3: $o,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 8.60/4.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ X3 ) )
% 8.60/4.77 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ X3 ) )
% 8.60/4.77 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X3 ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1788_vebt__mint_Osimps_I1_J,axiom,
% 8.60/4.77 ! [A: $o,B: $o] :
% 8.60/4.77 ( ( A
% 8.60/4.77 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A
% 8.60/4.77 => ( ( B
% 8.60/4.77 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B
% 8.60/4.77 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 8.60/4.77 = none_nat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1789_vebt__maxt_Osimps_I1_J,axiom,
% 8.60/4.77 ! [B: $o,A: $o] :
% 8.60/4.77 ( ( B
% 8.60/4.77 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B
% 8.60/4.77 => ( ( A
% 8.60/4.77 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A
% 8.60/4.77 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 8.60/4.77 = none_nat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1790_geqmaxNone,axiom,
% 8.60/4.77 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_nat @ Ma @ X )
% 8.60/4.77 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.60/4.77 = none_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1791_vebt__pred_Ocases,axiom,
% 8.60/4.77 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.77 ( ! [Uu2: $o,Uv2: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 8.60/4.77 => ( ! [A3: $o,Uw: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) )
% 8.60/4.77 => ( ! [A3: $o,B3: $o,Va: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) )
% 8.60/4.77 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT,Vb2: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) @ Vb2 ) )
% 8.60/4.77 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf ) )
% 8.60/4.77 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1792_vebt__succ_Ocases,axiom,
% 8.60/4.77 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.77 ( ! [Uu2: $o,B3: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) )
% 8.60/4.77 => ( ! [Uv2: $o,Uw: $o,N3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw ) @ ( suc @ N3 ) ) )
% 8.60/4.77 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va2: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Va2 ) )
% 8.60/4.77 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Ve ) )
% 8.60/4.77 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1793_vebt__delete_Ocases,axiom,
% 8.60/4.77 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.77 ( ! [A3: $o,B3: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) )
% 8.60/4.77 => ( ! [A3: $o,B3: $o] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) )
% 8.60/4.77 => ( ! [A3: $o,B3: $o,N3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 8.60/4.77 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Uu2 ) )
% 8.60/4.77 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X3 ) )
% 8.60/4.77 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X3 ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1794_vebt__insert_Ocases,axiom,
% 8.60/4.77 ! [X: produc9072475918466114483BT_nat] :
% 8.60/4.77 ( ! [A3: $o,B3: $o,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ X3 ) )
% 8.60/4.77 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X3 ) )
% 8.60/4.77 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X3 ) )
% 8.60/4.77 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) @ X3 ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,X3: nat] :
% 8.60/4.77 ( X
% 8.60/4.77 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ X3 ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1795_succ__correct,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.77 => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.60/4.77 = ( some_nat @ Sx ) )
% 8.60/4.77 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1796_pred__correct,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.77 => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.60/4.77 = ( some_nat @ Sx ) )
% 8.60/4.77 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1797_pred__corr,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.77 => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.60/4.77 = ( some_nat @ Px ) )
% 8.60/4.77 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1798_succ__corr,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.77 => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.60/4.77 = ( some_nat @ Sx ) )
% 8.60/4.77 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1799_sum__squares__eq__zero__iff,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 8.60/4.77 = zero_zero_real )
% 8.60/4.77 = ( ( X = zero_zero_real )
% 8.60/4.77 & ( Y = zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1800_sum__squares__eq__zero__iff,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 8.60/4.77 = zero_zero_rat )
% 8.60/4.77 = ( ( X = zero_zero_rat )
% 8.60/4.77 & ( Y = zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1801_sum__squares__eq__zero__iff,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 8.60/4.77 = zero_zero_int )
% 8.60/4.77 = ( ( X = zero_zero_int )
% 8.60/4.77 & ( Y = zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1802_vebt__succ_Osimps_I2_J,axiom,
% 8.60/4.77 ! [Uv: $o,Uw2: $o,N: nat] :
% 8.60/4.77 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw2 ) @ ( suc @ N ) )
% 8.60/4.77 = none_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1803_vebt__pred_Osimps_I1_J,axiom,
% 8.60/4.77 ! [Uu: $o,Uv: $o] :
% 8.60/4.77 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 8.60/4.77 = none_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1804_vebt__succ_Osimps_I4_J,axiom,
% 8.60/4.77 ! [V2: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 8.60/4.77 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc @ Vd2 ) @ Ve2 )
% 8.60/4.77 = none_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1805_vebt__pred_Osimps_I5_J,axiom,
% 8.60/4.77 ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 8.60/4.77 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 )
% 8.60/4.77 = none_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1806_vebt__pred_Osimps_I6_J,axiom,
% 8.60/4.77 ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 8.60/4.77 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 )
% 8.60/4.77 = none_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1807_vebt__succ_Osimps_I5_J,axiom,
% 8.60/4.77 ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 8.60/4.77 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 )
% 8.60/4.77 = none_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1808_vebt__pred_Osimps_I2_J,axiom,
% 8.60/4.77 ! [A: $o,Uw2: $o] :
% 8.60/4.77 ( ( A
% 8.60/4.77 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A
% 8.60/4.77 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw2 ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.77 = none_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1809_vebt__succ_Osimps_I1_J,axiom,
% 8.60/4.77 ! [B: $o,Uu: $o] :
% 8.60/4.77 ( ( B
% 8.60/4.77 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B
% 8.60/4.77 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 8.60/4.77 = none_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1810_vebt__pred_Osimps_I3_J,axiom,
% 8.60/4.77 ! [B: $o,A: $o,Va3: nat] :
% 8.60/4.77 ( ( B
% 8.60/4.77 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B
% 8.60/4.77 => ( ( A
% 8.60/4.77 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A
% 8.60/4.77 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va3 ) ) )
% 8.60/4.77 = none_nat ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1811_vebt__delete_Osimps_I3_J,axiom,
% 8.60/4.77 ! [A: $o,B: $o,N: nat] :
% 8.60/4.77 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 8.60/4.77 = ( vEBT_Leaf @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1812_vebt__delete_Osimps_I1_J,axiom,
% 8.60/4.77 ! [A: $o,B: $o] :
% 8.60/4.77 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 8.60/4.77 = ( vEBT_Leaf @ $false @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1813_is__pred__in__set__def,axiom,
% 8.60/4.77 ( vEBT_is_pred_in_set
% 8.60/4.77 = ( ^ [Xs: set_nat,X4: nat,Y4: nat] :
% 8.60/4.77 ( ( member_nat @ Y4 @ Xs )
% 8.60/4.77 & ( ord_less_nat @ Y4 @ X4 )
% 8.60/4.77 & ! [Z4: nat] :
% 8.60/4.77 ( ( member_nat @ Z4 @ Xs )
% 8.60/4.77 => ( ( ord_less_nat @ Z4 @ X4 )
% 8.60/4.77 => ( ord_less_eq_nat @ Z4 @ Y4 ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1814_is__succ__in__set__def,axiom,
% 8.60/4.77 ( vEBT_is_succ_in_set
% 8.60/4.77 = ( ^ [Xs: set_nat,X4: nat,Y4: nat] :
% 8.60/4.77 ( ( member_nat @ Y4 @ Xs )
% 8.60/4.77 & ( ord_less_nat @ X4 @ Y4 )
% 8.60/4.77 & ! [Z4: nat] :
% 8.60/4.77 ( ( member_nat @ Z4 @ Xs )
% 8.60/4.77 => ( ( ord_less_nat @ X4 @ Z4 )
% 8.60/4.77 => ( ord_less_eq_nat @ Y4 @ Z4 ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1815_sum__squares__le__zero__iff,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 8.60/4.77 = ( ( X = zero_zero_real )
% 8.60/4.77 & ( Y = zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1816_sum__squares__le__zero__iff,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 8.60/4.77 = ( ( X = zero_zero_rat )
% 8.60/4.77 & ( Y = zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1817_sum__squares__le__zero__iff,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 8.60/4.77 = ( ( X = zero_zero_int )
% 8.60/4.77 & ( Y = zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1818_sum__squares__gt__zero__iff,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 8.60/4.77 = ( ( X != zero_zero_real )
% 8.60/4.77 | ( Y != zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1819_sum__squares__gt__zero__iff,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 8.60/4.77 = ( ( X != zero_zero_rat )
% 8.60/4.77 | ( Y != zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1820_sum__squares__gt__zero__iff,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 8.60/4.77 = ( ( X != zero_zero_int )
% 8.60/4.77 | ( Y != zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1821_vebt__delete_Osimps_I2_J,axiom,
% 8.60/4.77 ! [A: $o,B: $o] :
% 8.60/4.77 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.77 = ( vEBT_Leaf @ A @ $false ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1822_vebt__delete_Osimps_I5_J,axiom,
% 8.60/4.77 ! [Mi: nat,Ma: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X: nat] :
% 8.60/4.77 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X )
% 8.60/4.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1823_vebt__delete_Osimps_I6_J,axiom,
% 8.60/4.77 ! [Mi: nat,Ma: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X: nat] :
% 8.60/4.77 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X )
% 8.60/4.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1824_add__def,axiom,
% 8.60/4.77 ( vEBT_VEBT_add
% 8.60/4.77 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1825_delete__correct,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.77 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 8.60/4.77 = ( minus_minus_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1826_double__eq__0__iff,axiom,
% 8.60/4.77 ! [A: real] :
% 8.60/4.77 ( ( ( plus_plus_real @ A @ A )
% 8.60/4.77 = zero_zero_real )
% 8.60/4.77 = ( A = zero_zero_real ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1827_double__eq__0__iff,axiom,
% 8.60/4.77 ! [A: rat] :
% 8.60/4.77 ( ( ( plus_plus_rat @ A @ A )
% 8.60/4.77 = zero_zero_rat )
% 8.60/4.77 = ( A = zero_zero_rat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1828_double__eq__0__iff,axiom,
% 8.60/4.77 ! [A: int] :
% 8.60/4.77 ( ( ( plus_plus_int @ A @ A )
% 8.60/4.77 = zero_zero_int )
% 8.60/4.77 = ( A = zero_zero_int ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1829_add__shift,axiom,
% 8.60/4.77 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.77 ( ( ( plus_plus_nat @ X @ Y )
% 8.60/4.77 = Z3 )
% 8.60/4.77 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 8.60/4.77 = ( some_nat @ Z3 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1830_delete__correct_H,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.77 => ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_delete @ T @ X ) )
% 8.60/4.77 = ( minus_minus_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1831_obtain__set__succ,axiom,
% 8.60/4.77 ! [X: nat,Z3: nat,A4: set_nat,B5: set_nat] :
% 8.60/4.77 ( ( ord_less_nat @ X @ Z3 )
% 8.60/4.77 => ( ( vEBT_VEBT_max_in_set @ A4 @ Z3 )
% 8.60/4.77 => ( ( finite_finite_nat @ B5 )
% 8.60/4.77 => ( ( A4 = B5 )
% 8.60/4.77 => ? [X_12: nat] : ( vEBT_is_succ_in_set @ A4 @ X @ X_12 ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1832_obtain__set__pred,axiom,
% 8.60/4.77 ! [Z3: nat,X: nat,A4: set_nat] :
% 8.60/4.77 ( ( ord_less_nat @ Z3 @ X )
% 8.60/4.77 => ( ( vEBT_VEBT_min_in_set @ A4 @ Z3 )
% 8.60/4.77 => ( ( finite_finite_nat @ A4 )
% 8.60/4.77 => ? [X_12: nat] : ( vEBT_is_pred_in_set @ A4 @ X @ X_12 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1833_length__pos__if__in__set,axiom,
% 8.60/4.77 ! [X: complex,Xs2: list_complex] :
% 8.60/4.77 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1834_length__pos__if__in__set,axiom,
% 8.60/4.77 ! [X: real,Xs2: list_real] :
% 8.60/4.77 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1835_length__pos__if__in__set,axiom,
% 8.60/4.77 ! [X: set_nat,Xs2: list_set_nat] :
% 8.60/4.77 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1836_length__pos__if__in__set,axiom,
% 8.60/4.77 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.77 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1837_length__pos__if__in__set,axiom,
% 8.60/4.77 ! [X: $o,Xs2: list_o] :
% 8.60/4.77 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1838_length__pos__if__in__set,axiom,
% 8.60/4.77 ! [X: nat,Xs2: list_nat] :
% 8.60/4.77 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1839_length__pos__if__in__set,axiom,
% 8.60/4.77 ! [X: int,Xs2: list_int] :
% 8.60/4.77 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.60/4.77 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1840_option_Osize__gen_I2_J,axiom,
% 8.60/4.77 ! [X: product_prod_nat_nat > nat,X2: product_prod_nat_nat] :
% 8.60/4.77 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X2 ) )
% 8.60/4.77 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1841_option_Osize__gen_I2_J,axiom,
% 8.60/4.77 ! [X: nat > nat,X2: nat] :
% 8.60/4.77 ( ( size_option_nat @ X @ ( some_nat @ X2 ) )
% 8.60/4.77 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1842_option_Osize__gen_I2_J,axiom,
% 8.60/4.77 ! [X: num > nat,X2: num] :
% 8.60/4.77 ( ( size_option_num @ X @ ( some_num @ X2 ) )
% 8.60/4.77 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1843_add__scale__eq__noteq,axiom,
% 8.60/4.77 ! [R3: complex,A: complex,B: complex,C2: complex,D: complex] :
% 8.60/4.77 ( ( R3 != zero_zero_complex )
% 8.60/4.77 => ( ( ( A = B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R3 @ C2 ) )
% 8.60/4.77 != ( plus_plus_complex @ B @ ( times_times_complex @ R3 @ D ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1844_add__scale__eq__noteq,axiom,
% 8.60/4.77 ! [R3: real,A: real,B: real,C2: real,D: real] :
% 8.60/4.77 ( ( R3 != zero_zero_real )
% 8.60/4.77 => ( ( ( A = B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 => ( ( plus_plus_real @ A @ ( times_times_real @ R3 @ C2 ) )
% 8.60/4.77 != ( plus_plus_real @ B @ ( times_times_real @ R3 @ D ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1845_add__scale__eq__noteq,axiom,
% 8.60/4.77 ! [R3: rat,A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.77 ( ( R3 != zero_zero_rat )
% 8.60/4.77 => ( ( ( A = B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C2 ) )
% 8.60/4.77 != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1846_add__scale__eq__noteq,axiom,
% 8.60/4.77 ! [R3: nat,A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.77 ( ( R3 != zero_zero_nat )
% 8.60/4.77 => ( ( ( A = B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C2 ) )
% 8.60/4.77 != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1847_add__scale__eq__noteq,axiom,
% 8.60/4.77 ! [R3: int,A: int,B: int,C2: int,D: int] :
% 8.60/4.77 ( ( R3 != zero_zero_int )
% 8.60/4.77 => ( ( ( A = B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C2 ) )
% 8.60/4.77 != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1848_set__vebt__finite,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT,N: nat] :
% 8.60/4.77 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.77 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1849_pred__none__empty,axiom,
% 8.60/4.77 ! [Xs2: set_nat,A: nat] :
% 8.60/4.77 ( ~ ? [X_12: nat] : ( vEBT_is_pred_in_set @ Xs2 @ A @ X_12 )
% 8.60/4.77 => ( ( finite_finite_nat @ Xs2 )
% 8.60/4.77 => ~ ? [X5: nat] :
% 8.60/4.77 ( ( member_nat @ X5 @ Xs2 )
% 8.60/4.77 & ( ord_less_nat @ X5 @ A ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1850_succ__none__empty,axiom,
% 8.60/4.77 ! [Xs2: set_nat,A: nat] :
% 8.60/4.77 ( ~ ? [X_12: nat] : ( vEBT_is_succ_in_set @ Xs2 @ A @ X_12 )
% 8.60/4.77 => ( ( finite_finite_nat @ Xs2 )
% 8.60/4.77 => ~ ? [X5: nat] :
% 8.60/4.77 ( ( member_nat @ X5 @ Xs2 )
% 8.60/4.77 & ( ord_less_nat @ A @ X5 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1851_diff__self,axiom,
% 8.60/4.77 ! [A: complex] :
% 8.60/4.77 ( ( minus_minus_complex @ A @ A )
% 8.60/4.77 = zero_zero_complex ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1852_diff__self,axiom,
% 8.60/4.77 ! [A: real] :
% 8.60/4.77 ( ( minus_minus_real @ A @ A )
% 8.60/4.77 = zero_zero_real ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1853_diff__self,axiom,
% 8.60/4.77 ! [A: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ A @ A )
% 8.60/4.77 = zero_zero_rat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1854_diff__self,axiom,
% 8.60/4.77 ! [A: int] :
% 8.60/4.77 ( ( minus_minus_int @ A @ A )
% 8.60/4.77 = zero_zero_int ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1855_diff__0__right,axiom,
% 8.60/4.77 ! [A: complex] :
% 8.60/4.77 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1856_diff__0__right,axiom,
% 8.60/4.77 ! [A: real] :
% 8.60/4.77 ( ( minus_minus_real @ A @ zero_zero_real )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1857_diff__0__right,axiom,
% 8.60/4.77 ! [A: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1858_diff__0__right,axiom,
% 8.60/4.77 ! [A: int] :
% 8.60/4.77 ( ( minus_minus_int @ A @ zero_zero_int )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1859_zero__diff,axiom,
% 8.60/4.77 ! [A: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 8.60/4.77 = zero_zero_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1860_diff__zero,axiom,
% 8.60/4.77 ! [A: complex] :
% 8.60/4.77 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1861_diff__zero,axiom,
% 8.60/4.77 ! [A: real] :
% 8.60/4.77 ( ( minus_minus_real @ A @ zero_zero_real )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1862_diff__zero,axiom,
% 8.60/4.77 ! [A: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1863_diff__zero,axiom,
% 8.60/4.77 ! [A: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1864_diff__zero,axiom,
% 8.60/4.77 ! [A: int] :
% 8.60/4.77 ( ( minus_minus_int @ A @ zero_zero_int )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1865_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.60/4.77 ! [A: complex] :
% 8.60/4.77 ( ( minus_minus_complex @ A @ A )
% 8.60/4.77 = zero_zero_complex ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1866_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.60/4.77 ! [A: real] :
% 8.60/4.77 ( ( minus_minus_real @ A @ A )
% 8.60/4.77 = zero_zero_real ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1867_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.60/4.77 ! [A: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ A @ A )
% 8.60/4.77 = zero_zero_rat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1868_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.60/4.77 ! [A: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ A @ A )
% 8.60/4.77 = zero_zero_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1869_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 8.60/4.77 ! [A: int] :
% 8.60/4.77 ( ( minus_minus_int @ A @ A )
% 8.60/4.77 = zero_zero_int ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1870_add__diff__cancel__right_H,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1871_add__diff__cancel__right_H,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1872_add__diff__cancel__right_H,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1873_add__diff__cancel__right_H,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1874_add__diff__cancel__right,axiom,
% 8.60/4.77 ! [A: real,C2: real,B: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_real @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1875_add__diff__cancel__right,axiom,
% 8.60/4.77 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_rat @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1876_add__diff__cancel__right,axiom,
% 8.60/4.77 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_nat @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1877_add__diff__cancel__right,axiom,
% 8.60/4.77 ! [A: int,C2: int,B: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_int @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1878_add__diff__cancel__left_H,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 8.60/4.77 = B ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1879_add__diff__cancel__left_H,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 8.60/4.77 = B ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1880_add__diff__cancel__left_H,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 8.60/4.77 = B ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1881_add__diff__cancel__left_H,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 8.60/4.77 = B ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1882_add__diff__cancel__left,axiom,
% 8.60/4.77 ! [C2: real,A: real,B: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( plus_plus_real @ C2 @ A ) @ ( plus_plus_real @ C2 @ B ) )
% 8.60/4.77 = ( minus_minus_real @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1883_add__diff__cancel__left,axiom,
% 8.60/4.77 ! [C2: rat,A: rat,B: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( plus_plus_rat @ C2 @ A ) @ ( plus_plus_rat @ C2 @ B ) )
% 8.60/4.77 = ( minus_minus_rat @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1884_add__diff__cancel__left,axiom,
% 8.60/4.77 ! [C2: nat,A: nat,B: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ ( plus_plus_nat @ C2 @ B ) )
% 8.60/4.77 = ( minus_minus_nat @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1885_add__diff__cancel__left,axiom,
% 8.60/4.77 ! [C2: int,A: int,B: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( plus_plus_int @ C2 @ A ) @ ( plus_plus_int @ C2 @ B ) )
% 8.60/4.77 = ( minus_minus_int @ A @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1886_diff__add__cancel,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1887_diff__add__cancel,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1888_diff__add__cancel,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1889_add__diff__cancel,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1890_add__diff__cancel,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1891_add__diff__cancel,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.60/4.77 = A ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1892_diff__ge__0__iff__ge,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 8.60/4.77 = ( ord_less_eq_real @ B @ A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1893_diff__ge__0__iff__ge,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.60/4.77 = ( ord_less_eq_rat @ B @ A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1894_diff__ge__0__iff__ge,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.60/4.77 = ( ord_less_eq_int @ B @ A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1895_diff__gt__0__iff__gt,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 8.60/4.77 = ( ord_less_real @ B @ A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1896_diff__gt__0__iff__gt,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 8.60/4.77 = ( ord_less_rat @ B @ A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1897_diff__gt__0__iff__gt,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 8.60/4.77 = ( ord_less_int @ B @ A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1898_le__add__diff__inverse2,axiom,
% 8.60/4.77 ! [B: real,A: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ B @ A )
% 8.60/4.77 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1899_le__add__diff__inverse2,axiom,
% 8.60/4.77 ! [B: rat,A: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.77 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1900_le__add__diff__inverse2,axiom,
% 8.60/4.77 ! [B: nat,A: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.77 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1901_le__add__diff__inverse2,axiom,
% 8.60/4.77 ! [B: int,A: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.77 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1902_le__add__diff__inverse,axiom,
% 8.60/4.77 ! [B: real,A: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ B @ A )
% 8.60/4.77 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1903_le__add__diff__inverse,axiom,
% 8.60/4.77 ! [B: rat,A: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.77 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1904_le__add__diff__inverse,axiom,
% 8.60/4.77 ! [B: nat,A: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ B @ A )
% 8.60/4.77 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1905_le__add__diff__inverse,axiom,
% 8.60/4.77 ! [B: int,A: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.77 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1906_diff__add__zero,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.60/4.77 = zero_zero_nat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1907_diff__numeral__special_I9_J,axiom,
% 8.60/4.77 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ one_one_Code_integer )
% 8.60/4.77 = zero_z3403309356797280102nteger ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1908_diff__numeral__special_I9_J,axiom,
% 8.60/4.77 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 8.60/4.77 = zero_zero_complex ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1909_diff__numeral__special_I9_J,axiom,
% 8.60/4.77 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 8.60/4.77 = zero_zero_real ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1910_diff__numeral__special_I9_J,axiom,
% 8.60/4.77 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 8.60/4.77 = zero_zero_rat ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1911_diff__numeral__special_I9_J,axiom,
% 8.60/4.77 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 8.60/4.77 = zero_zero_int ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1912_neq__if__length__neq,axiom,
% 8.60/4.77 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.60/4.77 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.77 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.77 => ( Xs2 != Ys ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1913_neq__if__length__neq,axiom,
% 8.60/4.77 ! [Xs2: list_o,Ys: list_o] :
% 8.60/4.77 ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.77 != ( size_size_list_o @ Ys ) )
% 8.60/4.77 => ( Xs2 != Ys ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1914_neq__if__length__neq,axiom,
% 8.60/4.77 ! [Xs2: list_nat,Ys: list_nat] :
% 8.60/4.77 ( ( ( size_size_list_nat @ Xs2 )
% 8.60/4.77 != ( size_size_list_nat @ Ys ) )
% 8.60/4.77 => ( Xs2 != Ys ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1915_neq__if__length__neq,axiom,
% 8.60/4.77 ! [Xs2: list_int,Ys: list_int] :
% 8.60/4.77 ( ( ( size_size_list_int @ Xs2 )
% 8.60/4.77 != ( size_size_list_int @ Ys ) )
% 8.60/4.77 => ( Xs2 != Ys ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1916_Ex__list__of__length,axiom,
% 8.60/4.77 ! [N: nat] :
% 8.60/4.77 ? [Xs3: list_VEBT_VEBT] :
% 8.60/4.77 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 8.60/4.77 = N ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1917_Ex__list__of__length,axiom,
% 8.60/4.77 ! [N: nat] :
% 8.60/4.77 ? [Xs3: list_o] :
% 8.60/4.77 ( ( size_size_list_o @ Xs3 )
% 8.60/4.77 = N ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1918_Ex__list__of__length,axiom,
% 8.60/4.77 ! [N: nat] :
% 8.60/4.77 ? [Xs3: list_nat] :
% 8.60/4.77 ( ( size_size_list_nat @ Xs3 )
% 8.60/4.77 = N ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1919_Ex__list__of__length,axiom,
% 8.60/4.77 ! [N: nat] :
% 8.60/4.77 ? [Xs3: list_int] :
% 8.60/4.77 ( ( size_size_list_int @ Xs3 )
% 8.60/4.77 = N ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1920_diff__right__commute,axiom,
% 8.60/4.77 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B )
% 8.60/4.77 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1921_diff__right__commute,axiom,
% 8.60/4.77 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C2 ) @ B )
% 8.60/4.77 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1922_diff__right__commute,axiom,
% 8.60/4.77 ! [A: int,C2: int,B: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B )
% 8.60/4.77 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1923_diff__eq__diff__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.77 ( ( ( minus_minus_rat @ A @ B )
% 8.60/4.77 = ( minus_minus_rat @ C2 @ D ) )
% 8.60/4.77 => ( ( A = B )
% 8.60/4.77 = ( C2 = D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1924_diff__eq__diff__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.77 ( ( ( minus_minus_int @ A @ B )
% 8.60/4.77 = ( minus_minus_int @ C2 @ D ) )
% 8.60/4.77 => ( ( A = B )
% 8.60/4.77 = ( C2 = D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1925_diff__mono,axiom,
% 8.60/4.77 ! [A: rat,B: rat,D: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_rat @ D @ C2 )
% 8.60/4.77 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1926_diff__mono,axiom,
% 8.60/4.77 ! [A: int,B: int,D: int,C2: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_int @ D @ C2 )
% 8.60/4.77 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1927_diff__left__mono,axiom,
% 8.60/4.77 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ B @ A )
% 8.60/4.77 => ( ord_less_eq_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1928_diff__left__mono,axiom,
% 8.60/4.77 ! [B: int,A: int,C2: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ B @ A )
% 8.60/4.77 => ( ord_less_eq_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1929_diff__right__mono,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.77 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1930_diff__right__mono,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.77 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1931_diff__eq__diff__less__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.77 ( ( ( minus_minus_rat @ A @ B )
% 8.60/4.77 = ( minus_minus_rat @ C2 @ D ) )
% 8.60/4.77 => ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.77 = ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1932_diff__eq__diff__less__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.77 ( ( ( minus_minus_int @ A @ B )
% 8.60/4.77 = ( minus_minus_int @ C2 @ D ) )
% 8.60/4.77 => ( ( ord_less_eq_int @ A @ B )
% 8.60/4.77 = ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1933_eq__iff__diff__eq__0,axiom,
% 8.60/4.77 ( ( ^ [Y5: complex,Z2: complex] : ( Y5 = Z2 ) )
% 8.60/4.77 = ( ^ [A5: complex,B4: complex] :
% 8.60/4.77 ( ( minus_minus_complex @ A5 @ B4 )
% 8.60/4.77 = zero_zero_complex ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1934_eq__iff__diff__eq__0,axiom,
% 8.60/4.77 ( ( ^ [Y5: real,Z2: real] : ( Y5 = Z2 ) )
% 8.60/4.77 = ( ^ [A5: real,B4: real] :
% 8.60/4.77 ( ( minus_minus_real @ A5 @ B4 )
% 8.60/4.77 = zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1935_eq__iff__diff__eq__0,axiom,
% 8.60/4.77 ( ( ^ [Y5: rat,Z2: rat] : ( Y5 = Z2 ) )
% 8.60/4.77 = ( ^ [A5: rat,B4: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ A5 @ B4 )
% 8.60/4.77 = zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1936_eq__iff__diff__eq__0,axiom,
% 8.60/4.77 ( ( ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 8.60/4.77 = ( ^ [A5: int,B4: int] :
% 8.60/4.77 ( ( minus_minus_int @ A5 @ B4 )
% 8.60/4.77 = zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1937_diff__strict__right__mono,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( ord_less_real @ A @ B )
% 8.60/4.77 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1938_diff__strict__right__mono,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ A @ B )
% 8.60/4.77 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1939_diff__strict__right__mono,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ord_less_int @ A @ B )
% 8.60/4.77 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1940_diff__strict__left__mono,axiom,
% 8.60/4.77 ! [B: real,A: real,C2: real] :
% 8.60/4.77 ( ( ord_less_real @ B @ A )
% 8.60/4.77 => ( ord_less_real @ ( minus_minus_real @ C2 @ A ) @ ( minus_minus_real @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1941_diff__strict__left__mono,axiom,
% 8.60/4.77 ! [B: rat,A: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ B @ A )
% 8.60/4.77 => ( ord_less_rat @ ( minus_minus_rat @ C2 @ A ) @ ( minus_minus_rat @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1942_diff__strict__left__mono,axiom,
% 8.60/4.77 ! [B: int,A: int,C2: int] :
% 8.60/4.77 ( ( ord_less_int @ B @ A )
% 8.60/4.77 => ( ord_less_int @ ( minus_minus_int @ C2 @ A ) @ ( minus_minus_int @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1943_diff__eq__diff__less,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.77 ( ( ( minus_minus_real @ A @ B )
% 8.60/4.77 = ( minus_minus_real @ C2 @ D ) )
% 8.60/4.77 => ( ( ord_less_real @ A @ B )
% 8.60/4.77 = ( ord_less_real @ C2 @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1944_diff__eq__diff__less,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.77 ( ( ( minus_minus_rat @ A @ B )
% 8.60/4.77 = ( minus_minus_rat @ C2 @ D ) )
% 8.60/4.77 => ( ( ord_less_rat @ A @ B )
% 8.60/4.77 = ( ord_less_rat @ C2 @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1945_diff__eq__diff__less,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.77 ( ( ( minus_minus_int @ A @ B )
% 8.60/4.77 = ( minus_minus_int @ C2 @ D ) )
% 8.60/4.77 => ( ( ord_less_int @ A @ B )
% 8.60/4.77 = ( ord_less_int @ C2 @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1946_diff__strict__mono,axiom,
% 8.60/4.77 ! [A: real,B: real,D: real,C2: real] :
% 8.60/4.77 ( ( ord_less_real @ A @ B )
% 8.60/4.77 => ( ( ord_less_real @ D @ C2 )
% 8.60/4.77 => ( ord_less_real @ ( minus_minus_real @ A @ C2 ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1947_diff__strict__mono,axiom,
% 8.60/4.77 ! [A: rat,B: rat,D: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ A @ B )
% 8.60/4.77 => ( ( ord_less_rat @ D @ C2 )
% 8.60/4.77 => ( ord_less_rat @ ( minus_minus_rat @ A @ C2 ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1948_diff__strict__mono,axiom,
% 8.60/4.77 ! [A: int,B: int,D: int,C2: int] :
% 8.60/4.77 ( ( ord_less_int @ A @ B )
% 8.60/4.77 => ( ( ord_less_int @ D @ C2 )
% 8.60/4.77 => ( ord_less_int @ ( minus_minus_int @ A @ C2 ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1949_left__diff__distrib,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1950_left__diff__distrib,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1951_left__diff__distrib,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1952_right__diff__distrib,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1953_right__diff__distrib,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1954_right__diff__distrib,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1955_left__diff__distrib_H,axiom,
% 8.60/4.77 ! [B: real,C2: real,A: real] :
% 8.60/4.77 ( ( times_times_real @ ( minus_minus_real @ B @ C2 ) @ A )
% 8.60/4.77 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C2 @ A ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1956_left__diff__distrib_H,axiom,
% 8.60/4.77 ! [B: rat,C2: rat,A: rat] :
% 8.60/4.77 ( ( times_times_rat @ ( minus_minus_rat @ B @ C2 ) @ A )
% 8.60/4.77 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C2 @ A ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1957_left__diff__distrib_H,axiom,
% 8.60/4.77 ! [B: nat,C2: nat,A: nat] :
% 8.60/4.77 ( ( times_times_nat @ ( minus_minus_nat @ B @ C2 ) @ A )
% 8.60/4.77 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C2 @ A ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1958_left__diff__distrib_H,axiom,
% 8.60/4.77 ! [B: int,C2: int,A: int] :
% 8.60/4.77 ( ( times_times_int @ ( minus_minus_int @ B @ C2 ) @ A )
% 8.60/4.77 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C2 @ A ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1959_right__diff__distrib_H,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1960_right__diff__distrib_H,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1961_right__diff__distrib_H,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1962_right__diff__distrib_H,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1963_diff__diff__eq,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1964_diff__diff__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1965_diff__diff__eq,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1966_diff__diff__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1967_add__implies__diff,axiom,
% 8.60/4.77 ! [C2: real,B: real,A: real] :
% 8.60/4.77 ( ( ( plus_plus_real @ C2 @ B )
% 8.60/4.77 = A )
% 8.60/4.77 => ( C2
% 8.60/4.77 = ( minus_minus_real @ A @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1968_add__implies__diff,axiom,
% 8.60/4.77 ! [C2: rat,B: rat,A: rat] :
% 8.60/4.77 ( ( ( plus_plus_rat @ C2 @ B )
% 8.60/4.77 = A )
% 8.60/4.77 => ( C2
% 8.60/4.77 = ( minus_minus_rat @ A @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1969_add__implies__diff,axiom,
% 8.60/4.77 ! [C2: nat,B: nat,A: nat] :
% 8.60/4.77 ( ( ( plus_plus_nat @ C2 @ B )
% 8.60/4.77 = A )
% 8.60/4.77 => ( C2
% 8.60/4.77 = ( minus_minus_nat @ A @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1970_add__implies__diff,axiom,
% 8.60/4.77 ! [C2: int,B: int,A: int] :
% 8.60/4.77 ( ( ( plus_plus_int @ C2 @ B )
% 8.60/4.77 = A )
% 8.60/4.77 => ( C2
% 8.60/4.77 = ( minus_minus_int @ A @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1971_diff__add__eq__diff__diff__swap,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_real @ ( minus_minus_real @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1972_diff__add__eq__diff__diff__swap,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1973_diff__add__eq__diff__diff__swap,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_int @ ( minus_minus_int @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1974_diff__add__eq,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1975_diff__add__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1976_diff__add__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 8.60/4.77 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1977_diff__diff__eq2,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_real @ ( plus_plus_real @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1978_diff__diff__eq2,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1979_diff__diff__eq2,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_int @ ( plus_plus_int @ A @ C2 ) @ B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1980_add__diff__eq,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1981_add__diff__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1982_add__diff__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C2 ) )
% 8.60/4.77 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1983_eq__diff__eq,axiom,
% 8.60/4.77 ! [A: real,C2: real,B: real] :
% 8.60/4.77 ( ( A
% 8.60/4.77 = ( minus_minus_real @ C2 @ B ) )
% 8.60/4.77 = ( ( plus_plus_real @ A @ B )
% 8.60/4.77 = C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1984_eq__diff__eq,axiom,
% 8.60/4.77 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.77 ( ( A
% 8.60/4.77 = ( minus_minus_rat @ C2 @ B ) )
% 8.60/4.77 = ( ( plus_plus_rat @ A @ B )
% 8.60/4.77 = C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1985_eq__diff__eq,axiom,
% 8.60/4.77 ! [A: int,C2: int,B: int] :
% 8.60/4.77 ( ( A
% 8.60/4.77 = ( minus_minus_int @ C2 @ B ) )
% 8.60/4.77 = ( ( plus_plus_int @ A @ B )
% 8.60/4.77 = C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1986_diff__eq__eq,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( ( minus_minus_real @ A @ B )
% 8.60/4.77 = C2 )
% 8.60/4.77 = ( A
% 8.60/4.77 = ( plus_plus_real @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1987_diff__eq__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ( minus_minus_rat @ A @ B )
% 8.60/4.77 = C2 )
% 8.60/4.77 = ( A
% 8.60/4.77 = ( plus_plus_rat @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1988_diff__eq__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ( minus_minus_int @ A @ B )
% 8.60/4.77 = C2 )
% 8.60/4.77 = ( A
% 8.60/4.77 = ( plus_plus_int @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1989_group__cancel_Osub1,axiom,
% 8.60/4.77 ! [A4: real,K2: real,A: real,B: real] :
% 8.60/4.77 ( ( A4
% 8.60/4.77 = ( plus_plus_real @ K2 @ A ) )
% 8.60/4.77 => ( ( minus_minus_real @ A4 @ B )
% 8.60/4.77 = ( plus_plus_real @ K2 @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1990_group__cancel_Osub1,axiom,
% 8.60/4.77 ! [A4: rat,K2: rat,A: rat,B: rat] :
% 8.60/4.77 ( ( A4
% 8.60/4.77 = ( plus_plus_rat @ K2 @ A ) )
% 8.60/4.77 => ( ( minus_minus_rat @ A4 @ B )
% 8.60/4.77 = ( plus_plus_rat @ K2 @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1991_group__cancel_Osub1,axiom,
% 8.60/4.77 ! [A4: int,K2: int,A: int,B: int] :
% 8.60/4.77 ( ( A4
% 8.60/4.77 = ( plus_plus_int @ K2 @ A ) )
% 8.60/4.77 => ( ( minus_minus_int @ A4 @ B )
% 8.60/4.77 = ( plus_plus_int @ K2 @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1992_finite__nat__set__iff__bounded,axiom,
% 8.60/4.77 ( finite_finite_nat
% 8.60/4.77 = ( ^ [N5: set_nat] :
% 8.60/4.77 ? [M6: nat] :
% 8.60/4.77 ! [X4: nat] :
% 8.60/4.77 ( ( member_nat @ X4 @ N5 )
% 8.60/4.77 => ( ord_less_nat @ X4 @ M6 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1993_bounded__nat__set__is__finite,axiom,
% 8.60/4.77 ! [N6: set_nat,N: nat] :
% 8.60/4.77 ( ! [X3: nat] :
% 8.60/4.77 ( ( member_nat @ X3 @ N6 )
% 8.60/4.77 => ( ord_less_nat @ X3 @ N ) )
% 8.60/4.77 => ( finite_finite_nat @ N6 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1994_finite__nat__set__iff__bounded__le,axiom,
% 8.60/4.77 ( finite_finite_nat
% 8.60/4.77 = ( ^ [N5: set_nat] :
% 8.60/4.77 ? [M6: nat] :
% 8.60/4.77 ! [X4: nat] :
% 8.60/4.77 ( ( member_nat @ X4 @ N5 )
% 8.60/4.77 => ( ord_less_eq_nat @ X4 @ M6 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1995_le__iff__diff__le__0,axiom,
% 8.60/4.77 ( ord_less_eq_real
% 8.60/4.77 = ( ^ [A5: real,B4: real] : ( ord_less_eq_real @ ( minus_minus_real @ A5 @ B4 ) @ zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1996_le__iff__diff__le__0,axiom,
% 8.60/4.77 ( ord_less_eq_rat
% 8.60/4.77 = ( ^ [A5: rat,B4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1997_le__iff__diff__le__0,axiom,
% 8.60/4.77 ( ord_less_eq_int
% 8.60/4.77 = ( ^ [A5: int,B4: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1998_less__iff__diff__less__0,axiom,
% 8.60/4.77 ( ord_less_real
% 8.60/4.77 = ( ^ [A5: real,B4: real] : ( ord_less_real @ ( minus_minus_real @ A5 @ B4 ) @ zero_zero_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_1999_less__iff__diff__less__0,axiom,
% 8.60/4.77 ( ord_less_rat
% 8.60/4.77 = ( ^ [A5: rat,B4: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B4 ) @ zero_zero_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2000_less__iff__diff__less__0,axiom,
% 8.60/4.77 ( ord_less_int
% 8.60/4.77 = ( ^ [A5: int,B4: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B4 ) @ zero_zero_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2001_add__le__add__imp__diff__le,axiom,
% 8.60/4.77 ! [I2: real,K2: real,N: real,J2: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K2 ) )
% 8.60/4.77 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J2 @ K2 ) )
% 8.60/4.77 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2002_add__le__add__imp__diff__le,axiom,
% 8.60/4.77 ! [I2: rat,K2: rat,N: rat,J2: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K2 ) )
% 8.60/4.77 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J2 @ K2 ) )
% 8.60/4.77 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2003_add__le__add__imp__diff__le,axiom,
% 8.60/4.77 ! [I2: nat,K2: nat,N: nat,J2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K2 ) )
% 8.60/4.77 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J2 @ K2 ) )
% 8.60/4.77 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2004_add__le__add__imp__diff__le,axiom,
% 8.60/4.77 ! [I2: int,K2: int,N: int,J2: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K2 ) )
% 8.60/4.77 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J2 @ K2 ) )
% 8.60/4.77 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K2 ) @ J2 ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2005_add__le__imp__le__diff,axiom,
% 8.60/4.77 ! [I2: real,K2: real,N: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N @ K2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2006_add__le__imp__le__diff,axiom,
% 8.60/4.77 ! [I2: rat,K2: rat,N: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N @ K2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2007_add__le__imp__le__diff,axiom,
% 8.60/4.77 ! [I2: nat,K2: nat,N: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N @ K2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2008_add__le__imp__le__diff,axiom,
% 8.60/4.77 ! [I2: int,K2: int,N: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K2 ) @ N )
% 8.60/4.77 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N @ K2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2009_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( ( minus_minus_nat @ B @ A )
% 8.60/4.77 = C2 )
% 8.60/4.77 = ( B
% 8.60/4.77 = ( plus_plus_nat @ C2 @ A ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2010_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 8.60/4.77 = B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2011_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( minus_minus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 8.60/4.77 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2012_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A )
% 8.60/4.77 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2013_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C2 )
% 8.60/4.77 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2014_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A )
% 8.60/4.77 = ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2015_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( plus_plus_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 8.60/4.77 = ( minus_minus_nat @ ( plus_plus_nat @ C2 @ B ) @ A ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2016_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ B @ A ) )
% 8.60/4.77 = ( ord_less_eq_nat @ ( plus_plus_nat @ C2 @ A ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2017_le__add__diff,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ord_less_eq_nat @ C2 @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C2 ) @ A ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2018_diff__add,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.77 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 8.60/4.77 = B ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2019_le__diff__eq,axiom,
% 8.60/4.77 ! [A: real,C2: real,B: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 8.60/4.77 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2020_le__diff__eq,axiom,
% 8.60/4.77 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 8.60/4.77 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2021_le__diff__eq,axiom,
% 8.60/4.77 ! [A: int,C2: int,B: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 8.60/4.77 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2022_diff__le__eq,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 8.60/4.77 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2023_diff__le__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 8.60/4.77 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2024_diff__le__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 8.60/4.77 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2025_less__diff__eq,axiom,
% 8.60/4.77 ! [A: real,C2: real,B: real] :
% 8.60/4.77 ( ( ord_less_real @ A @ ( minus_minus_real @ C2 @ B ) )
% 8.60/4.77 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2026_less__diff__eq,axiom,
% 8.60/4.77 ! [A: rat,C2: rat,B: rat] :
% 8.60/4.77 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C2 @ B ) )
% 8.60/4.77 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2027_less__diff__eq,axiom,
% 8.60/4.77 ! [A: int,C2: int,B: int] :
% 8.60/4.77 ( ( ord_less_int @ A @ ( minus_minus_int @ C2 @ B ) )
% 8.60/4.77 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2028_diff__less__eq,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real] :
% 8.60/4.77 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C2 )
% 8.60/4.77 = ( ord_less_real @ A @ ( plus_plus_real @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2029_diff__less__eq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat] :
% 8.60/4.77 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C2 )
% 8.60/4.77 = ( ord_less_rat @ A @ ( plus_plus_rat @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2030_diff__less__eq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int] :
% 8.60/4.77 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 8.60/4.77 = ( ord_less_int @ A @ ( plus_plus_int @ C2 @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2031_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.60/4.77 ! [A: real,B: real] :
% 8.60/4.77 ( ~ ( ord_less_real @ A @ B )
% 8.60/4.77 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2032_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.60/4.77 ! [A: rat,B: rat] :
% 8.60/4.77 ( ~ ( ord_less_rat @ A @ B )
% 8.60/4.77 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2033_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.60/4.77 ! [A: nat,B: nat] :
% 8.60/4.77 ( ~ ( ord_less_nat @ A @ B )
% 8.60/4.77 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2034_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 8.60/4.77 ! [A: int,B: int] :
% 8.60/4.77 ( ~ ( ord_less_int @ A @ B )
% 8.60/4.77 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 8.60/4.77 = A ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2035_square__diff__square__factored,axiom,
% 8.60/4.77 ! [X: real,Y: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 8.60/4.77 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2036_square__diff__square__factored,axiom,
% 8.60/4.77 ! [X: rat,Y: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 8.60/4.77 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2037_square__diff__square__factored,axiom,
% 8.60/4.77 ! [X: int,Y: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 8.60/4.77 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2038_eq__add__iff2,axiom,
% 8.60/4.77 ! [A: real,E: real,C2: real,B: real,D: real] :
% 8.60/4.77 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 )
% 8.60/4.77 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.60/4.77 = ( C2
% 8.60/4.77 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2039_eq__add__iff2,axiom,
% 8.60/4.77 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 8.60/4.77 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 8.60/4.77 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.60/4.77 = ( C2
% 8.60/4.77 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2040_eq__add__iff2,axiom,
% 8.60/4.77 ! [A: int,E: int,C2: int,B: int,D: int] :
% 8.60/4.77 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 8.60/4.77 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.60/4.77 = ( C2
% 8.60/4.77 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2041_eq__add__iff1,axiom,
% 8.60/4.77 ! [A: real,E: real,C2: real,B: real,D: real] :
% 8.60/4.77 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 )
% 8.60/4.77 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.60/4.77 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 )
% 8.60/4.77 = D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2042_eq__add__iff1,axiom,
% 8.60/4.77 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 8.60/4.77 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 )
% 8.60/4.77 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.60/4.77 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 )
% 8.60/4.77 = D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2043_eq__add__iff1,axiom,
% 8.60/4.77 ! [A: int,E: int,C2: int,B: int,D: int] :
% 8.60/4.77 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 )
% 8.60/4.77 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.60/4.77 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 )
% 8.60/4.77 = D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2044_ordered__ring__class_Ole__add__iff2,axiom,
% 8.60/4.77 ! [A: real,E: real,C2: real,B: real,D: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_eq_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2045_ordered__ring__class_Ole__add__iff2,axiom,
% 8.60/4.77 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_eq_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2046_ordered__ring__class_Ole__add__iff2,axiom,
% 8.60/4.77 ! [A: int,E: int,C2: int,B: int,D: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_eq_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2047_ordered__ring__class_Ole__add__iff1,axiom,
% 8.60/4.77 ! [A: real,E: real,C2: real,B: real,D: real] :
% 8.60/4.77 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2048_ordered__ring__class_Ole__add__iff1,axiom,
% 8.60/4.77 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 8.60/4.77 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2049_ordered__ring__class_Ole__add__iff1,axiom,
% 8.60/4.77 ! [A: int,E: int,C2: int,B: int,D: int] :
% 8.60/4.77 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2050_less__add__iff1,axiom,
% 8.60/4.77 ! [A: real,E: real,C2: real,B: real,D: real] :
% 8.60/4.77 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2051_less__add__iff1,axiom,
% 8.60/4.77 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 8.60/4.77 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2052_less__add__iff1,axiom,
% 8.60/4.77 ! [A: int,E: int,C2: int,B: int,D: int] :
% 8.60/4.77 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C2 ) @ D ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2053_less__add__iff2,axiom,
% 8.60/4.77 ! [A: real,E: real,C2: real,B: real,D: real] :
% 8.60/4.77 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_real @ C2 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2054_less__add__iff2,axiom,
% 8.60/4.77 ! [A: rat,E: rat,C2: rat,B: rat,D: rat] :
% 8.60/4.77 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_rat @ C2 @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2055_less__add__iff2,axiom,
% 8.60/4.77 ! [A: int,E: int,C2: int,B: int,D: int] :
% 8.60/4.77 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 8.60/4.77 = ( ord_less_int @ C2 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2056_square__diff__one__factored,axiom,
% 8.60/4.77 ! [X: code_integer] :
% 8.60/4.77 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 8.60/4.77 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2057_square__diff__one__factored,axiom,
% 8.60/4.77 ! [X: complex] :
% 8.60/4.77 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 8.60/4.77 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2058_square__diff__one__factored,axiom,
% 8.60/4.77 ! [X: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 8.60/4.77 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2059_square__diff__one__factored,axiom,
% 8.60/4.77 ! [X: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 8.60/4.77 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2060_square__diff__one__factored,axiom,
% 8.60/4.77 ! [X: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 8.60/4.77 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2061_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_complex,P2: set_complex > $o,F2: complex > rat] :
% 8.60/4.77 ( ( finite3207457112153483333omplex @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_complex )
% 8.60/4.77 => ( ! [X3: complex,S4: set_complex] :
% 8.60/4.77 ( ( finite3207457112153483333omplex @ S4 )
% 8.60/4.77 => ( ! [Y6: complex] :
% 8.60/4.77 ( ( member_complex @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2062_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_nat,P2: set_nat > $o,F2: nat > rat] :
% 8.60/4.77 ( ( finite_finite_nat @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_nat )
% 8.60/4.77 => ( ! [X3: nat,S4: set_nat] :
% 8.60/4.77 ( ( finite_finite_nat @ S4 )
% 8.60/4.77 => ( ! [Y6: nat] :
% 8.60/4.77 ( ( member_nat @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2063_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_int,P2: set_int > $o,F2: int > rat] :
% 8.60/4.77 ( ( finite_finite_int @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_int )
% 8.60/4.77 => ( ! [X3: int,S4: set_int] :
% 8.60/4.77 ( ( finite_finite_int @ S4 )
% 8.60/4.77 => ( ! [Y6: int] :
% 8.60/4.77 ( ( member_int @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2064_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_real,P2: set_real > $o,F2: real > rat] :
% 8.60/4.77 ( ( finite_finite_real @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_real )
% 8.60/4.77 => ( ! [X3: real,S4: set_real] :
% 8.60/4.77 ( ( finite_finite_real @ S4 )
% 8.60/4.77 => ( ! [Y6: real] :
% 8.60/4.77 ( ( member_real @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_rat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2065_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_complex,P2: set_complex > $o,F2: complex > num] :
% 8.60/4.77 ( ( finite3207457112153483333omplex @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_complex )
% 8.60/4.77 => ( ! [X3: complex,S4: set_complex] :
% 8.60/4.77 ( ( finite3207457112153483333omplex @ S4 )
% 8.60/4.77 => ( ! [Y6: complex] :
% 8.60/4.77 ( ( member_complex @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2066_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_nat,P2: set_nat > $o,F2: nat > num] :
% 8.60/4.77 ( ( finite_finite_nat @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_nat )
% 8.60/4.77 => ( ! [X3: nat,S4: set_nat] :
% 8.60/4.77 ( ( finite_finite_nat @ S4 )
% 8.60/4.77 => ( ! [Y6: nat] :
% 8.60/4.77 ( ( member_nat @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2067_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_int,P2: set_int > $o,F2: int > num] :
% 8.60/4.77 ( ( finite_finite_int @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_int )
% 8.60/4.77 => ( ! [X3: int,S4: set_int] :
% 8.60/4.77 ( ( finite_finite_int @ S4 )
% 8.60/4.77 => ( ! [Y6: int] :
% 8.60/4.77 ( ( member_int @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_int @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2068_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_real,P2: set_real > $o,F2: real > num] :
% 8.60/4.77 ( ( finite_finite_real @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_real )
% 8.60/4.77 => ( ! [X3: real,S4: set_real] :
% 8.60/4.77 ( ( finite_finite_real @ S4 )
% 8.60/4.77 => ( ! [Y6: real] :
% 8.60/4.77 ( ( member_real @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_num @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_real @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2069_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_complex,P2: set_complex > $o,F2: complex > nat] :
% 8.60/4.77 ( ( finite3207457112153483333omplex @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_complex )
% 8.60/4.77 => ( ! [X3: complex,S4: set_complex] :
% 8.60/4.77 ( ( finite3207457112153483333omplex @ S4 )
% 8.60/4.77 => ( ! [Y6: complex] :
% 8.60/4.77 ( ( member_complex @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_nat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_complex @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2070_finite__ranking__induct,axiom,
% 8.60/4.77 ! [S3: set_nat,P2: set_nat > $o,F2: nat > nat] :
% 8.60/4.77 ( ( finite_finite_nat @ S3 )
% 8.60/4.77 => ( ( P2 @ bot_bot_set_nat )
% 8.60/4.77 => ( ! [X3: nat,S4: set_nat] :
% 8.60/4.77 ( ( finite_finite_nat @ S4 )
% 8.60/4.77 => ( ! [Y6: nat] :
% 8.60/4.77 ( ( member_nat @ Y6 @ S4 )
% 8.60/4.77 => ( ord_less_eq_nat @ ( F2 @ Y6 ) @ ( F2 @ X3 ) ) )
% 8.60/4.77 => ( ( P2 @ S4 )
% 8.60/4.77 => ( P2 @ ( insert_nat @ X3 @ S4 ) ) ) ) )
% 8.60/4.77 => ( P2 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2071_length__induct,axiom,
% 8.60/4.77 ! [P2: list_VEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 8.60/4.77 ( ! [Xs3: list_VEBT_VEBT] :
% 8.60/4.77 ( ! [Ys2: list_VEBT_VEBT] :
% 8.60/4.77 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Ys2 ) )
% 8.60/4.77 => ( P2 @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Xs2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2072_length__induct,axiom,
% 8.60/4.77 ! [P2: list_o > $o,Xs2: list_o] :
% 8.60/4.77 ( ! [Xs3: list_o] :
% 8.60/4.77 ( ! [Ys2: list_o] :
% 8.60/4.77 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Ys2 ) )
% 8.60/4.77 => ( P2 @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Xs2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2073_length__induct,axiom,
% 8.60/4.77 ! [P2: list_nat > $o,Xs2: list_nat] :
% 8.60/4.77 ( ! [Xs3: list_nat] :
% 8.60/4.77 ( ! [Ys2: list_nat] :
% 8.60/4.77 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Ys2 ) )
% 8.60/4.77 => ( P2 @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Xs2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2074_length__induct,axiom,
% 8.60/4.77 ! [P2: list_int > $o,Xs2: list_int] :
% 8.60/4.77 ( ! [Xs3: list_int] :
% 8.60/4.77 ( ! [Ys2: list_int] :
% 8.60/4.77 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Ys2 ) )
% 8.60/4.77 => ( P2 @ Xs3 ) )
% 8.60/4.77 => ( P2 @ Xs2 ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2075_add__0__iff,axiom,
% 8.60/4.77 ! [B: complex,A: complex] :
% 8.60/4.77 ( ( B
% 8.60/4.77 = ( plus_plus_complex @ B @ A ) )
% 8.60/4.77 = ( A = zero_zero_complex ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2076_add__0__iff,axiom,
% 8.60/4.77 ! [B: real,A: real] :
% 8.60/4.77 ( ( B
% 8.60/4.77 = ( plus_plus_real @ B @ A ) )
% 8.60/4.77 = ( A = zero_zero_real ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2077_add__0__iff,axiom,
% 8.60/4.77 ! [B: rat,A: rat] :
% 8.60/4.77 ( ( B
% 8.60/4.77 = ( plus_plus_rat @ B @ A ) )
% 8.60/4.77 = ( A = zero_zero_rat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2078_add__0__iff,axiom,
% 8.60/4.77 ! [B: nat,A: nat] :
% 8.60/4.77 ( ( B
% 8.60/4.77 = ( plus_plus_nat @ B @ A ) )
% 8.60/4.77 = ( A = zero_zero_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2079_add__0__iff,axiom,
% 8.60/4.77 ! [B: int,A: int] :
% 8.60/4.77 ( ( B
% 8.60/4.77 = ( plus_plus_int @ B @ A ) )
% 8.60/4.77 = ( A = zero_zero_int ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2080_crossproduct__eq,axiom,
% 8.60/4.77 ! [W2: real,Y: real,X: real,Z3: real] :
% 8.60/4.77 ( ( ( plus_plus_real @ ( times_times_real @ W2 @ Y ) @ ( times_times_real @ X @ Z3 ) )
% 8.60/4.77 = ( plus_plus_real @ ( times_times_real @ W2 @ Z3 ) @ ( times_times_real @ X @ Y ) ) )
% 8.60/4.77 = ( ( W2 = X )
% 8.60/4.77 | ( Y = Z3 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2081_crossproduct__eq,axiom,
% 8.60/4.77 ! [W2: rat,Y: rat,X: rat,Z3: rat] :
% 8.60/4.77 ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X @ Z3 ) )
% 8.60/4.77 = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z3 ) @ ( times_times_rat @ X @ Y ) ) )
% 8.60/4.77 = ( ( W2 = X )
% 8.60/4.77 | ( Y = Z3 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2082_crossproduct__eq,axiom,
% 8.60/4.77 ! [W2: nat,Y: nat,X: nat,Z3: nat] :
% 8.60/4.77 ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X @ Z3 ) )
% 8.60/4.77 = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z3 ) @ ( times_times_nat @ X @ Y ) ) )
% 8.60/4.77 = ( ( W2 = X )
% 8.60/4.77 | ( Y = Z3 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2083_crossproduct__eq,axiom,
% 8.60/4.77 ! [W2: int,Y: int,X: int,Z3: int] :
% 8.60/4.77 ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X @ Z3 ) )
% 8.60/4.77 = ( plus_plus_int @ ( times_times_int @ W2 @ Z3 ) @ ( times_times_int @ X @ Y ) ) )
% 8.60/4.77 = ( ( W2 = X )
% 8.60/4.77 | ( Y = Z3 ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2084_crossproduct__noteq,axiom,
% 8.60/4.77 ! [A: real,B: real,C2: real,D: real] :
% 8.60/4.77 ( ( ( A != B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 = ( ( plus_plus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) )
% 8.60/4.77 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2085_crossproduct__noteq,axiom,
% 8.60/4.77 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.60/4.77 ( ( ( A != B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) )
% 8.60/4.77 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2086_crossproduct__noteq,axiom,
% 8.60/4.77 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.60/4.77 ( ( ( A != B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) )
% 8.60/4.77 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2087_crossproduct__noteq,axiom,
% 8.60/4.77 ! [A: int,B: int,C2: int,D: int] :
% 8.60/4.77 ( ( ( A != B )
% 8.60/4.77 & ( C2 != D ) )
% 8.60/4.77 = ( ( plus_plus_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) )
% 8.60/4.77 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C2 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2088_option_Osize__gen_I1_J,axiom,
% 8.60/4.77 ! [X: nat > nat] :
% 8.60/4.77 ( ( size_option_nat @ X @ none_nat )
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2089_option_Osize__gen_I1_J,axiom,
% 8.60/4.77 ! [X: product_prod_nat_nat > nat] :
% 8.60/4.77 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2090_option_Osize__gen_I1_J,axiom,
% 8.60/4.77 ! [X: num > nat] :
% 8.60/4.77 ( ( size_option_num @ X @ none_num )
% 8.60/4.77 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2091_finite__has__minimal,axiom,
% 8.60/4.77 ! [A4: set_real] :
% 8.60/4.77 ( ( finite_finite_real @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_real )
% 8.60/4.77 => ? [X3: real] :
% 8.60/4.77 ( ( member_real @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: real] :
% 8.60/4.77 ( ( member_real @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_real @ Xa @ X3 )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2092_finite__has__minimal,axiom,
% 8.60/4.77 ! [A4: set_set_nat] :
% 8.60/4.77 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_set_nat )
% 8.60/4.77 => ? [X3: set_nat] :
% 8.60/4.77 ( ( member_set_nat @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: set_nat] :
% 8.60/4.77 ( ( member_set_nat @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2093_finite__has__minimal,axiom,
% 8.60/4.77 ! [A4: set_rat] :
% 8.60/4.77 ( ( finite_finite_rat @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_rat )
% 8.60/4.77 => ? [X3: rat] :
% 8.60/4.77 ( ( member_rat @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: rat] :
% 8.60/4.77 ( ( member_rat @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2094_finite__has__minimal,axiom,
% 8.60/4.77 ! [A4: set_num] :
% 8.60/4.77 ( ( finite_finite_num @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_num )
% 8.60/4.77 => ? [X3: num] :
% 8.60/4.77 ( ( member_num @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: num] :
% 8.60/4.77 ( ( member_num @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_num @ Xa @ X3 )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2095_finite__has__minimal,axiom,
% 8.60/4.77 ! [A4: set_nat] :
% 8.60/4.77 ( ( finite_finite_nat @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_nat )
% 8.60/4.77 => ? [X3: nat] :
% 8.60/4.77 ( ( member_nat @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: nat] :
% 8.60/4.77 ( ( member_nat @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2096_finite__has__minimal,axiom,
% 8.60/4.77 ! [A4: set_int] :
% 8.60/4.77 ( ( finite_finite_int @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_int )
% 8.60/4.77 => ? [X3: int] :
% 8.60/4.77 ( ( member_int @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: int] :
% 8.60/4.77 ( ( member_int @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_int @ Xa @ X3 )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2097_finite__has__maximal,axiom,
% 8.60/4.77 ! [A4: set_real] :
% 8.60/4.77 ( ( finite_finite_real @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_real )
% 8.60/4.77 => ? [X3: real] :
% 8.60/4.77 ( ( member_real @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: real] :
% 8.60/4.77 ( ( member_real @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_real @ X3 @ Xa )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2098_finite__has__maximal,axiom,
% 8.60/4.77 ! [A4: set_set_nat] :
% 8.60/4.77 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_set_nat )
% 8.60/4.77 => ? [X3: set_nat] :
% 8.60/4.77 ( ( member_set_nat @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: set_nat] :
% 8.60/4.77 ( ( member_set_nat @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2099_finite__has__maximal,axiom,
% 8.60/4.77 ! [A4: set_rat] :
% 8.60/4.77 ( ( finite_finite_rat @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_rat )
% 8.60/4.77 => ? [X3: rat] :
% 8.60/4.77 ( ( member_rat @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: rat] :
% 8.60/4.77 ( ( member_rat @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2100_finite__has__maximal,axiom,
% 8.60/4.77 ! [A4: set_num] :
% 8.60/4.77 ( ( finite_finite_num @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_num )
% 8.60/4.77 => ? [X3: num] :
% 8.60/4.77 ( ( member_num @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: num] :
% 8.60/4.77 ( ( member_num @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_num @ X3 @ Xa )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2101_finite__has__maximal,axiom,
% 8.60/4.77 ! [A4: set_nat] :
% 8.60/4.77 ( ( finite_finite_nat @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_nat )
% 8.60/4.77 => ? [X3: nat] :
% 8.60/4.77 ( ( member_nat @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: nat] :
% 8.60/4.77 ( ( member_nat @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2102_finite__has__maximal,axiom,
% 8.60/4.77 ! [A4: set_int] :
% 8.60/4.77 ( ( finite_finite_int @ A4 )
% 8.60/4.77 => ( ( A4 != bot_bot_set_int )
% 8.60/4.77 => ? [X3: int] :
% 8.60/4.77 ( ( member_int @ X3 @ A4 )
% 8.60/4.77 & ! [Xa: int] :
% 8.60/4.77 ( ( member_int @ Xa @ A4 )
% 8.60/4.77 => ( ( ord_less_eq_int @ X3 @ Xa )
% 8.60/4.77 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2103_mult__diff__mult,axiom,
% 8.60/4.77 ! [X: real,Y: real,A: real,B: real] :
% 8.60/4.77 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 8.60/4.77 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2104_mult__diff__mult,axiom,
% 8.60/4.77 ! [X: rat,Y: rat,A: rat,B: rat] :
% 8.60/4.77 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 8.60/4.77 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2105_mult__diff__mult,axiom,
% 8.60/4.77 ! [X: int,Y: int,A: int,B: int] :
% 8.60/4.77 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 8.60/4.77 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2106_diff__shunt__var,axiom,
% 8.60/4.77 ! [X: set_int,Y: set_int] :
% 8.60/4.77 ( ( ( minus_minus_set_int @ X @ Y )
% 8.60/4.77 = bot_bot_set_int )
% 8.60/4.77 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2107_diff__shunt__var,axiom,
% 8.60/4.77 ! [X: set_real,Y: set_real] :
% 8.60/4.77 ( ( ( minus_minus_set_real @ X @ Y )
% 8.60/4.77 = bot_bot_set_real )
% 8.60/4.77 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2108_diff__shunt__var,axiom,
% 8.60/4.77 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 8.60/4.77 ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 8.60/4.77 = bot_bo2099793752762293965at_nat )
% 8.60/4.77 = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2109_diff__shunt__var,axiom,
% 8.60/4.77 ! [X: set_nat,Y: set_nat] :
% 8.60/4.77 ( ( ( minus_minus_set_nat @ X @ Y )
% 8.60/4.77 = bot_bot_set_nat )
% 8.60/4.77 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2110_minNullmin,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT] :
% 8.60/4.77 ( ( vEBT_VEBT_minNull @ T )
% 8.60/4.77 => ( ( vEBT_vebt_mint @ T )
% 8.60/4.77 = none_nat ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2111_minminNull,axiom,
% 8.60/4.77 ! [T: vEBT_VEBT] :
% 8.60/4.77 ( ( ( vEBT_vebt_mint @ T )
% 8.60/4.77 = none_nat )
% 8.60/4.77 => ( vEBT_VEBT_minNull @ T ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2112_vebt__maxt_Opelims,axiom,
% 8.60/4.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 8.60/4.77 ( ( ( vEBT_vebt_maxt @ X )
% 8.60/4.77 = Y )
% 8.60/4.77 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 8.60/4.77 => ( ! [A3: $o,B3: $o] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.60/4.77 => ( ( ( B3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B3
% 8.60/4.77 => ( ( A3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A3
% 8.60/4.77 => ( Y = none_nat ) ) ) ) )
% 8.60/4.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 8.60/4.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.60/4.77 => ( ( Y = none_nat )
% 8.60/4.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) ) ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 8.60/4.77 => ( ( Y
% 8.60/4.77 = ( some_nat @ Ma2 ) )
% 8.60/4.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2113_vebt__mint_Opelims,axiom,
% 8.60/4.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 8.60/4.77 ( ( ( vEBT_vebt_mint @ X )
% 8.60/4.77 = Y )
% 8.60/4.77 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 8.60/4.77 => ( ! [A3: $o,B3: $o] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.60/4.77 => ( ( ( A3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ zero_zero_nat ) ) )
% 8.60/4.77 & ( ~ A3
% 8.60/4.77 => ( ( B3
% 8.60/4.77 => ( Y
% 8.60/4.77 = ( some_nat @ one_one_nat ) ) )
% 8.60/4.77 & ( ~ B3
% 8.60/4.77 => ( Y = none_nat ) ) ) ) )
% 8.60/4.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 8.60/4.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.60/4.77 => ( ( Y = none_nat )
% 8.60/4.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) ) ) )
% 8.60/4.77 => ~ ! [Mi2: nat,Ma2: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.60/4.77 ( ( X
% 8.60/4.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) )
% 8.60/4.77 => ( ( Y
% 8.60/4.77 = ( some_nat @ Mi2 ) )
% 8.60/4.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux @ Uy @ Uz2 ) ) ) ) ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2114_infinite__nat__iff__unbounded__le,axiom,
% 8.60/4.77 ! [S3: set_nat] :
% 8.60/4.77 ( ( ~ ( finite_finite_nat @ S3 ) )
% 8.60/4.77 = ( ! [M6: nat] :
% 8.60/4.77 ? [N4: nat] :
% 8.60/4.77 ( ( ord_less_eq_nat @ M6 @ N4 )
% 8.60/4.77 & ( member_nat @ N4 @ S3 ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2115_inthall,axiom,
% 8.60/4.77 ! [Xs2: list_complex,P2: complex > $o,N: nat] :
% 8.60/4.77 ( ! [X3: complex] :
% 8.60/4.77 ( ( member_complex @ X3 @ ( set_complex2 @ Xs2 ) )
% 8.60/4.77 => ( P2 @ X3 ) )
% 8.60/4.77 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.60/4.77 => ( P2 @ ( nth_complex @ Xs2 @ N ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2116_inthall,axiom,
% 8.60/4.77 ! [Xs2: list_real,P2: real > $o,N: nat] :
% 8.60/4.77 ( ! [X3: real] :
% 8.60/4.77 ( ( member_real @ X3 @ ( set_real2 @ Xs2 ) )
% 8.60/4.77 => ( P2 @ X3 ) )
% 8.60/4.77 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 8.60/4.77 => ( P2 @ ( nth_real @ Xs2 @ N ) ) ) ) ).
% 8.60/4.77
% 8.60/4.77 thf(fact_2117_inthall,axiom,
% 8.60/4.77 ! [Xs2: list_set_nat,P2: set_nat > $o,N: nat] :
% 8.60/4.77 ( ! [X3: set_nat] :
% 8.60/4.77 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs2 ) )
% 8.60/4.77 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_set_nat @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2118_inthall,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o,N: nat] :
% 8.60/4.78 ( ! [X3: vEBT_VEBT] :
% 8.60/4.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2119_inthall,axiom,
% 8.60/4.78 ! [Xs2: list_o,P2: $o > $o,N: nat] :
% 8.60/4.78 ( ! [X3: $o] :
% 8.60/4.78 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2120_inthall,axiom,
% 8.60/4.78 ! [Xs2: list_nat,P2: nat > $o,N: nat] :
% 8.60/4.78 ( ! [X3: nat] :
% 8.60/4.78 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2121_inthall,axiom,
% 8.60/4.78 ! [Xs2: list_int,P2: int > $o,N: nat] :
% 8.60/4.78 ( ! [X3: int] :
% 8.60/4.78 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2122_not__min__Null__member,axiom,
% 8.60/4.78 ! [T: vEBT_VEBT] :
% 8.60/4.78 ( ~ ( vEBT_VEBT_minNull @ T )
% 8.60/4.78 => ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_12 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2123_min__Null__member,axiom,
% 8.60/4.78 ! [T: vEBT_VEBT,X: nat] :
% 8.60/4.78 ( ( vEBT_VEBT_minNull @ T )
% 8.60/4.78 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2124_Suc__diff__diff,axiom,
% 8.60/4.78 ! [M2: nat,N: nat,K2: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( suc @ K2 ) )
% 8.60/4.78 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ N ) @ K2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2125_diff__Suc__Suc,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 8.60/4.78 = ( minus_minus_nat @ M2 @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2126_diff__0__eq__0,axiom,
% 8.60/4.78 ! [N: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 8.60/4.78 = zero_zero_nat ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2127_diff__self__eq__0,axiom,
% 8.60/4.78 ! [M2: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ M2 @ M2 )
% 8.60/4.78 = zero_zero_nat ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2128_diff__diff__cancel,axiom,
% 8.60/4.78 ! [I2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ I2 @ N )
% 8.60/4.78 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I2 ) )
% 8.60/4.78 = I2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2129_diff__diff__left,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 8.60/4.78 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2130_zero__less__diff,axiom,
% 8.60/4.78 ! [N: nat,M2: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M2 ) )
% 8.60/4.78 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2131_diff__is__0__eq_H,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.78 => ( ( minus_minus_nat @ M2 @ N )
% 8.60/4.78 = zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2132_diff__is__0__eq,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] :
% 8.60/4.78 ( ( ( minus_minus_nat @ M2 @ N )
% 8.60/4.78 = zero_zero_nat )
% 8.60/4.78 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2133_Nat_Oadd__diff__assoc,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 8.60/4.78 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2134_Nat_Oadd__diff__assoc2,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 8.60/4.78 = ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2135_Nat_Odiff__diff__right,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 8.60/4.78 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2136_diff__Suc__1,axiom,
% 8.60/4.78 ! [N: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 8.60/4.78 = N ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2137_Suc__pred,axiom,
% 8.60/4.78 ! [N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 8.60/4.78 = N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2138_diff__Suc__diff__eq1,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) )
% 8.60/4.78 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K2 ) @ ( suc @ J2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2139_diff__Suc__diff__eq2,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J2 @ K2 ) ) @ I2 )
% 8.60/4.78 = ( minus_minus_nat @ ( suc @ J2 ) @ ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2140_Suc__diff__1,axiom,
% 8.60/4.78 ! [N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 = N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2141_zero__induct__lemma,axiom,
% 8.60/4.78 ! [P2: nat > $o,K2: nat,I2: nat] :
% 8.60/4.78 ( ( P2 @ K2 )
% 8.60/4.78 => ( ! [N3: nat] :
% 8.60/4.78 ( ( P2 @ ( suc @ N3 ) )
% 8.60/4.78 => ( P2 @ N3 ) )
% 8.60/4.78 => ( P2 @ ( minus_minus_nat @ K2 @ I2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2142_minus__nat_Odiff__0,axiom,
% 8.60/4.78 ! [M2: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ M2 @ zero_zero_nat )
% 8.60/4.78 = M2 ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2143_diffs0__imp__equal,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] :
% 8.60/4.78 ( ( ( minus_minus_nat @ M2 @ N )
% 8.60/4.78 = zero_zero_nat )
% 8.60/4.78 => ( ( ( minus_minus_nat @ N @ M2 )
% 8.60/4.78 = zero_zero_nat )
% 8.60/4.78 => ( M2 = N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2144_diff__less__mono2,axiom,
% 8.60/4.78 ! [M2: nat,N: nat,L: nat] :
% 8.60/4.78 ( ( ord_less_nat @ M2 @ N )
% 8.60/4.78 => ( ( ord_less_nat @ M2 @ L )
% 8.60/4.78 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2145_less__imp__diff__less,axiom,
% 8.60/4.78 ! [J2: nat,K2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J2 @ K2 )
% 8.60/4.78 => ( ord_less_nat @ ( minus_minus_nat @ J2 @ N ) @ K2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2146_diff__le__mono2,axiom,
% 8.60/4.78 ! [M2: nat,N: nat,L: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.78 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2147_le__diff__iff_H,axiom,
% 8.60/4.78 ! [A: nat,C2: nat,B: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ A @ C2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ B @ C2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C2 @ A ) @ ( minus_minus_nat @ C2 @ B ) )
% 8.60/4.78 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2148_diff__le__self,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2149_diff__le__mono,axiom,
% 8.60/4.78 ! [M2: nat,N: nat,L: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ M2 @ N )
% 8.60/4.78 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2150_Nat_Odiff__diff__eq,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ M2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.60/4.78 => ( ( minus_minus_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 8.60/4.78 = ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2151_le__diff__iff,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ M2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 8.60/4.78 = ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2152_eq__diff__iff,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ M2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.60/4.78 => ( ( ( minus_minus_nat @ M2 @ K2 )
% 8.60/4.78 = ( minus_minus_nat @ N @ K2 ) )
% 8.60/4.78 = ( M2 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2153_Nat_Odiff__cancel,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( plus_plus_nat @ K2 @ M2 ) @ ( plus_plus_nat @ K2 @ N ) )
% 8.60/4.78 = ( minus_minus_nat @ M2 @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2154_diff__cancel2,axiom,
% 8.60/4.78 ! [M2: nat,K2: nat,N: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) )
% 8.60/4.78 = ( minus_minus_nat @ M2 @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2155_diff__add__inverse,axiom,
% 8.60/4.78 ! [N: nat,M2: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M2 ) @ N )
% 8.60/4.78 = M2 ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2156_diff__add__inverse2,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ N )
% 8.60/4.78 = M2 ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2157_diff__mult__distrib,axiom,
% 8.60/4.78 ! [M2: nat,N: nat,K2: nat] :
% 8.60/4.78 ( ( times_times_nat @ ( minus_minus_nat @ M2 @ N ) @ K2 )
% 8.60/4.78 = ( minus_minus_nat @ ( times_times_nat @ M2 @ K2 ) @ ( times_times_nat @ N @ K2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2158_diff__mult__distrib2,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( times_times_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 8.60/4.78 = ( minus_minus_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2159_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 8.60/4.78 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2160_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 8.60/4.78 ! [Uv: $o] :
% 8.60/4.78 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2161_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 8.60/4.78 ! [Uu: $o] :
% 8.60/4.78 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2162_list__eq__iff__nth__eq,axiom,
% 8.60/4.78 ( ( ^ [Y5: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y5 = Z2 ) )
% 8.60/4.78 = ( ^ [Xs: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.60/4.78 => ( ( nth_VEBT_VEBT @ Xs @ I )
% 8.60/4.78 = ( nth_VEBT_VEBT @ Ys3 @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2163_list__eq__iff__nth__eq,axiom,
% 8.60/4.78 ( ( ^ [Y5: list_o,Z2: list_o] : ( Y5 = Z2 ) )
% 8.60/4.78 = ( ^ [Xs: list_o,Ys3: list_o] :
% 8.60/4.78 ( ( ( size_size_list_o @ Xs )
% 8.60/4.78 = ( size_size_list_o @ Ys3 ) )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 8.60/4.78 => ( ( nth_o @ Xs @ I )
% 8.60/4.78 = ( nth_o @ Ys3 @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2164_list__eq__iff__nth__eq,axiom,
% 8.60/4.78 ( ( ^ [Y5: list_nat,Z2: list_nat] : ( Y5 = Z2 ) )
% 8.60/4.78 = ( ^ [Xs: list_nat,Ys3: list_nat] :
% 8.60/4.78 ( ( ( size_size_list_nat @ Xs )
% 8.60/4.78 = ( size_size_list_nat @ Ys3 ) )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 8.60/4.78 => ( ( nth_nat @ Xs @ I )
% 8.60/4.78 = ( nth_nat @ Ys3 @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2165_list__eq__iff__nth__eq,axiom,
% 8.60/4.78 ( ( ^ [Y5: list_int,Z2: list_int] : ( Y5 = Z2 ) )
% 8.60/4.78 = ( ^ [Xs: list_int,Ys3: list_int] :
% 8.60/4.78 ( ( ( size_size_list_int @ Xs )
% 8.60/4.78 = ( size_size_list_int @ Ys3 ) )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 8.60/4.78 => ( ( nth_int @ Xs @ I )
% 8.60/4.78 = ( nth_int @ Ys3 @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2166_Skolem__list__nth,axiom,
% 8.60/4.78 ! [K2: nat,P2: nat > vEBT_VEBT > $o] :
% 8.60/4.78 ( ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ? [X7: vEBT_VEBT] : ( P2 @ I @ X7 ) ) )
% 8.60/4.78 = ( ? [Xs: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.60/4.78 = K2 )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ( P2 @ I @ ( nth_VEBT_VEBT @ Xs @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2167_Skolem__list__nth,axiom,
% 8.60/4.78 ! [K2: nat,P2: nat > $o > $o] :
% 8.60/4.78 ( ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ? [X7: $o] : ( P2 @ I @ X7 ) ) )
% 8.60/4.78 = ( ? [Xs: list_o] :
% 8.60/4.78 ( ( ( size_size_list_o @ Xs )
% 8.60/4.78 = K2 )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ( P2 @ I @ ( nth_o @ Xs @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2168_Skolem__list__nth,axiom,
% 8.60/4.78 ! [K2: nat,P2: nat > nat > $o] :
% 8.60/4.78 ( ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ? [X7: nat] : ( P2 @ I @ X7 ) ) )
% 8.60/4.78 = ( ? [Xs: list_nat] :
% 8.60/4.78 ( ( ( size_size_list_nat @ Xs )
% 8.60/4.78 = K2 )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ( P2 @ I @ ( nth_nat @ Xs @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2169_Skolem__list__nth,axiom,
% 8.60/4.78 ! [K2: nat,P2: nat > int > $o] :
% 8.60/4.78 ( ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ? [X7: int] : ( P2 @ I @ X7 ) ) )
% 8.60/4.78 = ( ? [Xs: list_int] :
% 8.60/4.78 ( ( ( size_size_list_int @ Xs )
% 8.60/4.78 = K2 )
% 8.60/4.78 & ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ K2 )
% 8.60/4.78 => ( P2 @ I @ ( nth_int @ Xs @ I ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2170_nth__equalityI,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ( nth_VEBT_VEBT @ Xs2 @ I3 )
% 8.60/4.78 = ( nth_VEBT_VEBT @ Ys @ I3 ) ) )
% 8.60/4.78 => ( Xs2 = Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2171_nth__equalityI,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_o] :
% 8.60/4.78 ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.78 = ( size_size_list_o @ Ys ) )
% 8.60/4.78 => ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ( nth_o @ Xs2 @ I3 )
% 8.60/4.78 = ( nth_o @ Ys @ I3 ) ) )
% 8.60/4.78 => ( Xs2 = Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2172_nth__equalityI,axiom,
% 8.60/4.78 ! [Xs2: list_nat,Ys: list_nat] :
% 8.60/4.78 ( ( ( size_size_list_nat @ Xs2 )
% 8.60/4.78 = ( size_size_list_nat @ Ys ) )
% 8.60/4.78 => ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( ( nth_nat @ Xs2 @ I3 )
% 8.60/4.78 = ( nth_nat @ Ys @ I3 ) ) )
% 8.60/4.78 => ( Xs2 = Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2173_nth__equalityI,axiom,
% 8.60/4.78 ! [Xs2: list_int,Ys: list_int] :
% 8.60/4.78 ( ( ( size_size_list_int @ Xs2 )
% 8.60/4.78 = ( size_size_list_int @ Ys ) )
% 8.60/4.78 => ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( ( nth_int @ Xs2 @ I3 )
% 8.60/4.78 = ( nth_int @ Ys @ I3 ) ) )
% 8.60/4.78 => ( Xs2 = Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2174_diff__less__Suc,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ ( suc @ M2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2175_Suc__diff__Suc,axiom,
% 8.60/4.78 ! [N: nat,M2: nat] :
% 8.60/4.78 ( ( ord_less_nat @ N @ M2 )
% 8.60/4.78 => ( ( suc @ ( minus_minus_nat @ M2 @ ( suc @ N ) ) )
% 8.60/4.78 = ( minus_minus_nat @ M2 @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2176_diff__less,axiom,
% 8.60/4.78 ! [N: nat,M2: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.60/4.78 => ( ord_less_nat @ ( minus_minus_nat @ M2 @ N ) @ M2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2177_Suc__diff__le,axiom,
% 8.60/4.78 ! [N: nat,M2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ N @ M2 )
% 8.60/4.78 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 8.60/4.78 = ( suc @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2178_less__diff__iff,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ M2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.60/4.78 => ( ( ord_less_nat @ ( minus_minus_nat @ M2 @ K2 ) @ ( minus_minus_nat @ N @ K2 ) )
% 8.60/4.78 = ( ord_less_nat @ M2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2179_diff__less__mono,axiom,
% 8.60/4.78 ! [A: nat,B: nat,C2: nat] :
% 8.60/4.78 ( ( ord_less_nat @ A @ B )
% 8.60/4.78 => ( ( ord_less_eq_nat @ C2 @ A )
% 8.60/4.78 => ( ord_less_nat @ ( minus_minus_nat @ A @ C2 ) @ ( minus_minus_nat @ B @ C2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2180_diff__add__0,axiom,
% 8.60/4.78 ! [N: nat,M2: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M2 ) )
% 8.60/4.78 = zero_zero_nat ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2181_finite__maxlen,axiom,
% 8.60/4.78 ! [M5: set_list_VEBT_VEBT] :
% 8.60/4.78 ( ( finite3004134309566078307T_VEBT @ M5 )
% 8.60/4.78 => ? [N3: nat] :
% 8.60/4.78 ! [X5: list_VEBT_VEBT] :
% 8.60/4.78 ( ( member2936631157270082147T_VEBT @ X5 @ M5 )
% 8.60/4.78 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X5 ) @ N3 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2182_finite__maxlen,axiom,
% 8.60/4.78 ! [M5: set_list_o] :
% 8.60/4.78 ( ( finite_finite_list_o @ M5 )
% 8.60/4.78 => ? [N3: nat] :
% 8.60/4.78 ! [X5: list_o] :
% 8.60/4.78 ( ( member_list_o @ X5 @ M5 )
% 8.60/4.78 => ( ord_less_nat @ ( size_size_list_o @ X5 ) @ N3 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2183_finite__maxlen,axiom,
% 8.60/4.78 ! [M5: set_list_nat] :
% 8.60/4.78 ( ( finite8100373058378681591st_nat @ M5 )
% 8.60/4.78 => ? [N3: nat] :
% 8.60/4.78 ! [X5: list_nat] :
% 8.60/4.78 ( ( member_list_nat @ X5 @ M5 )
% 8.60/4.78 => ( ord_less_nat @ ( size_size_list_nat @ X5 ) @ N3 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2184_finite__maxlen,axiom,
% 8.60/4.78 ! [M5: set_list_int] :
% 8.60/4.78 ( ( finite3922522038869484883st_int @ M5 )
% 8.60/4.78 => ? [N3: nat] :
% 8.60/4.78 ! [X5: list_int] :
% 8.60/4.78 ( ( member_list_int @ X5 @ M5 )
% 8.60/4.78 => ( ord_less_nat @ ( size_size_list_int @ X5 ) @ N3 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2185_less__diff__conv,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 8.60/4.78 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2186_add__diff__inverse__nat,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] :
% 8.60/4.78 ( ~ ( ord_less_nat @ M2 @ N )
% 8.60/4.78 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M2 @ N ) )
% 8.60/4.78 = M2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2187_le__diff__conv,axiom,
% 8.60/4.78 ! [J2: nat,K2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 8.60/4.78 = ( ord_less_eq_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2188_Nat_Ole__diff__conv2,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) )
% 8.60/4.78 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K2 ) @ J2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2189_Nat_Odiff__add__assoc,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J2 ) @ K2 )
% 8.60/4.78 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J2 @ K2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2190_Nat_Odiff__add__assoc2,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( minus_minus_nat @ ( plus_plus_nat @ J2 @ I2 ) @ K2 )
% 8.60/4.78 = ( plus_plus_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2191_Nat_Ole__imp__diff__is__add,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.78 => ( ( ( minus_minus_nat @ J2 @ I2 )
% 8.60/4.78 = K2 )
% 8.60/4.78 = ( J2
% 8.60/4.78 = ( plus_plus_nat @ K2 @ I2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2192_diff__Suc__eq__diff__pred,axiom,
% 8.60/4.78 ! [M2: nat,N: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 8.60/4.78 = ( minus_minus_nat @ ( minus_minus_nat @ M2 @ one_one_nat ) @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2193_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 8.60/4.78 ! [Uz: product_prod_nat_nat,Va3: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 8.60/4.78 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va3 @ Vb @ Vc ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2194_nth__mem,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_complex] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.60/4.78 => ( member_complex @ ( nth_complex @ Xs2 @ N ) @ ( set_complex2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2195_nth__mem,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_real] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 8.60/4.78 => ( member_real @ ( nth_real @ Xs2 @ N ) @ ( set_real2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2196_nth__mem,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_set_nat] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.60/4.78 => ( member_set_nat @ ( nth_set_nat @ Xs2 @ N ) @ ( set_set_nat2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2197_nth__mem,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ ( set_VEBT_VEBT2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2198_nth__mem,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_o] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( member_o @ ( nth_o @ Xs2 @ N ) @ ( set_o2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2199_nth__mem,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( member_nat @ ( nth_nat @ Xs2 @ N ) @ ( set_nat2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2200_nth__mem,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_int] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( member_int @ ( nth_int @ Xs2 @ N ) @ ( set_int2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2201_list__ball__nth,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ! [X3: vEBT_VEBT] :
% 8.60/4.78 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2202_list__ball__nth,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_o,P2: $o > $o] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ! [X3: $o] :
% 8.60/4.78 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( P2 @ ( nth_o @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2203_list__ball__nth,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_nat,P2: nat > $o] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( ! [X3: nat] :
% 8.60/4.78 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( P2 @ ( nth_nat @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2204_list__ball__nth,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_int,P2: int > $o] :
% 8.60/4.78 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( ! [X3: int] :
% 8.60/4.78 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( P2 @ ( nth_int @ Xs2 @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2205_in__set__conv__nth,axiom,
% 8.60/4.78 ! [X: complex,Xs2: list_complex] :
% 8.60/4.78 ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.60/4.78 & ( ( nth_complex @ Xs2 @ I )
% 8.60/4.78 = X ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2206_in__set__conv__nth,axiom,
% 8.60/4.78 ! [X: real,Xs2: list_real] :
% 8.60/4.78 ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_real @ Xs2 ) )
% 8.60/4.78 & ( ( nth_real @ Xs2 @ I )
% 8.60/4.78 = X ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2207_in__set__conv__nth,axiom,
% 8.60/4.78 ! [X: set_nat,Xs2: list_set_nat] :
% 8.60/4.78 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.60/4.78 & ( ( nth_set_nat @ Xs2 @ I )
% 8.60/4.78 = X ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2208_in__set__conv__nth,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 & ( ( nth_VEBT_VEBT @ Xs2 @ I )
% 8.60/4.78 = X ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2209_in__set__conv__nth,axiom,
% 8.60/4.78 ! [X: $o,Xs2: list_o] :
% 8.60/4.78 ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 & ( ( nth_o @ Xs2 @ I )
% 8.60/4.78 = X ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2210_in__set__conv__nth,axiom,
% 8.60/4.78 ! [X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 & ( ( nth_nat @ Xs2 @ I )
% 8.60/4.78 = X ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2211_in__set__conv__nth,axiom,
% 8.60/4.78 ! [X: int,Xs2: list_int] :
% 8.60/4.78 ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 & ( ( nth_int @ Xs2 @ I )
% 8.60/4.78 = X ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2212_all__nth__imp__all__set,axiom,
% 8.60/4.78 ! [Xs2: list_complex,P2: complex > $o,X: complex] :
% 8.60/4.78 ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_complex @ Xs2 @ I3 ) ) )
% 8.60/4.78 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2213_all__nth__imp__all__set,axiom,
% 8.60/4.78 ! [Xs2: list_real,P2: real > $o,X: real] :
% 8.60/4.78 ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_real @ Xs2 @ I3 ) ) )
% 8.60/4.78 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2214_all__nth__imp__all__set,axiom,
% 8.60/4.78 ! [Xs2: list_set_nat,P2: set_nat > $o,X: set_nat] :
% 8.60/4.78 ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_set_nat @ Xs2 @ I3 ) ) )
% 8.60/4.78 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2215_all__nth__imp__all__set,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 8.60/4.78 ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I3 ) ) )
% 8.60/4.78 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2216_all__nth__imp__all__set,axiom,
% 8.60/4.78 ! [Xs2: list_o,P2: $o > $o,X: $o] :
% 8.60/4.78 ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_o @ Xs2 @ I3 ) ) )
% 8.60/4.78 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2217_all__nth__imp__all__set,axiom,
% 8.60/4.78 ! [Xs2: list_nat,P2: nat > $o,X: nat] :
% 8.60/4.78 ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_nat @ Xs2 @ I3 ) ) )
% 8.60/4.78 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2218_all__nth__imp__all__set,axiom,
% 8.60/4.78 ! [Xs2: list_int,P2: int > $o,X: int] :
% 8.60/4.78 ( ! [I3: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_int @ Xs2 @ I3 ) ) )
% 8.60/4.78 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2219_all__set__conv__all__nth,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,P2: vEBT_VEBT > $o] :
% 8.60/4.78 ( ( ! [X4: vEBT_VEBT] :
% 8.60/4.78 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X4 ) ) )
% 8.60/4.78 = ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2220_all__set__conv__all__nth,axiom,
% 8.60/4.78 ! [Xs2: list_o,P2: $o > $o] :
% 8.60/4.78 ( ( ! [X4: $o] :
% 8.60/4.78 ( ( member_o @ X4 @ ( set_o2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X4 ) ) )
% 8.60/4.78 = ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_o @ Xs2 @ I ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2221_all__set__conv__all__nth,axiom,
% 8.60/4.78 ! [Xs2: list_nat,P2: nat > $o] :
% 8.60/4.78 ( ( ! [X4: nat] :
% 8.60/4.78 ( ( member_nat @ X4 @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X4 ) ) )
% 8.60/4.78 = ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_nat @ Xs2 @ I ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2222_all__set__conv__all__nth,axiom,
% 8.60/4.78 ! [Xs2: list_int,P2: int > $o] :
% 8.60/4.78 ( ( ! [X4: int] :
% 8.60/4.78 ( ( member_int @ X4 @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ( P2 @ X4 ) ) )
% 8.60/4.78 = ( ! [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( P2 @ ( nth_int @ Xs2 @ I ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2223_diff__Suc__less,axiom,
% 8.60/4.78 ! [N: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I2 ) ) @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2224_nat__diff__split,axiom,
% 8.60/4.78 ! [P2: nat > $o,A: nat,B: nat] :
% 8.60/4.78 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 8.60/4.78 = ( ( ( ord_less_nat @ A @ B )
% 8.60/4.78 => ( P2 @ zero_zero_nat ) )
% 8.60/4.78 & ! [D2: nat] :
% 8.60/4.78 ( ( A
% 8.60/4.78 = ( plus_plus_nat @ B @ D2 ) )
% 8.60/4.78 => ( P2 @ D2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2225_nat__diff__split__asm,axiom,
% 8.60/4.78 ! [P2: nat > $o,A: nat,B: nat] :
% 8.60/4.78 ( ( P2 @ ( minus_minus_nat @ A @ B ) )
% 8.60/4.78 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 8.60/4.78 & ~ ( P2 @ zero_zero_nat ) )
% 8.60/4.78 | ? [D2: nat] :
% 8.60/4.78 ( ( A
% 8.60/4.78 = ( plus_plus_nat @ B @ D2 ) )
% 8.60/4.78 & ~ ( P2 @ D2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2226_less__diff__conv2,axiom,
% 8.60/4.78 ! [K2: nat,J2: nat,I2: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K2 @ J2 )
% 8.60/4.78 => ( ( ord_less_nat @ ( minus_minus_nat @ J2 @ K2 ) @ I2 )
% 8.60/4.78 = ( ord_less_nat @ J2 @ ( plus_plus_nat @ I2 @ K2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2227_nat__eq__add__iff1,axiom,
% 8.60/4.78 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ J2 @ I2 )
% 8.60/4.78 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 )
% 8.60/4.78 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 )
% 8.60/4.78 = N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2228_nat__eq__add__iff2,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.78 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 )
% 8.60/4.78 = ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( M2
% 8.60/4.78 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2229_nat__le__add__iff1,axiom,
% 8.60/4.78 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ J2 @ I2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2230_nat__le__add__iff2,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2231_nat__diff__add__eq1,axiom,
% 8.60/4.78 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ J2 @ I2 )
% 8.60/4.78 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2232_nat__diff__add__eq2,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.78 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( minus_minus_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2233_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT] :
% 8.60/4.78 ( ~ ( vEBT_VEBT_minNull @ X )
% 8.60/4.78 => ( ! [Uv2: $o] :
% 8.60/4.78 ( X
% 8.60/4.78 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.60/4.78 => ( ! [Uu2: $o] :
% 8.60/4.78 ( X
% 8.60/4.78 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.60/4.78 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.60/4.78 ( X
% 8.60/4.78 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2234_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT] :
% 8.60/4.78 ( ( vEBT_VEBT_minNull @ X )
% 8.60/4.78 => ( ( X
% 8.60/4.78 != ( vEBT_Leaf @ $false @ $false ) )
% 8.60/4.78 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.60/4.78 ( X
% 8.60/4.78 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2235_Suc__pred_H,axiom,
% 8.60/4.78 ! [N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( N
% 8.60/4.78 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2236_Suc__diff__eq__diff__pred,axiom,
% 8.60/4.78 ! [N: nat,M2: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( minus_minus_nat @ ( suc @ M2 ) @ N )
% 8.60/4.78 = ( minus_minus_nat @ M2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2237_add__eq__if,axiom,
% 8.60/4.78 ( plus_plus_nat
% 8.60/4.78 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2238_nat__less__add__iff1,axiom,
% 8.60/4.78 ! [J2: nat,I2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ J2 @ I2 )
% 8.60/4.78 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J2 ) @ U ) @ M2 ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2239_nat__less__add__iff2,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,U: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.60/4.78 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M2 ) @ ( plus_plus_nat @ ( times_times_nat @ J2 @ U ) @ N ) )
% 8.60/4.78 = ( ord_less_nat @ M2 @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J2 @ I2 ) @ U ) @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2240_mult__eq__if,axiom,
% 8.60/4.78 ( times_times_nat
% 8.60/4.78 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N4 @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N4 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2241_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Y: $o] :
% 8.60/4.78 ( ( ( vEBT_VEBT_minNull @ X )
% 8.60/4.78 = Y )
% 8.60/4.78 => ( ( ( X
% 8.60/4.78 = ( vEBT_Leaf @ $false @ $false ) )
% 8.60/4.78 => ~ Y )
% 8.60/4.78 => ( ( ? [Uv2: $o] :
% 8.60/4.78 ( X
% 8.60/4.78 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.60/4.78 => Y )
% 8.60/4.78 => ( ( ? [Uu2: $o] :
% 8.60/4.78 ( X
% 8.60/4.78 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.60/4.78 => Y )
% 8.60/4.78 => ( ( ? [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.60/4.78 ( X
% 8.60/4.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 8.60/4.78 => ~ Y )
% 8.60/4.78 => ~ ( ? [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.60/4.78 ( X
% 8.60/4.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 8.60/4.78 => Y ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2242_field__lbound__gt__zero,axiom,
% 8.60/4.78 ! [D1: real,D22: real] :
% 8.60/4.78 ( ( ord_less_real @ zero_zero_real @ D1 )
% 8.60/4.78 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 8.60/4.78 => ? [E2: real] :
% 8.60/4.78 ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.60/4.78 & ( ord_less_real @ E2 @ D1 )
% 8.60/4.78 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2243_field__lbound__gt__zero,axiom,
% 8.60/4.78 ! [D1: rat,D22: rat] :
% 8.60/4.78 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 8.60/4.78 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 8.60/4.78 => ? [E2: rat] :
% 8.60/4.78 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 8.60/4.78 & ( ord_less_rat @ E2 @ D1 )
% 8.60/4.78 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2244_finite__has__minimal2,axiom,
% 8.60/4.78 ! [A4: set_real,A: real] :
% 8.60/4.78 ( ( finite_finite_real @ A4 )
% 8.60/4.78 => ( ( member_real @ A @ A4 )
% 8.60/4.78 => ? [X3: real] :
% 8.60/4.78 ( ( member_real @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_real @ X3 @ A )
% 8.60/4.78 & ! [Xa: real] :
% 8.60/4.78 ( ( member_real @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_real @ Xa @ X3 )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2245_finite__has__minimal2,axiom,
% 8.60/4.78 ! [A4: set_set_nat,A: set_nat] :
% 8.60/4.78 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.78 => ( ( member_set_nat @ A @ A4 )
% 8.60/4.78 => ? [X3: set_nat] :
% 8.60/4.78 ( ( member_set_nat @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_set_nat @ X3 @ A )
% 8.60/4.78 & ! [Xa: set_nat] :
% 8.60/4.78 ( ( member_set_nat @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_set_nat @ Xa @ X3 )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2246_finite__has__minimal2,axiom,
% 8.60/4.78 ! [A4: set_rat,A: rat] :
% 8.60/4.78 ( ( finite_finite_rat @ A4 )
% 8.60/4.78 => ( ( member_rat @ A @ A4 )
% 8.60/4.78 => ? [X3: rat] :
% 8.60/4.78 ( ( member_rat @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_rat @ X3 @ A )
% 8.60/4.78 & ! [Xa: rat] :
% 8.60/4.78 ( ( member_rat @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_rat @ Xa @ X3 )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2247_finite__has__minimal2,axiom,
% 8.60/4.78 ! [A4: set_num,A: num] :
% 8.60/4.78 ( ( finite_finite_num @ A4 )
% 8.60/4.78 => ( ( member_num @ A @ A4 )
% 8.60/4.78 => ? [X3: num] :
% 8.60/4.78 ( ( member_num @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_num @ X3 @ A )
% 8.60/4.78 & ! [Xa: num] :
% 8.60/4.78 ( ( member_num @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_num @ Xa @ X3 )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2248_finite__has__minimal2,axiom,
% 8.60/4.78 ! [A4: set_nat,A: nat] :
% 8.60/4.78 ( ( finite_finite_nat @ A4 )
% 8.60/4.78 => ( ( member_nat @ A @ A4 )
% 8.60/4.78 => ? [X3: nat] :
% 8.60/4.78 ( ( member_nat @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_nat @ X3 @ A )
% 8.60/4.78 & ! [Xa: nat] :
% 8.60/4.78 ( ( member_nat @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ Xa @ X3 )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2249_finite__has__minimal2,axiom,
% 8.60/4.78 ! [A4: set_int,A: int] :
% 8.60/4.78 ( ( finite_finite_int @ A4 )
% 8.60/4.78 => ( ( member_int @ A @ A4 )
% 8.60/4.78 => ? [X3: int] :
% 8.60/4.78 ( ( member_int @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_int @ X3 @ A )
% 8.60/4.78 & ! [Xa: int] :
% 8.60/4.78 ( ( member_int @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_int @ Xa @ X3 )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2250_finite__has__maximal2,axiom,
% 8.60/4.78 ! [A4: set_real,A: real] :
% 8.60/4.78 ( ( finite_finite_real @ A4 )
% 8.60/4.78 => ( ( member_real @ A @ A4 )
% 8.60/4.78 => ? [X3: real] :
% 8.60/4.78 ( ( member_real @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_real @ A @ X3 )
% 8.60/4.78 & ! [Xa: real] :
% 8.60/4.78 ( ( member_real @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_real @ X3 @ Xa )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2251_finite__has__maximal2,axiom,
% 8.60/4.78 ! [A4: set_set_nat,A: set_nat] :
% 8.60/4.78 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.78 => ( ( member_set_nat @ A @ A4 )
% 8.60/4.78 => ? [X3: set_nat] :
% 8.60/4.78 ( ( member_set_nat @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_set_nat @ A @ X3 )
% 8.60/4.78 & ! [Xa: set_nat] :
% 8.60/4.78 ( ( member_set_nat @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_set_nat @ X3 @ Xa )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2252_finite__has__maximal2,axiom,
% 8.60/4.78 ! [A4: set_rat,A: rat] :
% 8.60/4.78 ( ( finite_finite_rat @ A4 )
% 8.60/4.78 => ( ( member_rat @ A @ A4 )
% 8.60/4.78 => ? [X3: rat] :
% 8.60/4.78 ( ( member_rat @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_rat @ A @ X3 )
% 8.60/4.78 & ! [Xa: rat] :
% 8.60/4.78 ( ( member_rat @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_rat @ X3 @ Xa )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2253_finite__has__maximal2,axiom,
% 8.60/4.78 ! [A4: set_num,A: num] :
% 8.60/4.78 ( ( finite_finite_num @ A4 )
% 8.60/4.78 => ( ( member_num @ A @ A4 )
% 8.60/4.78 => ? [X3: num] :
% 8.60/4.78 ( ( member_num @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_num @ A @ X3 )
% 8.60/4.78 & ! [Xa: num] :
% 8.60/4.78 ( ( member_num @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_num @ X3 @ Xa )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2254_finite__has__maximal2,axiom,
% 8.60/4.78 ! [A4: set_nat,A: nat] :
% 8.60/4.78 ( ( finite_finite_nat @ A4 )
% 8.60/4.78 => ( ( member_nat @ A @ A4 )
% 8.60/4.78 => ? [X3: nat] :
% 8.60/4.78 ( ( member_nat @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_nat @ A @ X3 )
% 8.60/4.78 & ! [Xa: nat] :
% 8.60/4.78 ( ( member_nat @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_nat @ X3 @ Xa )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2255_finite__has__maximal2,axiom,
% 8.60/4.78 ! [A4: set_int,A: int] :
% 8.60/4.78 ( ( finite_finite_int @ A4 )
% 8.60/4.78 => ( ( member_int @ A @ A4 )
% 8.60/4.78 => ? [X3: int] :
% 8.60/4.78 ( ( member_int @ X3 @ A4 )
% 8.60/4.78 & ( ord_less_eq_int @ A @ X3 )
% 8.60/4.78 & ! [Xa: int] :
% 8.60/4.78 ( ( member_int @ Xa @ A4 )
% 8.60/4.78 => ( ( ord_less_eq_int @ X3 @ Xa )
% 8.60/4.78 => ( X3 = Xa ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2256_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Y: $o] :
% 8.60/4.78 ( ( ( vEBT_VEBT_minNull @ X )
% 8.60/4.78 = Y )
% 8.60/4.78 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 8.60/4.78 => ( ( ( X
% 8.60/4.78 = ( vEBT_Leaf @ $false @ $false ) )
% 8.60/4.78 => ( Y
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 8.60/4.78 => ( ! [Uv2: $o] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.60/4.78 => ( ~ Y
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 8.60/4.78 => ( ! [Uu2: $o] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.60/4.78 => ( ~ Y
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 8.60/4.78 => ( ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 8.60/4.78 => ( Y
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) )
% 8.60/4.78 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 8.60/4.78 => ( ~ Y
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2257_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT] :
% 8.60/4.78 ( ( vEBT_VEBT_minNull @ X )
% 8.60/4.78 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 8.60/4.78 => ( ( ( X
% 8.60/4.78 = ( vEBT_Leaf @ $false @ $false ) )
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 8.60/4.78 => ~ ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) )
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2258_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT] :
% 8.60/4.78 ( ~ ( vEBT_VEBT_minNull @ X )
% 8.60/4.78 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 8.60/4.78 => ( ! [Uv2: $o] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 8.60/4.78 => ( ! [Uu2: $o] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 8.60/4.78 => ~ ! [Uz2: product_prod_nat_nat,Va2: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.60/4.78 ( ( X
% 8.60/4.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) )
% 8.60/4.78 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va2 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2259_nth__enumerate__eq,axiom,
% 8.60/4.78 ! [M2: nat,Xs2: list_VEBT_VEBT,N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ M2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ( nth_Pr744662078594809490T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs2 ) @ M2 )
% 8.60/4.78 = ( produc599794634098209291T_VEBT @ ( plus_plus_nat @ N @ M2 ) @ ( nth_VEBT_VEBT @ Xs2 @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2260_nth__enumerate__eq,axiom,
% 8.60/4.78 ! [M2: nat,Xs2: list_o,N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ M2 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N @ Xs2 ) @ M2 )
% 8.60/4.78 = ( product_Pair_nat_o @ ( plus_plus_nat @ N @ M2 ) @ ( nth_o @ Xs2 @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2261_nth__enumerate__eq,axiom,
% 8.60/4.78 ! [M2: nat,Xs2: list_nat,N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ M2 @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N @ Xs2 ) @ M2 )
% 8.60/4.78 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N @ M2 ) @ ( nth_nat @ Xs2 @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2262_nth__enumerate__eq,axiom,
% 8.60/4.78 ! [M2: nat,Xs2: list_int,N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ M2 @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N @ Xs2 ) @ M2 )
% 8.60/4.78 = ( product_Pair_nat_int @ ( plus_plus_nat @ N @ M2 ) @ ( nth_int @ Xs2 @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2263_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_complex,Y: complex,F2: complex > rat] :
% 8.60/4.78 ( ( finite3207457112153483333omplex @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_complex )
% 8.60/4.78 => ( ( member_complex @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_rat @ ( F2 @ ( lattic4729654577720512673ex_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2264_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_nat,Y: nat,F2: nat > rat] :
% 8.60/4.78 ( ( finite_finite_nat @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_nat )
% 8.60/4.78 => ( ( member_nat @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_rat @ ( F2 @ ( lattic6811802900495863747at_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2265_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_int,Y: int,F2: int > rat] :
% 8.60/4.78 ( ( finite_finite_int @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_int )
% 8.60/4.78 => ( ( member_int @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_rat @ ( F2 @ ( lattic7811156612396918303nt_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2266_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_real,Y: real,F2: real > rat] :
% 8.60/4.78 ( ( finite_finite_real @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_real )
% 8.60/4.78 => ( ( member_real @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_rat @ ( F2 @ ( lattic4420706379359479199al_rat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2267_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_complex,Y: complex,F2: complex > num] :
% 8.60/4.78 ( ( finite3207457112153483333omplex @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_complex )
% 8.60/4.78 => ( ( member_complex @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_num @ ( F2 @ ( lattic1922116423962787043ex_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2268_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_nat,Y: nat,F2: nat > num] :
% 8.60/4.78 ( ( finite_finite_nat @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_nat )
% 8.60/4.78 => ( ( member_nat @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_num @ ( F2 @ ( lattic4004264746738138117at_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2269_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_int,Y: int,F2: int > num] :
% 8.60/4.78 ( ( finite_finite_int @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_int )
% 8.60/4.78 => ( ( member_int @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_num @ ( F2 @ ( lattic5003618458639192673nt_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2270_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_real,Y: real,F2: real > num] :
% 8.60/4.78 ( ( finite_finite_real @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_real )
% 8.60/4.78 => ( ( member_real @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_num @ ( F2 @ ( lattic1613168225601753569al_num @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2271_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_complex,Y: complex,F2: complex > nat] :
% 8.60/4.78 ( ( finite3207457112153483333omplex @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_complex )
% 8.60/4.78 => ( ( member_complex @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_nat @ ( F2 @ ( lattic5364784637807008409ex_nat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2272_arg__min__least,axiom,
% 8.60/4.78 ! [S3: set_nat,Y: nat,F2: nat > nat] :
% 8.60/4.78 ( ( finite_finite_nat @ S3 )
% 8.60/4.78 => ( ( S3 != bot_bot_set_nat )
% 8.60/4.78 => ( ( member_nat @ Y @ S3 )
% 8.60/4.78 => ( ord_less_eq_nat @ ( F2 @ ( lattic7446932960582359483at_nat @ F2 @ S3 ) ) @ ( F2 @ Y ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2273_Euclid__induct,axiom,
% 8.60/4.78 ! [P2: nat > nat > $o,A: nat,B: nat] :
% 8.60/4.78 ( ! [A3: nat,B3: nat] :
% 8.60/4.78 ( ( P2 @ A3 @ B3 )
% 8.60/4.78 = ( P2 @ B3 @ A3 ) )
% 8.60/4.78 => ( ! [A3: nat] : ( P2 @ A3 @ zero_zero_nat )
% 8.60/4.78 => ( ! [A3: nat,B3: nat] :
% 8.60/4.78 ( ( P2 @ A3 @ B3 )
% 8.60/4.78 => ( P2 @ A3 @ ( plus_plus_nat @ A3 @ B3 ) ) )
% 8.60/4.78 => ( P2 @ A @ B ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2274_nat__descend__induct,axiom,
% 8.60/4.78 ! [N: nat,P2: nat > $o,M2: nat] :
% 8.60/4.78 ( ! [K: nat] :
% 8.60/4.78 ( ( ord_less_nat @ N @ K )
% 8.60/4.78 => ( P2 @ K ) )
% 8.60/4.78 => ( ! [K: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ K @ N )
% 8.60/4.78 => ( ! [I4: nat] :
% 8.60/4.78 ( ( ord_less_nat @ K @ I4 )
% 8.60/4.78 => ( P2 @ I4 ) )
% 8.60/4.78 => ( P2 @ K ) ) )
% 8.60/4.78 => ( P2 @ M2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2275_length__mul__elem,axiom,
% 8.60/4.78 ! [Xs2: list_list_VEBT_VEBT,N: nat] :
% 8.60/4.78 ( ! [X3: list_VEBT_VEBT] :
% 8.60/4.78 ( ( member2936631157270082147T_VEBT @ X3 @ ( set_list_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ( ( size_s6755466524823107622T_VEBT @ X3 )
% 8.60/4.78 = N ) )
% 8.60/4.78 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs2 ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs2 ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2276_length__mul__elem,axiom,
% 8.60/4.78 ! [Xs2: list_list_o,N: nat] :
% 8.60/4.78 ( ! [X3: list_o] :
% 8.60/4.78 ( ( member_list_o @ X3 @ ( set_list_o2 @ Xs2 ) )
% 8.60/4.78 => ( ( size_size_list_o @ X3 )
% 8.60/4.78 = N ) )
% 8.60/4.78 => ( ( size_size_list_o @ ( concat_o @ Xs2 ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs2 ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2277_length__mul__elem,axiom,
% 8.60/4.78 ! [Xs2: list_list_nat,N: nat] :
% 8.60/4.78 ( ! [X3: list_nat] :
% 8.60/4.78 ( ( member_list_nat @ X3 @ ( set_list_nat2 @ Xs2 ) )
% 8.60/4.78 => ( ( size_size_list_nat @ X3 )
% 8.60/4.78 = N ) )
% 8.60/4.78 => ( ( size_size_list_nat @ ( concat_nat @ Xs2 ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs2 ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2278_length__mul__elem,axiom,
% 8.60/4.78 ! [Xs2: list_list_int,N: nat] :
% 8.60/4.78 ( ! [X3: list_int] :
% 8.60/4.78 ( ( member_list_int @ X3 @ ( set_list_int2 @ Xs2 ) )
% 8.60/4.78 => ( ( size_size_list_int @ X3 )
% 8.60/4.78 = N ) )
% 8.60/4.78 => ( ( size_size_list_int @ ( concat_int @ Xs2 ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs2 ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2279_triangle__Suc,axiom,
% 8.60/4.78 ! [N: nat] :
% 8.60/4.78 ( ( nat_triangle @ ( suc @ N ) )
% 8.60/4.78 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2280_length__enumerate,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( size_s4762443039079500285T_VEBT @ ( enumerate_VEBT_VEBT @ N @ Xs2 ) )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2281_length__enumerate,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_o] :
% 8.60/4.78 ( ( size_s6491369823275344609_nat_o @ ( enumerate_o @ N @ Xs2 ) )
% 8.60/4.78 = ( size_size_list_o @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2282_length__enumerate,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( size_s5460976970255530739at_nat @ ( enumerate_nat @ N @ Xs2 ) )
% 8.60/4.78 = ( size_size_list_nat @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2283_length__enumerate,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_int] :
% 8.60/4.78 ( ( size_s2970893825323803983at_int @ ( enumerate_int @ N @ Xs2 ) )
% 8.60/4.78 = ( size_size_list_int @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2284_triangle__0,axiom,
% 8.60/4.78 ( ( nat_triangle @ zero_zero_nat )
% 8.60/4.78 = zero_zero_nat ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2285_diff__commute,axiom,
% 8.60/4.78 ! [I2: nat,J2: nat,K2: nat] :
% 8.60/4.78 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J2 ) @ K2 )
% 8.60/4.78 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K2 ) @ J2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2286_prod__decode__aux_Oelims,axiom,
% 8.60/4.78 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 8.60/4.78 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 8.60/4.78 = Y )
% 8.60/4.78 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 8.60/4.78 => ( Y
% 8.60/4.78 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 8.60/4.78 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 8.60/4.78 => ( Y
% 8.60/4.78 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2287_prod__decode__aux_Osimps,axiom,
% 8.60/4.78 ( nat_prod_decode_aux
% 8.60/4.78 = ( ^ [K3: nat,M6: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M6 @ K3 ) @ ( product_Pair_nat_nat @ M6 @ ( minus_minus_nat @ K3 @ M6 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M6 @ ( suc @ K3 ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2288_prod__encode__prod__decode__aux,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat] :
% 8.60/4.78 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K2 @ M2 ) )
% 8.60/4.78 = ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2289_prod__decode__triangle__add,axiom,
% 8.60/4.78 ! [K2: nat,M2: nat] :
% 8.60/4.78 ( ( nat_prod_decode @ ( plus_plus_nat @ ( nat_triangle @ K2 ) @ M2 ) )
% 8.60/4.78 = ( nat_prod_decode_aux @ K2 @ M2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2290_in__set__product__lists__length,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Xss: list_list_VEBT_VEBT] :
% 8.60/4.78 ( ( member2936631157270082147T_VEBT @ Xs2 @ ( set_list_VEBT_VEBT2 @ ( produc3021084454716106787T_VEBT @ Xss ) ) )
% 8.60/4.78 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_s8217280938318005548T_VEBT @ Xss ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2291_in__set__product__lists__length,axiom,
% 8.60/4.78 ! [Xs2: list_o,Xss: list_list_o] :
% 8.60/4.78 ( ( member_list_o @ Xs2 @ ( set_list_o2 @ ( product_lists_o @ Xss ) ) )
% 8.60/4.78 => ( ( size_size_list_o @ Xs2 )
% 8.60/4.78 = ( size_s2710708370519433104list_o @ Xss ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2292_in__set__product__lists__length,axiom,
% 8.60/4.78 ! [Xs2: list_nat,Xss: list_list_nat] :
% 8.60/4.78 ( ( member_list_nat @ Xs2 @ ( set_list_nat2 @ ( product_lists_nat @ Xss ) ) )
% 8.60/4.78 => ( ( size_size_list_nat @ Xs2 )
% 8.60/4.78 = ( size_s3023201423986296836st_nat @ Xss ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2293_in__set__product__lists__length,axiom,
% 8.60/4.78 ! [Xs2: list_int,Xss: list_list_int] :
% 8.60/4.78 ( ( member_list_int @ Xs2 @ ( set_list_int2 @ ( product_lists_int @ Xss ) ) )
% 8.60/4.78 => ( ( size_size_list_int @ Xs2 )
% 8.60/4.78 = ( size_s533118279054570080st_int @ Xss ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2294_Gcd__remove0__nat,axiom,
% 8.60/4.78 ! [M5: set_nat] :
% 8.60/4.78 ( ( finite_finite_nat @ M5 )
% 8.60/4.78 => ( ( gcd_Gcd_nat @ M5 )
% 8.60/4.78 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2295_inf__period_I2_J,axiom,
% 8.60/4.78 ! [P2: real > $o,D3: real,Q: real > $o] :
% 8.60/4.78 ( ! [X3: real,K: real] :
% 8.60/4.78 ( ( P2 @ X3 )
% 8.60/4.78 = ( P2 @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 8.60/4.78 => ( ! [X3: real,K: real] :
% 8.60/4.78 ( ( Q @ X3 )
% 8.60/4.78 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 8.60/4.78 => ! [X5: real,K4: real] :
% 8.60/4.78 ( ( ( P2 @ X5 )
% 8.60/4.78 | ( Q @ X5 ) )
% 8.60/4.78 = ( ( P2 @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 8.60/4.78 | ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2296_inf__period_I2_J,axiom,
% 8.60/4.78 ! [P2: rat > $o,D3: rat,Q: rat > $o] :
% 8.60/4.78 ( ! [X3: rat,K: rat] :
% 8.60/4.78 ( ( P2 @ X3 )
% 8.60/4.78 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 8.60/4.78 => ( ! [X3: rat,K: rat] :
% 8.60/4.78 ( ( Q @ X3 )
% 8.60/4.78 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 8.60/4.78 => ! [X5: rat,K4: rat] :
% 8.60/4.78 ( ( ( P2 @ X5 )
% 8.60/4.78 | ( Q @ X5 ) )
% 8.60/4.78 = ( ( P2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 8.60/4.78 | ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2297_inf__period_I2_J,axiom,
% 8.60/4.78 ! [P2: int > $o,D3: int,Q: int > $o] :
% 8.60/4.78 ( ! [X3: int,K: int] :
% 8.60/4.78 ( ( P2 @ X3 )
% 8.60/4.78 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 8.60/4.78 => ( ! [X3: int,K: int] :
% 8.60/4.78 ( ( Q @ X3 )
% 8.60/4.78 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 8.60/4.78 => ! [X5: int,K4: int] :
% 8.60/4.78 ( ( ( P2 @ X5 )
% 8.60/4.78 | ( Q @ X5 ) )
% 8.60/4.78 = ( ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 8.60/4.78 | ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2298_inf__period_I1_J,axiom,
% 8.60/4.78 ! [P2: real > $o,D3: real,Q: real > $o] :
% 8.60/4.78 ( ! [X3: real,K: real] :
% 8.60/4.78 ( ( P2 @ X3 )
% 8.60/4.78 = ( P2 @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 8.60/4.78 => ( ! [X3: real,K: real] :
% 8.60/4.78 ( ( Q @ X3 )
% 8.60/4.78 = ( Q @ ( minus_minus_real @ X3 @ ( times_times_real @ K @ D3 ) ) ) )
% 8.60/4.78 => ! [X5: real,K4: real] :
% 8.60/4.78 ( ( ( P2 @ X5 )
% 8.60/4.78 & ( Q @ X5 ) )
% 8.60/4.78 = ( ( P2 @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) )
% 8.60/4.78 & ( Q @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2299_inf__period_I1_J,axiom,
% 8.60/4.78 ! [P2: rat > $o,D3: rat,Q: rat > $o] :
% 8.60/4.78 ( ! [X3: rat,K: rat] :
% 8.60/4.78 ( ( P2 @ X3 )
% 8.60/4.78 = ( P2 @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 8.60/4.78 => ( ! [X3: rat,K: rat] :
% 8.60/4.78 ( ( Q @ X3 )
% 8.60/4.78 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K @ D3 ) ) ) )
% 8.60/4.78 => ! [X5: rat,K4: rat] :
% 8.60/4.78 ( ( ( P2 @ X5 )
% 8.60/4.78 & ( Q @ X5 ) )
% 8.60/4.78 = ( ( P2 @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) )
% 8.60/4.78 & ( Q @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2300_inf__period_I1_J,axiom,
% 8.60/4.78 ! [P2: int > $o,D3: int,Q: int > $o] :
% 8.60/4.78 ( ! [X3: int,K: int] :
% 8.60/4.78 ( ( P2 @ X3 )
% 8.60/4.78 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 8.60/4.78 => ( ! [X3: int,K: int] :
% 8.60/4.78 ( ( Q @ X3 )
% 8.60/4.78 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 8.60/4.78 => ! [X5: int,K4: int] :
% 8.60/4.78 ( ( ( P2 @ X5 )
% 8.60/4.78 & ( Q @ X5 ) )
% 8.60/4.78 = ( ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) )
% 8.60/4.78 & ( Q @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2301_verit__sum__simplify,axiom,
% 8.60/4.78 ! [A: complex] :
% 8.60/4.78 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 8.60/4.78 = A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2302_verit__sum__simplify,axiom,
% 8.60/4.78 ! [A: real] :
% 8.60/4.78 ( ( plus_plus_real @ A @ zero_zero_real )
% 8.60/4.78 = A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2303_verit__sum__simplify,axiom,
% 8.60/4.78 ! [A: rat] :
% 8.60/4.78 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 8.60/4.78 = A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2304_verit__sum__simplify,axiom,
% 8.60/4.78 ! [A: nat] :
% 8.60/4.78 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 8.60/4.78 = A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2305_verit__sum__simplify,axiom,
% 8.60/4.78 ! [A: int] :
% 8.60/4.78 ( ( plus_plus_int @ A @ zero_zero_int )
% 8.60/4.78 = A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2306_Gcd__empty,axiom,
% 8.60/4.78 ( ( gcd_Gcd_nat @ bot_bot_set_nat )
% 8.60/4.78 = zero_zero_nat ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2307_Gcd__empty,axiom,
% 8.60/4.78 ( ( gcd_Gcd_int @ bot_bot_set_int )
% 8.60/4.78 = zero_zero_int ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2308_Gcd__0__iff,axiom,
% 8.60/4.78 ! [A4: set_int] :
% 8.60/4.78 ( ( ( gcd_Gcd_int @ A4 )
% 8.60/4.78 = zero_zero_int )
% 8.60/4.78 = ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2309_Gcd__0__iff,axiom,
% 8.60/4.78 ! [A4: set_nat] :
% 8.60/4.78 ( ( ( gcd_Gcd_nat @ A4 )
% 8.60/4.78 = zero_zero_nat )
% 8.60/4.78 = ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2310_verit__la__disequality,axiom,
% 8.60/4.78 ! [A: rat,B: rat] :
% 8.60/4.78 ( ( A = B )
% 8.60/4.78 | ~ ( ord_less_eq_rat @ A @ B )
% 8.60/4.78 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2311_verit__la__disequality,axiom,
% 8.60/4.78 ! [A: num,B: num] :
% 8.60/4.78 ( ( A = B )
% 8.60/4.78 | ~ ( ord_less_eq_num @ A @ B )
% 8.60/4.78 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2312_verit__la__disequality,axiom,
% 8.60/4.78 ! [A: nat,B: nat] :
% 8.60/4.78 ( ( A = B )
% 8.60/4.78 | ~ ( ord_less_eq_nat @ A @ B )
% 8.60/4.78 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2313_verit__la__disequality,axiom,
% 8.60/4.78 ! [A: int,B: int] :
% 8.60/4.78 ( ( A = B )
% 8.60/4.78 | ~ ( ord_less_eq_int @ A @ B )
% 8.60/4.78 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2314_verit__comp__simplify1_I2_J,axiom,
% 8.60/4.78 ! [A: set_nat] : ( ord_less_eq_set_nat @ A @ A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2315_verit__comp__simplify1_I2_J,axiom,
% 8.60/4.78 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2316_verit__comp__simplify1_I2_J,axiom,
% 8.60/4.78 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2317_verit__comp__simplify1_I2_J,axiom,
% 8.60/4.78 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2318_verit__comp__simplify1_I2_J,axiom,
% 8.60/4.78 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2319_prod__decode__def,axiom,
% 8.60/4.78 ( nat_prod_decode
% 8.60/4.78 = ( nat_prod_decode_aux @ zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2320_verit__comp__simplify1_I3_J,axiom,
% 8.60/4.78 ! [B2: real,A2: real] :
% 8.60/4.78 ( ( ~ ( ord_less_eq_real @ B2 @ A2 ) )
% 8.60/4.78 = ( ord_less_real @ A2 @ B2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2321_verit__comp__simplify1_I3_J,axiom,
% 8.60/4.78 ! [B2: rat,A2: rat] :
% 8.60/4.78 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 8.60/4.78 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2322_verit__comp__simplify1_I3_J,axiom,
% 8.60/4.78 ! [B2: num,A2: num] :
% 8.60/4.78 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 8.60/4.78 = ( ord_less_num @ A2 @ B2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2323_verit__comp__simplify1_I3_J,axiom,
% 8.60/4.78 ! [B2: nat,A2: nat] :
% 8.60/4.78 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 8.60/4.78 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2324_verit__comp__simplify1_I3_J,axiom,
% 8.60/4.78 ! [B2: int,A2: int] :
% 8.60/4.78 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 8.60/4.78 = ( ord_less_int @ A2 @ B2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2325_pinf_I6_J,axiom,
% 8.60/4.78 ! [T: real] :
% 8.60/4.78 ? [Z: real] :
% 8.60/4.78 ! [X5: real] :
% 8.60/4.78 ( ( ord_less_real @ Z @ X5 )
% 8.60/4.78 => ~ ( ord_less_eq_real @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2326_pinf_I6_J,axiom,
% 8.60/4.78 ! [T: rat] :
% 8.60/4.78 ? [Z: rat] :
% 8.60/4.78 ! [X5: rat] :
% 8.60/4.78 ( ( ord_less_rat @ Z @ X5 )
% 8.60/4.78 => ~ ( ord_less_eq_rat @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2327_pinf_I6_J,axiom,
% 8.60/4.78 ! [T: num] :
% 8.60/4.78 ? [Z: num] :
% 8.60/4.78 ! [X5: num] :
% 8.60/4.78 ( ( ord_less_num @ Z @ X5 )
% 8.60/4.78 => ~ ( ord_less_eq_num @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2328_pinf_I6_J,axiom,
% 8.60/4.78 ! [T: nat] :
% 8.60/4.78 ? [Z: nat] :
% 8.60/4.78 ! [X5: nat] :
% 8.60/4.78 ( ( ord_less_nat @ Z @ X5 )
% 8.60/4.78 => ~ ( ord_less_eq_nat @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2329_pinf_I6_J,axiom,
% 8.60/4.78 ! [T: int] :
% 8.60/4.78 ? [Z: int] :
% 8.60/4.78 ! [X5: int] :
% 8.60/4.78 ( ( ord_less_int @ Z @ X5 )
% 8.60/4.78 => ~ ( ord_less_eq_int @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2330_pinf_I8_J,axiom,
% 8.60/4.78 ! [T: real] :
% 8.60/4.78 ? [Z: real] :
% 8.60/4.78 ! [X5: real] :
% 8.60/4.78 ( ( ord_less_real @ Z @ X5 )
% 8.60/4.78 => ( ord_less_eq_real @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2331_pinf_I8_J,axiom,
% 8.60/4.78 ! [T: rat] :
% 8.60/4.78 ? [Z: rat] :
% 8.60/4.78 ! [X5: rat] :
% 8.60/4.78 ( ( ord_less_rat @ Z @ X5 )
% 8.60/4.78 => ( ord_less_eq_rat @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2332_pinf_I8_J,axiom,
% 8.60/4.78 ! [T: num] :
% 8.60/4.78 ? [Z: num] :
% 8.60/4.78 ! [X5: num] :
% 8.60/4.78 ( ( ord_less_num @ Z @ X5 )
% 8.60/4.78 => ( ord_less_eq_num @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2333_pinf_I8_J,axiom,
% 8.60/4.78 ! [T: nat] :
% 8.60/4.78 ? [Z: nat] :
% 8.60/4.78 ! [X5: nat] :
% 8.60/4.78 ( ( ord_less_nat @ Z @ X5 )
% 8.60/4.78 => ( ord_less_eq_nat @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2334_pinf_I8_J,axiom,
% 8.60/4.78 ! [T: int] :
% 8.60/4.78 ? [Z: int] :
% 8.60/4.78 ! [X5: int] :
% 8.60/4.78 ( ( ord_less_int @ Z @ X5 )
% 8.60/4.78 => ( ord_less_eq_int @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2335_minf_I6_J,axiom,
% 8.60/4.78 ! [T: real] :
% 8.60/4.78 ? [Z: real] :
% 8.60/4.78 ! [X5: real] :
% 8.60/4.78 ( ( ord_less_real @ X5 @ Z )
% 8.60/4.78 => ( ord_less_eq_real @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2336_minf_I6_J,axiom,
% 8.60/4.78 ! [T: rat] :
% 8.60/4.78 ? [Z: rat] :
% 8.60/4.78 ! [X5: rat] :
% 8.60/4.78 ( ( ord_less_rat @ X5 @ Z )
% 8.60/4.78 => ( ord_less_eq_rat @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2337_minf_I6_J,axiom,
% 8.60/4.78 ! [T: num] :
% 8.60/4.78 ? [Z: num] :
% 8.60/4.78 ! [X5: num] :
% 8.60/4.78 ( ( ord_less_num @ X5 @ Z )
% 8.60/4.78 => ( ord_less_eq_num @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2338_minf_I6_J,axiom,
% 8.60/4.78 ! [T: nat] :
% 8.60/4.78 ? [Z: nat] :
% 8.60/4.78 ! [X5: nat] :
% 8.60/4.78 ( ( ord_less_nat @ X5 @ Z )
% 8.60/4.78 => ( ord_less_eq_nat @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2339_minf_I6_J,axiom,
% 8.60/4.78 ! [T: int] :
% 8.60/4.78 ? [Z: int] :
% 8.60/4.78 ! [X5: int] :
% 8.60/4.78 ( ( ord_less_int @ X5 @ Z )
% 8.60/4.78 => ( ord_less_eq_int @ X5 @ T ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2340_minf_I8_J,axiom,
% 8.60/4.78 ! [T: real] :
% 8.60/4.78 ? [Z: real] :
% 8.60/4.78 ! [X5: real] :
% 8.60/4.78 ( ( ord_less_real @ X5 @ Z )
% 8.60/4.78 => ~ ( ord_less_eq_real @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2341_minf_I8_J,axiom,
% 8.60/4.78 ! [T: rat] :
% 8.60/4.78 ? [Z: rat] :
% 8.60/4.78 ! [X5: rat] :
% 8.60/4.78 ( ( ord_less_rat @ X5 @ Z )
% 8.60/4.78 => ~ ( ord_less_eq_rat @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2342_minf_I8_J,axiom,
% 8.60/4.78 ! [T: num] :
% 8.60/4.78 ? [Z: num] :
% 8.60/4.78 ! [X5: num] :
% 8.60/4.78 ( ( ord_less_num @ X5 @ Z )
% 8.60/4.78 => ~ ( ord_less_eq_num @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2343_minf_I8_J,axiom,
% 8.60/4.78 ! [T: nat] :
% 8.60/4.78 ? [Z: nat] :
% 8.60/4.78 ! [X5: nat] :
% 8.60/4.78 ( ( ord_less_nat @ X5 @ Z )
% 8.60/4.78 => ~ ( ord_less_eq_nat @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2344_minf_I8_J,axiom,
% 8.60/4.78 ! [T: int] :
% 8.60/4.78 ? [Z: int] :
% 8.60/4.78 ! [X5: int] :
% 8.60/4.78 ( ( ord_less_int @ X5 @ Z )
% 8.60/4.78 => ~ ( ord_less_eq_int @ T @ X5 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2345_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2346_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_o] :
% 8.60/4.78 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2347_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 8.60/4.78 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2348_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_int] :
% 8.60/4.78 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2349_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2350_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_o] :
% 8.60/4.78 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2351_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_nat] :
% 8.60/4.78 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2352_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_int] :
% 8.60/4.78 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2353_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2354_length__product,axiom,
% 8.60/4.78 ! [Xs2: list_nat,Ys: list_o] :
% 8.60/4.78 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs2 @ Ys ) )
% 8.60/4.78 = ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_o @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2355_complete__interval,axiom,
% 8.60/4.78 ! [A: real,B: real,P2: real > $o] :
% 8.60/4.78 ( ( ord_less_real @ A @ B )
% 8.60/4.78 => ( ( P2 @ A )
% 8.60/4.78 => ( ~ ( P2 @ B )
% 8.60/4.78 => ? [C: real] :
% 8.60/4.78 ( ( ord_less_eq_real @ A @ C )
% 8.60/4.78 & ( ord_less_eq_real @ C @ B )
% 8.60/4.78 & ! [X5: real] :
% 8.60/4.78 ( ( ( ord_less_eq_real @ A @ X5 )
% 8.60/4.78 & ( ord_less_real @ X5 @ C ) )
% 8.60/4.78 => ( P2 @ X5 ) )
% 8.60/4.78 & ! [D4: real] :
% 8.60/4.78 ( ! [X3: real] :
% 8.60/4.78 ( ( ( ord_less_eq_real @ A @ X3 )
% 8.60/4.78 & ( ord_less_real @ X3 @ D4 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ord_less_eq_real @ D4 @ C ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2356_complete__interval,axiom,
% 8.60/4.78 ! [A: nat,B: nat,P2: nat > $o] :
% 8.60/4.78 ( ( ord_less_nat @ A @ B )
% 8.60/4.78 => ( ( P2 @ A )
% 8.60/4.78 => ( ~ ( P2 @ B )
% 8.60/4.78 => ? [C: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ A @ C )
% 8.60/4.78 & ( ord_less_eq_nat @ C @ B )
% 8.60/4.78 & ! [X5: nat] :
% 8.60/4.78 ( ( ( ord_less_eq_nat @ A @ X5 )
% 8.60/4.78 & ( ord_less_nat @ X5 @ C ) )
% 8.60/4.78 => ( P2 @ X5 ) )
% 8.60/4.78 & ! [D4: nat] :
% 8.60/4.78 ( ! [X3: nat] :
% 8.60/4.78 ( ( ( ord_less_eq_nat @ A @ X3 )
% 8.60/4.78 & ( ord_less_nat @ X3 @ D4 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ord_less_eq_nat @ D4 @ C ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2357_complete__interval,axiom,
% 8.60/4.78 ! [A: int,B: int,P2: int > $o] :
% 8.60/4.78 ( ( ord_less_int @ A @ B )
% 8.60/4.78 => ( ( P2 @ A )
% 8.60/4.78 => ( ~ ( P2 @ B )
% 8.60/4.78 => ? [C: int] :
% 8.60/4.78 ( ( ord_less_eq_int @ A @ C )
% 8.60/4.78 & ( ord_less_eq_int @ C @ B )
% 8.60/4.78 & ! [X5: int] :
% 8.60/4.78 ( ( ( ord_less_eq_int @ A @ X5 )
% 8.60/4.78 & ( ord_less_int @ X5 @ C ) )
% 8.60/4.78 => ( P2 @ X5 ) )
% 8.60/4.78 & ! [D4: int] :
% 8.60/4.78 ( ! [X3: int] :
% 8.60/4.78 ( ( ( ord_less_eq_int @ A @ X3 )
% 8.60/4.78 & ( ord_less_int @ X3 @ D4 ) )
% 8.60/4.78 => ( P2 @ X3 ) )
% 8.60/4.78 => ( ord_less_eq_int @ D4 @ C ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2358_vebt__insert_Osimps_I4_J,axiom,
% 8.60/4.78 ! [V2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.60/4.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary ) @ X )
% 8.60/4.78 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList2 @ Summary ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2359_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_s3445333598471063425nteger @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_s3445333598471063425nteger @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr2304437835452373666nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ I2 ) @ ( nth_Code_integer @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2360_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr4953567300277697838T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2361_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr4606735188037164562VEBT_o @ ( zip_VEBT_VEBT_o @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_o @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2362_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr1791586995822124652BT_nat @ ( zip_VEBT_VEBT_nat @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2363_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr6837108013167703752BT_int @ ( zip_VEBT_VEBT_int @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2364_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr6777367263587873994T_VEBT @ ( zip_o_VEBT_VEBT @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2365_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_o,Ys: list_o] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Ys ) )
% 8.60/4.78 => ( ( nth_Product_prod_o_o @ ( zip_o_o @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ I2 ) @ ( nth_o @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2366_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_o,Ys: list_nat] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr5826913651314560976_o_nat @ ( zip_o_nat @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ I2 ) @ ( nth_nat @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2367_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_o,Ys: list_int] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr1649062631805364268_o_int @ ( zip_o_int @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ I2 ) @ ( nth_int @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2368_nth__zip,axiom,
% 8.60/4.78 ! [I2: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( nth_Pr744662078594809490T_VEBT @ ( zip_nat_VEBT_VEBT @ Xs2 @ Ys ) @ I2 )
% 8.60/4.78 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ I2 ) @ ( nth_VEBT_VEBT @ Ys @ I2 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2369_find__Some__iff2,axiom,
% 8.60/4.78 ! [X: product_prod_nat_nat,P2: product_prod_nat_nat > $o,Xs2: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( ( some_P7363390416028606310at_nat @ X )
% 8.60/4.78 = ( find_P8199882355184865565at_nat @ P2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2370_find__Some__iff2,axiom,
% 8.60/4.78 ! [X: num,P2: num > $o,Xs2: list_num] :
% 8.60/4.78 ( ( ( some_num @ X )
% 8.60/4.78 = ( find_num @ P2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_num @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_num @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_num @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2371_find__Some__iff2,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,P2: vEBT_VEBT > $o,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ( some_VEBT_VEBT @ X )
% 8.60/4.78 = ( find_VEBT_VEBT @ P2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2372_find__Some__iff2,axiom,
% 8.60/4.78 ! [X: $o,P2: $o > $o,Xs2: list_o] :
% 8.60/4.78 ( ( ( some_o @ X )
% 8.60/4.78 = ( find_o @ P2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_o @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_o @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_o @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2373_find__Some__iff2,axiom,
% 8.60/4.78 ! [X: nat,P2: nat > $o,Xs2: list_nat] :
% 8.60/4.78 ( ( ( some_nat @ X )
% 8.60/4.78 = ( find_nat @ P2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_nat @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_nat @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2374_find__Some__iff2,axiom,
% 8.60/4.78 ! [X: int,P2: int > $o,Xs2: list_int] :
% 8.60/4.78 ( ( ( some_int @ X )
% 8.60/4.78 = ( find_int @ P2 @ Xs2 ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_int @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_int @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_int @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2375_find__Some__iff,axiom,
% 8.60/4.78 ! [P2: product_prod_nat_nat > $o,Xs2: list_P6011104703257516679at_nat,X: product_prod_nat_nat] :
% 8.60/4.78 ( ( ( find_P8199882355184865565at_nat @ P2 @ Xs2 )
% 8.60/4.78 = ( some_P7363390416028606310at_nat @ X ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_Pr7617993195940197384at_nat @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2376_find__Some__iff,axiom,
% 8.60/4.78 ! [P2: num > $o,Xs2: list_num,X: num] :
% 8.60/4.78 ( ( ( find_num @ P2 @ Xs2 )
% 8.60/4.78 = ( some_num @ X ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_num @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_num @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_num @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_num @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2377_find__Some__iff,axiom,
% 8.60/4.78 ! [P2: vEBT_VEBT > $o,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.60/4.78 ( ( ( find_VEBT_VEBT @ P2 @ Xs2 )
% 8.60/4.78 = ( some_VEBT_VEBT @ X ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_VEBT_VEBT @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_VEBT_VEBT @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2378_find__Some__iff,axiom,
% 8.60/4.78 ! [P2: $o > $o,Xs2: list_o,X: $o] :
% 8.60/4.78 ( ( ( find_o @ P2 @ Xs2 )
% 8.60/4.78 = ( some_o @ X ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_o @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_o @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_o @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2379_find__Some__iff,axiom,
% 8.60/4.78 ! [P2: nat > $o,Xs2: list_nat,X: nat] :
% 8.60/4.78 ( ( ( find_nat @ P2 @ Xs2 )
% 8.60/4.78 = ( some_nat @ X ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_nat @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_nat @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_nat @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2380_find__Some__iff,axiom,
% 8.60/4.78 ! [P2: int > $o,Xs2: list_int,X: int] :
% 8.60/4.78 ( ( ( find_int @ P2 @ Xs2 )
% 8.60/4.78 = ( some_int @ X ) )
% 8.60/4.78 = ( ? [I: nat] :
% 8.60/4.78 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 & ( P2 @ ( nth_int @ Xs2 @ I ) )
% 8.60/4.78 & ( X
% 8.60/4.78 = ( nth_int @ Xs2 @ I ) )
% 8.60/4.78 & ! [J: nat] :
% 8.60/4.78 ( ( ord_less_nat @ J @ I )
% 8.60/4.78 => ~ ( P2 @ ( nth_int @ Xs2 @ J ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2381_nth__Cons__pos,axiom,
% 8.60/4.78 ! [N: nat,X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 8.60/4.78 = ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2382_nth__Cons__pos,axiom,
% 8.60/4.78 ! [N: nat,X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 8.60/4.78 = ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2383_rotate1__length01,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ one_one_nat )
% 8.60/4.78 => ( ( rotate1_VEBT_VEBT @ Xs2 )
% 8.60/4.78 = Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2384_rotate1__length01,axiom,
% 8.60/4.78 ! [Xs2: list_o] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ one_one_nat )
% 8.60/4.78 => ( ( rotate1_o @ Xs2 )
% 8.60/4.78 = Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2385_rotate1__length01,axiom,
% 8.60/4.78 ! [Xs2: list_nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ one_one_nat )
% 8.60/4.78 => ( ( rotate1_nat @ Xs2 )
% 8.60/4.78 = Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2386_rotate1__length01,axiom,
% 8.60/4.78 ! [Xs2: list_int] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ one_one_nat )
% 8.60/4.78 => ( ( rotate1_int @ Xs2 )
% 8.60/4.78 = Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2387_length__rotate1,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( size_s6755466524823107622T_VEBT @ ( rotate1_VEBT_VEBT @ Xs2 ) )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2388_length__rotate1,axiom,
% 8.60/4.78 ! [Xs2: list_o] :
% 8.60/4.78 ( ( size_size_list_o @ ( rotate1_o @ Xs2 ) )
% 8.60/4.78 = ( size_size_list_o @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2389_length__rotate1,axiom,
% 8.60/4.78 ! [Xs2: list_nat] :
% 8.60/4.78 ( ( size_size_list_nat @ ( rotate1_nat @ Xs2 ) )
% 8.60/4.78 = ( size_size_list_nat @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2390_length__rotate1,axiom,
% 8.60/4.78 ! [Xs2: list_int] :
% 8.60/4.78 ( ( size_size_list_int @ ( rotate1_int @ Xs2 ) )
% 8.60/4.78 = ( size_size_list_int @ Xs2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2391_nth__Cons__Suc,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 8.60/4.78 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( suc @ N ) )
% 8.60/4.78 = ( nth_VEBT_VEBT @ Xs2 @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2392_nth__Cons__Suc,axiom,
% 8.60/4.78 ! [X: nat,Xs2: list_nat,N: nat] :
% 8.60/4.78 ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ ( suc @ N ) )
% 8.60/4.78 = ( nth_nat @ Xs2 @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2393_nth__Cons__0,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ zero_zero_nat )
% 8.60/4.78 = X ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2394_nth__Cons__0,axiom,
% 8.60/4.78 ! [X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ zero_zero_nat )
% 8.60/4.78 = X ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2395_zip__Cons__Cons,axiom,
% 8.60/4.78 ! [X: code_integer,Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer] :
% 8.60/4.78 ( ( zip_Co3543743374963494515nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) )
% 8.60/4.78 = ( cons_P9044669534377732177nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2396_zip__Cons__Cons,axiom,
% 8.60/4.78 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( zip_Pr4664179122662387191at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) )
% 8.60/4.78 = ( cons_P8732206157123786781at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2397_zip__Cons__Cons,axiom,
% 8.60/4.78 ! [X: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat] :
% 8.60/4.78 ( ( zip_se5600341670672612855at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) )
% 8.60/4.78 = ( cons_P3940603068885512221at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2398_zip__Cons__Cons,axiom,
% 8.60/4.78 ! [X: nat,Xs2: list_nat,Y: nat,Ys: list_nat] :
% 8.60/4.78 ( ( zip_nat_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) )
% 8.60/4.78 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( zip_nat_nat @ Xs2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2399_zip__Cons__Cons,axiom,
% 8.60/4.78 ! [X: int,Xs2: list_int,Y: int,Ys: list_int] :
% 8.60/4.78 ( ( zip_int_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) )
% 8.60/4.78 = ( cons_P3334398858971670639nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( zip_int_int @ Xs2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2400_enumerate__simps_I2_J,axiom,
% 8.60/4.78 ! [N: nat,X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( enumerate_nat @ N @ ( cons_nat @ X @ Xs2 ) )
% 8.60/4.78 = ( cons_P6512896166579812791at_nat @ ( product_Pair_nat_nat @ N @ X ) @ ( enumerate_nat @ ( suc @ N ) @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2401_zip__eq__ConsE,axiom,
% 8.60/4.78 ! [Xs2: list_Code_integer,Ys: list_Code_integer,Xy: produc8923325533196201883nteger,Xys: list_P5578671422887162913nteger] :
% 8.60/4.78 ( ( ( zip_Co3543743374963494515nteger @ Xs2 @ Ys )
% 8.60/4.78 = ( cons_P9044669534377732177nteger @ Xy @ Xys ) )
% 8.60/4.78 => ~ ! [X3: code_integer,Xs4: list_Code_integer] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_Code_integer @ X3 @ Xs4 ) )
% 8.60/4.78 => ! [Y3: code_integer,Ys4: list_Code_integer] :
% 8.60/4.78 ( ( Ys
% 8.60/4.78 = ( cons_Code_integer @ Y3 @ Ys4 ) )
% 8.60/4.78 => ( ( Xy
% 8.60/4.78 = ( produc1086072967326762835nteger @ X3 @ Y3 ) )
% 8.60/4.78 => ( Xys
% 8.60/4.78 != ( zip_Co3543743374963494515nteger @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2402_zip__eq__ConsE,axiom,
% 8.60/4.78 ! [Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat,Xy: produc859450856879609959at_nat,Xys: list_P8469869581646625389at_nat] :
% 8.60/4.78 ( ( ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys )
% 8.60/4.78 = ( cons_P8732206157123786781at_nat @ Xy @ Xys ) )
% 8.60/4.78 => ~ ! [X3: product_prod_nat_nat,Xs4: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_P6512896166579812791at_nat @ X3 @ Xs4 ) )
% 8.60/4.78 => ! [Y3: product_prod_nat_nat,Ys4: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( Ys
% 8.60/4.78 = ( cons_P6512896166579812791at_nat @ Y3 @ Ys4 ) )
% 8.60/4.78 => ( ( Xy
% 8.60/4.78 = ( produc6161850002892822231at_nat @ X3 @ Y3 ) )
% 8.60/4.78 => ( Xys
% 8.60/4.78 != ( zip_Pr4664179122662387191at_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2403_zip__eq__ConsE,axiom,
% 8.60/4.78 ! [Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat,Xy: produc3843707927480180839at_nat,Xys: list_P5464809261938338413at_nat] :
% 8.60/4.78 ( ( ( zip_se5600341670672612855at_nat @ Xs2 @ Ys )
% 8.60/4.78 = ( cons_P3940603068885512221at_nat @ Xy @ Xys ) )
% 8.60/4.78 => ~ ! [X3: set_Pr1261947904930325089at_nat,Xs4: list_s1210847774152347623at_nat] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_s6881495754146722583at_nat @ X3 @ Xs4 ) )
% 8.60/4.78 => ! [Y3: set_Pr1261947904930325089at_nat,Ys4: list_s1210847774152347623at_nat] :
% 8.60/4.78 ( ( Ys
% 8.60/4.78 = ( cons_s6881495754146722583at_nat @ Y3 @ Ys4 ) )
% 8.60/4.78 => ( ( Xy
% 8.60/4.78 = ( produc2922128104949294807at_nat @ X3 @ Y3 ) )
% 8.60/4.78 => ( Xys
% 8.60/4.78 != ( zip_se5600341670672612855at_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2404_zip__eq__ConsE,axiom,
% 8.60/4.78 ! [Xs2: list_nat,Ys: list_nat,Xy: product_prod_nat_nat,Xys: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( ( zip_nat_nat @ Xs2 @ Ys )
% 8.60/4.78 = ( cons_P6512896166579812791at_nat @ Xy @ Xys ) )
% 8.60/4.78 => ~ ! [X3: nat,Xs4: list_nat] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_nat @ X3 @ Xs4 ) )
% 8.60/4.78 => ! [Y3: nat,Ys4: list_nat] :
% 8.60/4.78 ( ( Ys
% 8.60/4.78 = ( cons_nat @ Y3 @ Ys4 ) )
% 8.60/4.78 => ( ( Xy
% 8.60/4.78 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 8.60/4.78 => ( Xys
% 8.60/4.78 != ( zip_nat_nat @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2405_zip__eq__ConsE,axiom,
% 8.60/4.78 ! [Xs2: list_int,Ys: list_int,Xy: product_prod_int_int,Xys: list_P5707943133018811711nt_int] :
% 8.60/4.78 ( ( ( zip_int_int @ Xs2 @ Ys )
% 8.60/4.78 = ( cons_P3334398858971670639nt_int @ Xy @ Xys ) )
% 8.60/4.78 => ~ ! [X3: int,Xs4: list_int] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_int @ X3 @ Xs4 ) )
% 8.60/4.78 => ! [Y3: int,Ys4: list_int] :
% 8.60/4.78 ( ( Ys
% 8.60/4.78 = ( cons_int @ Y3 @ Ys4 ) )
% 8.60/4.78 => ( ( Xy
% 8.60/4.78 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 8.60/4.78 => ( Xys
% 8.60/4.78 != ( zip_int_int @ Xs4 @ Ys4 ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2406_find_Osimps_I2_J,axiom,
% 8.60/4.78 ! [P2: product_prod_nat_nat > $o,X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( ( P2 @ X )
% 8.60/4.78 => ( ( find_P8199882355184865565at_nat @ P2 @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) )
% 8.60/4.78 = ( some_P7363390416028606310at_nat @ X ) ) )
% 8.60/4.78 & ( ~ ( P2 @ X )
% 8.60/4.78 => ( ( find_P8199882355184865565at_nat @ P2 @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) )
% 8.60/4.78 = ( find_P8199882355184865565at_nat @ P2 @ Xs2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2407_find_Osimps_I2_J,axiom,
% 8.60/4.78 ! [P2: nat > $o,X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( ( P2 @ X )
% 8.60/4.78 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs2 ) )
% 8.60/4.78 = ( some_nat @ X ) ) )
% 8.60/4.78 & ( ~ ( P2 @ X )
% 8.60/4.78 => ( ( find_nat @ P2 @ ( cons_nat @ X @ Xs2 ) )
% 8.60/4.78 = ( find_nat @ P2 @ Xs2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2408_find_Osimps_I2_J,axiom,
% 8.60/4.78 ! [P2: num > $o,X: num,Xs2: list_num] :
% 8.60/4.78 ( ( ( P2 @ X )
% 8.60/4.78 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs2 ) )
% 8.60/4.78 = ( some_num @ X ) ) )
% 8.60/4.78 & ( ~ ( P2 @ X )
% 8.60/4.78 => ( ( find_num @ P2 @ ( cons_num @ X @ Xs2 ) )
% 8.60/4.78 = ( find_num @ P2 @ Xs2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2409_set__zip__rightD,axiom,
% 8.60/4.78 ! [X: code_integer,Y: code_integer,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 8.60/4.78 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member_Code_integer @ Y @ ( set_Code_integer2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2410_set__zip__rightD,axiom,
% 8.60/4.78 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member8440522571783428010at_nat @ Y @ ( set_Pr5648618587558075414at_nat @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2411_set__zip__rightD,axiom,
% 8.60/4.78 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 8.60/4.78 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member2643936169264416010at_nat @ Y @ ( set_se5049602875457034614at_nat @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2412_set__zip__rightD,axiom,
% 8.60/4.78 ! [X: nat,Y: nat,Xs2: list_nat,Ys: list_nat] :
% 8.60/4.78 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member_nat @ Y @ ( set_nat2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2413_set__zip__rightD,axiom,
% 8.60/4.78 ! [X: int,Y: int,Xs2: list_int,Ys: list_int] :
% 8.60/4.78 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2414_set__zip__leftD,axiom,
% 8.60/4.78 ! [X: code_integer,Y: code_integer,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 8.60/4.78 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member_Code_integer @ X @ ( set_Code_integer2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2415_set__zip__leftD,axiom,
% 8.60/4.78 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2416_set__zip__leftD,axiom,
% 8.60/4.78 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 8.60/4.78 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member2643936169264416010at_nat @ X @ ( set_se5049602875457034614at_nat @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2417_set__zip__leftD,axiom,
% 8.60/4.78 ! [X: nat,Y: nat,Xs2: list_nat,Ys: list_nat] :
% 8.60/4.78 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member_nat @ X @ ( set_nat2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2418_set__zip__leftD,axiom,
% 8.60/4.78 ! [X: int,Y: int,Xs2: list_int,Ys: list_int] :
% 8.60/4.78 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ( member_int @ X @ ( set_int2 @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2419_in__set__zipE,axiom,
% 8.60/4.78 ! [X: complex,Y: complex,Xs2: list_complex,Ys: list_complex] :
% 8.60/4.78 ( ( member5793383173714906214omplex @ ( produc101793102246108661omplex @ X @ Y ) @ ( set_Pr8199049879907524818omplex @ ( zip_complex_complex @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2420_in__set__zipE,axiom,
% 8.60/4.78 ! [X: complex,Y: real,Xs2: list_complex,Ys: list_real] :
% 8.60/4.78 ( ( member47443559803733732x_real @ ( produc1746590499379883635x_real @ X @ Y ) @ ( set_Pr1225976482156248400x_real @ ( zip_complex_real @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2421_in__set__zipE,axiom,
% 8.60/4.78 ! [X: complex,Y: int,Xs2: list_complex,Ys: list_int] :
% 8.60/4.78 ( ( member595073364599660772ex_int @ ( produc1367138851071493491ex_int @ X @ Y ) @ ( set_Pr4995810437751016784ex_int @ ( zip_complex_int @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2422_in__set__zipE,axiom,
% 8.60/4.78 ! [X: real,Y: complex,Xs2: list_real,Ys: list_complex] :
% 8.60/4.78 ( ( member7358116576843751780omplex @ ( produc1693001998875562995omplex @ X @ Y ) @ ( set_Pr8536649499196266448omplex @ ( zip_real_complex @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2423_in__set__zipE,axiom,
% 8.60/4.78 ! [X: real,Y: real,Xs2: list_real,Ys: list_real] :
% 8.60/4.78 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ X @ Y ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2424_in__set__zipE,axiom,
% 8.60/4.78 ! [X: real,Y: int,Xs2: list_real,Ys: list_int] :
% 8.60/4.78 ( ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X @ Y ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_int @ Y @ ( set_int2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2425_in__set__zipE,axiom,
% 8.60/4.78 ! [X: int,Y: complex,Xs2: list_int,Ys: list_complex] :
% 8.60/4.78 ( ( member8811922270175639012omplex @ ( produc7948753499206759283omplex @ X @ Y ) @ ( set_Pr3989287306472219216omplex @ ( zip_int_complex @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_complex @ Y @ ( set_complex2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2426_in__set__zipE,axiom,
% 8.60/4.78 ! [X: int,Y: real,Xs2: list_int,Ys: list_real] :
% 8.60/4.78 ( ( member2744130022092475746t_real @ ( produc801115645435158769t_real @ X @ Y ) @ ( set_Pr112895574167722958t_real @ ( zip_int_real @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_real @ Y @ ( set_real2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2427_in__set__zipE,axiom,
% 8.60/4.78 ! [X: complex,Y: vEBT_VEBT,Xs2: list_complex,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( member1978952105866562066T_VEBT @ ( produc2757191886755552429T_VEBT @ X @ Y ) @ ( set_Pr5158653123227461798T_VEBT @ ( zip_co9157518722488180109T_VEBT @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2428_in__set__zipE,axiom,
% 8.60/4.78 ! [X: real,Y: vEBT_VEBT,Xs2: list_real,Ys: list_VEBT_VEBT] :
% 8.60/4.78 ( ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X @ Y ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs2 @ Ys ) ) )
% 8.60/4.78 => ~ ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2429_zip__same,axiom,
% 8.60/4.78 ! [A: complex,B: complex,Xs2: list_complex] :
% 8.60/4.78 ( ( member5793383173714906214omplex @ ( produc101793102246108661omplex @ A @ B ) @ ( set_Pr8199049879907524818omplex @ ( zip_complex_complex @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member_complex @ A @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2430_zip__same,axiom,
% 8.60/4.78 ! [A: real,B: real,Xs2: list_real] :
% 8.60/4.78 ( ( member7849222048561428706l_real @ ( produc4511245868158468465l_real @ A @ B ) @ ( set_Pr5999470521830281550l_real @ ( zip_real_real @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member_real @ A @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2431_zip__same,axiom,
% 8.60/4.78 ! [A: set_nat,B: set_nat,Xs2: list_set_nat] :
% 8.60/4.78 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A @ B ) @ ( set_Pr9040384385603167362et_nat @ ( zip_set_nat_set_nat @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member_set_nat @ A @ ( set_set_nat2 @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2432_zip__same,axiom,
% 8.60/4.78 ! [A: vEBT_VEBT,B: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ A @ B ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member_VEBT_VEBT @ A @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2433_zip__same,axiom,
% 8.60/4.78 ! [A: code_integer,B: code_integer,Xs2: list_Code_integer] :
% 8.60/4.78 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ A @ B ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member_Code_integer @ A @ ( set_Code_integer2 @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2434_zip__same,axiom,
% 8.60/4.78 ! [A: product_prod_nat_nat,B: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat] :
% 8.60/4.78 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ A @ B ) @ ( set_Pr5518436109238095868at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member8440522571783428010at_nat @ A @ ( set_Pr5648618587558075414at_nat @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2435_zip__same,axiom,
% 8.60/4.78 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat] :
% 8.60/4.78 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A @ B ) @ ( set_Pr3765526544606949372at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member2643936169264416010at_nat @ A @ ( set_se5049602875457034614at_nat @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2436_zip__same,axiom,
% 8.60/4.78 ! [A: nat,B: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ ( set_Pr5648618587558075414at_nat @ ( zip_nat_nat @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member_nat @ A @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2437_zip__same,axiom,
% 8.60/4.78 ! [A: int,B: int,Xs2: list_int] :
% 8.60/4.78 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ ( set_Pr2470121279949933262nt_int @ ( zip_int_int @ Xs2 @ Xs2 ) ) )
% 8.60/4.78 = ( ( member_int @ A @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 & ( A = B ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2438_Suc__length__conv,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ( suc @ N )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2439_Suc__length__conv,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_o] :
% 8.60/4.78 ( ( ( suc @ N )
% 8.60/4.78 = ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 = ( ? [Y4: $o,Ys3: list_o] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_o @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_size_list_o @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2440_Suc__length__conv,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( ( suc @ N )
% 8.60/4.78 = ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 = ( ? [Y4: nat,Ys3: list_nat] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_nat @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_size_list_nat @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2441_Suc__length__conv,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_int] :
% 8.60/4.78 ( ( ( suc @ N )
% 8.60/4.78 = ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 = ( ? [Y4: int,Ys3: list_int] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_int @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_size_list_int @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2442_length__Suc__conv,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,N: nat] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( suc @ N ) )
% 8.60/4.78 = ( ? [Y4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_VEBT_VEBT @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_s6755466524823107622T_VEBT @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2443_length__Suc__conv,axiom,
% 8.60/4.78 ! [Xs2: list_o,N: nat] :
% 8.60/4.78 ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.78 = ( suc @ N ) )
% 8.60/4.78 = ( ? [Y4: $o,Ys3: list_o] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_o @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_size_list_o @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2444_length__Suc__conv,axiom,
% 8.60/4.78 ! [Xs2: list_nat,N: nat] :
% 8.60/4.78 ( ( ( size_size_list_nat @ Xs2 )
% 8.60/4.78 = ( suc @ N ) )
% 8.60/4.78 = ( ? [Y4: nat,Ys3: list_nat] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_nat @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_size_list_nat @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2445_length__Suc__conv,axiom,
% 8.60/4.78 ! [Xs2: list_int,N: nat] :
% 8.60/4.78 ( ( ( size_size_list_int @ Xs2 )
% 8.60/4.78 = ( suc @ N ) )
% 8.60/4.78 = ( ? [Y4: int,Ys3: list_int] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_int @ Y4 @ Ys3 ) )
% 8.60/4.78 & ( ( size_size_list_int @ Ys3 )
% 8.60/4.78 = N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2446_impossible__Cons,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( Xs2
% 8.60/4.78 != ( cons_VEBT_VEBT @ X @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2447_impossible__Cons,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_o,X: $o] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) )
% 8.60/4.78 => ( Xs2
% 8.60/4.78 != ( cons_o @ X @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2448_impossible__Cons,axiom,
% 8.60/4.78 ! [Xs2: list_nat,Ys: list_nat,X: nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_size_list_nat @ Ys ) )
% 8.60/4.78 => ( Xs2
% 8.60/4.78 != ( cons_nat @ X @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2449_impossible__Cons,axiom,
% 8.60/4.78 ! [Xs2: list_int,Ys: list_int,X: int] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ ( size_size_list_int @ Ys ) )
% 8.60/4.78 => ( Xs2
% 8.60/4.78 != ( cons_int @ X @ Ys ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2450_vebt__insert_Osimps_I2_J,axiom,
% 8.60/4.78 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 8.60/4.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) @ X )
% 8.60/4.78 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2451_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_Code_integer,Ys: list_Code_integer,X: code_integer] :
% 8.60/4.78 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 8.60/4.78 = ( size_s3445333598471063425nteger @ Ys ) )
% 8.60/4.78 => ( ( member_Code_integer @ X @ ( set_Code_integer2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: code_integer] :
% 8.60/4.78 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y3 ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2452_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_complex,Ys: list_VEBT_VEBT,X: complex] :
% 8.60/4.78 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member1978952105866562066T_VEBT @ ( produc2757191886755552429T_VEBT @ X @ Y3 ) @ ( set_Pr5158653123227461798T_VEBT @ ( zip_co9157518722488180109T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2453_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_real,Ys: list_VEBT_VEBT,X: real] :
% 8.60/4.78 ( ( ( size_size_list_real @ Xs2 )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member7262085504369356948T_VEBT @ ( produc6931449550656315951T_VEBT @ X @ Y3 ) @ ( set_Pr8897343066327330088T_VEBT @ ( zip_real_VEBT_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2454_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_complex,Ys: list_o,X: complex] :
% 8.60/4.78 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 8.60/4.78 = ( size_size_list_o @ Ys ) )
% 8.60/4.78 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: $o] :
% 8.60/4.78 ~ ( member6487239523555734774plex_o @ ( produc2908979694703026321plex_o @ X @ Y3 ) @ ( set_Pr6829704231520703882plex_o @ ( zip_complex_o @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2455_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_real,Ys: list_o,X: real] :
% 8.60/4.78 ( ( ( size_size_list_real @ Xs2 )
% 8.60/4.78 = ( size_size_list_o @ Ys ) )
% 8.60/4.78 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: $o] :
% 8.60/4.78 ~ ( member772602641336174712real_o @ ( product_Pair_real_o @ X @ Y3 ) @ ( set_Pr5196769464307566348real_o @ ( zip_real_o @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2456_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_complex,Ys: list_nat,X: complex] :
% 8.60/4.78 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 8.60/4.78 = ( size_size_list_nat @ Ys ) )
% 8.60/4.78 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: nat] :
% 8.60/4.78 ~ ( member4772924384108857480ex_nat @ ( produc1369629321580543767ex_nat @ X @ Y3 ) @ ( set_Pr9173661457260213492ex_nat @ ( zip_complex_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2457_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_real,Ys: list_nat,X: real] :
% 8.60/4.78 ( ( ( size_size_list_real @ Xs2 )
% 8.60/4.78 = ( size_size_list_nat @ Ys ) )
% 8.60/4.78 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: nat] :
% 8.60/4.78 ~ ( member5805532792777349510al_nat @ ( produc3181502643871035669al_nat @ X @ Y3 ) @ ( set_Pr3174298344852596722al_nat @ ( zip_real_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2458_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_complex,Ys: list_int,X: complex] :
% 8.60/4.78 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 8.60/4.78 = ( size_size_list_int @ Ys ) )
% 8.60/4.78 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: int] :
% 8.60/4.78 ~ ( member595073364599660772ex_int @ ( produc1367138851071493491ex_int @ X @ Y3 ) @ ( set_Pr4995810437751016784ex_int @ ( zip_complex_int @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2459_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_real,Ys: list_int,X: real] :
% 8.60/4.78 ( ( ( size_size_list_real @ Xs2 )
% 8.60/4.78 = ( size_size_list_int @ Ys ) )
% 8.60/4.78 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: int] :
% 8.60/4.78 ~ ( member1627681773268152802al_int @ ( produc3179012173361985393al_int @ X @ Y3 ) @ ( set_Pr8219819362198175822al_int @ ( zip_real_int @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2460_in__set__impl__in__set__zip1,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ~ ! [Y3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y3 ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2461_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_Code_integer,Ys: list_Code_integer,Y: code_integer] :
% 8.60/4.78 ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 8.60/4.78 = ( size_s3445333598471063425nteger @ Ys ) )
% 8.60/4.78 => ( ( member_Code_integer @ Y @ ( set_Code_integer2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: code_integer] :
% 8.60/4.78 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y ) @ ( set_Pr920681315882439344nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2462_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_complex,Y: complex] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_s3451745648224563538omplex @ Ys ) )
% 8.60/4.78 => ( ( member_complex @ Y @ ( set_complex2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member3207599676835851048omplex @ ( produc5617778602380981643omplex @ X3 @ Y ) @ ( set_Pr6387300694196750780omplex @ ( zip_VE2794733401258833515omplex @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2463_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_real,Y: real] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_size_list_real @ Ys ) )
% 8.60/4.78 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member8675245146396747942T_real @ ( produc8117437818029410057T_real @ X3 @ Y ) @ ( set_Pr1087130671499945274T_real @ ( zip_VEBT_VEBT_real @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2464_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X3 @ Y ) @ ( set_Pr9182192707038809660T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2465_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_o,Y: $o] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_size_list_o @ Ys ) )
% 8.60/4.78 => ( ( member_o @ Y @ ( set_o2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ X3 @ Y ) @ ( set_Pr7708085864119495200VEBT_o @ ( zip_VEBT_VEBT_o @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2466_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,Y: nat] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_size_list_nat @ Ys ) )
% 8.60/4.78 => ( ( member_nat @ Y @ ( set_nat2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ X3 @ Y ) @ ( set_Pr7031586669278753246BT_nat @ ( zip_VEBT_VEBT_nat @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2467_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_VEBT_VEBT,Ys: list_int,Y: int] :
% 8.60/4.78 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.78 = ( size_size_list_int @ Ys ) )
% 8.60/4.78 => ( ( member_int @ Y @ ( set_int2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: vEBT_VEBT] :
% 8.60/4.78 ~ ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ X3 @ Y ) @ ( set_Pr2853735649769556538BT_int @ ( zip_VEBT_VEBT_int @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2468_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_complex,Y: complex] :
% 8.60/4.78 ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.78 = ( size_s3451745648224563538omplex @ Ys ) )
% 8.60/4.78 => ( ( member_complex @ Y @ ( set_complex2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: $o] :
% 8.60/4.78 ~ ( member1046615901120239500omplex @ ( produc414345526774272751omplex @ X3 @ Y ) @ ( set_Pr1389080609085208608omplex @ ( zip_o_complex @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2469_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_real,Y: real] :
% 8.60/4.78 ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.78 = ( size_size_list_real @ Ys ) )
% 8.60/4.78 => ( ( member_real @ Y @ ( set_real2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: $o] :
% 8.60/4.78 ~ ( member7400031367953476362o_real @ ( product_Pair_o_real @ X3 @ Y ) @ ( set_Pr2600826154070092190o_real @ ( zip_o_real @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2470_in__set__impl__in__set__zip2,axiom,
% 8.60/4.78 ! [Xs2: list_o,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 8.60/4.78 ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.78 => ( ( member_VEBT_VEBT @ Y @ ( set_VEBT_VEBT2 @ Ys ) )
% 8.60/4.78 => ~ ! [X3: $o] :
% 8.60/4.78 ~ ( member5477980866518848620T_VEBT @ ( produc2982872950893828659T_VEBT @ X3 @ Y ) @ ( set_Pr655345902815428824T_VEBT @ ( zip_o_VEBT_VEBT @ Xs2 @ Ys ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2471_Suc__le__length__iff,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 = ( ? [X4: vEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_VEBT_VEBT @ X4 @ Ys3 ) )
% 8.60/4.78 & ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2472_Suc__le__length__iff,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_o] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 = ( ? [X4: $o,Ys3: list_o] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_o @ X4 @ Ys3 ) )
% 8.60/4.78 & ( ord_less_eq_nat @ N @ ( size_size_list_o @ Ys3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2473_Suc__le__length__iff,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 = ( ? [X4: nat,Ys3: list_nat] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_nat @ X4 @ Ys3 ) )
% 8.60/4.78 & ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2474_Suc__le__length__iff,axiom,
% 8.60/4.78 ! [N: nat,Xs2: list_int] :
% 8.60/4.78 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 = ( ? [X4: int,Ys3: list_int] :
% 8.60/4.78 ( ( Xs2
% 8.60/4.78 = ( cons_int @ X4 @ Ys3 ) )
% 8.60/4.78 & ( ord_less_eq_nat @ N @ ( size_size_list_int @ Ys3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2475_VEBT__internal_Oinsert_H_Osimps_I1_J,axiom,
% 8.60/4.78 ! [A: $o,B: $o,X: nat] :
% 8.60/4.78 ( ( vEBT_VEBT_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.60/4.78 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2476_vebt__insert_Osimps_I3_J,axiom,
% 8.60/4.78 ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 8.60/4.78 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) @ X )
% 8.60/4.78 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S2 ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2477_vebt__insert_Osimps_I1_J,axiom,
% 8.60/4.78 ! [X: nat,A: $o,B: $o] :
% 8.60/4.78 ( ( ( X = zero_zero_nat )
% 8.60/4.78 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.60/4.78 = ( vEBT_Leaf @ $true @ B ) ) )
% 8.60/4.78 & ( ( X != zero_zero_nat )
% 8.60/4.78 => ( ( ( X = one_one_nat )
% 8.60/4.78 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.60/4.78 = ( vEBT_Leaf @ A @ $true ) ) )
% 8.60/4.78 & ( ( X != one_one_nat )
% 8.60/4.78 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 8.60/4.78 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2478_list_Osize_I4_J,axiom,
% 8.60/4.78 ! [X21: vEBT_VEBT,X22: list_VEBT_VEBT] :
% 8.60/4.78 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X21 @ X22 ) )
% 8.60/4.78 = ( plus_plus_nat @ ( size_s6755466524823107622T_VEBT @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2479_list_Osize_I4_J,axiom,
% 8.60/4.78 ! [X21: $o,X22: list_o] :
% 8.60/4.78 ( ( size_size_list_o @ ( cons_o @ X21 @ X22 ) )
% 8.60/4.78 = ( plus_plus_nat @ ( size_size_list_o @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2480_list_Osize_I4_J,axiom,
% 8.60/4.78 ! [X21: nat,X22: list_nat] :
% 8.60/4.78 ( ( size_size_list_nat @ ( cons_nat @ X21 @ X22 ) )
% 8.60/4.78 = ( plus_plus_nat @ ( size_size_list_nat @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2481_list_Osize_I4_J,axiom,
% 8.60/4.78 ! [X21: int,X22: list_int] :
% 8.60/4.78 ( ( size_size_list_int @ ( cons_int @ X21 @ X22 ) )
% 8.60/4.78 = ( plus_plus_nat @ ( size_size_list_int @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2482_nth__Cons_H,axiom,
% 8.60/4.78 ! [N: nat,X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( ( N = zero_zero_nat )
% 8.60/4.78 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 8.60/4.78 = X ) )
% 8.60/4.78 & ( ( N != zero_zero_nat )
% 8.60/4.78 => ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 8.60/4.78 = ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2483_nth__Cons_H,axiom,
% 8.60/4.78 ! [N: nat,X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( ( N = zero_zero_nat )
% 8.60/4.78 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 8.60/4.78 = X ) )
% 8.60/4.78 & ( ( N != zero_zero_nat )
% 8.60/4.78 => ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 8.60/4.78 = ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2484_nth__equal__first__eq,axiom,
% 8.60/4.78 ! [X: complex,Xs2: list_complex,N: nat] :
% 8.60/4.78 ( ~ ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_eq_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.60/4.78 => ( ( ( nth_complex @ ( cons_complex @ X @ Xs2 ) @ N )
% 8.60/4.78 = X )
% 8.60/4.78 = ( N = zero_zero_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2485_nth__equal__first__eq,axiom,
% 8.60/4.78 ! [X: real,Xs2: list_real,N: nat] :
% 8.60/4.78 ( ~ ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_eq_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 8.60/4.78 => ( ( ( nth_real @ ( cons_real @ X @ Xs2 ) @ N )
% 8.60/4.78 = X )
% 8.60/4.78 = ( N = zero_zero_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2486_nth__equal__first__eq,axiom,
% 8.60/4.78 ! [X: set_nat,Xs2: list_set_nat,N: nat] :
% 8.60/4.78 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_eq_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.60/4.78 => ( ( ( nth_set_nat @ ( cons_set_nat @ X @ Xs2 ) @ N )
% 8.60/4.78 = X )
% 8.60/4.78 = ( N = zero_zero_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2487_nth__equal__first__eq,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 8.60/4.78 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_eq_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.78 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 8.60/4.78 = X )
% 8.60/4.78 = ( N = zero_zero_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2488_nth__equal__first__eq,axiom,
% 8.60/4.78 ! [X: $o,Xs2: list_o,N: nat] :
% 8.60/4.78 ( ~ ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_eq_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.78 => ( ( ( nth_o @ ( cons_o @ X @ Xs2 ) @ N )
% 8.60/4.78 = X )
% 8.60/4.78 = ( N = zero_zero_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2489_nth__equal__first__eq,axiom,
% 8.60/4.78 ! [X: nat,Xs2: list_nat,N: nat] :
% 8.60/4.78 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_eq_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.78 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 8.60/4.78 = X )
% 8.60/4.78 = ( N = zero_zero_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2490_nth__equal__first__eq,axiom,
% 8.60/4.78 ! [X: int,Xs2: list_int,N: nat] :
% 8.60/4.78 ( ~ ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ( ( ord_less_eq_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 8.60/4.78 => ( ( ( nth_int @ ( cons_int @ X @ Xs2 ) @ N )
% 8.60/4.78 = X )
% 8.60/4.78 = ( N = zero_zero_nat ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2491_nth__non__equal__first__eq,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Y: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat] :
% 8.60/4.78 ( ( X != Y )
% 8.60/4.78 => ( ( ( nth_VEBT_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ N )
% 8.60/4.78 = Y )
% 8.60/4.78 = ( ( ( nth_VEBT_VEBT @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 = Y )
% 8.60/4.78 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2492_nth__non__equal__first__eq,axiom,
% 8.60/4.78 ! [X: nat,Y: nat,Xs2: list_nat,N: nat] :
% 8.60/4.78 ( ( X != Y )
% 8.60/4.78 => ( ( ( nth_nat @ ( cons_nat @ X @ Xs2 ) @ N )
% 8.60/4.78 = Y )
% 8.60/4.78 = ( ( ( nth_nat @ Xs2 @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 = Y )
% 8.60/4.78 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2493_length__Cons,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ( size_s6755466524823107622T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) )
% 8.60/4.78 = ( suc @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2494_length__Cons,axiom,
% 8.60/4.78 ! [X: $o,Xs2: list_o] :
% 8.60/4.78 ( ( size_size_list_o @ ( cons_o @ X @ Xs2 ) )
% 8.60/4.78 = ( suc @ ( size_size_list_o @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2495_length__Cons,axiom,
% 8.60/4.78 ! [X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ( size_size_list_nat @ ( cons_nat @ X @ Xs2 ) )
% 8.60/4.78 = ( suc @ ( size_size_list_nat @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2496_length__Cons,axiom,
% 8.60/4.78 ! [X: int,Xs2: list_int] :
% 8.60/4.78 ( ( size_size_list_int @ ( cons_int @ X @ Xs2 ) )
% 8.60/4.78 = ( suc @ ( size_size_list_int @ Xs2 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2497_dbl__inc__simps_I2_J,axiom,
% 8.60/4.78 ( ( neg_nu5831290666863070958nteger @ zero_z3403309356797280102nteger )
% 8.60/4.78 = one_one_Code_integer ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2498_dbl__inc__simps_I2_J,axiom,
% 8.60/4.78 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 8.60/4.78 = one_one_complex ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2499_dbl__inc__simps_I2_J,axiom,
% 8.60/4.78 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 8.60/4.78 = one_one_real ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2500_dbl__inc__simps_I2_J,axiom,
% 8.60/4.78 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 8.60/4.78 = one_one_rat ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2501_dbl__inc__simps_I2_J,axiom,
% 8.60/4.78 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 8.60/4.78 = one_one_int ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2502_enumerate__Suc_H,axiom,
% 8.60/4.78 ! [S3: set_nat,N: nat] :
% 8.60/4.78 ( ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) )
% 8.60/4.78 = ( infini8530281810654367211te_nat @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ ( infini8530281810654367211te_nat @ S3 @ zero_zero_nat ) @ bot_bot_set_nat ) ) @ N ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2503_dbl__dec__def,axiom,
% 8.60/4.78 ( neg_nu7757733837767384882nteger
% 8.60/4.78 = ( ^ [X4: code_integer] : ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ X4 @ X4 ) @ one_one_Code_integer ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2504_dbl__dec__def,axiom,
% 8.60/4.78 ( neg_nu6511756317524482435omplex
% 8.60/4.78 = ( ^ [X4: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X4 @ X4 ) @ one_one_complex ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2505_dbl__dec__def,axiom,
% 8.60/4.78 ( neg_nu6075765906172075777c_real
% 8.60/4.78 = ( ^ [X4: real] : ( minus_minus_real @ ( plus_plus_real @ X4 @ X4 ) @ one_one_real ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2506_dbl__dec__def,axiom,
% 8.60/4.78 ( neg_nu3179335615603231917ec_rat
% 8.60/4.78 = ( ^ [X4: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X4 @ X4 ) @ one_one_rat ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2507_dbl__dec__def,axiom,
% 8.60/4.78 ( neg_nu3811975205180677377ec_int
% 8.60/4.78 = ( ^ [X4: int] : ( minus_minus_int @ ( plus_plus_int @ X4 @ X4 ) @ one_one_int ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2508_Gcd__fin__0__iff,axiom,
% 8.60/4.78 ! [A4: set_int] :
% 8.60/4.78 ( ( ( semiri4256215615220890538in_int @ A4 )
% 8.60/4.78 = zero_zero_int )
% 8.60/4.78 = ( ( ord_less_eq_set_int @ A4 @ ( insert_int @ zero_zero_int @ bot_bot_set_int ) )
% 8.60/4.78 & ( finite_finite_int @ A4 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2509_Gcd__fin__0__iff,axiom,
% 8.60/4.78 ! [A4: set_nat] :
% 8.60/4.78 ( ( ( semiri4258706085729940814in_nat @ A4 )
% 8.60/4.78 = zero_zero_nat )
% 8.60/4.78 = ( ( ord_less_eq_set_nat @ A4 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) )
% 8.60/4.78 & ( finite_finite_nat @ A4 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2510_power__decreasing__iff,axiom,
% 8.60/4.78 ! [B: code_integer,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.60/4.78 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 8.60/4.78 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 8.60/4.78 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2511_power__decreasing__iff,axiom,
% 8.60/4.78 ! [B: real,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_real @ zero_zero_real @ B )
% 8.60/4.78 => ( ( ord_less_real @ B @ one_one_real )
% 8.60/4.78 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 8.60/4.78 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2512_power__decreasing__iff,axiom,
% 8.60/4.78 ! [B: rat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.60/4.78 => ( ( ord_less_rat @ B @ one_one_rat )
% 8.60/4.78 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 8.60/4.78 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2513_power__decreasing__iff,axiom,
% 8.60/4.78 ! [B: nat,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.60/4.78 => ( ( ord_less_nat @ B @ one_one_nat )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 8.60/4.78 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2514_power__decreasing__iff,axiom,
% 8.60/4.78 ! [B: int,M2: nat,N: nat] :
% 8.60/4.78 ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.78 => ( ( ord_less_int @ B @ one_one_int )
% 8.60/4.78 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 8.60/4.78 = ( ord_less_eq_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2515_card__insert__le__m1,axiom,
% 8.60/4.78 ! [N: nat,Y: set_real,X: real] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( finite_card_real @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 => ( ord_less_eq_nat @ ( finite_card_real @ ( insert_real @ X @ Y ) ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2516_card__insert__le__m1,axiom,
% 8.60/4.78 ! [N: nat,Y: set_nat,X: nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( finite_card_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 => ( ord_less_eq_nat @ ( finite_card_nat @ ( insert_nat @ X @ Y ) ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2517_card__insert__le__m1,axiom,
% 8.60/4.78 ! [N: nat,Y: set_complex,X: complex] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( finite_card_complex @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 => ( ord_less_eq_nat @ ( finite_card_complex @ ( insert_complex @ X @ Y ) ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2518_card__insert__le__m1,axiom,
% 8.60/4.78 ! [N: nat,Y: set_int,X: int] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( finite_card_int @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 => ( ord_less_eq_nat @ ( finite_card_int @ ( insert_int @ X @ Y ) ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2519_card__insert__le__m1,axiom,
% 8.60/4.78 ! [N: nat,Y: set_list_nat,X: list_nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( insert_list_nat @ X @ Y ) ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2520_card__insert__le__m1,axiom,
% 8.60/4.78 ! [N: nat,Y: set_set_nat,X: set_nat] :
% 8.60/4.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.78 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ Y ) @ ( minus_minus_nat @ N @ one_one_nat ) )
% 8.60/4.78 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( insert_set_nat @ X @ Y ) ) @ N ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2521_count__notin,axiom,
% 8.60/4.78 ! [X: complex,Xs2: list_complex] :
% 8.60/4.78 ( ~ ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.60/4.78 => ( ( count_list_complex @ Xs2 @ X )
% 8.60/4.78 = zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2522_count__notin,axiom,
% 8.60/4.78 ! [X: real,Xs2: list_real] :
% 8.60/4.78 ( ~ ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.60/4.78 => ( ( count_list_real @ Xs2 @ X )
% 8.60/4.78 = zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2523_count__notin,axiom,
% 8.60/4.78 ! [X: set_nat,Xs2: list_set_nat] :
% 8.60/4.78 ( ~ ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( ( count_list_set_nat @ Xs2 @ X )
% 8.60/4.78 = zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2524_count__notin,axiom,
% 8.60/4.78 ! [X: int,Xs2: list_int] :
% 8.60/4.78 ( ~ ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.60/4.78 => ( ( count_list_int @ Xs2 @ X )
% 8.60/4.78 = zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2525_count__notin,axiom,
% 8.60/4.78 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT] :
% 8.60/4.78 ( ~ ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.60/4.78 => ( ( count_list_VEBT_VEBT @ Xs2 @ X )
% 8.60/4.78 = zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2526_count__notin,axiom,
% 8.60/4.78 ! [X: nat,Xs2: list_nat] :
% 8.60/4.78 ( ~ ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 8.60/4.78 => ( ( count_list_nat @ Xs2 @ X )
% 8.60/4.78 = zero_zero_nat ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2527_Cons__lenlex__iff,axiom,
% 8.60/4.78 ! [M2: code_integer,Ms: list_Code_integer,N: code_integer,Ns: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 8.60/4.78 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ M2 @ Ms ) @ ( cons_Code_integer @ N @ Ns ) ) @ ( lenlex_Code_integer @ R3 ) )
% 8.60/4.78 = ( ( ord_less_nat @ ( size_s3445333598471063425nteger @ Ms ) @ ( size_s3445333598471063425nteger @ Ns ) )
% 8.60/4.78 | ( ( ( size_s3445333598471063425nteger @ Ms )
% 8.60/4.78 = ( size_s3445333598471063425nteger @ Ns ) )
% 8.60/4.78 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ M2 @ N ) @ R3 ) )
% 8.60/4.78 | ( ( M2 = N )
% 8.60/4.78 & ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Ms @ Ns ) @ ( lenlex_Code_integer @ R3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2528_Cons__lenlex__iff,axiom,
% 8.60/4.78 ! [M2: product_prod_nat_nat,Ms: list_P6011104703257516679at_nat,N: product_prod_nat_nat,Ns: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 8.60/4.78 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ M2 @ Ms ) @ ( cons_P6512896166579812791at_nat @ N @ Ns ) ) @ ( lenlex325483962726685836at_nat @ R3 ) )
% 8.60/4.78 = ( ( ord_less_nat @ ( size_s5460976970255530739at_nat @ Ms ) @ ( size_s5460976970255530739at_nat @ Ns ) )
% 8.60/4.78 | ( ( ( size_s5460976970255530739at_nat @ Ms )
% 8.60/4.78 = ( size_s5460976970255530739at_nat @ Ns ) )
% 8.60/4.78 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ M2 @ N ) @ R3 ) )
% 8.60/4.78 | ( ( M2 = N )
% 8.60/4.78 & ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Ms @ Ns ) @ ( lenlex325483962726685836at_nat @ R3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2529_Cons__lenlex__iff,axiom,
% 8.60/4.78 ! [M2: set_Pr1261947904930325089at_nat,Ms: list_s1210847774152347623at_nat,N: set_Pr1261947904930325089at_nat,Ns: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 8.60/4.78 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ M2 @ Ms ) @ ( cons_s6881495754146722583at_nat @ N @ Ns ) ) @ ( lenlex1357538814655152620at_nat @ R3 ) )
% 8.60/4.78 = ( ( ord_less_nat @ ( size_s8736152011456118867at_nat @ Ms ) @ ( size_s8736152011456118867at_nat @ Ns ) )
% 8.60/4.78 | ( ( ( size_s8736152011456118867at_nat @ Ms )
% 8.60/4.78 = ( size_s8736152011456118867at_nat @ Ns ) )
% 8.60/4.78 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ M2 @ N ) @ R3 ) )
% 8.60/4.78 | ( ( M2 = N )
% 8.60/4.78 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ms @ Ns ) @ ( lenlex1357538814655152620at_nat @ R3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2530_Cons__lenlex__iff,axiom,
% 8.60/4.78 ! [M2: vEBT_VEBT,Ms: list_VEBT_VEBT,N: vEBT_VEBT,Ns: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 8.60/4.78 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ M2 @ Ms ) @ ( cons_VEBT_VEBT @ N @ Ns ) ) @ ( lenlex_VEBT_VEBT @ R3 ) )
% 8.60/4.78 = ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) )
% 8.60/4.78 | ( ( ( size_s6755466524823107622T_VEBT @ Ms )
% 8.60/4.78 = ( size_s6755466524823107622T_VEBT @ Ns ) )
% 8.60/4.78 & ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ M2 @ N ) @ R3 ) )
% 8.60/4.78 | ( ( M2 = N )
% 8.60/4.78 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2531_Cons__lenlex__iff,axiom,
% 8.60/4.78 ! [M2: $o,Ms: list_o,N: $o,Ns: list_o,R3: set_Product_prod_o_o] :
% 8.60/4.78 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ M2 @ Ms ) @ ( cons_o @ N @ Ns ) ) @ ( lenlex_o @ R3 ) )
% 8.60/4.78 = ( ( ord_less_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) )
% 8.60/4.78 | ( ( ( size_size_list_o @ Ms )
% 8.60/4.78 = ( size_size_list_o @ Ns ) )
% 8.60/4.78 & ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ M2 @ N ) @ R3 ) )
% 8.60/4.78 | ( ( M2 = N )
% 8.60/4.78 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2532_Cons__lenlex__iff,axiom,
% 8.60/4.78 ! [M2: nat,Ms: list_nat,N: nat,Ns: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 8.60/4.78 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ M2 @ Ms ) @ ( cons_nat @ N @ Ns ) ) @ ( lenlex_nat @ R3 ) )
% 8.60/4.78 = ( ( ord_less_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) )
% 8.60/4.78 | ( ( ( size_size_list_nat @ Ms )
% 8.60/4.78 = ( size_size_list_nat @ Ns ) )
% 8.60/4.78 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ R3 ) )
% 8.60/4.78 | ( ( M2 = N )
% 8.60/4.78 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2533_Cons__lenlex__iff,axiom,
% 8.60/4.78 ! [M2: int,Ms: list_int,N: int,Ns: list_int,R3: set_Pr958786334691620121nt_int] :
% 8.60/4.78 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ M2 @ Ms ) @ ( cons_int @ N @ Ns ) ) @ ( lenlex_int @ R3 ) )
% 8.60/4.78 = ( ( ord_less_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) )
% 8.60/4.78 | ( ( ( size_size_list_int @ Ms )
% 8.60/4.78 = ( size_size_list_int @ Ns ) )
% 8.60/4.78 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ M2 @ N ) @ R3 ) )
% 8.60/4.78 | ( ( M2 = N )
% 8.60/4.78 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R3 ) ) ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2534_power__shift,axiom,
% 8.60/4.78 ! [X: nat,Y: nat,Z3: nat] :
% 8.60/4.78 ( ( ( power_power_nat @ X @ Y )
% 8.60/4.78 = Z3 )
% 8.60/4.78 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 8.60/4.78 = ( some_nat @ Z3 ) ) ) ).
% 8.60/4.78
% 8.60/4.78 thf(fact_2535_local_Opower__def,axiom,
% 8.60/4.78 ( vEBT_VEBT_power
% 8.60/4.78 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2536_nat__power__eq__Suc__0__iff,axiom,
% 8.60/4.79 ! [X: nat,M2: nat] :
% 8.60/4.79 ( ( ( power_power_nat @ X @ M2 )
% 8.60/4.79 = ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ( M2 = zero_zero_nat )
% 8.60/4.79 | ( X
% 8.60/4.79 = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2537_power__Suc__0,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.60/4.79 = ( suc @ zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2538_nat__zero__less__power__iff,axiom,
% 8.60/4.79 ! [X: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 8.60/4.79 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.60/4.79 | ( N = zero_zero_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2539_dbl__dec__simps_I3_J,axiom,
% 8.60/4.79 ( ( neg_nu7757733837767384882nteger @ one_one_Code_integer )
% 8.60/4.79 = one_one_Code_integer ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2540_dbl__dec__simps_I3_J,axiom,
% 8.60/4.79 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 8.60/4.79 = one_one_complex ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2541_dbl__dec__simps_I3_J,axiom,
% 8.60/4.79 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 8.60/4.79 = one_one_real ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2542_dbl__dec__simps_I3_J,axiom,
% 8.60/4.79 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 8.60/4.79 = one_one_int ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2543_power__0__Suc,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 8.60/4.79 = zero_zero_rat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2544_power__0__Suc,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2545_power__0__Suc,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 8.60/4.79 = zero_zero_real ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2546_power__0__Suc,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 8.60/4.79 = zero_zero_int ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2547_power__0__Suc,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 8.60/4.79 = zero_zero_complex ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2548_power__Suc0__right,axiom,
% 8.60/4.79 ! [A: nat] :
% 8.60/4.79 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = A ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2549_power__Suc0__right,axiom,
% 8.60/4.79 ! [A: real] :
% 8.60/4.79 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = A ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2550_power__Suc0__right,axiom,
% 8.60/4.79 ! [A: int] :
% 8.60/4.79 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = A ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2551_power__Suc0__right,axiom,
% 8.60/4.79 ! [A: complex] :
% 8.60/4.79 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = A ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2552_card_Oempty,axiom,
% 8.60/4.79 ( ( finite_card_complex @ bot_bot_set_complex )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2553_card_Oempty,axiom,
% 8.60/4.79 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2554_card_Oempty,axiom,
% 8.60/4.79 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2555_card_Oempty,axiom,
% 8.60/4.79 ( ( finite_card_nat @ bot_bot_set_nat )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2556_card_Oempty,axiom,
% 8.60/4.79 ( ( finite_card_int @ bot_bot_set_int )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2557_card_Oempty,axiom,
% 8.60/4.79 ( ( finite_card_real @ bot_bot_set_real )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2558_card_Oinfinite,axiom,
% 8.60/4.79 ! [A4: set_list_nat] :
% 8.60/4.79 ( ~ ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2559_card_Oinfinite,axiom,
% 8.60/4.79 ! [A4: set_set_nat] :
% 8.60/4.79 ( ~ ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2560_card_Oinfinite,axiom,
% 8.60/4.79 ! [A4: set_nat] :
% 8.60/4.79 ( ~ ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( finite_card_nat @ A4 )
% 8.60/4.79 = zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2561_card_Oinfinite,axiom,
% 8.60/4.79 ! [A4: set_int] :
% 8.60/4.79 ( ~ ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( finite_card_int @ A4 )
% 8.60/4.79 = zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2562_card_Oinfinite,axiom,
% 8.60/4.79 ! [A4: set_complex] :
% 8.60/4.79 ( ~ ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( finite_card_complex @ A4 )
% 8.60/4.79 = zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2563_Gcd__fin_Oempty,axiom,
% 8.60/4.79 ( ( semiri4258706085729940814in_nat @ bot_bot_set_nat )
% 8.60/4.79 = zero_zero_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2564_Gcd__fin_Oempty,axiom,
% 8.60/4.79 ( ( semiri4256215615220890538in_int @ bot_bot_set_int )
% 8.60/4.79 = zero_zero_int ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2565_power__eq__0__iff,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ( power_power_rat @ A @ N )
% 8.60/4.79 = zero_zero_rat )
% 8.60/4.79 = ( ( A = zero_zero_rat )
% 8.60/4.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2566_power__eq__0__iff,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ( power_power_nat @ A @ N )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( ( A = zero_zero_nat )
% 8.60/4.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2567_power__eq__0__iff,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ( power_power_real @ A @ N )
% 8.60/4.79 = zero_zero_real )
% 8.60/4.79 = ( ( A = zero_zero_real )
% 8.60/4.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2568_power__eq__0__iff,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ( power_power_int @ A @ N )
% 8.60/4.79 = zero_zero_int )
% 8.60/4.79 = ( ( A = zero_zero_int )
% 8.60/4.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2569_power__eq__0__iff,axiom,
% 8.60/4.79 ! [A: complex,N: nat] :
% 8.60/4.79 ( ( ( power_power_complex @ A @ N )
% 8.60/4.79 = zero_zero_complex )
% 8.60/4.79 = ( ( A = zero_zero_complex )
% 8.60/4.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2570_card__0__eq,axiom,
% 8.60/4.79 ! [A4: set_list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( A4 = bot_bot_set_list_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2571_card__0__eq,axiom,
% 8.60/4.79 ! [A4: set_set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( A4 = bot_bot_set_set_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2572_card__0__eq,axiom,
% 8.60/4.79 ! [A4: set_complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( ( finite_card_complex @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( A4 = bot_bot_set_complex ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2573_card__0__eq,axiom,
% 8.60/4.79 ! [A4: set_nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( ( finite_card_nat @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( A4 = bot_bot_set_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2574_card__0__eq,axiom,
% 8.60/4.79 ! [A4: set_int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( ( finite_card_int @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( A4 = bot_bot_set_int ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2575_card__0__eq,axiom,
% 8.60/4.79 ! [A4: set_real] :
% 8.60/4.79 ( ( finite_finite_real @ A4 )
% 8.60/4.79 => ( ( ( finite_card_real @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( A4 = bot_bot_set_real ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2576_card__insert__disjoint,axiom,
% 8.60/4.79 ! [A4: set_real,X: real] :
% 8.60/4.79 ( ( finite_finite_real @ A4 )
% 8.60/4.79 => ( ~ ( member_real @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2577_card__insert__disjoint,axiom,
% 8.60/4.79 ! [A4: set_list_nat,X: list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ~ ( member_list_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2578_card__insert__disjoint,axiom,
% 8.60/4.79 ! [A4: set_set_nat,X: set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ~ ( member_set_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2579_card__insert__disjoint,axiom,
% 8.60/4.79 ! [A4: set_nat,X: nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ~ ( member_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2580_card__insert__disjoint,axiom,
% 8.60/4.79 ! [A4: set_int,X: int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ~ ( member_int @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2581_card__insert__disjoint,axiom,
% 8.60/4.79 ! [A4: set_complex,X: complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ~ ( member_complex @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2582_power__strict__decreasing__iff,axiom,
% 8.60/4.79 ! [B: code_integer,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.60/4.79 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 8.60/4.79 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M2 ) @ ( power_8256067586552552935nteger @ B @ N ) )
% 8.60/4.79 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2583_power__strict__decreasing__iff,axiom,
% 8.60/4.79 ! [B: real,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ zero_zero_real @ B )
% 8.60/4.79 => ( ( ord_less_real @ B @ one_one_real )
% 8.60/4.79 => ( ( ord_less_real @ ( power_power_real @ B @ M2 ) @ ( power_power_real @ B @ N ) )
% 8.60/4.79 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2584_power__strict__decreasing__iff,axiom,
% 8.60/4.79 ! [B: rat,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ zero_zero_rat @ B )
% 8.60/4.79 => ( ( ord_less_rat @ B @ one_one_rat )
% 8.60/4.79 => ( ( ord_less_rat @ ( power_power_rat @ B @ M2 ) @ ( power_power_rat @ B @ N ) )
% 8.60/4.79 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2585_power__strict__decreasing__iff,axiom,
% 8.60/4.79 ! [B: nat,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.60/4.79 => ( ( ord_less_nat @ B @ one_one_nat )
% 8.60/4.79 => ( ( ord_less_nat @ ( power_power_nat @ B @ M2 ) @ ( power_power_nat @ B @ N ) )
% 8.60/4.79 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2586_power__strict__decreasing__iff,axiom,
% 8.60/4.79 ! [B: int,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ zero_zero_int @ B )
% 8.60/4.79 => ( ( ord_less_int @ B @ one_one_int )
% 8.60/4.79 => ( ( ord_less_int @ ( power_power_int @ B @ M2 ) @ ( power_power_int @ B @ N ) )
% 8.60/4.79 = ( ord_less_nat @ N @ M2 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2587_power__increasing__iff,axiom,
% 8.60/4.79 ! [B: code_integer,X: nat,Y: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 8.60/4.79 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 8.60/4.79 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2588_power__increasing__iff,axiom,
% 8.60/4.79 ! [B: real,X: nat,Y: nat] :
% 8.60/4.79 ( ( ord_less_real @ one_one_real @ B )
% 8.60/4.79 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 8.60/4.79 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2589_power__increasing__iff,axiom,
% 8.60/4.79 ! [B: rat,X: nat,Y: nat] :
% 8.60/4.79 ( ( ord_less_rat @ one_one_rat @ B )
% 8.60/4.79 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 8.60/4.79 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2590_power__increasing__iff,axiom,
% 8.60/4.79 ! [B: nat,X: nat,Y: nat] :
% 8.60/4.79 ( ( ord_less_nat @ one_one_nat @ B )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 8.60/4.79 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2591_power__increasing__iff,axiom,
% 8.60/4.79 ! [B: int,X: nat,Y: nat] :
% 8.60/4.79 ( ( ord_less_int @ one_one_int @ B )
% 8.60/4.79 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 8.60/4.79 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2592_power__mono__iff,axiom,
% 8.60/4.79 ! [A: real,B: real,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 8.60/4.79 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2593_power__mono__iff,axiom,
% 8.60/4.79 ! [A: rat,B: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 8.60/4.79 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2594_power__mono__iff,axiom,
% 8.60/4.79 ! [A: nat,B: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.60/4.79 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2595_power__mono__iff,axiom,
% 8.60/4.79 ! [A: int,B: int,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.60/4.79 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2596_power__not__zero,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( A != zero_zero_rat )
% 8.60/4.79 => ( ( power_power_rat @ A @ N )
% 8.60/4.79 != zero_zero_rat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2597_power__not__zero,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( A != zero_zero_nat )
% 8.60/4.79 => ( ( power_power_nat @ A @ N )
% 8.60/4.79 != zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2598_power__not__zero,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( A != zero_zero_real )
% 8.60/4.79 => ( ( power_power_real @ A @ N )
% 8.60/4.79 != zero_zero_real ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2599_power__not__zero,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( A != zero_zero_int )
% 8.60/4.79 => ( ( power_power_int @ A @ N )
% 8.60/4.79 != zero_zero_int ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2600_power__not__zero,axiom,
% 8.60/4.79 ! [A: complex,N: nat] :
% 8.60/4.79 ( ( A != zero_zero_complex )
% 8.60/4.79 => ( ( power_power_complex @ A @ N )
% 8.60/4.79 != zero_zero_complex ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2601_power__commuting__commutes,axiom,
% 8.60/4.79 ! [X: complex,Y: complex,N: nat] :
% 8.60/4.79 ( ( ( times_times_complex @ X @ Y )
% 8.60/4.79 = ( times_times_complex @ Y @ X ) )
% 8.60/4.79 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y )
% 8.60/4.79 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2602_power__commuting__commutes,axiom,
% 8.60/4.79 ! [X: real,Y: real,N: nat] :
% 8.60/4.79 ( ( ( times_times_real @ X @ Y )
% 8.60/4.79 = ( times_times_real @ Y @ X ) )
% 8.60/4.79 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y )
% 8.60/4.79 = ( times_times_real @ Y @ ( power_power_real @ X @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2603_power__commuting__commutes,axiom,
% 8.60/4.79 ! [X: rat,Y: rat,N: nat] :
% 8.60/4.79 ( ( ( times_times_rat @ X @ Y )
% 8.60/4.79 = ( times_times_rat @ Y @ X ) )
% 8.60/4.79 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 8.60/4.79 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2604_power__commuting__commutes,axiom,
% 8.60/4.79 ! [X: nat,Y: nat,N: nat] :
% 8.60/4.79 ( ( ( times_times_nat @ X @ Y )
% 8.60/4.79 = ( times_times_nat @ Y @ X ) )
% 8.60/4.79 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 8.60/4.79 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2605_power__commuting__commutes,axiom,
% 8.60/4.79 ! [X: int,Y: int,N: nat] :
% 8.60/4.79 ( ( ( times_times_int @ X @ Y )
% 8.60/4.79 = ( times_times_int @ Y @ X ) )
% 8.60/4.79 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 8.60/4.79 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2606_power__mult__distrib,axiom,
% 8.60/4.79 ! [A: complex,B: complex,N: nat] :
% 8.60/4.79 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 8.60/4.79 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2607_power__mult__distrib,axiom,
% 8.60/4.79 ! [A: real,B: real,N: nat] :
% 8.60/4.79 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 8.60/4.79 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2608_power__mult__distrib,axiom,
% 8.60/4.79 ! [A: rat,B: rat,N: nat] :
% 8.60/4.79 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 8.60/4.79 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2609_power__mult__distrib,axiom,
% 8.60/4.79 ! [A: nat,B: nat,N: nat] :
% 8.60/4.79 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 8.60/4.79 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2610_power__mult__distrib,axiom,
% 8.60/4.79 ! [A: int,B: int,N: nat] :
% 8.60/4.79 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 8.60/4.79 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2611_power__commutes,axiom,
% 8.60/4.79 ! [A: complex,N: nat] :
% 8.60/4.79 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 8.60/4.79 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2612_power__commutes,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 8.60/4.79 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2613_power__commutes,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 8.60/4.79 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2614_power__commutes,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 8.60/4.79 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2615_power__commutes,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 8.60/4.79 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2616_power__mult,axiom,
% 8.60/4.79 ! [A: nat,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_nat @ A @ ( times_times_nat @ M2 @ N ) )
% 8.60/4.79 = ( power_power_nat @ ( power_power_nat @ A @ M2 ) @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2617_power__mult,axiom,
% 8.60/4.79 ! [A: real,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_real @ A @ ( times_times_nat @ M2 @ N ) )
% 8.60/4.79 = ( power_power_real @ ( power_power_real @ A @ M2 ) @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2618_power__mult,axiom,
% 8.60/4.79 ! [A: int,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_int @ A @ ( times_times_nat @ M2 @ N ) )
% 8.60/4.79 = ( power_power_int @ ( power_power_int @ A @ M2 ) @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2619_power__mult,axiom,
% 8.60/4.79 ! [A: complex,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_complex @ A @ ( times_times_nat @ M2 @ N ) )
% 8.60/4.79 = ( power_power_complex @ ( power_power_complex @ A @ M2 ) @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2620_finite__le__enumerate,axiom,
% 8.60/4.79 ! [S3: set_nat,N: nat] :
% 8.60/4.79 ( ( finite_finite_nat @ S3 )
% 8.60/4.79 => ( ( ord_less_nat @ N @ ( finite_card_nat @ S3 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2621_lenlex__irreflexive,axiom,
% 8.60/4.79 ! [R3: set_Pr4811707699266497531nteger,Xs2: list_Code_integer] :
% 8.60/4.79 ( ! [X3: code_integer] :
% 8.60/4.79 ~ ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ X3 ) @ R3 )
% 8.60/4.79 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Xs2 ) @ ( lenlex_Code_integer @ R3 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2622_lenlex__irreflexive,axiom,
% 8.60/4.79 ! [R3: set_Pr8693737435421807431at_nat,Xs2: list_P6011104703257516679at_nat] :
% 8.60/4.79 ( ! [X3: product_prod_nat_nat] :
% 8.60/4.79 ~ ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ X3 ) @ R3 )
% 8.60/4.79 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Xs2 ) @ ( lenlex325483962726685836at_nat @ R3 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2623_lenlex__irreflexive,axiom,
% 8.60/4.79 ! [R3: set_Pr4329608150637261639at_nat,Xs2: list_s1210847774152347623at_nat] :
% 8.60/4.79 ( ! [X3: set_Pr1261947904930325089at_nat] :
% 8.60/4.79 ~ ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ X3 ) @ R3 )
% 8.60/4.79 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Xs2 ) @ ( lenlex1357538814655152620at_nat @ R3 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2624_lenlex__irreflexive,axiom,
% 8.60/4.79 ! [R3: set_Pr1261947904930325089at_nat,Xs2: list_nat] :
% 8.60/4.79 ( ! [X3: nat] :
% 8.60/4.79 ~ ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ X3 ) @ R3 )
% 8.60/4.79 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Xs2 ) @ ( lenlex_nat @ R3 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2625_lenlex__irreflexive,axiom,
% 8.60/4.79 ! [R3: set_Pr958786334691620121nt_int,Xs2: list_int] :
% 8.60/4.79 ( ! [X3: int] :
% 8.60/4.79 ~ ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ X3 ) @ R3 )
% 8.60/4.79 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Xs2 ) @ ( lenlex_int @ R3 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2626_zero__le__power,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2627_zero__le__power,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2628_zero__le__power,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2629_zero__le__power,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2630_power__mono,axiom,
% 8.60/4.79 ! [A: real,B: real,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_real @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2631_power__mono,axiom,
% 8.60/4.79 ! [A: rat,B: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2632_power__mono,axiom,
% 8.60/4.79 ! [A: nat,B: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2633_power__mono,axiom,
% 8.60/4.79 ! [A: int,B: int,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_int @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2634_finite__enumerate__step,axiom,
% 8.60/4.79 ! [S3: set_nat,N: nat] :
% 8.60/4.79 ( ( finite_finite_nat @ S3 )
% 8.60/4.79 => ( ( ord_less_nat @ ( suc @ N ) @ ( finite_card_nat @ S3 ) )
% 8.60/4.79 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2635_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_real,A4: set_real,R3: real > real > $o] :
% 8.60/4.79 ( ( finite_finite_real @ B5 )
% 8.60/4.79 => ( ! [A3: real] :
% 8.60/4.79 ( ( member_real @ A3 @ A4 )
% 8.60/4.79 => ? [B6: real] :
% 8.60/4.79 ( ( member_real @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: real,A22: real,B3: real] :
% 8.60/4.79 ( ( member_real @ A1 @ A4 )
% 8.60/4.79 => ( ( member_real @ A22 @ A4 )
% 8.60/4.79 => ( ( member_real @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2636_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_real,A4: set_nat,R3: nat > real > $o] :
% 8.60/4.79 ( ( finite_finite_real @ B5 )
% 8.60/4.79 => ( ! [A3: nat] :
% 8.60/4.79 ( ( member_nat @ A3 @ A4 )
% 8.60/4.79 => ? [B6: real] :
% 8.60/4.79 ( ( member_real @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: nat,A22: nat,B3: real] :
% 8.60/4.79 ( ( member_nat @ A1 @ A4 )
% 8.60/4.79 => ( ( member_nat @ A22 @ A4 )
% 8.60/4.79 => ( ( member_real @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2637_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_real,A4: set_complex,R3: complex > real > $o] :
% 8.60/4.79 ( ( finite_finite_real @ B5 )
% 8.60/4.79 => ( ! [A3: complex] :
% 8.60/4.79 ( ( member_complex @ A3 @ A4 )
% 8.60/4.79 => ? [B6: real] :
% 8.60/4.79 ( ( member_real @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: complex,A22: complex,B3: real] :
% 8.60/4.79 ( ( member_complex @ A1 @ A4 )
% 8.60/4.79 => ( ( member_complex @ A22 @ A4 )
% 8.60/4.79 => ( ( member_real @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2638_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_real,A4: set_int,R3: int > real > $o] :
% 8.60/4.79 ( ( finite_finite_real @ B5 )
% 8.60/4.79 => ( ! [A3: int] :
% 8.60/4.79 ( ( member_int @ A3 @ A4 )
% 8.60/4.79 => ? [B6: real] :
% 8.60/4.79 ( ( member_real @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: int,A22: int,B3: real] :
% 8.60/4.79 ( ( member_int @ A1 @ A4 )
% 8.60/4.79 => ( ( member_int @ A22 @ A4 )
% 8.60/4.79 => ( ( member_real @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_real @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2639_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_nat,A4: set_real,R3: real > nat > $o] :
% 8.60/4.79 ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ! [A3: real] :
% 8.60/4.79 ( ( member_real @ A3 @ A4 )
% 8.60/4.79 => ? [B6: nat] :
% 8.60/4.79 ( ( member_nat @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: real,A22: real,B3: nat] :
% 8.60/4.79 ( ( member_real @ A1 @ A4 )
% 8.60/4.79 => ( ( member_real @ A22 @ A4 )
% 8.60/4.79 => ( ( member_nat @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2640_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_nat,A4: set_nat,R3: nat > nat > $o] :
% 8.60/4.79 ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ! [A3: nat] :
% 8.60/4.79 ( ( member_nat @ A3 @ A4 )
% 8.60/4.79 => ? [B6: nat] :
% 8.60/4.79 ( ( member_nat @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: nat,A22: nat,B3: nat] :
% 8.60/4.79 ( ( member_nat @ A1 @ A4 )
% 8.60/4.79 => ( ( member_nat @ A22 @ A4 )
% 8.60/4.79 => ( ( member_nat @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2641_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_nat,A4: set_complex,R3: complex > nat > $o] :
% 8.60/4.79 ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ! [A3: complex] :
% 8.60/4.79 ( ( member_complex @ A3 @ A4 )
% 8.60/4.79 => ? [B6: nat] :
% 8.60/4.79 ( ( member_nat @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: complex,A22: complex,B3: nat] :
% 8.60/4.79 ( ( member_complex @ A1 @ A4 )
% 8.60/4.79 => ( ( member_complex @ A22 @ A4 )
% 8.60/4.79 => ( ( member_nat @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2642_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_nat,A4: set_int,R3: int > nat > $o] :
% 8.60/4.79 ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ! [A3: int] :
% 8.60/4.79 ( ( member_int @ A3 @ A4 )
% 8.60/4.79 => ? [B6: nat] :
% 8.60/4.79 ( ( member_nat @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: int,A22: int,B3: nat] :
% 8.60/4.79 ( ( member_int @ A1 @ A4 )
% 8.60/4.79 => ( ( member_int @ A22 @ A4 )
% 8.60/4.79 => ( ( member_nat @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2643_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_int,A4: set_real,R3: real > int > $o] :
% 8.60/4.79 ( ( finite_finite_int @ B5 )
% 8.60/4.79 => ( ! [A3: real] :
% 8.60/4.79 ( ( member_real @ A3 @ A4 )
% 8.60/4.79 => ? [B6: int] :
% 8.60/4.79 ( ( member_int @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: real,A22: real,B3: int] :
% 8.60/4.79 ( ( member_real @ A1 @ A4 )
% 8.60/4.79 => ( ( member_real @ A22 @ A4 )
% 8.60/4.79 => ( ( member_int @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2644_card__le__if__inj__on__rel,axiom,
% 8.60/4.79 ! [B5: set_int,A4: set_nat,R3: nat > int > $o] :
% 8.60/4.79 ( ( finite_finite_int @ B5 )
% 8.60/4.79 => ( ! [A3: nat] :
% 8.60/4.79 ( ( member_nat @ A3 @ A4 )
% 8.60/4.79 => ? [B6: int] :
% 8.60/4.79 ( ( member_int @ B6 @ B5 )
% 8.60/4.79 & ( R3 @ A3 @ B6 ) ) )
% 8.60/4.79 => ( ! [A1: nat,A22: nat,B3: int] :
% 8.60/4.79 ( ( member_nat @ A1 @ A4 )
% 8.60/4.79 => ( ( member_nat @ A22 @ A4 )
% 8.60/4.79 => ( ( member_int @ B3 @ B5 )
% 8.60/4.79 => ( ( R3 @ A1 @ B3 )
% 8.60/4.79 => ( ( R3 @ A22 @ B3 )
% 8.60/4.79 => ( A1 = A22 ) ) ) ) ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2645_zero__less__power,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2646_zero__less__power,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2647_zero__less__power,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2648_zero__less__power,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2649_card__insert__le,axiom,
% 8.60/4.79 ! [A4: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ ( finite_card_real @ ( insert_real @ X @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2650_card__insert__le,axiom,
% 8.60/4.79 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ ( insert_nat @ X @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2651_card__insert__le,axiom,
% 8.60/4.79 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ ( insert_complex @ X @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2652_card__insert__le,axiom,
% 8.60/4.79 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ ( insert_int @ X @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2653_card__insert__le,axiom,
% 8.60/4.79 ! [A4: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2654_card__insert__le,axiom,
% 8.60/4.79 ! [A4: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2655_one__le__power,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2656_one__le__power,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_real @ one_one_real @ A )
% 8.60/4.79 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2657_one__le__power,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2658_one__le__power,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2659_one__le__power,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_int @ one_one_int @ A )
% 8.60/4.79 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2660_left__right__inverse__power,axiom,
% 8.60/4.79 ! [X: code_integer,Y: code_integer,N: nat] :
% 8.60/4.79 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 8.60/4.79 = one_one_Code_integer )
% 8.60/4.79 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) )
% 8.60/4.79 = one_one_Code_integer ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2661_left__right__inverse__power,axiom,
% 8.60/4.79 ! [X: complex,Y: complex,N: nat] :
% 8.60/4.79 ( ( ( times_times_complex @ X @ Y )
% 8.60/4.79 = one_one_complex )
% 8.60/4.79 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 8.60/4.79 = one_one_complex ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2662_left__right__inverse__power,axiom,
% 8.60/4.79 ! [X: real,Y: real,N: nat] :
% 8.60/4.79 ( ( ( times_times_real @ X @ Y )
% 8.60/4.79 = one_one_real )
% 8.60/4.79 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 8.60/4.79 = one_one_real ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2663_left__right__inverse__power,axiom,
% 8.60/4.79 ! [X: rat,Y: rat,N: nat] :
% 8.60/4.79 ( ( ( times_times_rat @ X @ Y )
% 8.60/4.79 = one_one_rat )
% 8.60/4.79 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 8.60/4.79 = one_one_rat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2664_left__right__inverse__power,axiom,
% 8.60/4.79 ! [X: nat,Y: nat,N: nat] :
% 8.60/4.79 ( ( ( times_times_nat @ X @ Y )
% 8.60/4.79 = one_one_nat )
% 8.60/4.79 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 8.60/4.79 = one_one_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2665_left__right__inverse__power,axiom,
% 8.60/4.79 ! [X: int,Y: int,N: nat] :
% 8.60/4.79 ( ( ( times_times_int @ X @ Y )
% 8.60/4.79 = one_one_int )
% 8.60/4.79 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 8.60/4.79 = one_one_int ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2666_finite__enum__subset,axiom,
% 8.60/4.79 ! [X8: set_nat,Y7: set_nat] :
% 8.60/4.79 ( ! [I3: nat] :
% 8.60/4.79 ( ( ord_less_nat @ I3 @ ( finite_card_nat @ X8 ) )
% 8.60/4.79 => ( ( infini8530281810654367211te_nat @ X8 @ I3 )
% 8.60/4.79 = ( infini8530281810654367211te_nat @ Y7 @ I3 ) ) )
% 8.60/4.79 => ( ( finite_finite_nat @ X8 )
% 8.60/4.79 => ( ( finite_finite_nat @ Y7 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_nat @ X8 ) @ ( finite_card_nat @ Y7 ) )
% 8.60/4.79 => ( ord_less_eq_set_nat @ X8 @ Y7 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2667_power__Suc,axiom,
% 8.60/4.79 ! [A: complex,N: nat] :
% 8.60/4.79 ( ( power_power_complex @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2668_power__Suc,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( power_power_real @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2669_power__Suc,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( power_power_rat @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2670_power__Suc,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( power_power_nat @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2671_power__Suc,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( power_power_int @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2672_power__Suc2,axiom,
% 8.60/4.79 ! [A: complex,N: nat] :
% 8.60/4.79 ( ( power_power_complex @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2673_power__Suc2,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( power_power_real @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2674_power__Suc2,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( power_power_rat @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2675_power__Suc2,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( power_power_nat @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2676_power__Suc2,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( power_power_int @ A @ ( suc @ N ) )
% 8.60/4.79 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2677_power__0,axiom,
% 8.60/4.79 ! [A: code_integer] :
% 8.60/4.79 ( ( power_8256067586552552935nteger @ A @ zero_zero_nat )
% 8.60/4.79 = one_one_Code_integer ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2678_power__0,axiom,
% 8.60/4.79 ! [A: nat] :
% 8.60/4.79 ( ( power_power_nat @ A @ zero_zero_nat )
% 8.60/4.79 = one_one_nat ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2679_power__0,axiom,
% 8.60/4.79 ! [A: real] :
% 8.60/4.79 ( ( power_power_real @ A @ zero_zero_nat )
% 8.60/4.79 = one_one_real ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2680_power__0,axiom,
% 8.60/4.79 ! [A: int] :
% 8.60/4.79 ( ( power_power_int @ A @ zero_zero_nat )
% 8.60/4.79 = one_one_int ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2681_power__0,axiom,
% 8.60/4.79 ! [A: complex] :
% 8.60/4.79 ( ( power_power_complex @ A @ zero_zero_nat )
% 8.60/4.79 = one_one_complex ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2682_power__add,axiom,
% 8.60/4.79 ! [A: complex,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_complex @ A @ ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.79 = ( times_times_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2683_power__add,axiom,
% 8.60/4.79 ! [A: real,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_real @ A @ ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.79 = ( times_times_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2684_power__add,axiom,
% 8.60/4.79 ! [A: rat,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_rat @ A @ ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.79 = ( times_times_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2685_power__add,axiom,
% 8.60/4.79 ! [A: nat,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_nat @ A @ ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.79 = ( times_times_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2686_power__add,axiom,
% 8.60/4.79 ! [A: int,M2: nat,N: nat] :
% 8.60/4.79 ( ( power_power_int @ A @ ( plus_plus_nat @ M2 @ N ) )
% 8.60/4.79 = ( times_times_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2687_nat__power__less__imp__less,axiom,
% 8.60/4.79 ! [I2: nat,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 8.60/4.79 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M2 ) @ ( power_power_nat @ I2 @ N ) )
% 8.60/4.79 => ( ord_less_nat @ M2 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2688_le__enumerate,axiom,
% 8.60/4.79 ! [S3: set_nat,N: nat] :
% 8.60/4.79 ( ~ ( finite_finite_nat @ S3 )
% 8.60/4.79 => ( ord_less_eq_nat @ N @ ( infini8530281810654367211te_nat @ S3 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2689_card__eq__0__iff,axiom,
% 8.60/4.79 ! [A4: set_list_nat] :
% 8.60/4.79 ( ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( ( A4 = bot_bot_set_list_nat )
% 8.60/4.79 | ~ ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2690_card__eq__0__iff,axiom,
% 8.60/4.79 ! [A4: set_set_nat] :
% 8.60/4.79 ( ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( ( A4 = bot_bot_set_set_nat )
% 8.60/4.79 | ~ ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2691_card__eq__0__iff,axiom,
% 8.60/4.79 ! [A4: set_complex] :
% 8.60/4.79 ( ( ( finite_card_complex @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( ( A4 = bot_bot_set_complex )
% 8.60/4.79 | ~ ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2692_card__eq__0__iff,axiom,
% 8.60/4.79 ! [A4: set_nat] :
% 8.60/4.79 ( ( ( finite_card_nat @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( ( A4 = bot_bot_set_nat )
% 8.60/4.79 | ~ ( finite_finite_nat @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2693_card__eq__0__iff,axiom,
% 8.60/4.79 ! [A4: set_int] :
% 8.60/4.79 ( ( ( finite_card_int @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( ( A4 = bot_bot_set_int )
% 8.60/4.79 | ~ ( finite_finite_int @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2694_card__eq__0__iff,axiom,
% 8.60/4.79 ! [A4: set_real] :
% 8.60/4.79 ( ( ( finite_card_real @ A4 )
% 8.60/4.79 = zero_zero_nat )
% 8.60/4.79 = ( ( A4 = bot_bot_set_real )
% 8.60/4.79 | ~ ( finite_finite_real @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2695_card__ge__0__finite,axiom,
% 8.60/4.79 ! [A4: set_list_nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 8.60/4.79 => ( finite8100373058378681591st_nat @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2696_card__ge__0__finite,axiom,
% 8.60/4.79 ! [A4: set_set_nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 8.60/4.79 => ( finite1152437895449049373et_nat @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2697_card__ge__0__finite,axiom,
% 8.60/4.79 ! [A4: set_nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 8.60/4.79 => ( finite_finite_nat @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2698_card__ge__0__finite,axiom,
% 8.60/4.79 ! [A4: set_int] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 8.60/4.79 => ( finite_finite_int @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2699_card__ge__0__finite,axiom,
% 8.60/4.79 ! [A4: set_complex] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 8.60/4.79 => ( finite3207457112153483333omplex @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2700_card__insert__if,axiom,
% 8.60/4.79 ! [A4: set_real,X: real] :
% 8.60/4.79 ( ( finite_finite_real @ A4 )
% 8.60/4.79 => ( ( ( member_real @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 8.60/4.79 = ( finite_card_real @ A4 ) ) )
% 8.60/4.79 & ( ~ ( member_real @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_real @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2701_card__insert__if,axiom,
% 8.60/4.79 ! [A4: set_list_nat,X: list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( ( member_list_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 8.60/4.79 = ( finite_card_list_nat @ A4 ) ) )
% 8.60/4.79 & ( ~ ( member_list_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2702_card__insert__if,axiom,
% 8.60/4.79 ! [A4: set_set_nat,X: set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( ( member_set_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 8.60/4.79 = ( finite_card_set_nat @ A4 ) ) )
% 8.60/4.79 & ( ~ ( member_set_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2703_card__insert__if,axiom,
% 8.60/4.79 ! [A4: set_nat,X: nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( ( member_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 8.60/4.79 = ( finite_card_nat @ A4 ) ) )
% 8.60/4.79 & ( ~ ( member_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2704_card__insert__if,axiom,
% 8.60/4.79 ! [A4: set_int,X: int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( ( member_int @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 8.60/4.79 = ( finite_card_int @ A4 ) ) )
% 8.60/4.79 & ( ~ ( member_int @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2705_card__insert__if,axiom,
% 8.60/4.79 ! [A4: set_complex,X: complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( ( member_complex @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 8.60/4.79 = ( finite_card_complex @ A4 ) ) )
% 8.60/4.79 & ( ~ ( member_complex @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2706_card__Suc__eq__finite,axiom,
% 8.60/4.79 ! [A4: set_real,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_real @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: real,B7: set_real] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_real @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_real @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_real @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( finite_finite_real @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2707_card__Suc__eq__finite,axiom,
% 8.60/4.79 ! [A4: set_list_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: list_nat,B7: set_list_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_list_nat @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_list_nat @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_list_nat @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( finite8100373058378681591st_nat @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2708_card__Suc__eq__finite,axiom,
% 8.60/4.79 ! [A4: set_set_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: set_nat,B7: set_set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_set_nat @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_set_nat @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_set_nat @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( finite1152437895449049373et_nat @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2709_card__Suc__eq__finite,axiom,
% 8.60/4.79 ! [A4: set_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: nat,B7: set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_nat @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_nat @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_nat @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2710_card__Suc__eq__finite,axiom,
% 8.60/4.79 ! [A4: set_int,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_int @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: int,B7: set_int] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_int @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_int @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_int @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( finite_finite_int @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2711_card__Suc__eq__finite,axiom,
% 8.60/4.79 ! [A4: set_complex,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_complex @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: complex,B7: set_complex] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_complex @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_complex @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_complex @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( finite3207457112153483333omplex @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2712_power__less__imp__less__base,axiom,
% 8.60/4.79 ! [A: real,N: nat,B: real] :
% 8.60/4.79 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.79 => ( ord_less_real @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2713_power__less__imp__less__base,axiom,
% 8.60/4.79 ! [A: rat,N: nat,B: rat] :
% 8.60/4.79 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.79 => ( ord_less_rat @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2714_power__less__imp__less__base,axiom,
% 8.60/4.79 ! [A: nat,N: nat,B: nat] :
% 8.60/4.79 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.79 => ( ord_less_nat @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2715_power__less__imp__less__base,axiom,
% 8.60/4.79 ! [A: int,N: nat,B: int] :
% 8.60/4.79 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.79 => ( ord_less_int @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2716_card__mono,axiom,
% 8.60/4.79 ! [B5: set_list_nat,A4: set_list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ B5 )
% 8.60/4.79 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2717_card__mono,axiom,
% 8.60/4.79 ! [B5: set_set_nat,A4: set_set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ B5 )
% 8.60/4.79 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2718_card__mono,axiom,
% 8.60/4.79 ! [B5: set_int,A4: set_int] :
% 8.60/4.79 ( ( finite_finite_int @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2719_card__mono,axiom,
% 8.60/4.79 ! [B5: set_complex,A4: set_complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ B5 )
% 8.60/4.79 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2720_card__mono,axiom,
% 8.60/4.79 ! [B5: set_nat,A4: set_nat] :
% 8.60/4.79 ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2721_card__seteq,axiom,
% 8.60/4.79 ! [B5: set_list_nat,A4: set_list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ B5 )
% 8.60/4.79 => ( ( ord_le6045566169113846134st_nat @ A4 @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B5 ) @ ( finite_card_list_nat @ A4 ) )
% 8.60/4.79 => ( A4 = B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2722_card__seteq,axiom,
% 8.60/4.79 ! [B5: set_set_nat,A4: set_set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ B5 )
% 8.60/4.79 => ( ( ord_le6893508408891458716et_nat @ A4 @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B5 ) @ ( finite_card_set_nat @ A4 ) )
% 8.60/4.79 => ( A4 = B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2723_card__seteq,axiom,
% 8.60/4.79 ! [B5: set_int,A4: set_int] :
% 8.60/4.79 ( ( finite_finite_int @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_int @ B5 ) @ ( finite_card_int @ A4 ) )
% 8.60/4.79 => ( A4 = B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2724_card__seteq,axiom,
% 8.60/4.79 ! [B5: set_complex,A4: set_complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ B5 )
% 8.60/4.79 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_complex @ B5 ) @ ( finite_card_complex @ A4 ) )
% 8.60/4.79 => ( A4 = B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2725_card__seteq,axiom,
% 8.60/4.79 ! [B5: set_nat,A4: set_nat] :
% 8.60/4.79 ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_set_nat @ A4 @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B5 ) @ ( finite_card_nat @ A4 ) )
% 8.60/4.79 => ( A4 = B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2726_finite__if__finite__subsets__card__bdd,axiom,
% 8.60/4.79 ! [F3: set_list_nat,C4: nat] :
% 8.60/4.79 ( ! [G: set_list_nat] :
% 8.60/4.79 ( ( ord_le6045566169113846134st_nat @ G @ F3 )
% 8.60/4.79 => ( ( finite8100373058378681591st_nat @ G )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G ) @ C4 ) ) )
% 8.60/4.79 => ( ( finite8100373058378681591st_nat @ F3 )
% 8.60/4.79 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F3 ) @ C4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2727_finite__if__finite__subsets__card__bdd,axiom,
% 8.60/4.79 ! [F3: set_set_nat,C4: nat] :
% 8.60/4.79 ( ! [G: set_set_nat] :
% 8.60/4.79 ( ( ord_le6893508408891458716et_nat @ G @ F3 )
% 8.60/4.79 => ( ( finite1152437895449049373et_nat @ G )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G ) @ C4 ) ) )
% 8.60/4.79 => ( ( finite1152437895449049373et_nat @ F3 )
% 8.60/4.79 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F3 ) @ C4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2728_finite__if__finite__subsets__card__bdd,axiom,
% 8.60/4.79 ! [F3: set_int,C4: nat] :
% 8.60/4.79 ( ! [G: set_int] :
% 8.60/4.79 ( ( ord_less_eq_set_int @ G @ F3 )
% 8.60/4.79 => ( ( finite_finite_int @ G )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_int @ G ) @ C4 ) ) )
% 8.60/4.79 => ( ( finite_finite_int @ F3 )
% 8.60/4.79 & ( ord_less_eq_nat @ ( finite_card_int @ F3 ) @ C4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2729_finite__if__finite__subsets__card__bdd,axiom,
% 8.60/4.79 ! [F3: set_complex,C4: nat] :
% 8.60/4.79 ( ! [G: set_complex] :
% 8.60/4.79 ( ( ord_le211207098394363844omplex @ G @ F3 )
% 8.60/4.79 => ( ( finite3207457112153483333omplex @ G )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_complex @ G ) @ C4 ) ) )
% 8.60/4.79 => ( ( finite3207457112153483333omplex @ F3 )
% 8.60/4.79 & ( ord_less_eq_nat @ ( finite_card_complex @ F3 ) @ C4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2730_finite__if__finite__subsets__card__bdd,axiom,
% 8.60/4.79 ! [F3: set_nat,C4: nat] :
% 8.60/4.79 ( ! [G: set_nat] :
% 8.60/4.79 ( ( ord_less_eq_set_nat @ G @ F3 )
% 8.60/4.79 => ( ( finite_finite_nat @ G )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_nat @ G ) @ C4 ) ) )
% 8.60/4.79 => ( ( finite_finite_nat @ F3 )
% 8.60/4.79 & ( ord_less_eq_nat @ ( finite_card_nat @ F3 ) @ C4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2731_obtain__subset__with__card__n,axiom,
% 8.60/4.79 ! [N: nat,S3: set_list_nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ S3 ) )
% 8.60/4.79 => ~ ! [T3: set_list_nat] :
% 8.60/4.79 ( ( ord_le6045566169113846134st_nat @ T3 @ S3 )
% 8.60/4.79 => ( ( ( finite_card_list_nat @ T3 )
% 8.60/4.79 = N )
% 8.60/4.79 => ~ ( finite8100373058378681591st_nat @ T3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2732_obtain__subset__with__card__n,axiom,
% 8.60/4.79 ! [N: nat,S3: set_set_nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ S3 ) )
% 8.60/4.79 => ~ ! [T3: set_set_nat] :
% 8.60/4.79 ( ( ord_le6893508408891458716et_nat @ T3 @ S3 )
% 8.60/4.79 => ( ( ( finite_card_set_nat @ T3 )
% 8.60/4.79 = N )
% 8.60/4.79 => ~ ( finite1152437895449049373et_nat @ T3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2733_obtain__subset__with__card__n,axiom,
% 8.60/4.79 ! [N: nat,S3: set_int] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ ( finite_card_int @ S3 ) )
% 8.60/4.79 => ~ ! [T3: set_int] :
% 8.60/4.79 ( ( ord_less_eq_set_int @ T3 @ S3 )
% 8.60/4.79 => ( ( ( finite_card_int @ T3 )
% 8.60/4.79 = N )
% 8.60/4.79 => ~ ( finite_finite_int @ T3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2734_obtain__subset__with__card__n,axiom,
% 8.60/4.79 ! [N: nat,S3: set_complex] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ ( finite_card_complex @ S3 ) )
% 8.60/4.79 => ~ ! [T3: set_complex] :
% 8.60/4.79 ( ( ord_le211207098394363844omplex @ T3 @ S3 )
% 8.60/4.79 => ( ( ( finite_card_complex @ T3 )
% 8.60/4.79 = N )
% 8.60/4.79 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2735_obtain__subset__with__card__n,axiom,
% 8.60/4.79 ! [N: nat,S3: set_nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ ( finite_card_nat @ S3 ) )
% 8.60/4.79 => ~ ! [T3: set_nat] :
% 8.60/4.79 ( ( ord_less_eq_set_nat @ T3 @ S3 )
% 8.60/4.79 => ( ( ( finite_card_nat @ T3 )
% 8.60/4.79 = N )
% 8.60/4.79 => ~ ( finite_finite_nat @ T3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2736_power__le__one,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.60/4.79 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.60/4.79 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2737_power__le__one,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ A @ one_one_real )
% 8.60/4.79 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2738_power__le__one,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.60/4.79 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2739_power__le__one,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.60/4.79 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2740_power__le__one,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.60/4.79 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2741_power__inject__base,axiom,
% 8.60/4.79 ! [A: real,N: nat,B: real] :
% 8.60/4.79 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 8.60/4.79 = ( power_power_real @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.79 => ( A = B ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2742_power__inject__base,axiom,
% 8.60/4.79 ! [A: rat,N: nat,B: rat] :
% 8.60/4.79 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 8.60/4.79 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.79 => ( A = B ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2743_power__inject__base,axiom,
% 8.60/4.79 ! [A: nat,N: nat,B: nat] :
% 8.60/4.79 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 8.60/4.79 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.79 => ( A = B ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2744_power__inject__base,axiom,
% 8.60/4.79 ! [A: int,N: nat,B: int] :
% 8.60/4.79 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 8.60/4.79 = ( power_power_int @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.79 => ( A = B ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2745_power__le__imp__le__base,axiom,
% 8.60/4.79 ! [A: real,N: nat,B: real] :
% 8.60/4.79 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.79 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2746_power__le__imp__le__base,axiom,
% 8.60/4.79 ! [A: rat,N: nat,B: rat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.79 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2747_power__le__imp__le__base,axiom,
% 8.60/4.79 ! [A: nat,N: nat,B: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.79 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2748_power__le__imp__le__base,axiom,
% 8.60/4.79 ! [A: int,N: nat,B: int] :
% 8.60/4.79 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.79 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2749_power__less__power__Suc,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2750_power__less__power__Suc,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ one_one_real @ A )
% 8.60/4.79 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2751_power__less__power__Suc,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2752_power__less__power__Suc,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2753_power__less__power__Suc,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ one_one_int @ A )
% 8.60/4.79 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2754_power__gt1__lemma,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2755_power__gt1__lemma,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ one_one_real @ A )
% 8.60/4.79 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2756_power__gt1__lemma,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2757_power__gt1__lemma,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2758_power__gt1__lemma,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ one_one_int @ A )
% 8.60/4.79 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2759_card__le__sym__Diff,axiom,
% 8.60/4.79 ! [A4: set_list_nat,B5: set_list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( finite8100373058378681591st_nat @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2760_card__le__sym__Diff,axiom,
% 8.60/4.79 ! [A4: set_set_nat,B5: set_set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( finite1152437895449049373et_nat @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2761_card__le__sym__Diff,axiom,
% 8.60/4.79 ! [A4: set_int,B5: set_int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( finite_finite_int @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B5 @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2762_card__le__sym__Diff,axiom,
% 8.60/4.79 ! [A4: set_complex,B5: set_complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( finite3207457112153483333omplex @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2763_card__le__sym__Diff,axiom,
% 8.60/4.79 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 8.60/4.79 ( ( finite6177210948735845034at_nat @ A4 )
% 8.60/4.79 => ( ( finite6177210948735845034at_nat @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2764_card__le__sym__Diff,axiom,
% 8.60/4.79 ! [A4: set_nat,B5: set_nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2765_card__length,axiom,
% 8.60/4.79 ! [Xs2: list_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( set_complex2 @ Xs2 ) ) @ ( size_s3451745648224563538omplex @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2766_card__length,axiom,
% 8.60/4.79 ! [Xs2: list_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) ) @ ( size_s3023201423986296836st_nat @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2767_card__length,axiom,
% 8.60/4.79 ! [Xs2: list_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) ) @ ( size_s3254054031482475050et_nat @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2768_card__length,axiom,
% 8.60/4.79 ! [Xs2: list_VEBT_VEBT] : ( ord_less_eq_nat @ ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2769_card__length,axiom,
% 8.60/4.79 ! [Xs2: list_o] : ( ord_less_eq_nat @ ( finite_card_o @ ( set_o2 @ Xs2 ) ) @ ( size_size_list_o @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2770_card__length,axiom,
% 8.60/4.79 ! [Xs2: list_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( set_nat2 @ Xs2 ) ) @ ( size_size_list_nat @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2771_card__length,axiom,
% 8.60/4.79 ! [Xs2: list_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( set_int2 @ Xs2 ) ) @ ( size_size_list_int @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2772_power__gt1,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2773_power__gt1,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ one_one_real @ A )
% 8.60/4.79 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2774_power__gt1,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2775_power__gt1,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2776_power__gt1,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ one_one_int @ A )
% 8.60/4.79 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2777_power__0__left,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ( N = zero_zero_nat )
% 8.60/4.79 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 8.60/4.79 = one_one_Code_integer ) )
% 8.60/4.79 & ( ( N != zero_zero_nat )
% 8.60/4.79 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N )
% 8.60/4.79 = zero_z3403309356797280102nteger ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2778_power__0__left,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ( N = zero_zero_nat )
% 8.60/4.79 => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.60/4.79 = one_one_rat ) )
% 8.60/4.79 & ( ( N != zero_zero_nat )
% 8.60/4.79 => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.60/4.79 = zero_zero_rat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2779_power__0__left,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ( N = zero_zero_nat )
% 8.60/4.79 => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.60/4.79 = one_one_nat ) )
% 8.60/4.79 & ( ( N != zero_zero_nat )
% 8.60/4.79 => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.60/4.79 = zero_zero_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2780_power__0__left,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ( N = zero_zero_nat )
% 8.60/4.79 => ( ( power_power_real @ zero_zero_real @ N )
% 8.60/4.79 = one_one_real ) )
% 8.60/4.79 & ( ( N != zero_zero_nat )
% 8.60/4.79 => ( ( power_power_real @ zero_zero_real @ N )
% 8.60/4.79 = zero_zero_real ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2781_power__0__left,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ( N = zero_zero_nat )
% 8.60/4.79 => ( ( power_power_int @ zero_zero_int @ N )
% 8.60/4.79 = one_one_int ) )
% 8.60/4.79 & ( ( N != zero_zero_nat )
% 8.60/4.79 => ( ( power_power_int @ zero_zero_int @ N )
% 8.60/4.79 = zero_zero_int ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2782_power__0__left,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ( N = zero_zero_nat )
% 8.60/4.79 => ( ( power_power_complex @ zero_zero_complex @ N )
% 8.60/4.79 = one_one_complex ) )
% 8.60/4.79 & ( ( N != zero_zero_nat )
% 8.60/4.79 => ( ( power_power_complex @ zero_zero_complex @ N )
% 8.60/4.79 = zero_zero_complex ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2783_power__increasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: code_integer] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ A @ N6 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2784_power__increasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: real] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_real @ one_one_real @ A )
% 8.60/4.79 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N6 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2785_power__increasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: rat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N6 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2786_power__increasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N6 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2787_power__increasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: int] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_int @ one_one_int @ A )
% 8.60/4.79 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N6 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2788_zero__power,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( power_power_rat @ zero_zero_rat @ N )
% 8.60/4.79 = zero_zero_rat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2789_zero__power,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( power_power_nat @ zero_zero_nat @ N )
% 8.60/4.79 = zero_zero_nat ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2790_zero__power,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( power_power_real @ zero_zero_real @ N )
% 8.60/4.79 = zero_zero_real ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2791_zero__power,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( power_power_int @ zero_zero_int @ N )
% 8.60/4.79 = zero_zero_int ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2792_zero__power,axiom,
% 8.60/4.79 ! [N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( power_power_complex @ zero_zero_complex @ N )
% 8.60/4.79 = zero_zero_complex ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2793_lenlex__length,axiom,
% 8.60/4.79 ! [Ms: list_VEBT_VEBT,Ns: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 8.60/4.79 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Ms @ Ns ) @ ( lenlex_VEBT_VEBT @ R3 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Ms ) @ ( size_s6755466524823107622T_VEBT @ Ns ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2794_lenlex__length,axiom,
% 8.60/4.79 ! [Ms: list_o,Ns: list_o,R3: set_Product_prod_o_o] :
% 8.60/4.79 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Ms @ Ns ) @ ( lenlex_o @ R3 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( size_size_list_o @ Ms ) @ ( size_size_list_o @ Ns ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2795_lenlex__length,axiom,
% 8.60/4.79 ! [Ms: list_nat,Ns: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 8.60/4.79 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ms @ Ns ) @ ( lenlex_nat @ R3 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( size_size_list_nat @ Ms ) @ ( size_size_list_nat @ Ns ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2796_lenlex__length,axiom,
% 8.60/4.79 ! [Ms: list_int,Ns: list_int,R3: set_Pr958786334691620121nt_int] :
% 8.60/4.79 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ms @ Ns ) @ ( lenlex_int @ R3 ) )
% 8.60/4.79 => ( ord_less_eq_nat @ ( size_size_list_int @ Ms ) @ ( size_size_list_int @ Ns ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2797_power__gt__expt,axiom,
% 8.60/4.79 ! [N: nat,K2: nat] :
% 8.60/4.79 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.60/4.79 => ( ord_less_nat @ K2 @ ( power_power_nat @ N @ K2 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2798_nat__one__le__power,axiom,
% 8.60/4.79 ! [I2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2799_enumerate__step,axiom,
% 8.60/4.79 ! [S3: set_nat,N: nat] :
% 8.60/4.79 ( ~ ( finite_finite_nat @ S3 )
% 8.60/4.79 => ( ord_less_nat @ ( infini8530281810654367211te_nat @ S3 @ N ) @ ( infini8530281810654367211te_nat @ S3 @ ( suc @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2800_card__gt__0__iff,axiom,
% 8.60/4.79 ! [A4: set_list_nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A4 ) )
% 8.60/4.79 = ( ( A4 != bot_bot_set_list_nat )
% 8.60/4.79 & ( finite8100373058378681591st_nat @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2801_card__gt__0__iff,axiom,
% 8.60/4.79 ! [A4: set_set_nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A4 ) )
% 8.60/4.79 = ( ( A4 != bot_bot_set_set_nat )
% 8.60/4.79 & ( finite1152437895449049373et_nat @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2802_card__gt__0__iff,axiom,
% 8.60/4.79 ! [A4: set_complex] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 8.60/4.79 = ( ( A4 != bot_bot_set_complex )
% 8.60/4.79 & ( finite3207457112153483333omplex @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2803_card__gt__0__iff,axiom,
% 8.60/4.79 ! [A4: set_nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 8.60/4.79 = ( ( A4 != bot_bot_set_nat )
% 8.60/4.79 & ( finite_finite_nat @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2804_card__gt__0__iff,axiom,
% 8.60/4.79 ! [A4: set_int] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 8.60/4.79 = ( ( A4 != bot_bot_set_int )
% 8.60/4.79 & ( finite_finite_int @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2805_card__gt__0__iff,axiom,
% 8.60/4.79 ! [A4: set_real] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 8.60/4.79 = ( ( A4 != bot_bot_set_real )
% 8.60/4.79 & ( finite_finite_real @ A4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2806_card__1__singleton__iff,axiom,
% 8.60/4.79 ! [A4: set_complex] :
% 8.60/4.79 ( ( ( finite_card_complex @ A4 )
% 8.60/4.79 = ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ? [X4: complex] :
% 8.60/4.79 ( A4
% 8.60/4.79 = ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2807_card__1__singleton__iff,axiom,
% 8.60/4.79 ! [A4: set_list_nat] :
% 8.60/4.79 ( ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ? [X4: list_nat] :
% 8.60/4.79 ( A4
% 8.60/4.79 = ( insert_list_nat @ X4 @ bot_bot_set_list_nat ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2808_card__1__singleton__iff,axiom,
% 8.60/4.79 ! [A4: set_set_nat] :
% 8.60/4.79 ( ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ? [X4: set_nat] :
% 8.60/4.79 ( A4
% 8.60/4.79 = ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2809_card__1__singleton__iff,axiom,
% 8.60/4.79 ! [A4: set_nat] :
% 8.60/4.79 ( ( ( finite_card_nat @ A4 )
% 8.60/4.79 = ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ? [X4: nat] :
% 8.60/4.79 ( A4
% 8.60/4.79 = ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2810_card__1__singleton__iff,axiom,
% 8.60/4.79 ! [A4: set_int] :
% 8.60/4.79 ( ( ( finite_card_int @ A4 )
% 8.60/4.79 = ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ? [X4: int] :
% 8.60/4.79 ( A4
% 8.60/4.79 = ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2811_card__1__singleton__iff,axiom,
% 8.60/4.79 ! [A4: set_real] :
% 8.60/4.79 ( ( ( finite_card_real @ A4 )
% 8.60/4.79 = ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ? [X4: real] :
% 8.60/4.79 ( A4
% 8.60/4.79 = ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2812_card__eq__SucD,axiom,
% 8.60/4.79 ! [A4: set_complex,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_complex @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 => ? [B3: complex,B8: set_complex] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_complex @ B3 @ B8 ) )
% 8.60/4.79 & ~ ( member_complex @ B3 @ B8 )
% 8.60/4.79 & ( ( finite_card_complex @ B8 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B8 = bot_bot_set_complex ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2813_card__eq__SucD,axiom,
% 8.60/4.79 ! [A4: set_list_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 => ? [B3: list_nat,B8: set_list_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_list_nat @ B3 @ B8 ) )
% 8.60/4.79 & ~ ( member_list_nat @ B3 @ B8 )
% 8.60/4.79 & ( ( finite_card_list_nat @ B8 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B8 = bot_bot_set_list_nat ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2814_card__eq__SucD,axiom,
% 8.60/4.79 ! [A4: set_set_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 => ? [B3: set_nat,B8: set_set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_set_nat @ B3 @ B8 ) )
% 8.60/4.79 & ~ ( member_set_nat @ B3 @ B8 )
% 8.60/4.79 & ( ( finite_card_set_nat @ B8 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B8 = bot_bot_set_set_nat ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2815_card__eq__SucD,axiom,
% 8.60/4.79 ! [A4: set_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 => ? [B3: nat,B8: set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_nat @ B3 @ B8 ) )
% 8.60/4.79 & ~ ( member_nat @ B3 @ B8 )
% 8.60/4.79 & ( ( finite_card_nat @ B8 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B8 = bot_bot_set_nat ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2816_card__eq__SucD,axiom,
% 8.60/4.79 ! [A4: set_int,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_int @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 => ? [B3: int,B8: set_int] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_int @ B3 @ B8 ) )
% 8.60/4.79 & ~ ( member_int @ B3 @ B8 )
% 8.60/4.79 & ( ( finite_card_int @ B8 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B8 = bot_bot_set_int ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2817_card__eq__SucD,axiom,
% 8.60/4.79 ! [A4: set_real,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_real @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 => ? [B3: real,B8: set_real] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_real @ B3 @ B8 ) )
% 8.60/4.79 & ~ ( member_real @ B3 @ B8 )
% 8.60/4.79 & ( ( finite_card_real @ B8 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B8 = bot_bot_set_real ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2818_card__Suc__eq,axiom,
% 8.60/4.79 ! [A4: set_complex,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_complex @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: complex,B7: set_complex] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_complex @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_complex @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_complex @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B7 = bot_bot_set_complex ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2819_card__Suc__eq,axiom,
% 8.60/4.79 ! [A4: set_list_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: list_nat,B7: set_list_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_list_nat @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_list_nat @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_list_nat @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B7 = bot_bot_set_list_nat ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2820_card__Suc__eq,axiom,
% 8.60/4.79 ! [A4: set_set_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: set_nat,B7: set_set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_set_nat @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_set_nat @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_set_nat @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B7 = bot_bot_set_set_nat ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2821_card__Suc__eq,axiom,
% 8.60/4.79 ! [A4: set_nat,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_nat @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: nat,B7: set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_nat @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_nat @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_nat @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B7 = bot_bot_set_nat ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2822_card__Suc__eq,axiom,
% 8.60/4.79 ! [A4: set_int,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_int @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: int,B7: set_int] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_int @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_int @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_int @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B7 = bot_bot_set_int ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2823_card__Suc__eq,axiom,
% 8.60/4.79 ! [A4: set_real,K2: nat] :
% 8.60/4.79 ( ( ( finite_card_real @ A4 )
% 8.60/4.79 = ( suc @ K2 ) )
% 8.60/4.79 = ( ? [B4: real,B7: set_real] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_real @ B4 @ B7 ) )
% 8.60/4.79 & ~ ( member_real @ B4 @ B7 )
% 8.60/4.79 & ( ( finite_card_real @ B7 )
% 8.60/4.79 = K2 )
% 8.60/4.79 & ( ( K2 = zero_zero_nat )
% 8.60/4.79 => ( B7 = bot_bot_set_real ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2824_card__le__Suc0__iff__eq,axiom,
% 8.60/4.79 ! [A4: set_list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ! [X4: list_nat] :
% 8.60/4.79 ( ( member_list_nat @ X4 @ A4 )
% 8.60/4.79 => ! [Y4: list_nat] :
% 8.60/4.79 ( ( member_list_nat @ Y4 @ A4 )
% 8.60/4.79 => ( X4 = Y4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2825_card__le__Suc0__iff__eq,axiom,
% 8.60/4.79 ! [A4: set_set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ! [X4: set_nat] :
% 8.60/4.79 ( ( member_set_nat @ X4 @ A4 )
% 8.60/4.79 => ! [Y4: set_nat] :
% 8.60/4.79 ( ( member_set_nat @ Y4 @ A4 )
% 8.60/4.79 => ( X4 = Y4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2826_card__le__Suc0__iff__eq,axiom,
% 8.60/4.79 ! [A4: set_nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ! [X4: nat] :
% 8.60/4.79 ( ( member_nat @ X4 @ A4 )
% 8.60/4.79 => ! [Y4: nat] :
% 8.60/4.79 ( ( member_nat @ Y4 @ A4 )
% 8.60/4.79 => ( X4 = Y4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2827_card__le__Suc0__iff__eq,axiom,
% 8.60/4.79 ! [A4: set_int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ! [X4: int] :
% 8.60/4.79 ( ( member_int @ X4 @ A4 )
% 8.60/4.79 => ! [Y4: int] :
% 8.60/4.79 ( ( member_int @ Y4 @ A4 )
% 8.60/4.79 => ( X4 = Y4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2828_card__le__Suc0__iff__eq,axiom,
% 8.60/4.79 ! [A4: set_complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ ( suc @ zero_zero_nat ) )
% 8.60/4.79 = ( ! [X4: complex] :
% 8.60/4.79 ( ( member_complex @ X4 @ A4 )
% 8.60/4.79 => ! [Y4: complex] :
% 8.60/4.79 ( ( member_complex @ Y4 @ A4 )
% 8.60/4.79 => ( X4 = Y4 ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2829_card__le__Suc__iff,axiom,
% 8.60/4.79 ! [N: nat,A4: set_real] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_real @ A4 ) )
% 8.60/4.79 = ( ? [A5: real,B7: set_real] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_real @ A5 @ B7 ) )
% 8.60/4.79 & ~ ( member_real @ A5 @ B7 )
% 8.60/4.79 & ( ord_less_eq_nat @ N @ ( finite_card_real @ B7 ) )
% 8.60/4.79 & ( finite_finite_real @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2830_card__le__Suc__iff,axiom,
% 8.60/4.79 ! [N: nat,A4: set_list_nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_list_nat @ A4 ) )
% 8.60/4.79 = ( ? [A5: list_nat,B7: set_list_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_list_nat @ A5 @ B7 ) )
% 8.60/4.79 & ~ ( member_list_nat @ A5 @ B7 )
% 8.60/4.79 & ( ord_less_eq_nat @ N @ ( finite_card_list_nat @ B7 ) )
% 8.60/4.79 & ( finite8100373058378681591st_nat @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2831_card__le__Suc__iff,axiom,
% 8.60/4.79 ! [N: nat,A4: set_set_nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_set_nat @ A4 ) )
% 8.60/4.79 = ( ? [A5: set_nat,B7: set_set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_set_nat @ A5 @ B7 ) )
% 8.60/4.79 & ~ ( member_set_nat @ A5 @ B7 )
% 8.60/4.79 & ( ord_less_eq_nat @ N @ ( finite_card_set_nat @ B7 ) )
% 8.60/4.79 & ( finite1152437895449049373et_nat @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2832_card__le__Suc__iff,axiom,
% 8.60/4.79 ! [N: nat,A4: set_nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_nat @ A4 ) )
% 8.60/4.79 = ( ? [A5: nat,B7: set_nat] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_nat @ A5 @ B7 ) )
% 8.60/4.79 & ~ ( member_nat @ A5 @ B7 )
% 8.60/4.79 & ( ord_less_eq_nat @ N @ ( finite_card_nat @ B7 ) )
% 8.60/4.79 & ( finite_finite_nat @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2833_card__le__Suc__iff,axiom,
% 8.60/4.79 ! [N: nat,A4: set_int] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_int @ A4 ) )
% 8.60/4.79 = ( ? [A5: int,B7: set_int] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_int @ A5 @ B7 ) )
% 8.60/4.79 & ~ ( member_int @ A5 @ B7 )
% 8.60/4.79 & ( ord_less_eq_nat @ N @ ( finite_card_int @ B7 ) )
% 8.60/4.79 & ( finite_finite_int @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2834_card__le__Suc__iff,axiom,
% 8.60/4.79 ! [N: nat,A4: set_complex] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( finite_card_complex @ A4 ) )
% 8.60/4.79 = ( ? [A5: complex,B7: set_complex] :
% 8.60/4.79 ( ( A4
% 8.60/4.79 = ( insert_complex @ A5 @ B7 ) )
% 8.60/4.79 & ~ ( member_complex @ A5 @ B7 )
% 8.60/4.79 & ( ord_less_eq_nat @ N @ ( finite_card_complex @ B7 ) )
% 8.60/4.79 & ( finite3207457112153483333omplex @ B7 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2835_power__Suc__less,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.60/4.79 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 8.60/4.79 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2836_power__Suc__less,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_real @ A @ one_one_real )
% 8.60/4.79 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2837_power__Suc__less,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_rat @ A @ one_one_rat )
% 8.60/4.79 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2838_power__Suc__less,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ A @ one_one_nat )
% 8.60/4.79 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2839_power__Suc__less,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_int @ A @ one_one_int )
% 8.60/4.79 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2840_power__Suc__le__self,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.60/4.79 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.60/4.79 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2841_power__Suc__le__self,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ A @ one_one_real )
% 8.60/4.79 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2842_power__Suc__le__self,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.60/4.79 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2843_power__Suc__le__self,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.60/4.79 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2844_power__Suc__le__self,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.60/4.79 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2845_power__Suc__less__one,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.60/4.79 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 8.60/4.79 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N ) ) @ one_one_Code_integer ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2846_power__Suc__less__one,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_real @ A @ one_one_real )
% 8.60/4.79 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2847_power__Suc__less__one,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_rat @ A @ one_one_rat )
% 8.60/4.79 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2848_power__Suc__less__one,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ A @ one_one_nat )
% 8.60/4.79 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2849_power__Suc__less__one,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_int @ A @ one_one_int )
% 8.60/4.79 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2850_card__Diff1__le,axiom,
% 8.60/4.79 ! [A4: set_complex,X: complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) @ ( finite_card_complex @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2851_card__Diff1__le,axiom,
% 8.60/4.79 ! [A4: set_list_nat,X: list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) @ ( finite_card_list_nat @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2852_card__Diff1__le,axiom,
% 8.60/4.79 ! [A4: set_set_nat,X: set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) @ ( finite_card_set_nat @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2853_card__Diff1__le,axiom,
% 8.60/4.79 ! [A4: set_int,X: int] : ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) @ ( finite_card_int @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2854_card__Diff1__le,axiom,
% 8.60/4.79 ! [A4: set_real,X: real] : ( ord_less_eq_nat @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) @ ( finite_card_real @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2855_card__Diff1__le,axiom,
% 8.60/4.79 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] : ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) @ ( finite711546835091564841at_nat @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2856_card__Diff1__le,axiom,
% 8.60/4.79 ! [A4: set_nat,X: nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) @ ( finite_card_nat @ A4 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2857_power__strict__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: code_integer] :
% 8.60/4.79 ( ( ord_less_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.60/4.79 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 8.60/4.79 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2858_power__strict__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: real] :
% 8.60/4.79 ( ( ord_less_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_real @ A @ one_one_real )
% 8.60/4.79 => ( ord_less_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2859_power__strict__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: rat] :
% 8.60/4.79 ( ( ord_less_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_rat @ A @ one_one_rat )
% 8.60/4.79 => ( ord_less_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2860_power__strict__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ A @ one_one_nat )
% 8.60/4.79 => ( ord_less_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2861_power__strict__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: int] :
% 8.60/4.79 ( ( ord_less_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_int @ A @ one_one_int )
% 8.60/4.79 => ( ord_less_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2862_power__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: code_integer] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.60/4.79 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 8.60/4.79 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N6 ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2863_power__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: real] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ A @ one_one_real )
% 8.60/4.79 => ( ord_less_eq_real @ ( power_power_real @ A @ N6 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2864_power__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: rat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 8.60/4.79 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N6 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2865_power__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 8.60/4.79 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N6 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2866_power__decreasing,axiom,
% 8.60/4.79 ! [N: nat,N6: nat,A: int] :
% 8.60/4.79 ( ( ord_less_eq_nat @ N @ N6 )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ A @ one_one_int )
% 8.60/4.79 => ( ord_less_eq_int @ ( power_power_int @ A @ N6 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2867_power__le__imp__le__exp,axiom,
% 8.60/4.79 ! [A: code_integer,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.60/4.79 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2868_power__le__imp__le__exp,axiom,
% 8.60/4.79 ! [A: real,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ one_one_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) )
% 8.60/4.79 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2869_power__le__imp__le__exp,axiom,
% 8.60/4.79 ! [A: rat,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) )
% 8.60/4.79 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2870_power__le__imp__le__exp,axiom,
% 8.60/4.79 ! [A: nat,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 8.60/4.79 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2871_power__le__imp__le__exp,axiom,
% 8.60/4.79 ! [A: int,M2: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ one_one_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 8.60/4.79 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2872_power__eq__iff__eq__base,axiom,
% 8.60/4.79 ! [N: nat,A: real,B: real] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.79 => ( ( ( power_power_real @ A @ N )
% 8.60/4.79 = ( power_power_real @ B @ N ) )
% 8.60/4.79 = ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2873_power__eq__iff__eq__base,axiom,
% 8.60/4.79 ! [N: nat,A: rat,B: rat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.79 => ( ( ( power_power_rat @ A @ N )
% 8.60/4.79 = ( power_power_rat @ B @ N ) )
% 8.60/4.79 = ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2874_power__eq__iff__eq__base,axiom,
% 8.60/4.79 ! [N: nat,A: nat,B: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.79 => ( ( ( power_power_nat @ A @ N )
% 8.60/4.79 = ( power_power_nat @ B @ N ) )
% 8.60/4.79 = ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2875_power__eq__iff__eq__base,axiom,
% 8.60/4.79 ! [N: nat,A: int,B: int] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.79 => ( ( ( power_power_int @ A @ N )
% 8.60/4.79 = ( power_power_int @ B @ N ) )
% 8.60/4.79 = ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2876_power__eq__imp__eq__base,axiom,
% 8.60/4.79 ! [A: real,N: nat,B: real] :
% 8.60/4.79 ( ( ( power_power_real @ A @ N )
% 8.60/4.79 = ( power_power_real @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2877_power__eq__imp__eq__base,axiom,
% 8.60/4.79 ! [A: rat,N: nat,B: rat] :
% 8.60/4.79 ( ( ( power_power_rat @ A @ N )
% 8.60/4.79 = ( power_power_rat @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2878_power__eq__imp__eq__base,axiom,
% 8.60/4.79 ! [A: nat,N: nat,B: nat] :
% 8.60/4.79 ( ( ( power_power_nat @ A @ N )
% 8.60/4.79 = ( power_power_nat @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2879_power__eq__imp__eq__base,axiom,
% 8.60/4.79 ! [A: int,N: nat,B: int] :
% 8.60/4.79 ( ( ( power_power_int @ A @ N )
% 8.60/4.79 = ( power_power_int @ B @ N ) )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( A = B ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2880_diff__card__le__card__Diff,axiom,
% 8.60/4.79 ! [B5: set_list_nat,A4: set_list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2881_diff__card__le__card__Diff,axiom,
% 8.60/4.79 ! [B5: set_set_nat,A4: set_set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2882_diff__card__le__card__Diff,axiom,
% 8.60/4.79 ! [B5: set_int,A4: set_int] :
% 8.60/4.79 ( ( finite_finite_int @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2883_diff__card__le__card__Diff,axiom,
% 8.60/4.79 ! [B5: set_complex,A4: set_complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2884_diff__card__le__card__Diff,axiom,
% 8.60/4.79 ! [B5: set_Pr1261947904930325089at_nat,A4: set_Pr1261947904930325089at_nat] :
% 8.60/4.79 ( ( finite6177210948735845034at_nat @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite711546835091564841at_nat @ A4 ) @ ( finite711546835091564841at_nat @ B5 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2885_diff__card__le__card__Diff,axiom,
% 8.60/4.79 ! [B5: set_nat,A4: set_nat] :
% 8.60/4.79 ( ( finite_finite_nat @ B5 )
% 8.60/4.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2886_self__le__power,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2887_self__le__power,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_real @ one_one_real @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2888_self__le__power,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2889_self__le__power,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2890_self__le__power,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_eq_int @ one_one_int @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2891_one__less__power,axiom,
% 8.60/4.79 ! [A: code_integer,N: nat] :
% 8.60/4.79 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2892_one__less__power,axiom,
% 8.60/4.79 ! [A: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ one_one_real @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2893_one__less__power,axiom,
% 8.60/4.79 ! [A: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ one_one_rat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2894_one__less__power,axiom,
% 8.60/4.79 ! [A: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ one_one_nat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2895_one__less__power,axiom,
% 8.60/4.79 ! [A: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ one_one_int @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2896_count__le__length,axiom,
% 8.60/4.79 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] : ( ord_less_eq_nat @ ( count_list_VEBT_VEBT @ Xs2 @ X ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2897_count__le__length,axiom,
% 8.60/4.79 ! [Xs2: list_o,X: $o] : ( ord_less_eq_nat @ ( count_list_o @ Xs2 @ X ) @ ( size_size_list_o @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2898_count__le__length,axiom,
% 8.60/4.79 ! [Xs2: list_nat,X: nat] : ( ord_less_eq_nat @ ( count_list_nat @ Xs2 @ X ) @ ( size_size_list_nat @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2899_count__le__length,axiom,
% 8.60/4.79 ! [Xs2: list_int,X: int] : ( ord_less_eq_nat @ ( count_list_int @ Xs2 @ X ) @ ( size_size_list_int @ Xs2 ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2900_dbl__inc__def,axiom,
% 8.60/4.79 ( neg_nu5831290666863070958nteger
% 8.60/4.79 = ( ^ [X4: code_integer] : ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ X4 @ X4 ) @ one_one_Code_integer ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2901_dbl__inc__def,axiom,
% 8.60/4.79 ( neg_nu8557863876264182079omplex
% 8.60/4.79 = ( ^ [X4: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X4 @ X4 ) @ one_one_complex ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2902_dbl__inc__def,axiom,
% 8.60/4.79 ( neg_nu8295874005876285629c_real
% 8.60/4.79 = ( ^ [X4: real] : ( plus_plus_real @ ( plus_plus_real @ X4 @ X4 ) @ one_one_real ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2903_dbl__inc__def,axiom,
% 8.60/4.79 ( neg_nu5219082963157363817nc_rat
% 8.60/4.79 = ( ^ [X4: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X4 @ X4 ) @ one_one_rat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2904_dbl__inc__def,axiom,
% 8.60/4.79 ( neg_nu5851722552734809277nc_int
% 8.60/4.79 = ( ^ [X4: int] : ( plus_plus_int @ ( plus_plus_int @ X4 @ X4 ) @ one_one_int ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2905_card_Oremove,axiom,
% 8.60/4.79 ! [A4: set_list_nat,X: list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( member_list_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_list_nat @ A4 )
% 8.60/4.79 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2906_card_Oremove,axiom,
% 8.60/4.79 ! [A4: set_set_nat,X: set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( member_set_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_set_nat @ A4 )
% 8.60/4.79 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2907_card_Oremove,axiom,
% 8.60/4.79 ! [A4: set_complex,X: complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( member_complex @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_complex @ A4 )
% 8.60/4.79 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2908_card_Oremove,axiom,
% 8.60/4.79 ! [A4: set_int,X: int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( member_int @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_int @ A4 )
% 8.60/4.79 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2909_card_Oremove,axiom,
% 8.60/4.79 ! [A4: set_real,X: real] :
% 8.60/4.79 ( ( finite_finite_real @ A4 )
% 8.60/4.79 => ( ( member_real @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_real @ A4 )
% 8.60/4.79 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2910_card_Oremove,axiom,
% 8.60/4.79 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 8.60/4.79 ( ( finite6177210948735845034at_nat @ A4 )
% 8.60/4.79 => ( ( member8440522571783428010at_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite711546835091564841at_nat @ A4 )
% 8.60/4.79 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2911_card_Oremove,axiom,
% 8.60/4.79 ! [A4: set_nat,X: nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( member_nat @ X @ A4 )
% 8.60/4.79 => ( ( finite_card_nat @ A4 )
% 8.60/4.79 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2912_card_Oinsert__remove,axiom,
% 8.60/4.79 ! [A4: set_list_nat,X: list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( finite_card_list_nat @ ( insert_list_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2913_card_Oinsert__remove,axiom,
% 8.60/4.79 ! [A4: set_set_nat,X: set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( finite_card_set_nat @ ( insert_set_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2914_card_Oinsert__remove,axiom,
% 8.60/4.79 ! [A4: set_complex,X: complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( finite_card_complex @ ( insert_complex @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2915_card_Oinsert__remove,axiom,
% 8.60/4.79 ! [A4: set_int,X: int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( finite_card_int @ ( insert_int @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2916_card_Oinsert__remove,axiom,
% 8.60/4.79 ! [A4: set_real,X: real] :
% 8.60/4.79 ( ( finite_finite_real @ A4 )
% 8.60/4.79 => ( ( finite_card_real @ ( insert_real @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2917_card_Oinsert__remove,axiom,
% 8.60/4.79 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 8.60/4.79 ( ( finite6177210948735845034at_nat @ A4 )
% 8.60/4.79 => ( ( finite711546835091564841at_nat @ ( insert8211810215607154385at_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2918_card_Oinsert__remove,axiom,
% 8.60/4.79 ! [A4: set_nat,X: nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( finite_card_nat @ ( insert_nat @ X @ A4 ) )
% 8.60/4.79 = ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2919_card__Suc__Diff1,axiom,
% 8.60/4.79 ! [A4: set_list_nat,X: list_nat] :
% 8.60/4.79 ( ( finite8100373058378681591st_nat @ A4 )
% 8.60/4.79 => ( ( member_list_nat @ X @ A4 )
% 8.60/4.79 => ( ( suc @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A4 @ ( insert_list_nat @ X @ bot_bot_set_list_nat ) ) ) )
% 8.60/4.79 = ( finite_card_list_nat @ A4 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2920_card__Suc__Diff1,axiom,
% 8.60/4.79 ! [A4: set_set_nat,X: set_nat] :
% 8.60/4.79 ( ( finite1152437895449049373et_nat @ A4 )
% 8.60/4.79 => ( ( member_set_nat @ X @ A4 )
% 8.60/4.79 => ( ( suc @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A4 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) ) )
% 8.60/4.79 = ( finite_card_set_nat @ A4 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2921_card__Suc__Diff1,axiom,
% 8.60/4.79 ! [A4: set_complex,X: complex] :
% 8.60/4.79 ( ( finite3207457112153483333omplex @ A4 )
% 8.60/4.79 => ( ( member_complex @ X @ A4 )
% 8.60/4.79 => ( ( suc @ ( finite_card_complex @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) )
% 8.60/4.79 = ( finite_card_complex @ A4 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2922_card__Suc__Diff1,axiom,
% 8.60/4.79 ! [A4: set_int,X: int] :
% 8.60/4.79 ( ( finite_finite_int @ A4 )
% 8.60/4.79 => ( ( member_int @ X @ A4 )
% 8.60/4.79 => ( ( suc @ ( finite_card_int @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) )
% 8.60/4.79 = ( finite_card_int @ A4 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2923_card__Suc__Diff1,axiom,
% 8.60/4.79 ! [A4: set_real,X: real] :
% 8.60/4.79 ( ( finite_finite_real @ A4 )
% 8.60/4.79 => ( ( member_real @ X @ A4 )
% 8.60/4.79 => ( ( suc @ ( finite_card_real @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) )
% 8.60/4.79 = ( finite_card_real @ A4 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2924_card__Suc__Diff1,axiom,
% 8.60/4.79 ! [A4: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 8.60/4.79 ( ( finite6177210948735845034at_nat @ A4 )
% 8.60/4.79 => ( ( member8440522571783428010at_nat @ X @ A4 )
% 8.60/4.79 => ( ( suc @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A4 @ ( insert8211810215607154385at_nat @ X @ bot_bo2099793752762293965at_nat ) ) ) )
% 8.60/4.79 = ( finite711546835091564841at_nat @ A4 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2925_card__Suc__Diff1,axiom,
% 8.60/4.79 ! [A4: set_nat,X: nat] :
% 8.60/4.79 ( ( finite_finite_nat @ A4 )
% 8.60/4.79 => ( ( member_nat @ X @ A4 )
% 8.60/4.79 => ( ( suc @ ( finite_card_nat @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) )
% 8.60/4.79 = ( finite_card_nat @ A4 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2926_power__strict__mono,axiom,
% 8.60/4.79 ! [A: real,B: real,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2927_power__strict__mono,axiom,
% 8.60/4.79 ! [A: rat,B: rat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2928_power__strict__mono,axiom,
% 8.60/4.79 ! [A: nat,B: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2929_power__strict__mono,axiom,
% 8.60/4.79 ! [A: int,B: int,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ A @ B )
% 8.60/4.79 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.60/4.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2930_power__eq__if,axiom,
% 8.60/4.79 ( power_8256067586552552935nteger
% 8.60/4.79 = ( ^ [P5: code_integer,M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P5 @ ( power_8256067586552552935nteger @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2931_power__eq__if,axiom,
% 8.60/4.79 ( power_power_complex
% 8.60/4.79 = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2932_power__eq__if,axiom,
% 8.60/4.79 ( power_power_real
% 8.60/4.79 = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2933_power__eq__if,axiom,
% 8.60/4.79 ( power_power_rat
% 8.60/4.79 = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2934_power__eq__if,axiom,
% 8.60/4.79 ( power_power_nat
% 8.60/4.79 = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2935_power__eq__if,axiom,
% 8.60/4.79 ( power_power_int
% 8.60/4.79 = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2936_power__minus__mult,axiom,
% 8.60/4.79 ! [N: nat,A: complex] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.60/4.79 = ( power_power_complex @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2937_power__minus__mult,axiom,
% 8.60/4.79 ! [N: nat,A: real] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.60/4.79 = ( power_power_real @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2938_power__minus__mult,axiom,
% 8.60/4.79 ! [N: nat,A: rat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.60/4.79 = ( power_power_rat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2939_power__minus__mult,axiom,
% 8.60/4.79 ! [N: nat,A: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.60/4.79 = ( power_power_nat @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2940_power__minus__mult,axiom,
% 8.60/4.79 ! [N: nat,A: int] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 8.60/4.79 = ( power_power_int @ A @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2941_Cons__in__lex,axiom,
% 8.60/4.79 ! [X: code_integer,Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 8.60/4.79 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) ) @ ( lex_Code_integer @ R3 ) )
% 8.60/4.79 = ( ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ R3 )
% 8.60/4.79 & ( ( size_s3445333598471063425nteger @ Xs2 )
% 8.60/4.79 = ( size_s3445333598471063425nteger @ Ys ) ) )
% 8.60/4.79 | ( ( X = Y )
% 8.60/4.79 & ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( lex_Code_integer @ R3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2942_Cons__in__lex,axiom,
% 8.60/4.79 ! [X: product_prod_nat_nat,Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 8.60/4.79 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( lex_Pr8571645452597969515at_nat @ R3 ) )
% 8.60/4.79 = ( ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R3 )
% 8.60/4.79 & ( ( size_s5460976970255530739at_nat @ Xs2 )
% 8.60/4.79 = ( size_s5460976970255530739at_nat @ Ys ) ) )
% 8.60/4.79 | ( ( X = Y )
% 8.60/4.79 & ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Ys ) @ ( lex_Pr8571645452597969515at_nat @ R3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2943_Cons__in__lex,axiom,
% 8.60/4.79 ! [X: set_Pr1261947904930325089at_nat,Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 8.60/4.79 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( lex_se2245640040323279819at_nat @ R3 ) )
% 8.60/4.79 = ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R3 )
% 8.60/4.79 & ( ( size_s8736152011456118867at_nat @ Xs2 )
% 8.60/4.79 = ( size_s8736152011456118867at_nat @ Ys ) ) )
% 8.60/4.79 | ( ( X = Y )
% 8.60/4.79 & ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Ys ) @ ( lex_se2245640040323279819at_nat @ R3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2944_Cons__in__lex,axiom,
% 8.60/4.79 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y: vEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 8.60/4.79 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( cons_VEBT_VEBT @ Y @ Ys ) ) @ ( lex_VEBT_VEBT @ R3 ) )
% 8.60/4.79 = ( ( ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ X @ Y ) @ R3 )
% 8.60/4.79 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.79 = ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 8.60/4.79 | ( ( X = Y )
% 8.60/4.79 & ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( lex_VEBT_VEBT @ R3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2945_Cons__in__lex,axiom,
% 8.60/4.79 ! [X: $o,Xs2: list_o,Y: $o,Ys: list_o,R3: set_Product_prod_o_o] :
% 8.60/4.79 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ ( cons_o @ X @ Xs2 ) @ ( cons_o @ Y @ Ys ) ) @ ( lex_o @ R3 ) )
% 8.60/4.79 = ( ( ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ X @ Y ) @ R3 )
% 8.60/4.79 & ( ( size_size_list_o @ Xs2 )
% 8.60/4.79 = ( size_size_list_o @ Ys ) ) )
% 8.60/4.79 | ( ( X = Y )
% 8.60/4.79 & ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( lex_o @ R3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2946_Cons__in__lex,axiom,
% 8.60/4.79 ! [X: nat,Xs2: list_nat,Y: nat,Ys: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 8.60/4.79 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) ) @ ( lex_nat @ R3 ) )
% 8.60/4.79 = ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 )
% 8.60/4.79 & ( ( size_size_list_nat @ Xs2 )
% 8.60/4.79 = ( size_size_list_nat @ Ys ) ) )
% 8.60/4.79 | ( ( X = Y )
% 8.60/4.79 & ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Ys ) @ ( lex_nat @ R3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2947_Cons__in__lex,axiom,
% 8.60/4.79 ! [X: int,Xs2: list_int,Y: int,Ys: list_int,R3: set_Pr958786334691620121nt_int] :
% 8.60/4.79 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) ) @ ( lex_int @ R3 ) )
% 8.60/4.79 = ( ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 )
% 8.60/4.79 & ( ( size_size_list_int @ Xs2 )
% 8.60/4.79 = ( size_size_list_int @ Ys ) ) )
% 8.60/4.79 | ( ( X = Y )
% 8.60/4.79 & ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Ys ) @ ( lex_int @ R3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2948_realpow__pos__nth__unique,axiom,
% 8.60/4.79 ! [N: nat,A: real] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.79 => ? [X3: real] :
% 8.60/4.79 ( ( ord_less_real @ zero_zero_real @ X3 )
% 8.60/4.79 & ( ( power_power_real @ X3 @ N )
% 8.60/4.79 = A )
% 8.60/4.79 & ! [Y6: real] :
% 8.60/4.79 ( ( ( ord_less_real @ zero_zero_real @ Y6 )
% 8.60/4.79 & ( ( power_power_real @ Y6 @ N )
% 8.60/4.79 = A ) )
% 8.60/4.79 => ( Y6 = X3 ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2949_realpow__pos__nth,axiom,
% 8.60/4.79 ! [N: nat,A: real] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.60/4.79 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.60/4.79 => ? [R4: real] :
% 8.60/4.79 ( ( ord_less_real @ zero_zero_real @ R4 )
% 8.60/4.79 & ( ( power_power_real @ R4 @ N )
% 8.60/4.79 = A ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2950_sprop1,axiom,
% 8.60/4.79 ( ( sa
% 8.60/4.79 = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 8.60/4.79 & ( deg
% 8.60/4.79 = ( plus_plus_nat @ na @ m ) )
% 8.60/4.79 & ( ( size_s6755466524823107622T_VEBT @ treeList )
% 8.60/4.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.60/4.79 & ( vEBT_invar_vebt @ summary @ m )
% 8.60/4.79 & ! [X5: vEBT_VEBT] :
% 8.60/4.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ treeList ) )
% 8.60/4.79 => ( vEBT_invar_vebt @ X5 @ na ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2951_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_Code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 8.60/4.79 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) )
% 8.60/4.79 = ( ( ( size_s3445333598471063425nteger @ Xs2 )
% 8.60/4.79 = ( size_s3445333598471063425nteger @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_s3445333598471063425nteger @ Xs2 ) )
% 8.60/4.79 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ N4 ) @ ( nth_Code_integer @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2952_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 8.60/4.79 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( listre1230615542750757617T_VEBT @ R3 ) )
% 8.60/4.79 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.79 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.79 => ( member568628332442017744T_VEBT @ ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2953_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_VEBT_VEBT,Ys: list_o,R3: set_Pr3175402225741728619VEBT_o] :
% 8.60/4.79 ( ( member3126162362653435956list_o @ ( produc2717590391345394939list_o @ Xs2 @ Ys ) @ ( listrel_VEBT_VEBT_o @ R3 ) )
% 8.60/4.79 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.79 = ( size_size_list_o @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.79 => ( member3307348790968139188VEBT_o @ ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_o @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2954_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,R3: set_Pr7556676689462069481BT_nat] :
% 8.60/4.79 ( ( member6193324644334088288st_nat @ ( produc5570133714943300547st_nat @ Xs2 @ Ys ) @ ( listre5900670229112895443BT_nat @ R3 ) )
% 8.60/4.79 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.79 = ( size_size_list_nat @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.79 => ( member373505688050248522BT_nat @ ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_nat @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2955_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_VEBT_VEBT,Ys: list_int,R3: set_Pr5066593544530342725BT_int] :
% 8.60/4.79 ( ( member3703241499402361532st_int @ ( produc1392282695434103839st_int @ Xs2 @ Ys ) @ ( listre5898179758603845167BT_int @ R3 ) )
% 8.60/4.79 = ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.60/4.79 = ( size_size_list_int @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.60/4.79 => ( member5419026705395827622BT_int @ ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ N4 ) @ ( nth_int @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2956_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_o,Ys: list_VEBT_VEBT,R3: set_Pr7543698050874017315T_VEBT] :
% 8.60/4.79 ( ( member1087064965665443052T_VEBT @ ( produc6043759678074843571T_VEBT @ Xs2 @ Ys ) @ ( listrel_o_VEBT_VEBT @ R3 ) )
% 8.60/4.79 = ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.79 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.79 => ( member5477980866518848620T_VEBT @ ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2957_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_o,Ys: list_o,R3: set_Product_prod_o_o] :
% 8.60/4.79 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( listrel_o_o @ R3 ) )
% 8.60/4.79 = ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.79 = ( size_size_list_o @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.79 => ( member7466972457876170832od_o_o @ ( product_Pair_o_o @ ( nth_o @ Xs2 @ N4 ) @ ( nth_o @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2958_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_o,Ys: list_nat,R3: set_Pr2101469702781467981_o_nat] :
% 8.60/4.79 ( ( member1519744053835550788st_nat @ ( produc7128876500814652583st_nat @ Xs2 @ Ys ) @ ( listrel_o_nat @ R3 ) )
% 8.60/4.79 = ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.79 = ( size_size_list_nat @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.79 => ( member2802428098988154798_o_nat @ ( product_Pair_o_nat @ ( nth_o @ Xs2 @ N4 ) @ ( nth_nat @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2959_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_o,Ys: list_int,R3: set_Pr8834758594704517033_o_int] :
% 8.60/4.79 ( ( member8253032945758599840st_int @ ( produc2951025481305455875st_int @ Xs2 @ Ys ) @ ( listrel_o_int @ R3 ) )
% 8.60/4.79 = ( ( ( size_size_list_o @ Xs2 )
% 8.60/4.79 = ( size_size_list_int @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_size_list_o @ Xs2 ) )
% 8.60/4.79 => ( member7847949116333733898_o_int @ ( product_Pair_o_int @ ( nth_o @ Xs2 @ N4 ) @ ( nth_int @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2960_listrel__iff__nth,axiom,
% 8.60/4.79 ! [Xs2: list_nat,Ys: list_VEBT_VEBT,R3: set_Pr6167073792073659919T_VEBT] :
% 8.60/4.79 ( ( member5968030670617646438T_VEBT @ ( produc8335345208264861441T_VEBT @ Xs2 @ Ys ) @ ( listre5761932458788874033T_VEBT @ R3 ) )
% 8.60/4.79 = ( ( ( size_size_list_nat @ Xs2 )
% 8.60/4.79 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 8.60/4.79 & ! [N4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ N4 @ ( size_size_list_nat @ Xs2 ) )
% 8.60/4.79 => ( member8549952807677709168T_VEBT @ ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ N4 ) @ ( nth_VEBT_VEBT @ Ys @ N4 ) ) @ R3 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2961_in__measures_I2_J,axiom,
% 8.60/4.79 ! [X: code_integer,Y: code_integer,F2: code_integer > nat,Fs: list_C4705013386053401436er_nat] :
% 8.60/4.79 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) )
% 8.60/4.79 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.60/4.79 | ( ( ( F2 @ X )
% 8.60/4.79 = ( F2 @ Y ) )
% 8.60/4.79 & ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ Fs ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2962_in__measures_I2_J,axiom,
% 8.60/4.79 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,F2: product_prod_nat_nat > nat,Fs: list_P9162950289778280392at_nat] :
% 8.60/4.79 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) )
% 8.60/4.79 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.60/4.79 | ( ( ( F2 @ X )
% 8.60/4.79 = ( F2 @ Y ) )
% 8.60/4.79 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ Fs ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2963_in__measures_I2_J,axiom,
% 8.60/4.79 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,F2: set_Pr1261947904930325089at_nat > nat,Fs: list_s9130966667114977576at_nat] :
% 8.60/4.79 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) )
% 8.60/4.79 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.60/4.79 | ( ( ( F2 @ X )
% 8.60/4.79 = ( F2 @ Y ) )
% 8.60/4.79 & ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ Fs ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2964_in__measures_I2_J,axiom,
% 8.60/4.79 ! [X: nat,Y: nat,F2: nat > nat,Fs: list_nat_nat] :
% 8.60/4.79 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) )
% 8.60/4.79 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.60/4.79 | ( ( ( F2 @ X )
% 8.60/4.79 = ( F2 @ Y ) )
% 8.60/4.79 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2965_in__measures_I2_J,axiom,
% 8.60/4.79 ! [X: int,Y: int,F2: int > nat,Fs: list_int_nat] :
% 8.60/4.79 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) )
% 8.60/4.79 = ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.60/4.79 | ( ( ( F2 @ X )
% 8.60/4.79 = ( F2 @ Y ) )
% 8.60/4.79 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2966_of__nat__zero__less__power__iff,axiom,
% 8.60/4.79 ! [X: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 8.60/4.79 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.60/4.79 | ( N = zero_zero_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2967_of__nat__zero__less__power__iff,axiom,
% 8.60/4.79 ! [X: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 8.60/4.79 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.60/4.79 | ( N = zero_zero_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2968_of__nat__zero__less__power__iff,axiom,
% 8.60/4.79 ! [X: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 8.60/4.79 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.60/4.79 | ( N = zero_zero_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2969_of__nat__zero__less__power__iff,axiom,
% 8.60/4.79 ! [X: nat,N: nat] :
% 8.60/4.79 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 8.60/4.79 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.60/4.79 | ( N = zero_zero_nat ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2970__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062treeList_H_Asummary_H_Ainfo_O_As_A_061_ANode_Ainfo_Adeg_AtreeList_H_Asummary_H_A_092_060and_062_Adeg_A_061_An_A_L_Am_A_092_060and_062_Alength_AtreeList_H_A_061_A2_A_094_Am_A_092_060and_062_Ainvar__vebt_Asummary_H_Am_A_092_060and_062_A_I_092_060forall_062t_092_060in_062set_AtreeList_H_O_Ainvar__vebt_At_An_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 8.60/4.79 ~ ! [TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Info: option4927543243414619207at_nat] :
% 8.60/4.79 ~ ( ( sa
% 8.60/4.79 = ( vEBT_Node @ Info @ deg @ TreeList3 @ Summary3 ) )
% 8.60/4.79 & ( deg
% 8.60/4.79 = ( plus_plus_nat @ na @ m ) )
% 8.60/4.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 8.60/4.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.60/4.79 & ( vEBT_invar_vebt @ Summary3 @ m )
% 8.60/4.79 & ! [X5: vEBT_VEBT] :
% 8.60/4.79 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 8.60/4.79 => ( vEBT_invar_vebt @ X5 @ na ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2971_intind,axiom,
% 8.60/4.79 ! [I2: nat,N: nat,P2: nat > $o,X: nat] :
% 8.60/4.79 ( ( ord_less_nat @ I2 @ N )
% 8.60/4.79 => ( ( P2 @ X )
% 8.60/4.79 => ( P2 @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I2 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2972_intind,axiom,
% 8.60/4.79 ! [I2: nat,N: nat,P2: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 8.60/4.79 ( ( ord_less_nat @ I2 @ N )
% 8.60/4.79 => ( ( P2 @ X )
% 8.60/4.79 => ( P2 @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I2 ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2973_numeral__eq__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ( numera1916890842035813515d_enat @ M2 )
% 8.60/4.79 = ( numera1916890842035813515d_enat @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2974_numeral__eq__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ( numera6690914467698888265omplex @ M2 )
% 8.60/4.79 = ( numera6690914467698888265omplex @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2975_numeral__eq__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ( numeral_numeral_real @ M2 )
% 8.60/4.79 = ( numeral_numeral_real @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2976_numeral__eq__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ( numeral_numeral_nat @ M2 )
% 8.60/4.79 = ( numeral_numeral_nat @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2977_numeral__eq__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ( numeral_numeral_int @ M2 )
% 8.60/4.79 = ( numeral_numeral_int @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2978_semiring__norm_I13_J,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( times_times_num @ ( bit0 @ M2 ) @ ( bit0 @ N ) )
% 8.60/4.79 = ( bit0 @ ( bit0 @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2979_semiring__norm_I11_J,axiom,
% 8.60/4.79 ! [M2: num] :
% 8.60/4.79 ( ( times_times_num @ M2 @ one )
% 8.60/4.79 = M2 ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2980_semiring__norm_I12_J,axiom,
% 8.60/4.79 ! [N: num] :
% 8.60/4.79 ( ( times_times_num @ one @ N )
% 8.60/4.79 = N ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2981_case4_I10_J,axiom,
% 8.60/4.79 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2982_case4_I4_J,axiom,
% 8.60/4.79 ( ( size_s6755466524823107622T_VEBT @ treeList2 )
% 8.60/4.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2983_of__nat__eq__iff,axiom,
% 8.60/4.79 ! [M2: nat,N: nat] :
% 8.60/4.79 ( ( ( semiri5074537144036343181t_real @ M2 )
% 8.60/4.79 = ( semiri5074537144036343181t_real @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2984_of__nat__eq__iff,axiom,
% 8.60/4.79 ! [M2: nat,N: nat] :
% 8.60/4.79 ( ( ( semiri1314217659103216013at_int @ M2 )
% 8.60/4.79 = ( semiri1314217659103216013at_int @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2985_of__nat__eq__iff,axiom,
% 8.60/4.79 ! [M2: nat,N: nat] :
% 8.60/4.79 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 8.60/4.79 = ( semiri1316708129612266289at_nat @ N ) )
% 8.60/4.79 = ( M2 = N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2986_a0,axiom,
% 8.60/4.79 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2987_case4_I7_J,axiom,
% 8.60/4.79 ! [I4: nat] :
% 8.60/4.79 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.60/4.79 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ X7 ) )
% 8.60/4.79 = ( vEBT_V8194947554948674370ptions @ summary2 @ I4 ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2988_member__bound,axiom,
% 8.60/4.79 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 8.60/4.79 ( ( vEBT_vebt_member @ Tree @ X )
% 8.60/4.79 => ( ( vEBT_invar_vebt @ Tree @ N )
% 8.60/4.79 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2989_valid__pres__insert,axiom,
% 8.60/4.79 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.79 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.79 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.60/4.79 => ( vEBT_invar_vebt @ ( vEBT_vebt_insert @ T @ X ) @ N ) ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2990_numeral__le__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 8.60/4.79 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2991_numeral__le__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 8.60/4.79 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2992_numeral__le__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 8.60/4.79 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2993_numeral__le__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.79 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2994_numeral__le__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 8.60/4.79 = ( ord_less_eq_num @ M2 @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2995_numeral__less__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 8.60/4.79 = ( ord_less_num @ M2 @ N ) ) ).
% 8.60/4.79
% 8.60/4.79 thf(fact_2996_numeral__less__iff,axiom,
% 8.60/4.79 ! [M2: num,N: num] :
% 8.60/4.79 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 8.60/4.79 = ( ord_less_num @ M2 @ N ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_2997_numeral__less__iff,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 8.60/4.80 = ( ord_less_num @ M2 @ N ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_2998_numeral__less__iff,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.80 = ( ord_less_num @ M2 @ N ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_2999_numeral__less__iff,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 8.60/4.80 = ( ord_less_num @ M2 @ N ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3000_numeral__times__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 8.60/4.80 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3001_numeral__times__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 8.60/4.80 = ( numera1916890842035813515d_enat @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3002_numeral__times__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 8.60/4.80 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3003_numeral__times__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 8.60/4.80 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3004_numeral__times__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( times_times_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.80 = ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3005_numeral__times__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 8.60/4.80 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3006_mult__numeral__left__semiring__numeral,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: rat] :
% 8.60/4.80 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3007_mult__numeral__left__semiring__numeral,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: extended_enat] :
% 8.60/4.80 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3008_mult__numeral__left__semiring__numeral,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: complex] :
% 8.60/4.80 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3009_mult__numeral__left__semiring__numeral,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: real] :
% 8.60/4.80 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3010_mult__numeral__left__semiring__numeral,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: nat] :
% 8.60/4.80 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3011_mult__numeral__left__semiring__numeral,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: int] :
% 8.60/4.80 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3012_add__numeral__left,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: rat] :
% 8.60/4.80 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V2 ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3013_add__numeral__left,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: extended_enat] :
% 8.60/4.80 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3014_add__numeral__left,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: complex] :
% 8.60/4.80 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3015_add__numeral__left,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: real] :
% 8.60/4.80 ( ( plus_plus_real @ ( numeral_numeral_real @ V2 ) @ ( plus_plus_real @ ( numeral_numeral_real @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3016_add__numeral__left,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: nat] :
% 8.60/4.80 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3017_add__numeral__left,axiom,
% 8.60/4.80 ! [V2: num,W2: num,Z3: int] :
% 8.60/4.80 ( ( plus_plus_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ ( numeral_numeral_int @ W2 ) @ Z3 ) )
% 8.60/4.80 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V2 @ W2 ) ) @ Z3 ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3018_numeral__plus__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) )
% 8.60/4.80 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3019_numeral__plus__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 8.60/4.80 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3020_numeral__plus__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) )
% 8.60/4.80 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3021_numeral__plus__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) )
% 8.60/4.80 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3022_numeral__plus__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.80 = ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3023_numeral__plus__numeral,axiom,
% 8.60/4.80 ! [M2: num,N: num] :
% 8.60/4.80 ( ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 8.60/4.80 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3024_num__double,axiom,
% 8.60/4.80 ! [N: num] :
% 8.60/4.80 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 8.60/4.80 = ( bit0 @ N ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3025_power__mult__numeral,axiom,
% 8.60/4.80 ! [A: nat,M2: num,N: num] :
% 8.60/4.80 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.80 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3026_power__mult__numeral,axiom,
% 8.60/4.80 ! [A: real,M2: num,N: num] :
% 8.60/4.80 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.80 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3027_power__mult__numeral,axiom,
% 8.60/4.80 ! [A: int,M2: num,N: num] :
% 8.60/4.80 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.80 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3028_power__mult__numeral,axiom,
% 8.60/4.80 ! [A: complex,M2: num,N: num] :
% 8.60/4.80 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) )
% 8.60/4.80 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3029_insert__simp__mima,axiom,
% 8.60/4.80 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.60/4.80 ( ( ( X = Mi )
% 8.60/4.80 | ( X = Ma ) )
% 8.60/4.80 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.60/4.80 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.60/4.80 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3030_misiz,axiom,
% 8.60/4.80 ! [T: vEBT_VEBT,N: nat,M2: nat] :
% 8.60/4.80 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.80 => ( ( ( some_nat @ M2 )
% 8.60/4.80 = ( vEBT_vebt_mint @ T ) )
% 8.60/4.80 => ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3031_not__real__square__gt__zero,axiom,
% 8.60/4.80 ! [X: real] :
% 8.60/4.80 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 8.60/4.80 = ( X = zero_zero_real ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3032_valid__insert__both__member__options__add,axiom,
% 8.60/4.80 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.60/4.80 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.80 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.60/4.80 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3033_valid__insert__both__member__options__pres,axiom,
% 8.60/4.80 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.60/4.80 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.80 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.60/4.80 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.60/4.80 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 8.60/4.80 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3034_helpypredd,axiom,
% 8.60/4.80 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.60/4.80 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.80 => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.60/4.80 = ( some_nat @ Y ) )
% 8.60/4.80 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3035_helpyd,axiom,
% 8.60/4.80 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.60/4.80 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.80 => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.60/4.80 = ( some_nat @ Y ) )
% 8.60/4.80 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3036_post__member__pre__member,axiom,
% 8.60/4.80 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 8.60/4.80 ( ( vEBT_invar_vebt @ T @ N )
% 8.60/4.80 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.60/4.80 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.60/4.80 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 8.60/4.80 => ( ( vEBT_vebt_member @ T @ Y )
% 8.60/4.80 | ( X = Y ) ) ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3037_replicate__eq__replicate,axiom,
% 8.60/4.80 ! [M2: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 8.60/4.80 ( ( ( replicate_VEBT_VEBT @ M2 @ X )
% 8.60/4.80 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 8.60/4.80 = ( ( M2 = N )
% 8.60/4.80 & ( ( M2 != zero_zero_nat )
% 8.60/4.80 => ( X = Y ) ) ) ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3038_length__replicate,axiom,
% 8.60/4.80 ! [N: nat,X: vEBT_VEBT] :
% 8.60/4.80 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.60/4.80 = N ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3039_length__replicate,axiom,
% 8.60/4.80 ! [N: nat,X: $o] :
% 8.60/4.80 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 8.60/4.80 = N ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3040_length__replicate,axiom,
% 8.60/4.80 ! [N: nat,X: nat] :
% 8.60/4.80 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 8.60/4.80 = N ) ).
% 8.60/4.80
% 8.60/4.80 thf(fact_3041_length__replicate,axiom,
% 8.60/4.80 ! [N: nat,X: int] :
% 8.60/4.80 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 8.64/4.80 = N ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3042_delt__out__of__range,axiom,
% 8.64/4.80 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.80 ( ( ( ord_less_nat @ X @ Mi )
% 8.64/4.80 | ( ord_less_nat @ Ma @ X ) )
% 8.64/4.80 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.80 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.80 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3043_del__single__cont,axiom,
% 8.64/4.80 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.80 ( ( ( X = Mi )
% 8.64/4.80 & ( X = Ma ) )
% 8.64/4.80 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.80 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.80 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3044_set__n__deg__not__0,axiom,
% 8.64/4.80 ! [TreeList2: list_VEBT_VEBT,N: nat,M2: nat] :
% 8.64/4.80 ( ! [X3: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.80 => ( vEBT_invar_vebt @ X3 @ N ) )
% 8.64/4.80 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.64/4.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.80 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3045_mi__ma__2__deg,axiom,
% 8.64/4.80 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.64/4.80 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.64/4.80 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 8.64/4.80 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3046_pred__max,axiom,
% 8.64/4.80 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.80 => ( ( ord_less_nat @ Ma @ X )
% 8.64/4.80 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.80 = ( some_nat @ Ma ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3047_succ__min,axiom,
% 8.64/4.80 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.80 => ( ( ord_less_nat @ X @ Mi )
% 8.64/4.80 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.80 = ( some_nat @ Mi ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3048_bit__concat__def,axiom,
% 8.64/4.80 ( vEBT_VEBT_bit_concat
% 8.64/4.80 = ( ^ [H2: nat,L2: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3049_distrib__left__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: rat,C2: rat] :
% 8.64/4.80 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( plus_plus_rat @ B @ C2 ) )
% 8.64/4.80 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3050_distrib__left__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: extended_enat,C2: extended_enat] :
% 8.64/4.80 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ ( plus_p3455044024723400733d_enat @ B @ C2 ) )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3051_distrib__left__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: complex,C2: complex] :
% 8.64/4.80 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( plus_plus_complex @ B @ C2 ) )
% 8.64/4.80 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3052_distrib__left__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: real,C2: real] :
% 8.64/4.80 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( plus_plus_real @ B @ C2 ) )
% 8.64/4.80 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3053_distrib__left__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: nat,C2: nat] :
% 8.64/4.80 ( ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ ( plus_plus_nat @ B @ C2 ) )
% 8.64/4.80 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3054_distrib__left__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: int,C2: int] :
% 8.64/4.80 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( plus_plus_int @ B @ C2 ) )
% 8.64/4.80 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3055_distrib__right__numeral,axiom,
% 8.64/4.80 ! [A: rat,B: rat,V2: num] :
% 8.64/4.80 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.80 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3056_distrib__right__numeral,axiom,
% 8.64/4.80 ! [A: extended_enat,B: extended_enat,V2: num] :
% 8.64/4.80 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V2 ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3057_distrib__right__numeral,axiom,
% 8.64/4.80 ! [A: complex,B: complex,V2: num] :
% 8.64/4.80 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V2 ) )
% 8.64/4.80 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3058_distrib__right__numeral,axiom,
% 8.64/4.80 ! [A: real,B: real,V2: num] :
% 8.64/4.80 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.80 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3059_distrib__right__numeral,axiom,
% 8.64/4.80 ! [A: nat,B: nat,V2: num] :
% 8.64/4.80 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V2 ) )
% 8.64/4.80 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V2 ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3060_distrib__right__numeral,axiom,
% 8.64/4.80 ! [A: int,B: int,V2: num] :
% 8.64/4.80 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.80 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3061_numeral__eq__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ( numera6620942414471956472nteger @ N )
% 8.64/4.80 = one_one_Code_integer )
% 8.64/4.80 = ( N = one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3062_numeral__eq__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ( numera1916890842035813515d_enat @ N )
% 8.64/4.80 = one_on7984719198319812577d_enat )
% 8.64/4.80 = ( N = one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3063_numeral__eq__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ( numera6690914467698888265omplex @ N )
% 8.64/4.80 = one_one_complex )
% 8.64/4.80 = ( N = one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3064_numeral__eq__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ( numeral_numeral_real @ N )
% 8.64/4.80 = one_one_real )
% 8.64/4.80 = ( N = one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3065_numeral__eq__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ( numeral_numeral_nat @ N )
% 8.64/4.80 = one_one_nat )
% 8.64/4.80 = ( N = one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3066_numeral__eq__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ( numeral_numeral_int @ N )
% 8.64/4.80 = one_one_int )
% 8.64/4.80 = ( N = one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3067_one__eq__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( one_one_Code_integer
% 8.64/4.80 = ( numera6620942414471956472nteger @ N ) )
% 8.64/4.80 = ( one = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3068_one__eq__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( one_on7984719198319812577d_enat
% 8.64/4.80 = ( numera1916890842035813515d_enat @ N ) )
% 8.64/4.80 = ( one = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3069_one__eq__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( one_one_complex
% 8.64/4.80 = ( numera6690914467698888265omplex @ N ) )
% 8.64/4.80 = ( one = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3070_one__eq__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( one_one_real
% 8.64/4.80 = ( numeral_numeral_real @ N ) )
% 8.64/4.80 = ( one = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3071_one__eq__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( one_one_nat
% 8.64/4.80 = ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( one = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3072_one__eq__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( one_one_int
% 8.64/4.80 = ( numeral_numeral_int @ N ) )
% 8.64/4.80 = ( one = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3073_left__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [A: rat,B: rat,V2: num] :
% 8.64/4.80 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.80 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3074_left__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [A: complex,B: complex,V2: num] :
% 8.64/4.80 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V2 ) )
% 8.64/4.80 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3075_left__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [A: real,B: real,V2: num] :
% 8.64/4.80 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.80 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3076_left__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [A: int,B: int,V2: num] :
% 8.64/4.80 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.80 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3077_right__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: rat,C2: rat] :
% 8.64/4.80 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( minus_minus_rat @ B @ C2 ) )
% 8.64/4.80 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3078_right__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: complex,C2: complex] :
% 8.64/4.80 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( minus_minus_complex @ B @ C2 ) )
% 8.64/4.80 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3079_right__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: real,C2: real] :
% 8.64/4.80 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( minus_minus_real @ B @ C2 ) )
% 8.64/4.80 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3080_right__diff__distrib__numeral,axiom,
% 8.64/4.80 ! [V2: num,B: int,C2: int] :
% 8.64/4.80 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( minus_minus_int @ B @ C2 ) )
% 8.64/4.80 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V2 ) @ C2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3081_power__zero__numeral,axiom,
% 8.64/4.80 ! [K2: num] :
% 8.64/4.80 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.80 = zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3082_power__zero__numeral,axiom,
% 8.64/4.80 ! [K2: num] :
% 8.64/4.80 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.80 = zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3083_power__zero__numeral,axiom,
% 8.64/4.80 ! [K2: num] :
% 8.64/4.80 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.80 = zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3084_power__zero__numeral,axiom,
% 8.64/4.80 ! [K2: num] :
% 8.64/4.80 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.80 = zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3085_power__zero__numeral,axiom,
% 8.64/4.80 ! [K2: num] :
% 8.64/4.80 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.80 = zero_zero_complex ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3086_Suc__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3087_power__add__numeral,axiom,
% 8.64/4.80 ! [A: complex,M2: num,N: num] :
% 8.64/4.80 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.64/4.80 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3088_power__add__numeral,axiom,
% 8.64/4.80 ! [A: real,M2: num,N: num] :
% 8.64/4.80 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.64/4.80 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3089_power__add__numeral,axiom,
% 8.64/4.80 ! [A: rat,M2: num,N: num] :
% 8.64/4.80 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.64/4.80 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3090_power__add__numeral,axiom,
% 8.64/4.80 ! [A: nat,M2: num,N: num] :
% 8.64/4.80 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.64/4.80 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3091_power__add__numeral,axiom,
% 8.64/4.80 ! [A: int,M2: num,N: num] :
% 8.64/4.80 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 8.64/4.80 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3092_power__add__numeral2,axiom,
% 8.64/4.80 ! [A: complex,M2: num,N: num,B: complex] :
% 8.64/4.80 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.64/4.80 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3093_power__add__numeral2,axiom,
% 8.64/4.80 ! [A: real,M2: num,N: num,B: real] :
% 8.64/4.80 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.64/4.80 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3094_power__add__numeral2,axiom,
% 8.64/4.80 ! [A: rat,M2: num,N: num,B: rat] :
% 8.64/4.80 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.64/4.80 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3095_power__add__numeral2,axiom,
% 8.64/4.80 ! [A: nat,M2: num,N: num,B: nat] :
% 8.64/4.80 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.64/4.80 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3096_power__add__numeral2,axiom,
% 8.64/4.80 ! [A: int,M2: num,N: num,B: int] :
% 8.64/4.80 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M2 ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 8.64/4.80 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M2 @ N ) ) ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3097_of__nat__eq__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ( semiri8010041392384452111omplex @ M2 )
% 8.64/4.80 = zero_zero_complex )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3098_of__nat__eq__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ( semiri681578069525770553at_rat @ M2 )
% 8.64/4.80 = zero_zero_rat )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3099_of__nat__eq__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ( semiri5074537144036343181t_real @ M2 )
% 8.64/4.80 = zero_zero_real )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3100_of__nat__eq__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ( semiri1314217659103216013at_int @ M2 )
% 8.64/4.80 = zero_zero_int )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3101_of__nat__eq__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ( semiri1316708129612266289at_nat @ M2 )
% 8.64/4.80 = zero_zero_nat )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3102_of__nat__0__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( zero_zero_complex
% 8.64/4.80 = ( semiri8010041392384452111omplex @ N ) )
% 8.64/4.80 = ( zero_zero_nat = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3103_of__nat__0__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( zero_zero_rat
% 8.64/4.80 = ( semiri681578069525770553at_rat @ N ) )
% 8.64/4.80 = ( zero_zero_nat = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3104_of__nat__0__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( zero_zero_real
% 8.64/4.80 = ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.80 = ( zero_zero_nat = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3105_of__nat__0__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( zero_zero_int
% 8.64/4.80 = ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.80 = ( zero_zero_nat = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3106_of__nat__0__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( zero_zero_nat
% 8.64/4.80 = ( semiri1316708129612266289at_nat @ N ) )
% 8.64/4.80 = ( zero_zero_nat = N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3107_of__nat__0,axiom,
% 8.64/4.80 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 8.64/4.80 = zero_zero_complex ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3108_of__nat__0,axiom,
% 8.64/4.80 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 8.64/4.80 = zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3109_of__nat__0,axiom,
% 8.64/4.80 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 8.64/4.80 = zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3110_of__nat__0,axiom,
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 8.64/4.80 = zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3111_of__nat__0,axiom,
% 8.64/4.80 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 8.64/4.80 = zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3112_of__nat__less__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.64/4.80 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3113_of__nat__less__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.80 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3114_of__nat__less__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.80 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3115_of__nat__less__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.64/4.80 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3116_of__nat__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( numera1916890842035813515d_enat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3117_of__nat__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( numera6690914467698888265omplex @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3118_of__nat__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( numeral_numeral_real @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3119_of__nat__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( numeral_numeral_int @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3120_of__nat__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( numeral_numeral_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3121_of__nat__le__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3122_of__nat__le__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3123_of__nat__le__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3124_of__nat__le__iff,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3125_of__nat__add,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.80 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3126_of__nat__add,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.80 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3127_of__nat__add,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.80 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3128_of__nat__add,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.80 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3129_of__nat__mult,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M2 @ N ) )
% 8.64/4.80 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3130_of__nat__mult,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M2 @ N ) )
% 8.64/4.80 = ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3131_of__nat__mult,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M2 @ N ) )
% 8.64/4.80 = ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3132_of__nat__mult,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M2 @ N ) )
% 8.64/4.80 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3133_of__nat__eq__1__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ( semiri4939895301339042750nteger @ N )
% 8.64/4.80 = one_one_Code_integer )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3134_of__nat__eq__1__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ( semiri8010041392384452111omplex @ N )
% 8.64/4.80 = one_one_complex )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3135_of__nat__eq__1__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ( semiri5074537144036343181t_real @ N )
% 8.64/4.80 = one_one_real )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3136_of__nat__eq__1__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ( semiri1314217659103216013at_int @ N )
% 8.64/4.80 = one_one_int )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3137_of__nat__eq__1__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ( semiri1316708129612266289at_nat @ N )
% 8.64/4.80 = one_one_nat )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3138_of__nat__1__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( one_one_Code_integer
% 8.64/4.80 = ( semiri4939895301339042750nteger @ N ) )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3139_of__nat__1__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( one_one_complex
% 8.64/4.80 = ( semiri8010041392384452111omplex @ N ) )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3140_of__nat__1__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( one_one_real
% 8.64/4.80 = ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3141_of__nat__1__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( one_one_int
% 8.64/4.80 = ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3142_of__nat__1__eq__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( one_one_nat
% 8.64/4.80 = ( semiri1316708129612266289at_nat @ N ) )
% 8.64/4.80 = ( N = one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3143_of__nat__1,axiom,
% 8.64/4.80 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 8.64/4.80 = one_one_Code_integer ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3144_of__nat__1,axiom,
% 8.64/4.80 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 8.64/4.80 = one_one_complex ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3145_of__nat__1,axiom,
% 8.64/4.80 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 8.64/4.80 = one_one_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3146_of__nat__1,axiom,
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 8.64/4.80 = one_one_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3147_of__nat__1,axiom,
% 8.64/4.80 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 8.64/4.80 = one_one_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3148_in__set__replicate,axiom,
% 8.64/4.80 ! [X: complex,N: nat,Y: complex] :
% 8.64/4.80 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 8.64/4.80 = ( ( X = Y )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3149_in__set__replicate,axiom,
% 8.64/4.80 ! [X: real,N: nat,Y: real] :
% 8.64/4.80 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 8.64/4.80 = ( ( X = Y )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3150_in__set__replicate,axiom,
% 8.64/4.80 ! [X: set_nat,N: nat,Y: set_nat] :
% 8.64/4.80 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 8.64/4.80 = ( ( X = Y )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3151_in__set__replicate,axiom,
% 8.64/4.80 ! [X: int,N: nat,Y: int] :
% 8.64/4.80 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 8.64/4.80 = ( ( X = Y )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3152_in__set__replicate,axiom,
% 8.64/4.80 ! [X: nat,N: nat,Y: nat] :
% 8.64/4.80 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 8.64/4.80 = ( ( X = Y )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3153_in__set__replicate,axiom,
% 8.64/4.80 ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 8.64/4.80 = ( ( X = Y )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3154_Bex__set__replicate,axiom,
% 8.64/4.80 ! [N: nat,A: nat,P2: nat > $o] :
% 8.64/4.80 ( ( ? [X4: nat] :
% 8.64/4.80 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 8.64/4.80 & ( P2 @ X4 ) ) )
% 8.64/4.80 = ( ( P2 @ A )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3155_Bex__set__replicate,axiom,
% 8.64/4.80 ! [N: nat,A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 8.64/4.80 ( ( ? [X4: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 8.64/4.80 & ( P2 @ X4 ) ) )
% 8.64/4.80 = ( ( P2 @ A )
% 8.64/4.80 & ( N != zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3156_Ball__set__replicate,axiom,
% 8.64/4.80 ! [N: nat,A: nat,P2: nat > $o] :
% 8.64/4.80 ( ( ! [X4: nat] :
% 8.64/4.80 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 8.64/4.80 => ( P2 @ X4 ) ) )
% 8.64/4.80 = ( ( P2 @ A )
% 8.64/4.80 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3157_Ball__set__replicate,axiom,
% 8.64/4.80 ! [N: nat,A: vEBT_VEBT,P2: vEBT_VEBT > $o] :
% 8.64/4.80 ( ( ! [X4: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 8.64/4.80 => ( P2 @ X4 ) ) )
% 8.64/4.80 = ( ( P2 @ A )
% 8.64/4.80 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3158_numeral__le__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 8.64/4.80 = ( ord_less_eq_num @ N @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3159_numeral__le__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 8.64/4.80 = ( ord_less_eq_num @ N @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3160_numeral__le__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 8.64/4.80 = ( ord_less_eq_num @ N @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3161_numeral__le__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 8.64/4.80 = ( ord_less_eq_num @ N @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3162_numeral__le__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 8.64/4.80 = ( ord_less_eq_num @ N @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3163_numeral__le__one__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 8.64/4.80 = ( ord_less_eq_num @ N @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3164_one__less__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 8.64/4.80 = ( ord_less_num @ one @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3165_one__less__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 8.64/4.80 = ( ord_less_num @ one @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3166_one__less__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 8.64/4.80 = ( ord_less_num @ one @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3167_one__less__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 8.64/4.80 = ( ord_less_num @ one @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3168_one__less__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( ord_less_num @ one @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3169_one__less__numeral__iff,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 8.64/4.80 = ( ord_less_num @ one @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3170_one__plus__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 8.64/4.80 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3171_one__plus__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 8.64/4.80 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3172_one__plus__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) )
% 8.64/4.80 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3173_one__plus__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 8.64/4.80 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3174_one__plus__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 8.64/4.80 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3175_one__plus__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 8.64/4.80 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3176_one__plus__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 8.64/4.80 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3177_numeral__plus__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer )
% 8.64/4.80 = ( numera6620942414471956472nteger @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3178_numeral__plus__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 8.64/4.80 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3179_numeral__plus__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat )
% 8.64/4.80 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3180_numeral__plus__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 8.64/4.80 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3181_numeral__plus__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 8.64/4.80 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3182_numeral__plus__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 8.64/4.80 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3183_numeral__plus__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 8.64/4.80 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3184_of__nat__le__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3185_of__nat__le__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3186_of__nat__le__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3187_of__nat__le__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int )
% 8.64/4.80 = ( M2 = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3188_of__nat__Suc,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( semiri4939895301339042750nteger @ ( suc @ M2 ) )
% 8.64/4.80 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3189_of__nat__Suc,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( semiri8010041392384452111omplex @ ( suc @ M2 ) )
% 8.64/4.80 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3190_of__nat__Suc,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( semiri681578069525770553at_rat @ ( suc @ M2 ) )
% 8.64/4.80 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3191_of__nat__Suc,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( semiri5074537144036343181t_real @ ( suc @ M2 ) )
% 8.64/4.80 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3192_of__nat__Suc,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( suc @ M2 ) )
% 8.64/4.80 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3193_of__nat__Suc,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ( ( semiri1316708129612266289at_nat @ ( suc @ M2 ) )
% 8.64/4.80 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3194_one__add__one,axiom,
% 8.64/4.80 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer )
% 8.64/4.80 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3195_one__add__one,axiom,
% 8.64/4.80 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 8.64/4.80 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3196_one__add__one,axiom,
% 8.64/4.80 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 8.64/4.80 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3197_one__add__one,axiom,
% 8.64/4.80 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 8.64/4.80 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3198_one__add__one,axiom,
% 8.64/4.80 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 8.64/4.80 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3199_one__add__one,axiom,
% 8.64/4.80 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3200_one__add__one,axiom,
% 8.64/4.80 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 8.64/4.80 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3201_zero__eq__power2,axiom,
% 8.64/4.80 ! [A: rat] :
% 8.64/4.80 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_rat )
% 8.64/4.80 = ( A = zero_zero_rat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3202_zero__eq__power2,axiom,
% 8.64/4.80 ! [A: nat] :
% 8.64/4.80 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_nat )
% 8.64/4.80 = ( A = zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3203_zero__eq__power2,axiom,
% 8.64/4.80 ! [A: real] :
% 8.64/4.80 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_real )
% 8.64/4.80 = ( A = zero_zero_real ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3204_zero__eq__power2,axiom,
% 8.64/4.80 ! [A: int] :
% 8.64/4.80 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_int )
% 8.64/4.80 = ( A = zero_zero_int ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3205_zero__eq__power2,axiom,
% 8.64/4.80 ! [A: complex] :
% 8.64/4.80 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_complex )
% 8.64/4.80 = ( A = zero_zero_complex ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3206_of__nat__0__less__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.64/4.80 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3207_of__nat__0__less__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.80 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3208_of__nat__0__less__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.80 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3209_of__nat__0__less__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 8.64/4.80 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3210_add__2__eq__Suc,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.80 = ( suc @ ( suc @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3211_add__2__eq__Suc_H,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( suc @ ( suc @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3212_Suc__1,axiom,
% 8.64/4.80 ( ( suc @ one_one_nat )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3213_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.64/4.80 ! [B: nat,W2: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) @ ( semiri5074537144036343181t_real @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3214_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.64/4.80 ! [B: nat,W2: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3215_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.64/4.80 ! [B: nat,W2: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3216_of__nat__le__of__nat__power__cancel__iff,axiom,
% 8.64/4.80 ! [B: nat,W2: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3217_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,B: nat,W2: nat] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W2 ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3218_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,B: nat,W2: nat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3219_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,B: nat,W2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3220_of__nat__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,B: nat,W2: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3221_set__replicate,axiom,
% 8.64/4.80 ! [N: nat,X: vEBT_VEBT] :
% 8.64/4.80 ( ( N != zero_zero_nat )
% 8.64/4.80 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.64/4.80 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3222_set__replicate,axiom,
% 8.64/4.80 ! [N: nat,X: nat] :
% 8.64/4.80 ( ( N != zero_zero_nat )
% 8.64/4.80 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 8.64/4.80 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3223_set__replicate,axiom,
% 8.64/4.80 ! [N: nat,X: int] :
% 8.64/4.80 ( ( N != zero_zero_nat )
% 8.64/4.80 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 8.64/4.80 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3224_set__replicate,axiom,
% 8.64/4.80 ! [N: nat,X: real] :
% 8.64/4.80 ( ( N != zero_zero_nat )
% 8.64/4.80 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 8.64/4.80 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3225_power2__eq__iff__nonneg,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.80 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.80 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3226_power2__eq__iff__nonneg,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.80 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.80 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3227_power2__eq__iff__nonneg,axiom,
% 8.64/4.80 ! [X: nat,Y: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.64/4.80 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.64/4.80 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3228_power2__eq__iff__nonneg,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.64/4.80 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.64/4.80 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3229_power2__less__eq__zero__iff,axiom,
% 8.64/4.80 ! [A: real] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 8.64/4.80 = ( A = zero_zero_real ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3230_power2__less__eq__zero__iff,axiom,
% 8.64/4.80 ! [A: rat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 8.64/4.80 = ( A = zero_zero_rat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3231_power2__less__eq__zero__iff,axiom,
% 8.64/4.80 ! [A: int] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 8.64/4.80 = ( A = zero_zero_int ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3232_zero__less__power2,axiom,
% 8.64/4.80 ! [A: real] :
% 8.64/4.80 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( A != zero_zero_real ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3233_zero__less__power2,axiom,
% 8.64/4.80 ! [A: rat] :
% 8.64/4.80 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( A != zero_zero_rat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3234_zero__less__power2,axiom,
% 8.64/4.80 ! [A: int] :
% 8.64/4.80 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( A != zero_zero_int ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3235_sum__power2__eq__zero__iff,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = zero_zero_rat )
% 8.64/4.80 = ( ( X = zero_zero_rat )
% 8.64/4.80 & ( Y = zero_zero_rat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3236_sum__power2__eq__zero__iff,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = zero_zero_real )
% 8.64/4.80 = ( ( X = zero_zero_real )
% 8.64/4.80 & ( Y = zero_zero_real ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3237_sum__power2__eq__zero__iff,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = zero_zero_int )
% 8.64/4.80 = ( ( X = zero_zero_int )
% 8.64/4.80 & ( Y = zero_zero_int ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3238_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [I2: num,N: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3239_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [I2: num,N: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3240_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [I2: num,N: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3241_numeral__power__le__of__nat__cancel__iff,axiom,
% 8.64/4.80 ! [I2: num,N: nat,X: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 8.64/4.80 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3242_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,I2: num,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3243_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,I2: num,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3244_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,I2: num,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3245_of__nat__le__numeral__power__cancel__iff,axiom,
% 8.64/4.80 ! [X: nat,I2: num,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3246_power2__nat__le__imp__le,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 8.64/4.80 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3247_power2__nat__le__eq__le,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( power_power_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3248_self__le__ge2__pow,axiom,
% 8.64/4.80 ! [K2: nat,M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 8.64/4.80 => ( ord_less_eq_nat @ M2 @ ( power_power_nat @ K2 @ M2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3249_card__2__iff_H,axiom,
% 8.64/4.80 ! [S3: set_nat] :
% 8.64/4.80 ( ( ( finite_card_nat @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: nat] :
% 8.64/4.80 ( ( member_nat @ X4 @ S3 )
% 8.64/4.80 & ? [Y4: nat] :
% 8.64/4.80 ( ( member_nat @ Y4 @ S3 )
% 8.64/4.80 & ( X4 != Y4 )
% 8.64/4.80 & ! [Z4: nat] :
% 8.64/4.80 ( ( member_nat @ Z4 @ S3 )
% 8.64/4.80 => ( ( Z4 = X4 )
% 8.64/4.80 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3250_card__2__iff_H,axiom,
% 8.64/4.80 ! [S3: set_complex] :
% 8.64/4.80 ( ( ( finite_card_complex @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: complex] :
% 8.64/4.80 ( ( member_complex @ X4 @ S3 )
% 8.64/4.80 & ? [Y4: complex] :
% 8.64/4.80 ( ( member_complex @ Y4 @ S3 )
% 8.64/4.80 & ( X4 != Y4 )
% 8.64/4.80 & ! [Z4: complex] :
% 8.64/4.80 ( ( member_complex @ Z4 @ S3 )
% 8.64/4.80 => ( ( Z4 = X4 )
% 8.64/4.80 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3251_card__2__iff_H,axiom,
% 8.64/4.80 ! [S3: set_int] :
% 8.64/4.80 ( ( ( finite_card_int @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: int] :
% 8.64/4.80 ( ( member_int @ X4 @ S3 )
% 8.64/4.80 & ? [Y4: int] :
% 8.64/4.80 ( ( member_int @ Y4 @ S3 )
% 8.64/4.80 & ( X4 != Y4 )
% 8.64/4.80 & ! [Z4: int] :
% 8.64/4.80 ( ( member_int @ Z4 @ S3 )
% 8.64/4.80 => ( ( Z4 = X4 )
% 8.64/4.80 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3252_card__2__iff_H,axiom,
% 8.64/4.80 ! [S3: set_list_nat] :
% 8.64/4.80 ( ( ( finite_card_list_nat @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: list_nat] :
% 8.64/4.80 ( ( member_list_nat @ X4 @ S3 )
% 8.64/4.80 & ? [Y4: list_nat] :
% 8.64/4.80 ( ( member_list_nat @ Y4 @ S3 )
% 8.64/4.80 & ( X4 != Y4 )
% 8.64/4.80 & ! [Z4: list_nat] :
% 8.64/4.80 ( ( member_list_nat @ Z4 @ S3 )
% 8.64/4.80 => ( ( Z4 = X4 )
% 8.64/4.80 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3253_card__2__iff_H,axiom,
% 8.64/4.80 ! [S3: set_set_nat] :
% 8.64/4.80 ( ( ( finite_card_set_nat @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: set_nat] :
% 8.64/4.80 ( ( member_set_nat @ X4 @ S3 )
% 8.64/4.80 & ? [Y4: set_nat] :
% 8.64/4.80 ( ( member_set_nat @ Y4 @ S3 )
% 8.64/4.80 & ( X4 != Y4 )
% 8.64/4.80 & ! [Z4: set_nat] :
% 8.64/4.80 ( ( member_set_nat @ Z4 @ S3 )
% 8.64/4.80 => ( ( Z4 = X4 )
% 8.64/4.80 | ( Z4 = Y4 ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3254_reals__Archimedean3,axiom,
% 8.64/4.80 ! [X: real] :
% 8.64/4.80 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.80 => ! [Y6: real] :
% 8.64/4.80 ? [N3: nat] : ( ord_less_real @ Y6 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3255_add__One__commute,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( plus_plus_num @ one @ N )
% 8.64/4.80 = ( plus_plus_num @ N @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3256_numeral__Bit0,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 8.64/4.80 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3257_numeral__Bit0,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3258_numeral__Bit0,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 8.64/4.80 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3259_numeral__Bit0,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 8.64/4.80 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3260_numeral__Bit0,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 8.64/4.80 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3261_numeral__Bit0,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 8.64/4.80 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3262_mult__numeral__1__right,axiom,
% 8.64/4.80 ! [A: rat] :
% 8.64/4.80 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3263_mult__numeral__1__right,axiom,
% 8.64/4.80 ! [A: extended_enat] :
% 8.64/4.80 ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3264_mult__numeral__1__right,axiom,
% 8.64/4.80 ! [A: complex] :
% 8.64/4.80 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3265_mult__numeral__1__right,axiom,
% 8.64/4.80 ! [A: real] :
% 8.64/4.80 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3266_mult__numeral__1__right,axiom,
% 8.64/4.80 ! [A: nat] :
% 8.64/4.80 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3267_mult__numeral__1__right,axiom,
% 8.64/4.80 ! [A: int] :
% 8.64/4.80 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3268_mult__numeral__1,axiom,
% 8.64/4.80 ! [A: rat] :
% 8.64/4.80 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3269_mult__numeral__1,axiom,
% 8.64/4.80 ! [A: extended_enat] :
% 8.64/4.80 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3270_mult__numeral__1,axiom,
% 8.64/4.80 ! [A: complex] :
% 8.64/4.80 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3271_mult__numeral__1,axiom,
% 8.64/4.80 ! [A: real] :
% 8.64/4.80 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3272_mult__numeral__1,axiom,
% 8.64/4.80 ! [A: nat] :
% 8.64/4.80 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3273_mult__numeral__1,axiom,
% 8.64/4.80 ! [A: int] :
% 8.64/4.80 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 8.64/4.80 = A ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3274_numeral__One,axiom,
% 8.64/4.80 ( ( numera6620942414471956472nteger @ one )
% 8.64/4.80 = one_one_Code_integer ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3275_numeral__One,axiom,
% 8.64/4.80 ( ( numera1916890842035813515d_enat @ one )
% 8.64/4.80 = one_on7984719198319812577d_enat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3276_numeral__One,axiom,
% 8.64/4.80 ( ( numera6690914467698888265omplex @ one )
% 8.64/4.80 = one_one_complex ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3277_numeral__One,axiom,
% 8.64/4.80 ( ( numeral_numeral_real @ one )
% 8.64/4.80 = one_one_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3278_numeral__One,axiom,
% 8.64/4.80 ( ( numeral_numeral_nat @ one )
% 8.64/4.80 = one_one_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3279_numeral__One,axiom,
% 8.64/4.80 ( ( numeral_numeral_int @ one )
% 8.64/4.80 = one_one_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3280_pos2,axiom,
% 8.64/4.80 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3281_numerals_I1_J,axiom,
% 8.64/4.80 ( ( numeral_numeral_nat @ one )
% 8.64/4.80 = one_one_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3282_le__num__One__iff,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( ord_less_eq_num @ X @ one )
% 8.64/4.80 = ( X = one ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3283_mult__2,axiom,
% 8.64/4.80 ! [Z3: rat] :
% 8.64/4.80 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 )
% 8.64/4.80 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3284_mult__2,axiom,
% 8.64/4.80 ! [Z3: extended_enat] :
% 8.64/4.80 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z3 )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3285_mult__2,axiom,
% 8.64/4.80 ! [Z3: complex] :
% 8.64/4.80 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 )
% 8.64/4.80 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3286_mult__2,axiom,
% 8.64/4.80 ! [Z3: real] :
% 8.64/4.80 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 )
% 8.64/4.80 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3287_mult__2,axiom,
% 8.64/4.80 ! [Z3: nat] :
% 8.64/4.80 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z3 )
% 8.64/4.80 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3288_mult__2,axiom,
% 8.64/4.80 ! [Z3: int] :
% 8.64/4.80 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z3 )
% 8.64/4.80 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3289_mult__2__right,axiom,
% 8.64/4.80 ! [Z3: rat] :
% 8.64/4.80 ( ( times_times_rat @ Z3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_rat @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3290_mult__2__right,axiom,
% 8.64/4.80 ! [Z3: extended_enat] :
% 8.64/4.80 ( ( times_7803423173614009249d_enat @ Z3 @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3291_mult__2__right,axiom,
% 8.64/4.80 ! [Z3: complex] :
% 8.64/4.80 ( ( times_times_complex @ Z3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_complex @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3292_mult__2__right,axiom,
% 8.64/4.80 ! [Z3: real] :
% 8.64/4.80 ( ( times_times_real @ Z3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_real @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3293_mult__2__right,axiom,
% 8.64/4.80 ! [Z3: nat] :
% 8.64/4.80 ( ( times_times_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_nat @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3294_mult__2__right,axiom,
% 8.64/4.80 ! [Z3: int] :
% 8.64/4.80 ( ( times_times_int @ Z3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_int @ Z3 @ Z3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3295_left__add__twice,axiom,
% 8.64/4.80 ! [A: rat,B: rat] :
% 8.64/4.80 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.64/4.80 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3296_left__add__twice,axiom,
% 8.64/4.80 ! [A: extended_enat,B: extended_enat] :
% 8.64/4.80 ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3297_left__add__twice,axiom,
% 8.64/4.80 ! [A: complex,B: complex] :
% 8.64/4.80 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 8.64/4.80 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3298_left__add__twice,axiom,
% 8.64/4.80 ! [A: real,B: real] :
% 8.64/4.80 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.64/4.80 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3299_left__add__twice,axiom,
% 8.64/4.80 ! [A: nat,B: nat] :
% 8.64/4.80 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.64/4.80 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3300_left__add__twice,axiom,
% 8.64/4.80 ! [A: int,B: int] :
% 8.64/4.80 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.64/4.80 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3301_zero__power2,axiom,
% 8.64/4.80 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3302_zero__power2,axiom,
% 8.64/4.80 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3303_zero__power2,axiom,
% 8.64/4.80 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3304_zero__power2,axiom,
% 8.64/4.80 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3305_zero__power2,axiom,
% 8.64/4.80 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = zero_zero_complex ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3306_power2__eq__square,axiom,
% 8.64/4.80 ! [A: complex] :
% 8.64/4.80 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( times_times_complex @ A @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3307_power2__eq__square,axiom,
% 8.64/4.80 ! [A: real] :
% 8.64/4.80 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( times_times_real @ A @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3308_power2__eq__square,axiom,
% 8.64/4.80 ! [A: rat] :
% 8.64/4.80 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( times_times_rat @ A @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3309_power2__eq__square,axiom,
% 8.64/4.80 ! [A: nat] :
% 8.64/4.80 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( times_times_nat @ A @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3310_power2__eq__square,axiom,
% 8.64/4.80 ! [A: int] :
% 8.64/4.80 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( times_times_int @ A @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3311_power4__eq__xxxx,axiom,
% 8.64/4.80 ! [X: complex] :
% 8.64/4.80 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3312_power4__eq__xxxx,axiom,
% 8.64/4.80 ! [X: real] :
% 8.64/4.80 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3313_power4__eq__xxxx,axiom,
% 8.64/4.80 ! [X: rat] :
% 8.64/4.80 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3314_power4__eq__xxxx,axiom,
% 8.64/4.80 ! [X: nat] :
% 8.64/4.80 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3315_power4__eq__xxxx,axiom,
% 8.64/4.80 ! [X: int] :
% 8.64/4.80 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.80 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3316_numeral__2__eq__2,axiom,
% 8.64/4.80 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 8.64/4.80 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3317_power__even__eq,axiom,
% 8.64/4.80 ! [A: nat,N: nat] :
% 8.64/4.80 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.80 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3318_power__even__eq,axiom,
% 8.64/4.80 ! [A: real,N: nat] :
% 8.64/4.80 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.80 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3319_power__even__eq,axiom,
% 8.64/4.80 ! [A: int,N: nat] :
% 8.64/4.80 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.80 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3320_power__even__eq,axiom,
% 8.64/4.80 ! [A: complex,N: nat] :
% 8.64/4.80 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.80 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3321_diff__le__diff__pow,axiom,
% 8.64/4.80 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 8.64/4.80 => ( ord_less_eq_nat @ ( minus_minus_nat @ M2 @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K2 @ M2 ) @ ( power_power_nat @ K2 @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3322_nat__1__add__1,axiom,
% 8.64/4.80 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3323_power2__sum,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3324_power2__sum,axiom,
% 8.64/4.80 ! [X: extended_enat,Y: extended_enat] :
% 8.64/4.80 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3325_power2__sum,axiom,
% 8.64/4.80 ! [X: complex,Y: complex] :
% 8.64/4.80 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3326_power2__sum,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3327_power2__sum,axiom,
% 8.64/4.80 ! [X: nat,Y: nat] :
% 8.64/4.80 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3328_power2__sum,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3329_sum__squares__bound,axiom,
% 8.64/4.80 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3330_sum__squares__bound,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3331_power2__diff,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3332_power2__diff,axiom,
% 8.64/4.80 ! [X: complex,Y: complex] :
% 8.64/4.80 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3333_power2__diff,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3334_power2__diff,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3335_power2__le__imp__le,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.80 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3336_power2__le__imp__le,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.80 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3337_power2__le__imp__le,axiom,
% 8.64/4.80 ! [X: nat,Y: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.64/4.80 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3338_power2__le__imp__le,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.64/4.80 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3339_power2__eq__imp__eq,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.80 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.80 => ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3340_power2__eq__imp__eq,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.80 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.80 => ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3341_power2__eq__imp__eq,axiom,
% 8.64/4.80 ! [X: nat,Y: nat] :
% 8.64/4.80 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.64/4.80 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.64/4.80 => ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3342_power2__eq__imp__eq,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.64/4.80 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.64/4.80 => ( X = Y ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3343_zero__le__power2,axiom,
% 8.64/4.80 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3344_zero__le__power2,axiom,
% 8.64/4.80 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3345_zero__le__power2,axiom,
% 8.64/4.80 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3346_power2__less__0,axiom,
% 8.64/4.80 ! [A: real] :
% 8.64/4.80 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3347_power2__less__0,axiom,
% 8.64/4.80 ! [A: rat] :
% 8.64/4.80 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3348_power2__less__0,axiom,
% 8.64/4.80 ! [A: int] :
% 8.64/4.80 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3349_less__2__cases,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 => ( ( N = zero_zero_nat )
% 8.64/4.80 | ( N
% 8.64/4.80 = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3350_less__2__cases__iff,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ( N = zero_zero_nat )
% 8.64/4.80 | ( N
% 8.64/4.80 = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3351_card__2__iff,axiom,
% 8.64/4.80 ! [S3: set_complex] :
% 8.64/4.80 ( ( ( finite_card_complex @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: complex,Y4: complex] :
% 8.64/4.80 ( ( S3
% 8.64/4.80 = ( insert_complex @ X4 @ ( insert_complex @ Y4 @ bot_bot_set_complex ) ) )
% 8.64/4.80 & ( X4 != Y4 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3352_card__2__iff,axiom,
% 8.64/4.80 ! [S3: set_list_nat] :
% 8.64/4.80 ( ( ( finite_card_list_nat @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: list_nat,Y4: list_nat] :
% 8.64/4.80 ( ( S3
% 8.64/4.80 = ( insert_list_nat @ X4 @ ( insert_list_nat @ Y4 @ bot_bot_set_list_nat ) ) )
% 8.64/4.80 & ( X4 != Y4 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3353_card__2__iff,axiom,
% 8.64/4.80 ! [S3: set_set_nat] :
% 8.64/4.80 ( ( ( finite_card_set_nat @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: set_nat,Y4: set_nat] :
% 8.64/4.80 ( ( S3
% 8.64/4.80 = ( insert_set_nat @ X4 @ ( insert_set_nat @ Y4 @ bot_bot_set_set_nat ) ) )
% 8.64/4.80 & ( X4 != Y4 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3354_card__2__iff,axiom,
% 8.64/4.80 ! [S3: set_nat] :
% 8.64/4.80 ( ( ( finite_card_nat @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: nat,Y4: nat] :
% 8.64/4.80 ( ( S3
% 8.64/4.80 = ( insert_nat @ X4 @ ( insert_nat @ Y4 @ bot_bot_set_nat ) ) )
% 8.64/4.80 & ( X4 != Y4 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3355_card__2__iff,axiom,
% 8.64/4.80 ! [S3: set_int] :
% 8.64/4.80 ( ( ( finite_card_int @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: int,Y4: int] :
% 8.64/4.80 ( ( S3
% 8.64/4.80 = ( insert_int @ X4 @ ( insert_int @ Y4 @ bot_bot_set_int ) ) )
% 8.64/4.80 & ( X4 != Y4 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3356_card__2__iff,axiom,
% 8.64/4.80 ! [S3: set_real] :
% 8.64/4.80 ( ( ( finite_card_real @ S3 )
% 8.64/4.80 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.80 = ( ? [X4: real,Y4: real] :
% 8.64/4.80 ( ( S3
% 8.64/4.80 = ( insert_real @ X4 @ ( insert_real @ Y4 @ bot_bot_set_real ) ) )
% 8.64/4.80 & ( X4 != Y4 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3357_numeral__1__eq__Suc__0,axiom,
% 8.64/4.80 ( ( numeral_numeral_nat @ one )
% 8.64/4.80 = ( suc @ zero_zero_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3358_Suc__nat__number__of__add,axiom,
% 8.64/4.80 ! [V2: num,N: nat] :
% 8.64/4.80 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V2 ) @ N ) )
% 8.64/4.80 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V2 @ one ) ) @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3359_real__arch__simple,axiom,
% 8.64/4.80 ! [X: real] :
% 8.64/4.80 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3360_real__arch__simple,axiom,
% 8.64/4.80 ! [X: rat] :
% 8.64/4.80 ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3361_reals__Archimedean2,axiom,
% 8.64/4.80 ! [X: rat] :
% 8.64/4.80 ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3362_reals__Archimedean2,axiom,
% 8.64/4.80 ! [X: real] :
% 8.64/4.80 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3363_mult__of__nat__commute,axiom,
% 8.64/4.80 ! [X: nat,Y: rat] :
% 8.64/4.80 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 8.64/4.80 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3364_mult__of__nat__commute,axiom,
% 8.64/4.80 ! [X: nat,Y: real] :
% 8.64/4.80 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 8.64/4.80 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3365_mult__of__nat__commute,axiom,
% 8.64/4.80 ! [X: nat,Y: int] :
% 8.64/4.80 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 8.64/4.80 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3366_mult__of__nat__commute,axiom,
% 8.64/4.80 ! [X: nat,Y: nat] :
% 8.64/4.80 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 8.64/4.80 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3367_zless__iff__Suc__zadd,axiom,
% 8.64/4.80 ( ord_less_int
% 8.64/4.80 = ( ^ [W3: int,Z4: int] :
% 8.64/4.80 ? [N4: nat] :
% 8.64/4.80 ( Z4
% 8.64/4.80 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N4 ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3368_int__Suc,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 8.64/4.80 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3369_int__ops_I4_J,axiom,
% 8.64/4.80 ! [A: nat] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 8.64/4.80 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3370_zero__neq__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( zero_zero_rat
% 8.64/4.80 != ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3371_zero__neq__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( zero_z5237406670263579293d_enat
% 8.64/4.80 != ( numera1916890842035813515d_enat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3372_zero__neq__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( zero_zero_complex
% 8.64/4.80 != ( numera6690914467698888265omplex @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3373_zero__neq__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( zero_zero_real
% 8.64/4.80 != ( numeral_numeral_real @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3374_zero__neq__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( zero_zero_nat
% 8.64/4.80 != ( numeral_numeral_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3375_zero__neq__numeral,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ( zero_zero_int
% 8.64/4.80 != ( numeral_numeral_int @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3376_int__ops_I1_J,axiom,
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 8.64/4.80 = zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3377_nat__le__real__less,axiom,
% 8.64/4.80 ( ord_less_eq_nat
% 8.64/4.80 = ( ^ [N4: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3378_zle__int,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.80 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3379_nat__int__comparison_I3_J,axiom,
% 8.64/4.80 ( ord_less_eq_nat
% 8.64/4.80 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3380_int__ops_I7_J,axiom,
% 8.64/4.80 ! [A: nat,B: nat] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 8.64/4.80 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3381_power2__less__imp__less,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.80 => ( ord_less_real @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3382_power2__less__imp__less,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.80 => ( ord_less_rat @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3383_power2__less__imp__less,axiom,
% 8.64/4.80 ! [X: nat,Y: nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 8.64/4.80 => ( ord_less_nat @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3384_power2__less__imp__less,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.80 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.64/4.80 => ( ord_less_int @ X @ Y ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3385_sum__power2__le__zero__iff,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 8.64/4.80 = ( ( X = zero_zero_real )
% 8.64/4.80 & ( Y = zero_zero_real ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3386_sum__power2__le__zero__iff,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 8.64/4.80 = ( ( X = zero_zero_rat )
% 8.64/4.80 & ( Y = zero_zero_rat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3387_sum__power2__le__zero__iff,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 8.64/4.80 = ( ( X = zero_zero_int )
% 8.64/4.80 & ( Y = zero_zero_int ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3388_sum__power2__ge__zero,axiom,
% 8.64/4.80 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3389_sum__power2__ge__zero,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3390_sum__power2__ge__zero,axiom,
% 8.64/4.80 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3391_sum__power2__gt__zero__iff,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.80 = ( ( X != zero_zero_real )
% 8.64/4.80 | ( Y != zero_zero_real ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3392_sum__power2__gt__zero__iff,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.80 = ( ( X != zero_zero_rat )
% 8.64/4.80 | ( Y != zero_zero_rat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3393_sum__power2__gt__zero__iff,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.80 = ( ( X != zero_zero_int )
% 8.64/4.80 | ( Y != zero_zero_int ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3394_not__sum__power2__lt__zero,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3395_not__sum__power2__lt__zero,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3396_not__sum__power2__lt__zero,axiom,
% 8.64/4.80 ! [X: int,Y: int] :
% 8.64/4.80 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3397_num_Osize_I4_J,axiom,
% 8.64/4.80 ( ( size_size_num @ one )
% 8.64/4.80 = zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3398_zero__le__even__power_H,axiom,
% 8.64/4.80 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3399_zero__le__even__power_H,axiom,
% 8.64/4.80 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3400_zero__le__even__power_H,axiom,
% 8.64/4.80 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3401_power__odd__eq,axiom,
% 8.64/4.80 ! [A: complex,N: nat] :
% 8.64/4.80 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.80 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3402_power__odd__eq,axiom,
% 8.64/4.80 ! [A: real,N: nat] :
% 8.64/4.80 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.80 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3403_power__odd__eq,axiom,
% 8.64/4.80 ! [A: rat,N: nat] :
% 8.64/4.80 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.80 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3404_power__odd__eq,axiom,
% 8.64/4.80 ! [A: nat,N: nat] :
% 8.64/4.80 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.80 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3405_power__odd__eq,axiom,
% 8.64/4.80 ! [A: int,N: nat] :
% 8.64/4.80 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.80 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3406_ex__power__ivl1,axiom,
% 8.64/4.80 ! [B: nat,K2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.64/4.80 => ( ( ord_less_eq_nat @ one_one_nat @ K2 )
% 8.64/4.80 => ? [N3: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K2 )
% 8.64/4.80 & ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3407_ex__power__ivl2,axiom,
% 8.64/4.80 ! [B: nat,K2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.64/4.80 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 8.64/4.80 => ? [N3: nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K2 )
% 8.64/4.80 & ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3408_VEBT__internal_Oinsert_H_Osimps_I2_J,axiom,
% 8.64/4.80 ! [Deg: nat,X: nat,Info2: option4927543243414619207at_nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.80 ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 8.64/4.80 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.80 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) )
% 8.64/4.80 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) @ X )
% 8.64/4.80 => ( ( vEBT_VEBT_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.80 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3409_odd__0__le__power__imp__0__le,axiom,
% 8.64/4.80 ! [A: real,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.80 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3410_odd__0__le__power__imp__0__le,axiom,
% 8.64/4.80 ! [A: rat,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.80 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3411_odd__0__le__power__imp__0__le,axiom,
% 8.64/4.80 ! [A: int,N: nat] :
% 8.64/4.80 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.80 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3412_odd__power__less__zero,axiom,
% 8.64/4.80 ! [A: real,N: nat] :
% 8.64/4.80 ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.80 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3413_odd__power__less__zero,axiom,
% 8.64/4.80 ! [A: rat,N: nat] :
% 8.64/4.80 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.80 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3414_odd__power__less__zero,axiom,
% 8.64/4.80 ! [A: int,N: nat] :
% 8.64/4.80 ( ( ord_less_int @ A @ zero_zero_int )
% 8.64/4.80 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3415_VEBT__internal_Oinsert_H_Oelims,axiom,
% 8.64/4.80 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.64/4.80 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 8.64/4.80 = Y )
% 8.64/4.80 => ( ! [A3: $o,B3: $o] :
% 8.64/4.80 ( ( X
% 8.64/4.80 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.80 => ( Y
% 8.64/4.80 != ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) )
% 8.64/4.80 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.80 ( ( X
% 8.64/4.80 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.80 => ~ ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 8.64/4.80 => ( Y
% 8.64/4.80 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 8.64/4.80 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 8.64/4.80 => ( Y
% 8.64/4.80 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3416_of__nat__0__le__iff,axiom,
% 8.64/4.80 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3417_of__nat__0__le__iff,axiom,
% 8.64/4.80 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3418_of__nat__0__le__iff,axiom,
% 8.64/4.80 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3419_of__nat__0__le__iff,axiom,
% 8.64/4.80 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3420_of__nat__less__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3421_of__nat__less__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3422_of__nat__less__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3423_of__nat__less__0__iff,axiom,
% 8.64/4.80 ! [M2: nat] :
% 8.64/4.80 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3424_of__nat__neq__0,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 8.64/4.80 != zero_zero_complex ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3425_of__nat__neq__0,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 8.64/4.80 != zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3426_of__nat__neq__0,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 8.64/4.80 != zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3427_of__nat__neq__0,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 8.64/4.80 != zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3428_of__nat__neq__0,axiom,
% 8.64/4.80 ! [N: nat] :
% 8.64/4.80 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 8.64/4.80 != zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3429_of__nat__less__imp__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) )
% 8.64/4.80 => ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3430_of__nat__less__imp__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.80 => ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3431_of__nat__less__imp__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.80 => ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3432_of__nat__less__imp__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) )
% 8.64/4.80 => ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3433_less__imp__of__nat__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ M2 @ N )
% 8.64/4.80 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3434_less__imp__of__nat__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ M2 @ N )
% 8.64/4.80 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3435_less__imp__of__nat__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ M2 @ N )
% 8.64/4.80 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3436_less__imp__of__nat__less,axiom,
% 8.64/4.80 ! [M2: nat,N: nat] :
% 8.64/4.80 ( ( ord_less_nat @ M2 @ N )
% 8.64/4.80 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3437_of__nat__mono,axiom,
% 8.64/4.80 ! [I2: nat,J2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.80 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3438_of__nat__mono,axiom,
% 8.64/4.80 ! [I2: nat,J2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.80 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3439_of__nat__mono,axiom,
% 8.64/4.80 ! [I2: nat,J2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.80 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3440_of__nat__mono,axiom,
% 8.64/4.80 ! [I2: nat,J2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.80 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3441_zero__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3442_zero__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3443_zero__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3444_zero__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3445_zero__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3446_not__numeral__le__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3447_not__numeral__le__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3448_not__numeral__le__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3449_not__numeral__le__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3450_not__numeral__le__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3451_not__numeral__less__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3452_not__numeral__less__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ zero_z5237406670263579293d_enat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3453_not__numeral__less__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3454_not__numeral__less__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3455_not__numeral__less__zero,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3456_zero__less__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3457_zero__less__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3458_zero__less__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3459_zero__less__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3460_zero__less__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3461_replicate__Suc,axiom,
% 8.64/4.80 ! [N: nat,X: nat] :
% 8.64/4.80 ( ( replicate_nat @ ( suc @ N ) @ X )
% 8.64/4.80 = ( cons_nat @ X @ ( replicate_nat @ N @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3462_replicate__Suc,axiom,
% 8.64/4.80 ! [N: nat,X: vEBT_VEBT] :
% 8.64/4.80 ( ( replicate_VEBT_VEBT @ ( suc @ N ) @ X )
% 8.64/4.80 = ( cons_VEBT_VEBT @ X @ ( replicate_VEBT_VEBT @ N @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3463_real__archimedian__rdiv__eq__0,axiom,
% 8.64/4.80 ! [X: real,C2: real] :
% 8.64/4.80 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.80 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.64/4.80 => ( ! [M: nat] :
% 8.64/4.80 ( ( ord_less_nat @ zero_zero_nat @ M )
% 8.64/4.80 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ X ) @ C2 ) )
% 8.64/4.80 => ( X = zero_zero_real ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3464_one__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3465_one__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3466_one__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3467_one__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3468_one__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3469_one__le__numeral,axiom,
% 8.64/4.80 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3470_pos__int__cases,axiom,
% 8.64/4.80 ! [K2: int] :
% 8.64/4.80 ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.80 => ~ ! [N3: nat] :
% 8.64/4.80 ( ( K2
% 8.64/4.80 = ( semiri1314217659103216013at_int @ N3 ) )
% 8.64/4.80 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3471_zero__less__imp__eq__int,axiom,
% 8.64/4.80 ! [K2: int] :
% 8.64/4.80 ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.80 => ? [N3: nat] :
% 8.64/4.80 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.64/4.80 & ( K2
% 8.64/4.80 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3472_zmult__zless__mono2__lemma,axiom,
% 8.64/4.80 ! [I2: int,J2: int,K2: nat] :
% 8.64/4.80 ( ( ord_less_int @ I2 @ J2 )
% 8.64/4.80 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.80 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K2 ) @ J2 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3473_not__numeral__less__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N ) @ one_one_Code_integer ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3474_not__numeral__less__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3475_not__numeral__less__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N ) @ one_on7984719198319812577d_enat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3476_not__numeral__less__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3477_not__numeral__less__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3478_not__numeral__less__one,axiom,
% 8.64/4.80 ! [N: num] :
% 8.64/4.80 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3479_one__plus__numeral__commute,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 8.64/4.80 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3480_one__plus__numeral__commute,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 8.64/4.80 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3481_one__plus__numeral__commute,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 8.64/4.80 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3482_one__plus__numeral__commute,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 8.64/4.80 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3483_one__plus__numeral__commute,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 8.64/4.80 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3484_one__plus__numeral__commute,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 8.64/4.80 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3485_one__plus__numeral__commute,axiom,
% 8.64/4.80 ! [X: num] :
% 8.64/4.80 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 8.64/4.80 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3486_replicate__length__same,axiom,
% 8.64/4.80 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.64/4.80 ( ! [X3: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.64/4.80 => ( X3 = X ) )
% 8.64/4.80 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ X )
% 8.64/4.80 = Xs2 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3487_replicate__length__same,axiom,
% 8.64/4.80 ! [Xs2: list_o,X: $o] :
% 8.64/4.80 ( ! [X3: $o] :
% 8.64/4.80 ( ( member_o @ X3 @ ( set_o2 @ Xs2 ) )
% 8.64/4.80 => ( X3 = X ) )
% 8.64/4.80 => ( ( replicate_o @ ( size_size_list_o @ Xs2 ) @ X )
% 8.64/4.80 = Xs2 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3488_replicate__length__same,axiom,
% 8.64/4.80 ! [Xs2: list_nat,X: nat] :
% 8.64/4.80 ( ! [X3: nat] :
% 8.64/4.80 ( ( member_nat @ X3 @ ( set_nat2 @ Xs2 ) )
% 8.64/4.80 => ( X3 = X ) )
% 8.64/4.80 => ( ( replicate_nat @ ( size_size_list_nat @ Xs2 ) @ X )
% 8.64/4.80 = Xs2 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3489_replicate__length__same,axiom,
% 8.64/4.80 ! [Xs2: list_int,X: int] :
% 8.64/4.80 ( ! [X3: int] :
% 8.64/4.80 ( ( member_int @ X3 @ ( set_int2 @ Xs2 ) )
% 8.64/4.80 => ( X3 = X ) )
% 8.64/4.80 => ( ( replicate_int @ ( size_size_list_int @ Xs2 ) @ X )
% 8.64/4.80 = Xs2 ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3490_replicate__eqI,axiom,
% 8.64/4.80 ! [Xs2: list_complex,N: nat,X: complex] :
% 8.64/4.80 ( ( ( size_s3451745648224563538omplex @ Xs2 )
% 8.64/4.80 = N )
% 8.64/4.80 => ( ! [Y3: complex] :
% 8.64/4.80 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs2 ) )
% 8.64/4.80 => ( Y3 = X ) )
% 8.64/4.80 => ( Xs2
% 8.64/4.80 = ( replicate_complex @ N @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3491_replicate__eqI,axiom,
% 8.64/4.80 ! [Xs2: list_real,N: nat,X: real] :
% 8.64/4.80 ( ( ( size_size_list_real @ Xs2 )
% 8.64/4.80 = N )
% 8.64/4.80 => ( ! [Y3: real] :
% 8.64/4.80 ( ( member_real @ Y3 @ ( set_real2 @ Xs2 ) )
% 8.64/4.80 => ( Y3 = X ) )
% 8.64/4.80 => ( Xs2
% 8.64/4.80 = ( replicate_real @ N @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3492_replicate__eqI,axiom,
% 8.64/4.80 ! [Xs2: list_set_nat,N: nat,X: set_nat] :
% 8.64/4.80 ( ( ( size_s3254054031482475050et_nat @ Xs2 )
% 8.64/4.80 = N )
% 8.64/4.80 => ( ! [Y3: set_nat] :
% 8.64/4.80 ( ( member_set_nat @ Y3 @ ( set_set_nat2 @ Xs2 ) )
% 8.64/4.80 => ( Y3 = X ) )
% 8.64/4.80 => ( Xs2
% 8.64/4.80 = ( replicate_set_nat @ N @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3493_replicate__eqI,axiom,
% 8.64/4.80 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 8.64/4.80 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.64/4.80 = N )
% 8.64/4.80 => ( ! [Y3: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.64/4.80 => ( Y3 = X ) )
% 8.64/4.80 => ( Xs2
% 8.64/4.80 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3494_replicate__eqI,axiom,
% 8.64/4.80 ! [Xs2: list_o,N: nat,X: $o] :
% 8.64/4.80 ( ( ( size_size_list_o @ Xs2 )
% 8.64/4.80 = N )
% 8.64/4.80 => ( ! [Y3: $o] :
% 8.64/4.80 ( ( member_o @ Y3 @ ( set_o2 @ Xs2 ) )
% 8.64/4.80 => ( Y3 = X ) )
% 8.64/4.80 => ( Xs2
% 8.64/4.80 = ( replicate_o @ N @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3495_replicate__eqI,axiom,
% 8.64/4.80 ! [Xs2: list_nat,N: nat,X: nat] :
% 8.64/4.80 ( ( ( size_size_list_nat @ Xs2 )
% 8.64/4.80 = N )
% 8.64/4.80 => ( ! [Y3: nat] :
% 8.64/4.80 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs2 ) )
% 8.64/4.80 => ( Y3 = X ) )
% 8.64/4.80 => ( Xs2
% 8.64/4.80 = ( replicate_nat @ N @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3496_replicate__eqI,axiom,
% 8.64/4.80 ! [Xs2: list_int,N: nat,X: int] :
% 8.64/4.80 ( ( ( size_size_list_int @ Xs2 )
% 8.64/4.80 = N )
% 8.64/4.80 => ( ! [Y3: int] :
% 8.64/4.80 ( ( member_int @ Y3 @ ( set_int2 @ Xs2 ) )
% 8.64/4.80 => ( Y3 = X ) )
% 8.64/4.80 => ( Xs2
% 8.64/4.80 = ( replicate_int @ N @ X ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3497_invar__vebt_Ointros_I2_J,axiom,
% 8.64/4.80 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 8.64/4.80 ( ! [X3: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.80 => ( vEBT_invar_vebt @ X3 @ N ) )
% 8.64/4.80 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 8.64/4.80 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.64/4.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.80 => ( ( M2 = N )
% 8.64/4.80 => ( ( Deg
% 8.64/4.80 = ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.80 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 8.64/4.80 => ( ! [X3: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.80 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 8.64/4.80 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3498_invar__vebt_Ointros_I3_J,axiom,
% 8.64/4.80 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat] :
% 8.64/4.80 ( ! [X3: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.80 => ( vEBT_invar_vebt @ X3 @ N ) )
% 8.64/4.80 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 8.64/4.80 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.64/4.80 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.80 => ( ( M2
% 8.64/4.80 = ( suc @ N ) )
% 8.64/4.80 => ( ( Deg
% 8.64/4.80 = ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.80 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 8.64/4.80 => ( ! [X3: vEBT_VEBT] :
% 8.64/4.80 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.80 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) )
% 8.64/4.80 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3499_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT,R3: set_Pr6192946355708809607T_VEBT] :
% 8.64/4.80 ( ( member4439316823752958928T_VEBT @ ( produc3897820843166775703T_VEBT @ Xs2 @ Ys ) @ ( listre1230615542750757617T_VEBT @ R3 ) )
% 8.64/4.80 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.64/4.80 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3500_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_VEBT_VEBT,Ys: list_o,R3: set_Pr3175402225741728619VEBT_o] :
% 8.64/4.80 ( ( member3126162362653435956list_o @ ( produc2717590391345394939list_o @ Xs2 @ Ys ) @ ( listrel_VEBT_VEBT_o @ R3 ) )
% 8.64/4.80 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.64/4.80 = ( size_size_list_o @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3501_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_VEBT_VEBT,Ys: list_nat,R3: set_Pr7556676689462069481BT_nat] :
% 8.64/4.80 ( ( member6193324644334088288st_nat @ ( produc5570133714943300547st_nat @ Xs2 @ Ys ) @ ( listre5900670229112895443BT_nat @ R3 ) )
% 8.64/4.80 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.64/4.80 = ( size_size_list_nat @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3502_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_VEBT_VEBT,Ys: list_int,R3: set_Pr5066593544530342725BT_int] :
% 8.64/4.80 ( ( member3703241499402361532st_int @ ( produc1392282695434103839st_int @ Xs2 @ Ys ) @ ( listre5898179758603845167BT_int @ R3 ) )
% 8.64/4.80 => ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 8.64/4.80 = ( size_size_list_int @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3503_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_o,Ys: list_VEBT_VEBT,R3: set_Pr7543698050874017315T_VEBT] :
% 8.64/4.80 ( ( member1087064965665443052T_VEBT @ ( produc6043759678074843571T_VEBT @ Xs2 @ Ys ) @ ( listrel_o_VEBT_VEBT @ R3 ) )
% 8.64/4.80 => ( ( size_size_list_o @ Xs2 )
% 8.64/4.80 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3504_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_o,Ys: list_o,R3: set_Product_prod_o_o] :
% 8.64/4.80 ( ( member4159035015898711888list_o @ ( produc8435520187683070743list_o @ Xs2 @ Ys ) @ ( listrel_o_o @ R3 ) )
% 8.64/4.80 => ( ( size_size_list_o @ Xs2 )
% 8.64/4.80 = ( size_size_list_o @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3505_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_o,Ys: list_nat,R3: set_Pr2101469702781467981_o_nat] :
% 8.64/4.80 ( ( member1519744053835550788st_nat @ ( produc7128876500814652583st_nat @ Xs2 @ Ys ) @ ( listrel_o_nat @ R3 ) )
% 8.64/4.80 => ( ( size_size_list_o @ Xs2 )
% 8.64/4.80 = ( size_size_list_nat @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3506_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_o,Ys: list_int,R3: set_Pr8834758594704517033_o_int] :
% 8.64/4.80 ( ( member8253032945758599840st_int @ ( produc2951025481305455875st_int @ Xs2 @ Ys ) @ ( listrel_o_int @ R3 ) )
% 8.64/4.80 => ( ( size_size_list_o @ Xs2 )
% 8.64/4.80 = ( size_size_list_int @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3507_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_nat,Ys: list_VEBT_VEBT,R3: set_Pr6167073792073659919T_VEBT] :
% 8.64/4.80 ( ( member5968030670617646438T_VEBT @ ( produc8335345208264861441T_VEBT @ Xs2 @ Ys ) @ ( listre5761932458788874033T_VEBT @ R3 ) )
% 8.64/4.80 => ( ( size_size_list_nat @ Xs2 )
% 8.64/4.80 = ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3508_listrel__eq__len,axiom,
% 8.64/4.80 ! [Xs2: list_nat,Ys: list_o,R3: set_Pr3149072824959771635_nat_o] :
% 8.64/4.80 ( ( member6688923169008879818list_o @ ( produc699922362453767013list_o @ Xs2 @ Ys ) @ ( listrel_nat_o @ R3 ) )
% 8.64/4.80 => ( ( size_size_list_nat @ Xs2 )
% 8.64/4.80 = ( size_size_list_o @ Ys ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3509_ex__less__of__nat__mult,axiom,
% 8.64/4.80 ! [X: rat,Y: rat] :
% 8.64/4.80 ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.64/4.80 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3510_ex__less__of__nat__mult,axiom,
% 8.64/4.80 ! [X: real,Y: real] :
% 8.64/4.80 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.80 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3511_of__nat__diff,axiom,
% 8.64/4.80 ! [N: nat,M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.80 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.80 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3512_of__nat__diff,axiom,
% 8.64/4.80 ! [N: nat,M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.80 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.80 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3513_of__nat__diff,axiom,
% 8.64/4.80 ! [N: nat,M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.80 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.80 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3514_of__nat__diff,axiom,
% 8.64/4.80 ! [N: nat,M2: nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.80 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.80 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3515_zdiff__int__split,axiom,
% 8.64/4.80 ! [P2: int > $o,X: nat,Y: nat] :
% 8.64/4.80 ( ( P2 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 8.64/4.80 = ( ( ( ord_less_eq_nat @ Y @ X )
% 8.64/4.80 => ( P2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 8.64/4.80 & ( ( ord_less_nat @ X @ Y )
% 8.64/4.80 => ( P2 @ zero_zero_int ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3516_num_Osize_I5_J,axiom,
% 8.64/4.80 ! [X2: num] :
% 8.64/4.80 ( ( size_size_num @ ( bit0 @ X2 ) )
% 8.64/4.80 = ( plus_plus_nat @ ( size_size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3517_realpow__pos__nth2,axiom,
% 8.64/4.80 ! [A: real,N: nat] :
% 8.64/4.80 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.80 => ? [R4: real] :
% 8.64/4.80 ( ( ord_less_real @ zero_zero_real @ R4 )
% 8.64/4.80 & ( ( power_power_real @ R4 @ ( suc @ N ) )
% 8.64/4.80 = A ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3518_listrel__Cons2,axiom,
% 8.64/4.80 ! [Xs2: list_Code_integer,Y: code_integer,Ys: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 8.64/4.80 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ ( cons_Code_integer @ Y @ Ys ) ) @ ( listre5734910445319291053nteger @ R3 ) )
% 8.64/4.80 => ~ ! [X3: code_integer,Xs3: list_Code_integer] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_Code_integer @ X3 @ Xs3 ) )
% 8.64/4.80 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X3 @ Y ) @ R3 )
% 8.64/4.80 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs3 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3519_listrel__Cons2,axiom,
% 8.64/4.80 ! [Xs2: list_P6011104703257516679at_nat,Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 8.64/4.80 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( listre818007680106770737at_nat @ R3 ) )
% 8.64/4.80 => ~ ! [X3: product_prod_nat_nat,Xs3: list_P6011104703257516679at_nat] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_P6512896166579812791at_nat @ X3 @ Xs3 ) )
% 8.64/4.80 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y ) @ R3 )
% 8.64/4.80 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs3 @ Ys ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3520_listrel__Cons2,axiom,
% 8.64/4.80 ! [Xs2: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 8.64/4.80 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 8.64/4.80 => ~ ! [X3: set_Pr1261947904930325089at_nat,Xs3: list_s1210847774152347623at_nat] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_s6881495754146722583at_nat @ X3 @ Xs3 ) )
% 8.64/4.80 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X3 @ Y ) @ R3 )
% 8.64/4.80 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs3 @ Ys ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3521_listrel__Cons2,axiom,
% 8.64/4.80 ! [Xs2: list_nat,Y: nat,Ys: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 8.64/4.80 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R3 ) )
% 8.64/4.80 => ~ ! [X3: nat,Xs3: list_nat] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_nat @ X3 @ Xs3 ) )
% 8.64/4.80 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y ) @ R3 )
% 8.64/4.80 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs3 @ Ys ) @ ( listrel_nat_nat @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3522_listrel__Cons2,axiom,
% 8.64/4.80 ! [Xs2: list_int,Y: int,Ys: list_int,R3: set_Pr958786334691620121nt_int] :
% 8.64/4.80 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R3 ) )
% 8.64/4.80 => ~ ! [X3: int,Xs3: list_int] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_int @ X3 @ Xs3 ) )
% 8.64/4.80 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X3 @ Y ) @ R3 )
% 8.64/4.80 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs3 @ Ys ) @ ( listrel_int_int @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3523_listrel__Cons1,axiom,
% 8.64/4.80 ! [Y: code_integer,Ys: list_Code_integer,Xs2: list_Code_integer,R3: set_Pr4811707699266497531nteger] :
% 8.64/4.80 ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ Y @ Ys ) @ Xs2 ) @ ( listre5734910445319291053nteger @ R3 ) )
% 8.64/4.80 => ~ ! [Y3: code_integer,Ys5: list_Code_integer] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_Code_integer @ Y3 @ Ys5 ) )
% 8.64/4.80 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ Y @ Y3 ) @ R3 )
% 8.64/4.80 => ~ ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Ys @ Ys5 ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3524_listrel__Cons1,axiom,
% 8.64/4.80 ! [Y: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,Xs2: list_P6011104703257516679at_nat,R3: set_Pr8693737435421807431at_nat] :
% 8.64/4.80 ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) @ Xs2 ) @ ( listre818007680106770737at_nat @ R3 ) )
% 8.64/4.80 => ~ ! [Y3: product_prod_nat_nat,Ys5: list_P6011104703257516679at_nat] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_P6512896166579812791at_nat @ Y3 @ Ys5 ) )
% 8.64/4.80 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ Y @ Y3 ) @ R3 )
% 8.64/4.80 => ~ ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Ys @ Ys5 ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3525_listrel__Cons1,axiom,
% 8.64/4.80 ! [Y: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,Xs2: list_s1210847774152347623at_nat,R3: set_Pr4329608150637261639at_nat] :
% 8.64/4.80 ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) @ Xs2 ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 8.64/4.80 => ~ ! [Y3: set_Pr1261947904930325089at_nat,Ys5: list_s1210847774152347623at_nat] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_s6881495754146722583at_nat @ Y3 @ Ys5 ) )
% 8.64/4.80 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ Y @ Y3 ) @ R3 )
% 8.64/4.80 => ~ ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Ys @ Ys5 ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3526_listrel__Cons1,axiom,
% 8.64/4.80 ! [Y: nat,Ys: list_nat,Xs2: list_nat,R3: set_Pr1261947904930325089at_nat] :
% 8.64/4.80 ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ Y @ Ys ) @ Xs2 ) @ ( listrel_nat_nat @ R3 ) )
% 8.64/4.80 => ~ ! [Y3: nat,Ys5: list_nat] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_nat @ Y3 @ Ys5 ) )
% 8.64/4.80 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y @ Y3 ) @ R3 )
% 8.64/4.80 => ~ ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Ys @ Ys5 ) @ ( listrel_nat_nat @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3527_listrel__Cons1,axiom,
% 8.64/4.80 ! [Y: int,Ys: list_int,Xs2: list_int,R3: set_Pr958786334691620121nt_int] :
% 8.64/4.80 ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ Y @ Ys ) @ Xs2 ) @ ( listrel_int_int @ R3 ) )
% 8.64/4.80 => ~ ! [Y3: int,Ys5: list_int] :
% 8.64/4.80 ( ( Xs2
% 8.64/4.80 = ( cons_int @ Y3 @ Ys5 ) )
% 8.64/4.80 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ Y @ Y3 ) @ R3 )
% 8.64/4.80 => ~ ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Ys @ Ys5 ) @ ( listrel_int_int @ R3 ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3528_listrel_OCons,axiom,
% 8.64/4.80 ! [X: code_integer,Y: code_integer,R3: set_Pr4811707699266497531nteger,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 8.64/4.80 ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ R3 )
% 8.64/4.80 => ( ( member749217712838834276nteger @ ( produc750622340256944499nteger @ Xs2 @ Ys ) @ ( listre5734910445319291053nteger @ R3 ) )
% 8.64/4.80 => ( member749217712838834276nteger @ ( produc750622340256944499nteger @ ( cons_Code_integer @ X @ Xs2 ) @ ( cons_Code_integer @ Y @ Ys ) ) @ ( listre5734910445319291053nteger @ R3 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3529_listrel_OCons,axiom,
% 8.64/4.80 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,R3: set_Pr8693737435421807431at_nat,Xs2: list_P6011104703257516679at_nat,Ys: list_P6011104703257516679at_nat] :
% 8.64/4.80 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ R3 )
% 8.64/4.80 => ( ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ Xs2 @ Ys ) @ ( listre818007680106770737at_nat @ R3 ) )
% 8.64/4.80 => ( member6693912407220327184at_nat @ ( produc5943733680697469783at_nat @ ( cons_P6512896166579812791at_nat @ X @ Xs2 ) @ ( cons_P6512896166579812791at_nat @ Y @ Ys ) ) @ ( listre818007680106770737at_nat @ R3 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3530_listrel_OCons,axiom,
% 8.64/4.80 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,R3: set_Pr4329608150637261639at_nat,Xs2: list_s1210847774152347623at_nat,Ys: list_s1210847774152347623at_nat] :
% 8.64/4.80 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ R3 )
% 8.64/4.80 => ( ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ Xs2 @ Ys ) @ ( listre2047417242196832561at_nat @ R3 ) )
% 8.64/4.80 => ( member4080735728053443344at_nat @ ( produc7536900900485677911at_nat @ ( cons_s6881495754146722583at_nat @ X @ Xs2 ) @ ( cons_s6881495754146722583at_nat @ Y @ Ys ) ) @ ( listre2047417242196832561at_nat @ R3 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3531_listrel_OCons,axiom,
% 8.64/4.80 ! [X: nat,Y: nat,R3: set_Pr1261947904930325089at_nat,Xs2: list_nat,Ys: list_nat] :
% 8.64/4.80 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R3 )
% 8.64/4.80 => ( ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ Xs2 @ Ys ) @ ( listrel_nat_nat @ R3 ) )
% 8.64/4.80 => ( member7340969449405702474st_nat @ ( produc2694037385005941721st_nat @ ( cons_nat @ X @ Xs2 ) @ ( cons_nat @ Y @ Ys ) ) @ ( listrel_nat_nat @ R3 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3532_listrel_OCons,axiom,
% 8.64/4.80 ! [X: int,Y: int,R3: set_Pr958786334691620121nt_int,Xs2: list_int,Ys: list_int] :
% 8.64/4.80 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ R3 )
% 8.64/4.80 => ( ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ Xs2 @ Ys ) @ ( listrel_int_int @ R3 ) )
% 8.64/4.80 => ( member6698963635872716290st_int @ ( produc364263696895485585st_int @ ( cons_int @ X @ Xs2 ) @ ( cons_int @ Y @ Ys ) ) @ ( listrel_int_int @ R3 ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3533_measures__less,axiom,
% 8.64/4.80 ! [F2: code_integer > nat,X: code_integer,Y: code_integer,Fs: list_C4705013386053401436er_nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.80 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3534_measures__less,axiom,
% 8.64/4.80 ! [F2: product_prod_nat_nat > nat,X: product_prod_nat_nat,Y: product_prod_nat_nat,Fs: list_P9162950289778280392at_nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.80 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3535_measures__less,axiom,
% 8.64/4.80 ! [F2: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Fs: list_s9130966667114977576at_nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.80 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3536_measures__less,axiom,
% 8.64/4.80 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.80 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3537_measures__less,axiom,
% 8.64/4.80 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 8.64/4.80 ( ( ord_less_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.80 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3538_measures__lesseq,axiom,
% 8.64/4.80 ! [F2: code_integer > nat,X: code_integer,Y: code_integer,Fs: list_C4705013386053401436er_nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.80 => ( ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ Fs ) )
% 8.64/4.80 => ( member157494554546826820nteger @ ( produc1086072967326762835nteger @ X @ Y ) @ ( measur8870801148506250077nteger @ ( cons_C1897838848541180310er_nat @ F2 @ Fs ) ) ) ) ) ).
% 8.64/4.80
% 8.64/4.80 thf(fact_3539_measures__lesseq,axiom,
% 8.64/4.80 ! [F2: product_prod_nat_nat > nat,X: product_prod_nat_nat,Y: product_prod_nat_nat,Fs: list_P9162950289778280392at_nat] :
% 8.64/4.80 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.80 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ Fs ) )
% 8.64/4.81 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ ( measur2679027848233739777at_nat @ ( cons_P4861729644591583992at_nat @ F2 @ Fs ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3540_measures__lesseq,axiom,
% 8.64/4.81 ! [F2: set_Pr1261947904930325089at_nat > nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Fs: list_s9130966667114977576at_nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.81 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ Fs ) )
% 8.64/4.81 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X @ Y ) @ ( measur2694323259624372065at_nat @ ( cons_s2538900923071588440at_nat @ F2 @ Fs ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3541_measures__lesseq,axiom,
% 8.64/4.81 ! [F2: nat > nat,X: nat,Y: nat,Fs: list_nat_nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.81 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ Fs ) )
% 8.64/4.81 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measures_nat @ ( cons_nat_nat @ F2 @ Fs ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3542_measures__lesseq,axiom,
% 8.64/4.81 ! [F2: int > nat,X: int,Y: int,Fs: list_int_nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ ( F2 @ X ) @ ( F2 @ Y ) )
% 8.64/4.81 => ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ Fs ) )
% 8.64/4.81 => ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X @ Y ) @ ( measures_int @ ( cons_int_nat @ F2 @ Fs ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3543_set__replicate__Suc,axiom,
% 8.64/4.81 ! [N: nat,X: vEBT_VEBT] :
% 8.64/4.81 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 8.64/4.81 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3544_set__replicate__Suc,axiom,
% 8.64/4.81 ! [N: nat,X: nat] :
% 8.64/4.81 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 8.64/4.81 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3545_set__replicate__Suc,axiom,
% 8.64/4.81 ! [N: nat,X: int] :
% 8.64/4.81 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 8.64/4.81 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3546_set__replicate__Suc,axiom,
% 8.64/4.81 ! [N: nat,X: real] :
% 8.64/4.81 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 8.64/4.81 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3547_set__replicate__conv__if,axiom,
% 8.64/4.81 ! [N: nat,X: vEBT_VEBT] :
% 8.64/4.81 ( ( ( N = zero_zero_nat )
% 8.64/4.81 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.64/4.81 = bot_bo8194388402131092736T_VEBT ) )
% 8.64/4.81 & ( ( N != zero_zero_nat )
% 8.64/4.81 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 8.64/4.81 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3548_set__replicate__conv__if,axiom,
% 8.64/4.81 ! [N: nat,X: nat] :
% 8.64/4.81 ( ( ( N = zero_zero_nat )
% 8.64/4.81 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 8.64/4.81 = bot_bot_set_nat ) )
% 8.64/4.81 & ( ( N != zero_zero_nat )
% 8.64/4.81 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 8.64/4.81 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3549_set__replicate__conv__if,axiom,
% 8.64/4.81 ! [N: nat,X: int] :
% 8.64/4.81 ( ( ( N = zero_zero_nat )
% 8.64/4.81 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 8.64/4.81 = bot_bot_set_int ) )
% 8.64/4.81 & ( ( N != zero_zero_nat )
% 8.64/4.81 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 8.64/4.81 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3550_set__replicate__conv__if,axiom,
% 8.64/4.81 ! [N: nat,X: real] :
% 8.64/4.81 ( ( ( N = zero_zero_nat )
% 8.64/4.81 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 8.64/4.81 = bot_bot_set_real ) )
% 8.64/4.81 & ( ( N != zero_zero_nat )
% 8.64/4.81 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 8.64/4.81 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3551_Cons__replicate__eq,axiom,
% 8.64/4.81 ! [X: nat,Xs2: list_nat,N: nat,Y: nat] :
% 8.64/4.81 ( ( ( cons_nat @ X @ Xs2 )
% 8.64/4.81 = ( replicate_nat @ N @ Y ) )
% 8.64/4.81 = ( ( X = Y )
% 8.64/4.81 & ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.81 & ( Xs2
% 8.64/4.81 = ( replicate_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ X ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3552_Cons__replicate__eq,axiom,
% 8.64/4.81 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 8.64/4.81 ( ( ( cons_VEBT_VEBT @ X @ Xs2 )
% 8.64/4.81 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 8.64/4.81 = ( ( X = Y )
% 8.64/4.81 & ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.81 & ( Xs2
% 8.64/4.81 = ( replicate_VEBT_VEBT @ ( minus_minus_nat @ N @ one_one_nat ) @ X ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3553_divmod__step__eq,axiom,
% 8.64/4.81 ! [L: num,R3: nat,Q2: nat] :
% 8.64/4.81 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 8.64/4.81 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 8.64/4.81 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 8.64/4.81 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 8.64/4.81 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q2 @ R3 ) )
% 8.64/4.81 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3554_divmod__step__eq,axiom,
% 8.64/4.81 ! [L: num,R3: int,Q2: int] :
% 8.64/4.81 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 8.64/4.81 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.81 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 8.64/4.81 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 8.64/4.81 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.81 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3555_divmod__step__eq,axiom,
% 8.64/4.81 ! [L: num,R3: code_integer,Q2: code_integer] :
% 8.64/4.81 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 8.64/4.81 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 8.64/4.81 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 8.64/4.81 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 8.64/4.81 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q2 @ R3 ) )
% 8.64/4.81 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3556_mintlistlength,axiom,
% 8.64/4.81 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.64/4.81 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.64/4.81 => ( ( Mi != Ma )
% 8.64/4.81 => ( ( ord_less_nat @ Mi @ Ma )
% 8.64/4.81 & ? [M: nat] :
% 8.64/4.81 ( ( ( some_nat @ M )
% 8.64/4.81 = ( vEBT_vebt_mint @ Summary ) )
% 8.64/4.81 & ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3557_insert__correct,axiom,
% 8.64/4.81 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.64/4.81 ( ( vEBT_invar_vebt @ T @ N )
% 8.64/4.81 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.81 => ( ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 8.64/4.81 = ( vEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3558_insert__corr,axiom,
% 8.64/4.81 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.64/4.81 ( ( vEBT_invar_vebt @ T @ N )
% 8.64/4.81 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.81 => ( ( sup_sup_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 8.64/4.81 = ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_insert @ T @ X ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3559_inrange,axiom,
% 8.64/4.81 ! [T: vEBT_VEBT,N: nat] :
% 8.64/4.81 ( ( vEBT_invar_vebt @ T @ N )
% 8.64/4.81 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3560_nat__bit__induct,axiom,
% 8.64/4.81 ! [P2: nat > $o,N: nat] :
% 8.64/4.81 ( ( P2 @ zero_zero_nat )
% 8.64/4.81 => ( ! [N3: nat] :
% 8.64/4.81 ( ( P2 @ N3 )
% 8.64/4.81 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.64/4.81 => ( P2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 8.64/4.81 => ( ! [N3: nat] :
% 8.64/4.81 ( ( P2 @ N3 )
% 8.64/4.81 => ( P2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 8.64/4.81 => ( P2 @ N ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3561_nat__induct2,axiom,
% 8.64/4.81 ! [P2: nat > $o,N: nat] :
% 8.64/4.81 ( ( P2 @ zero_zero_nat )
% 8.64/4.81 => ( ( P2 @ one_one_nat )
% 8.64/4.81 => ( ! [N3: nat] :
% 8.64/4.81 ( ( P2 @ N3 )
% 8.64/4.81 => ( P2 @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.81 => ( P2 @ N ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3562_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 8.64/4.81 ! [N: nat,M2: nat] :
% 8.64/4.81 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.81 != zero_zero_nat )
% 8.64/4.81 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 8.64/4.81 != zero_zero_nat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3563_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 8.64/4.81 ! [N: nat,M2: nat] :
% 8.64/4.81 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.64/4.81 != zero_zero_int )
% 8.64/4.81 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) )
% 8.64/4.81 != zero_zero_int ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3564_exp__add__not__zero__imp__left,axiom,
% 8.64/4.81 ! [M2: nat,N: nat] :
% 8.64/4.81 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.81 != zero_zero_nat )
% 8.64/4.81 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 8.64/4.81 != zero_zero_nat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3565_exp__add__not__zero__imp__left,axiom,
% 8.64/4.81 ! [M2: nat,N: nat] :
% 8.64/4.81 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.81 != zero_zero_int )
% 8.64/4.81 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 8.64/4.81 != zero_zero_int ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3566_pow__sum,axiom,
% 8.64/4.81 ! [A: nat,B: nat] :
% 8.64/4.81 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 8.64/4.81 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3567_power__minus__is__div,axiom,
% 8.64/4.81 ! [B: nat,A: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.81 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 8.64/4.81 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3568_bits__div__by__0,axiom,
% 8.64/4.81 ! [A: nat] :
% 8.64/4.81 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 8.64/4.81 = zero_zero_nat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3569_bits__div__by__0,axiom,
% 8.64/4.81 ! [A: int] :
% 8.64/4.81 ( ( divide_divide_int @ A @ zero_zero_int )
% 8.64/4.81 = zero_zero_int ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3570_bits__div__0,axiom,
% 8.64/4.81 ! [A: nat] :
% 8.64/4.81 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 8.64/4.81 = zero_zero_nat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3571_bits__div__0,axiom,
% 8.64/4.81 ! [A: int] :
% 8.64/4.81 ( ( divide_divide_int @ zero_zero_int @ A )
% 8.64/4.81 = zero_zero_int ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3572_div__by__0,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 8.64/4.81 = zero_zero_complex ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3573_div__by__0,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( divide_divide_real @ A @ zero_zero_real )
% 8.64/4.81 = zero_zero_real ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3574_div__by__0,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 8.64/4.81 = zero_zero_rat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3575_div__by__0,axiom,
% 8.64/4.81 ! [A: nat] :
% 8.64/4.81 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 8.64/4.81 = zero_zero_nat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3576_div__by__0,axiom,
% 8.64/4.81 ! [A: int] :
% 8.64/4.81 ( ( divide_divide_int @ A @ zero_zero_int )
% 8.64/4.81 = zero_zero_int ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3577_div__0,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 8.64/4.81 = zero_zero_complex ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3578_div__0,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( divide_divide_real @ zero_zero_real @ A )
% 8.64/4.81 = zero_zero_real ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3579_div__0,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 8.64/4.81 = zero_zero_rat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3580_div__0,axiom,
% 8.64/4.81 ! [A: nat] :
% 8.64/4.81 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 8.64/4.81 = zero_zero_nat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3581_div__0,axiom,
% 8.64/4.81 ! [A: int] :
% 8.64/4.81 ( ( divide_divide_int @ zero_zero_int @ A )
% 8.64/4.81 = zero_zero_int ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3582_division__ring__divide__zero,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 8.64/4.81 = zero_zero_complex ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3583_division__ring__divide__zero,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( divide_divide_real @ A @ zero_zero_real )
% 8.64/4.81 = zero_zero_real ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3584_division__ring__divide__zero,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 8.64/4.81 = zero_zero_rat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3585_divide__cancel__right,axiom,
% 8.64/4.81 ! [A: complex,C2: complex,B: complex] :
% 8.64/4.81 ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 8.64/4.81 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.81 = ( ( C2 = zero_zero_complex )
% 8.64/4.81 | ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3586_divide__cancel__right,axiom,
% 8.64/4.81 ! [A: real,C2: real,B: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ A @ C2 )
% 8.64/4.81 = ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( C2 = zero_zero_real )
% 8.64/4.81 | ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3587_divide__cancel__right,axiom,
% 8.64/4.81 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ A @ C2 )
% 8.64/4.81 = ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( C2 = zero_zero_rat )
% 8.64/4.81 | ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3588_divide__cancel__left,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( ( divide1717551699836669952omplex @ C2 @ A )
% 8.64/4.81 = ( divide1717551699836669952omplex @ C2 @ B ) )
% 8.64/4.81 = ( ( C2 = zero_zero_complex )
% 8.64/4.81 | ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3589_divide__cancel__left,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ C2 @ A )
% 8.64/4.81 = ( divide_divide_real @ C2 @ B ) )
% 8.64/4.81 = ( ( C2 = zero_zero_real )
% 8.64/4.81 | ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3590_divide__cancel__left,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ C2 @ A )
% 8.64/4.81 = ( divide_divide_rat @ C2 @ B ) )
% 8.64/4.81 = ( ( C2 = zero_zero_rat )
% 8.64/4.81 | ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3591_divide__eq__0__iff,axiom,
% 8.64/4.81 ! [A: complex,B: complex] :
% 8.64/4.81 ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.64/4.81 = zero_zero_complex )
% 8.64/4.81 = ( ( A = zero_zero_complex )
% 8.64/4.81 | ( B = zero_zero_complex ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3592_divide__eq__0__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ A @ B )
% 8.64/4.81 = zero_zero_real )
% 8.64/4.81 = ( ( A = zero_zero_real )
% 8.64/4.81 | ( B = zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3593_divide__eq__0__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ A @ B )
% 8.64/4.81 = zero_zero_rat )
% 8.64/4.81 = ( ( A = zero_zero_rat )
% 8.64/4.81 | ( B = zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3594_times__divide__eq__right,axiom,
% 8.64/4.81 ! [A: complex,B: complex,C2: complex] :
% 8.64/4.81 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C2 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3595_times__divide__eq__right,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C2 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3596_times__divide__eq__right,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C2 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3597_divide__divide__eq__right,axiom,
% 8.64/4.81 ! [A: complex,B: complex,C2: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3598_divide__divide__eq__right,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3599_divide__divide__eq__right,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3600_divide__divide__eq__left,axiom,
% 8.64/4.81 ! [A: complex,B: complex,C2: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C2 )
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3601_divide__divide__eq__left,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C2 )
% 8.64/4.81 = ( divide_divide_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3602_divide__divide__eq__left,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C2 )
% 8.64/4.81 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3603_times__divide__eq__left,axiom,
% 8.64/4.81 ! [B: complex,C2: complex,A: complex] :
% 8.64/4.81 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C2 ) @ A )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C2 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3604_times__divide__eq__left,axiom,
% 8.64/4.81 ! [B: real,C2: real,A: real] :
% 8.64/4.81 ( ( times_times_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 8.64/4.81 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C2 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3605_times__divide__eq__left,axiom,
% 8.64/4.81 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.81 ( ( times_times_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 8.64/4.81 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C2 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3606_div__by__1,axiom,
% 8.64/4.81 ! [A: code_integer] :
% 8.64/4.81 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3607_div__by__1,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3608_div__by__1,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( divide_divide_real @ A @ one_one_real )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3609_div__by__1,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ A @ one_one_rat )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3610_div__by__1,axiom,
% 8.64/4.81 ! [A: nat] :
% 8.64/4.81 ( ( divide_divide_nat @ A @ one_one_nat )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3611_div__by__1,axiom,
% 8.64/4.81 ! [A: int] :
% 8.64/4.81 ( ( divide_divide_int @ A @ one_one_int )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3612_atLeastAtMost__iff,axiom,
% 8.64/4.81 ! [I2: set_nat,L: set_nat,U: set_nat] :
% 8.64/4.81 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 8.64/4.81 = ( ( ord_less_eq_set_nat @ L @ I2 )
% 8.64/4.81 & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3613_atLeastAtMost__iff,axiom,
% 8.64/4.81 ! [I2: rat,L: rat,U: rat] :
% 8.64/4.81 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 8.64/4.81 = ( ( ord_less_eq_rat @ L @ I2 )
% 8.64/4.81 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3614_atLeastAtMost__iff,axiom,
% 8.64/4.81 ! [I2: num,L: num,U: num] :
% 8.64/4.81 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 8.64/4.81 = ( ( ord_less_eq_num @ L @ I2 )
% 8.64/4.81 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3615_atLeastAtMost__iff,axiom,
% 8.64/4.81 ! [I2: nat,L: nat,U: nat] :
% 8.64/4.81 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 8.64/4.81 = ( ( ord_less_eq_nat @ L @ I2 )
% 8.64/4.81 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3616_atLeastAtMost__iff,axiom,
% 8.64/4.81 ! [I2: int,L: int,U: int] :
% 8.64/4.81 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 8.64/4.81 = ( ( ord_less_eq_int @ L @ I2 )
% 8.64/4.81 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3617_atLeastAtMost__iff,axiom,
% 8.64/4.81 ! [I2: real,L: real,U: real] :
% 8.64/4.81 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L @ U ) )
% 8.64/4.81 = ( ( ord_less_eq_real @ L @ I2 )
% 8.64/4.81 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3618_Icc__eq__Icc,axiom,
% 8.64/4.81 ! [L: set_nat,H: set_nat,L3: set_nat,H3: set_nat] :
% 8.64/4.81 ( ( ( set_or4548717258645045905et_nat @ L @ H )
% 8.64/4.81 = ( set_or4548717258645045905et_nat @ L3 @ H3 ) )
% 8.64/4.81 = ( ( ( L = L3 )
% 8.64/4.81 & ( H = H3 ) )
% 8.64/4.81 | ( ~ ( ord_less_eq_set_nat @ L @ H )
% 8.64/4.81 & ~ ( ord_less_eq_set_nat @ L3 @ H3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3619_Icc__eq__Icc,axiom,
% 8.64/4.81 ! [L: rat,H: rat,L3: rat,H3: rat] :
% 8.64/4.81 ( ( ( set_or633870826150836451st_rat @ L @ H )
% 8.64/4.81 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 8.64/4.81 = ( ( ( L = L3 )
% 8.64/4.81 & ( H = H3 ) )
% 8.64/4.81 | ( ~ ( ord_less_eq_rat @ L @ H )
% 8.64/4.81 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3620_Icc__eq__Icc,axiom,
% 8.64/4.81 ! [L: num,H: num,L3: num,H3: num] :
% 8.64/4.81 ( ( ( set_or7049704709247886629st_num @ L @ H )
% 8.64/4.81 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 8.64/4.81 = ( ( ( L = L3 )
% 8.64/4.81 & ( H = H3 ) )
% 8.64/4.81 | ( ~ ( ord_less_eq_num @ L @ H )
% 8.64/4.81 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3621_Icc__eq__Icc,axiom,
% 8.64/4.81 ! [L: nat,H: nat,L3: nat,H3: nat] :
% 8.64/4.81 ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 8.64/4.81 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 8.64/4.81 = ( ( ( L = L3 )
% 8.64/4.81 & ( H = H3 ) )
% 8.64/4.81 | ( ~ ( ord_less_eq_nat @ L @ H )
% 8.64/4.81 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3622_Icc__eq__Icc,axiom,
% 8.64/4.81 ! [L: int,H: int,L3: int,H3: int] :
% 8.64/4.81 ( ( ( set_or1266510415728281911st_int @ L @ H )
% 8.64/4.81 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 8.64/4.81 = ( ( ( L = L3 )
% 8.64/4.81 & ( H = H3 ) )
% 8.64/4.81 | ( ~ ( ord_less_eq_int @ L @ H )
% 8.64/4.81 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3623_Icc__eq__Icc,axiom,
% 8.64/4.81 ! [L: real,H: real,L3: real,H3: real] :
% 8.64/4.81 ( ( ( set_or1222579329274155063t_real @ L @ H )
% 8.64/4.81 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 8.64/4.81 = ( ( ( L = L3 )
% 8.64/4.81 & ( H = H3 ) )
% 8.64/4.81 | ( ~ ( ord_less_eq_real @ L @ H )
% 8.64/4.81 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3624_finite__atLeastAtMost,axiom,
% 8.64/4.81 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3625_nonzero__mult__div__cancel__left,axiom,
% 8.64/4.81 ! [A: complex,B: complex] :
% 8.64/4.81 ( ( A != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 8.64/4.81 = B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3626_nonzero__mult__div__cancel__left,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( A != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 8.64/4.81 = B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3627_nonzero__mult__div__cancel__left,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( A != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 8.64/4.81 = B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3628_nonzero__mult__div__cancel__left,axiom,
% 8.64/4.81 ! [A: nat,B: nat] :
% 8.64/4.81 ( ( A != zero_zero_nat )
% 8.64/4.81 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 8.64/4.81 = B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3629_nonzero__mult__div__cancel__left,axiom,
% 8.64/4.81 ! [A: int,B: int] :
% 8.64/4.81 ( ( A != zero_zero_int )
% 8.64/4.81 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 8.64/4.81 = B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3630_nonzero__mult__div__cancel__right,axiom,
% 8.64/4.81 ! [B: complex,A: complex] :
% 8.64/4.81 ( ( B != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 8.64/4.81 = A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3631_nonzero__mult__div__cancel__right,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( B != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 8.64/4.81 = A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3632_nonzero__mult__div__cancel__right,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( B != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 8.64/4.81 = A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3633_nonzero__mult__div__cancel__right,axiom,
% 8.64/4.81 ! [B: nat,A: nat] :
% 8.64/4.81 ( ( B != zero_zero_nat )
% 8.64/4.81 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 8.64/4.81 = A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3634_nonzero__mult__div__cancel__right,axiom,
% 8.64/4.81 ! [B: int,A: int] :
% 8.64/4.81 ( ( B != zero_zero_int )
% 8.64/4.81 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 8.64/4.81 = A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3635_mult__divide__mult__cancel__left__if,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( ( C2 = zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 8.64/4.81 = zero_zero_complex ) )
% 8.64/4.81 & ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3636_mult__divide__mult__cancel__left__if,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( ( C2 = zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.64/4.81 = zero_zero_real ) )
% 8.64/4.81 & ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.64/4.81 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3637_mult__divide__mult__cancel__left__if,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ( C2 = zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.64/4.81 = zero_zero_rat ) )
% 8.64/4.81 & ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.64/4.81 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3638_nonzero__mult__divide__mult__cancel__left,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3639_nonzero__mult__divide__mult__cancel__left,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.64/4.81 = ( divide_divide_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3640_nonzero__mult__divide__mult__cancel__left,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.64/4.81 = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3641_nonzero__mult__divide__mult__cancel__left2,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ B @ C2 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3642_nonzero__mult__divide__mult__cancel__left2,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3643_nonzero__mult__divide__mult__cancel__left2,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3644_nonzero__mult__divide__mult__cancel__right,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ B @ C2 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3645_nonzero__mult__divide__mult__cancel__right,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3646_nonzero__mult__divide__mult__cancel__right,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3647_nonzero__mult__divide__mult__cancel__right2,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ C2 @ B ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3648_nonzero__mult__divide__mult__cancel__right2,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ C2 @ B ) )
% 8.64/4.81 = ( divide_divide_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3649_nonzero__mult__divide__mult__cancel__right2,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ C2 @ B ) )
% 8.64/4.81 = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3650_div__self,axiom,
% 8.64/4.81 ! [A: code_integer] :
% 8.64/4.81 ( ( A != zero_z3403309356797280102nteger )
% 8.64/4.81 => ( ( divide6298287555418463151nteger @ A @ A )
% 8.64/4.81 = one_one_Code_integer ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3651_div__self,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( A != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ A @ A )
% 8.64/4.81 = one_one_complex ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3652_div__self,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( A != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ A @ A )
% 8.64/4.81 = one_one_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3653_div__self,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( A != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ A @ A )
% 8.64/4.81 = one_one_rat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3654_div__self,axiom,
% 8.64/4.81 ! [A: nat] :
% 8.64/4.81 ( ( A != zero_zero_nat )
% 8.64/4.81 => ( ( divide_divide_nat @ A @ A )
% 8.64/4.81 = one_one_nat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3655_div__self,axiom,
% 8.64/4.81 ! [A: int] :
% 8.64/4.81 ( ( A != zero_zero_int )
% 8.64/4.81 => ( ( divide_divide_int @ A @ A )
% 8.64/4.81 = one_one_int ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3656_zero__eq__1__divide__iff,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( zero_zero_real
% 8.64/4.81 = ( divide_divide_real @ one_one_real @ A ) )
% 8.64/4.81 = ( A = zero_zero_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3657_zero__eq__1__divide__iff,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( zero_zero_rat
% 8.64/4.81 = ( divide_divide_rat @ one_one_rat @ A ) )
% 8.64/4.81 = ( A = zero_zero_rat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3658_one__divide__eq__0__iff,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ one_one_real @ A )
% 8.64/4.81 = zero_zero_real )
% 8.64/4.81 = ( A = zero_zero_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3659_one__divide__eq__0__iff,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 8.64/4.81 = zero_zero_rat )
% 8.64/4.81 = ( A = zero_zero_rat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3660_eq__divide__eq__1,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( one_one_real
% 8.64/4.81 = ( divide_divide_real @ B @ A ) )
% 8.64/4.81 = ( ( A != zero_zero_real )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3661_eq__divide__eq__1,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( one_one_rat
% 8.64/4.81 = ( divide_divide_rat @ B @ A ) )
% 8.64/4.81 = ( ( A != zero_zero_rat )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3662_divide__eq__eq__1,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ B @ A )
% 8.64/4.81 = one_one_real )
% 8.64/4.81 = ( ( A != zero_zero_real )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3663_divide__eq__eq__1,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ B @ A )
% 8.64/4.81 = one_one_rat )
% 8.64/4.81 = ( ( A != zero_zero_rat )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3664_divide__self__if,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( ( A = zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ A @ A )
% 8.64/4.81 = zero_zero_complex ) )
% 8.64/4.81 & ( ( A != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ A @ A )
% 8.64/4.81 = one_one_complex ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3665_divide__self__if,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( ( A = zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ A @ A )
% 8.64/4.81 = zero_zero_real ) )
% 8.64/4.81 & ( ( A != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ A @ A )
% 8.64/4.81 = one_one_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3666_divide__self__if,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( ( A = zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ A @ A )
% 8.64/4.81 = zero_zero_rat ) )
% 8.64/4.81 & ( ( A != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ A @ A )
% 8.64/4.81 = one_one_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3667_divide__self,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( A != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ A @ A )
% 8.64/4.81 = one_one_complex ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3668_divide__self,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( A != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ A @ A )
% 8.64/4.81 = one_one_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3669_divide__self,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( A != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ A @ A )
% 8.64/4.81 = one_one_rat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3670_one__eq__divide__iff,axiom,
% 8.64/4.81 ! [A: complex,B: complex] :
% 8.64/4.81 ( ( one_one_complex
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ B ) )
% 8.64/4.81 = ( ( B != zero_zero_complex )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3671_one__eq__divide__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( one_one_real
% 8.64/4.81 = ( divide_divide_real @ A @ B ) )
% 8.64/4.81 = ( ( B != zero_zero_real )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3672_one__eq__divide__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( one_one_rat
% 8.64/4.81 = ( divide_divide_rat @ A @ B ) )
% 8.64/4.81 = ( ( B != zero_zero_rat )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3673_divide__eq__1__iff,axiom,
% 8.64/4.81 ! [A: complex,B: complex] :
% 8.64/4.81 ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.64/4.81 = one_one_complex )
% 8.64/4.81 = ( ( B != zero_zero_complex )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3674_divide__eq__1__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ A @ B )
% 8.64/4.81 = one_one_real )
% 8.64/4.81 = ( ( B != zero_zero_real )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3675_divide__eq__1__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ A @ B )
% 8.64/4.81 = one_one_rat )
% 8.64/4.81 = ( ( B != zero_zero_rat )
% 8.64/4.81 & ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3676_atLeastatMost__empty__iff,axiom,
% 8.64/4.81 ! [A: set_nat,B: set_nat] :
% 8.64/4.81 ( ( ( set_or4548717258645045905et_nat @ A @ B )
% 8.64/4.81 = bot_bot_set_set_nat )
% 8.64/4.81 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3677_atLeastatMost__empty__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 8.64/4.81 = bot_bot_set_rat )
% 8.64/4.81 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3678_atLeastatMost__empty__iff,axiom,
% 8.64/4.81 ! [A: num,B: num] :
% 8.64/4.81 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 8.64/4.81 = bot_bot_set_num )
% 8.64/4.81 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3679_atLeastatMost__empty__iff,axiom,
% 8.64/4.81 ! [A: nat,B: nat] :
% 8.64/4.81 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.64/4.81 = bot_bot_set_nat )
% 8.64/4.81 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3680_atLeastatMost__empty__iff,axiom,
% 8.64/4.81 ! [A: int,B: int] :
% 8.64/4.81 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 8.64/4.81 = bot_bot_set_int )
% 8.64/4.81 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3681_atLeastatMost__empty__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 8.64/4.81 = bot_bot_set_real )
% 8.64/4.81 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3682_atLeastatMost__empty__iff2,axiom,
% 8.64/4.81 ! [A: set_nat,B: set_nat] :
% 8.64/4.81 ( ( bot_bot_set_set_nat
% 8.64/4.81 = ( set_or4548717258645045905et_nat @ A @ B ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_set_nat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3683_atLeastatMost__empty__iff2,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( bot_bot_set_rat
% 8.64/4.81 = ( set_or633870826150836451st_rat @ A @ B ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3684_atLeastatMost__empty__iff2,axiom,
% 8.64/4.81 ! [A: num,B: num] :
% 8.64/4.81 ( ( bot_bot_set_num
% 8.64/4.81 = ( set_or7049704709247886629st_num @ A @ B ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3685_atLeastatMost__empty__iff2,axiom,
% 8.64/4.81 ! [A: nat,B: nat] :
% 8.64/4.81 ( ( bot_bot_set_nat
% 8.64/4.81 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3686_atLeastatMost__empty__iff2,axiom,
% 8.64/4.81 ! [A: int,B: int] :
% 8.64/4.81 ( ( bot_bot_set_int
% 8.64/4.81 = ( set_or1266510415728281911st_int @ A @ B ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3687_atLeastatMost__empty__iff2,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( bot_bot_set_real
% 8.64/4.81 = ( set_or1222579329274155063t_real @ A @ B ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3688_atLeastatMost__subset__iff,axiom,
% 8.64/4.81 ! [A: set_nat,B: set_nat,C2: set_nat,D: set_nat] :
% 8.64/4.81 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C2 @ D ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_set_nat @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_set_nat @ B @ D ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3689_atLeastatMost__subset__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.64/4.81 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_rat @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3690_atLeastatMost__subset__iff,axiom,
% 8.64/4.81 ! [A: num,B: num,C2: num,D: num] :
% 8.64/4.81 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_num @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_num @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3691_atLeastatMost__subset__iff,axiom,
% 8.64/4.81 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.64/4.81 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_nat @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3692_atLeastatMost__subset__iff,axiom,
% 8.64/4.81 ! [A: int,B: int,C2: int,D: int] :
% 8.64/4.81 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_int @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3693_atLeastatMost__subset__iff,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real,D: real] :
% 8.64/4.81 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C2 @ D ) )
% 8.64/4.81 = ( ~ ( ord_less_eq_real @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_real @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3694_atLeastatMost__empty,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ B @ A )
% 8.64/4.81 => ( ( set_or633870826150836451st_rat @ A @ B )
% 8.64/4.81 = bot_bot_set_rat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3695_atLeastatMost__empty,axiom,
% 8.64/4.81 ! [B: num,A: num] :
% 8.64/4.81 ( ( ord_less_num @ B @ A )
% 8.64/4.81 => ( ( set_or7049704709247886629st_num @ A @ B )
% 8.64/4.81 = bot_bot_set_num ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3696_atLeastatMost__empty,axiom,
% 8.64/4.81 ! [B: nat,A: nat] :
% 8.64/4.81 ( ( ord_less_nat @ B @ A )
% 8.64/4.81 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.64/4.81 = bot_bot_set_nat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3697_atLeastatMost__empty,axiom,
% 8.64/4.81 ! [B: int,A: int] :
% 8.64/4.81 ( ( ord_less_int @ B @ A )
% 8.64/4.81 => ( ( set_or1266510415728281911st_int @ A @ B )
% 8.64/4.81 = bot_bot_set_int ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3698_atLeastatMost__empty,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ B @ A )
% 8.64/4.81 => ( ( set_or1222579329274155063t_real @ A @ B )
% 8.64/4.81 = bot_bot_set_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3699_infinite__Icc__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 8.64/4.81 = ( ord_less_rat @ A @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3700_infinite__Icc__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 8.64/4.81 = ( ord_less_real @ A @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3701_atLeastAtMost__singleton,axiom,
% 8.64/4.81 ! [A: nat] :
% 8.64/4.81 ( ( set_or1269000886237332187st_nat @ A @ A )
% 8.64/4.81 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3702_atLeastAtMost__singleton,axiom,
% 8.64/4.81 ! [A: int] :
% 8.64/4.81 ( ( set_or1266510415728281911st_int @ A @ A )
% 8.64/4.81 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3703_atLeastAtMost__singleton,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( set_or1222579329274155063t_real @ A @ A )
% 8.64/4.81 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3704_atLeastAtMost__singleton__iff,axiom,
% 8.64/4.81 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.81 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.64/4.81 = ( insert_nat @ C2 @ bot_bot_set_nat ) )
% 8.64/4.81 = ( ( A = B )
% 8.64/4.81 & ( B = C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3705_atLeastAtMost__singleton__iff,axiom,
% 8.64/4.81 ! [A: int,B: int,C2: int] :
% 8.64/4.81 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 8.64/4.81 = ( insert_int @ C2 @ bot_bot_set_int ) )
% 8.64/4.81 = ( ( A = B )
% 8.64/4.81 & ( B = C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3706_atLeastAtMost__singleton__iff,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 8.64/4.81 = ( insert_real @ C2 @ bot_bot_set_real ) )
% 8.64/4.81 = ( ( A = B )
% 8.64/4.81 & ( B = C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3707_nat__mult__div__cancel__disj,axiom,
% 8.64/4.81 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.81 ( ( ( K2 = zero_zero_nat )
% 8.64/4.81 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.64/4.81 = zero_zero_nat ) )
% 8.64/4.81 & ( ( K2 != zero_zero_nat )
% 8.64/4.81 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.64/4.81 = ( divide_divide_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3708_zero__le__divide__1__iff,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 8.64/4.81 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3709_zero__le__divide__1__iff,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 8.64/4.81 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3710_divide__le__0__1__iff,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 8.64/4.81 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3711_divide__le__0__1__iff,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 8.64/4.81 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3712_zero__less__divide__1__iff,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 8.64/4.81 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3713_zero__less__divide__1__iff,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 8.64/4.81 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3714_less__divide__eq__1__pos,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.64/4.81 = ( ord_less_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3715_less__divide__eq__1__pos,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.64/4.81 = ( ord_less_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3716_less__divide__eq__1__neg,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.64/4.81 = ( ord_less_real @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3717_less__divide__eq__1__neg,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.64/4.81 = ( ord_less_rat @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3718_divide__less__eq__1__pos,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.64/4.81 = ( ord_less_real @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3719_divide__less__eq__1__pos,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.64/4.81 = ( ord_less_rat @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3720_divide__less__eq__1__neg,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.64/4.81 = ( ord_less_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3721_divide__less__eq__1__neg,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.64/4.81 = ( ord_less_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3722_divide__less__0__1__iff,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 8.64/4.81 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3723_divide__less__0__1__iff,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 8.64/4.81 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3724_divide__le__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [B: real,W2: num,A: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 8.64/4.81 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3725_divide__le__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [B: rat,W2: num,A: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 8.64/4.81 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3726_le__divide__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [A: real,B: real,W2: num] :
% 8.64/4.81 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.81 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3727_le__divide__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [A: rat,B: rat,W2: num] :
% 8.64/4.81 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.81 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3728_divide__eq__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [B: complex,W2: num,A: complex] :
% 8.64/4.81 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.81 = A )
% 8.64/4.81 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 8.64/4.81 != zero_zero_complex )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 8.64/4.81 & ( ( ( numera6690914467698888265omplex @ W2 )
% 8.64/4.81 = zero_zero_complex )
% 8.64/4.81 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3729_divide__eq__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [B: real,W2: num,A: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.81 = A )
% 8.64/4.81 = ( ( ( ( numeral_numeral_real @ W2 )
% 8.64/4.81 != zero_zero_real )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) )
% 8.64/4.81 & ( ( ( numeral_numeral_real @ W2 )
% 8.64/4.81 = zero_zero_real )
% 8.64/4.81 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3730_divide__eq__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [B: rat,W2: num,A: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.81 = A )
% 8.64/4.81 = ( ( ( ( numeral_numeral_rat @ W2 )
% 8.64/4.81 != zero_zero_rat )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.64/4.81 & ( ( ( numeral_numeral_rat @ W2 )
% 8.64/4.81 = zero_zero_rat )
% 8.64/4.81 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3731_eq__divide__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [A: complex,B: complex,W2: num] :
% 8.64/4.81 ( ( A
% 8.64/4.81 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W2 ) ) )
% 8.64/4.81 = ( ( ( ( numera6690914467698888265omplex @ W2 )
% 8.64/4.81 != zero_zero_complex )
% 8.64/4.81 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( ( numera6690914467698888265omplex @ W2 )
% 8.64/4.81 = zero_zero_complex )
% 8.64/4.81 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3732_eq__divide__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [A: real,B: real,W2: num] :
% 8.64/4.81 ( ( A
% 8.64/4.81 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.81 = ( ( ( ( numeral_numeral_real @ W2 )
% 8.64/4.81 != zero_zero_real )
% 8.64/4.81 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( ( numeral_numeral_real @ W2 )
% 8.64/4.81 = zero_zero_real )
% 8.64/4.81 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3733_eq__divide__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [A: rat,B: rat,W2: num] :
% 8.64/4.81 ( ( A
% 8.64/4.81 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.81 = ( ( ( ( numeral_numeral_rat @ W2 )
% 8.64/4.81 != zero_zero_rat )
% 8.64/4.81 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( ( numeral_numeral_rat @ W2 )
% 8.64/4.81 = zero_zero_rat )
% 8.64/4.81 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3734_less__divide__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [A: real,B: real,W2: num] :
% 8.64/4.81 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.81 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3735_less__divide__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [A: rat,B: rat,W2: num] :
% 8.64/4.81 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.81 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3736_divide__less__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [B: real,W2: num,A: real] :
% 8.64/4.81 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W2 ) ) @ A )
% 8.64/4.81 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3737_divide__less__eq__numeral1_I1_J,axiom,
% 8.64/4.81 ! [B: rat,W2: num,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 8.64/4.81 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3738_nonzero__divide__mult__cancel__left,axiom,
% 8.64/4.81 ! [A: complex,B: complex] :
% 8.64/4.81 ( ( A != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3739_nonzero__divide__mult__cancel__left,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( A != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 8.64/4.81 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3740_nonzero__divide__mult__cancel__left,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( A != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 8.64/4.81 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3741_nonzero__divide__mult__cancel__right,axiom,
% 8.64/4.81 ! [B: complex,A: complex] :
% 8.64/4.81 ( ( B != zero_zero_complex )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3742_nonzero__divide__mult__cancel__right,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( B != zero_zero_real )
% 8.64/4.81 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 8.64/4.81 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3743_nonzero__divide__mult__cancel__right,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( B != zero_zero_rat )
% 8.64/4.81 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 8.64/4.81 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3744_numeral__le__real__of__nat__iff,axiom,
% 8.64/4.81 ! [N: num,M2: nat] :
% 8.64/4.81 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M2 ) )
% 8.64/4.81 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M2 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3745_card__atLeastAtMost,axiom,
% 8.64/4.81 ! [L: nat,U: nat] :
% 8.64/4.81 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 8.64/4.81 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3746_le__divide__eq__1__pos,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.64/4.81 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3747_le__divide__eq__1__pos,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.64/4.81 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3748_le__divide__eq__1__neg,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.64/4.81 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3749_le__divide__eq__1__neg,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.64/4.81 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3750_divide__le__eq__1__pos,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.64/4.81 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3751_divide__le__eq__1__pos,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.64/4.81 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3752_divide__le__eq__1__neg,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.64/4.81 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3753_divide__le__eq__1__neg,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.64/4.81 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3754_bits__1__div__2,axiom,
% 8.64/4.81 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.81 = zero_z3403309356797280102nteger ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3755_bits__1__div__2,axiom,
% 8.64/4.81 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.81 = zero_zero_nat ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3756_bits__1__div__2,axiom,
% 8.64/4.81 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.81 = zero_zero_int ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3757_decr__mult__lemma,axiom,
% 8.64/4.81 ! [D: int,P2: int > $o,K2: int] :
% 8.64/4.81 ( ( ord_less_int @ zero_zero_int @ D )
% 8.64/4.81 => ( ! [X3: int] :
% 8.64/4.81 ( ( P2 @ X3 )
% 8.64/4.81 => ( P2 @ ( minus_minus_int @ X3 @ D ) ) )
% 8.64/4.81 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 8.64/4.81 => ! [X5: int] :
% 8.64/4.81 ( ( P2 @ X5 )
% 8.64/4.81 => ( P2 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3758_minusinfinity,axiom,
% 8.64/4.81 ! [D: int,P1: int > $o,P2: int > $o] :
% 8.64/4.81 ( ( ord_less_int @ zero_zero_int @ D )
% 8.64/4.81 => ( ! [X3: int,K: int] :
% 8.64/4.81 ( ( P1 @ X3 )
% 8.64/4.81 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 8.64/4.81 => ( ? [Z5: int] :
% 8.64/4.81 ! [X3: int] :
% 8.64/4.81 ( ( ord_less_int @ X3 @ Z5 )
% 8.64/4.81 => ( ( P2 @ X3 )
% 8.64/4.81 = ( P1 @ X3 ) ) )
% 8.64/4.81 => ( ? [X_1: int] : ( P1 @ X_1 )
% 8.64/4.81 => ? [X_12: int] : ( P2 @ X_12 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3759_plusinfinity,axiom,
% 8.64/4.81 ! [D: int,P6: int > $o,P2: int > $o] :
% 8.64/4.81 ( ( ord_less_int @ zero_zero_int @ D )
% 8.64/4.81 => ( ! [X3: int,K: int] :
% 8.64/4.81 ( ( P6 @ X3 )
% 8.64/4.81 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 8.64/4.81 => ( ? [Z5: int] :
% 8.64/4.81 ! [X3: int] :
% 8.64/4.81 ( ( ord_less_int @ Z5 @ X3 )
% 8.64/4.81 => ( ( P2 @ X3 )
% 8.64/4.81 = ( P6 @ X3 ) ) )
% 8.64/4.81 => ( ? [X_1: int] : ( P6 @ X_1 )
% 8.64/4.81 => ? [X_12: int] : ( P2 @ X_12 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3760_times__int__code_I2_J,axiom,
% 8.64/4.81 ! [L: int] :
% 8.64/4.81 ( ( times_times_int @ zero_zero_int @ L )
% 8.64/4.81 = zero_zero_int ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3761_times__int__code_I1_J,axiom,
% 8.64/4.81 ! [K2: int] :
% 8.64/4.81 ( ( times_times_int @ K2 @ zero_zero_int )
% 8.64/4.81 = zero_zero_int ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3762_pos__zmult__eq__1__iff,axiom,
% 8.64/4.81 ! [M2: int,N: int] :
% 8.64/4.81 ( ( ord_less_int @ zero_zero_int @ M2 )
% 8.64/4.81 => ( ( ( times_times_int @ M2 @ N )
% 8.64/4.81 = one_one_int )
% 8.64/4.81 = ( ( M2 = one_one_int )
% 8.64/4.81 & ( N = one_one_int ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3763_zmult__zless__mono2,axiom,
% 8.64/4.81 ! [I2: int,J2: int,K2: int] :
% 8.64/4.81 ( ( ord_less_int @ I2 @ J2 )
% 8.64/4.81 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.81 => ( ord_less_int @ ( times_times_int @ K2 @ I2 ) @ ( times_times_int @ K2 @ J2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3764_unique__quotient__lemma__neg,axiom,
% 8.64/4.81 ! [B: int,Q4: int,R5: int,Q2: int,R3: int] :
% 8.64/4.81 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 8.64/4.81 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 8.64/4.81 => ( ( ord_less_int @ B @ R3 )
% 8.64/4.81 => ( ( ord_less_int @ B @ R5 )
% 8.64/4.81 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3765_unique__quotient__lemma,axiom,
% 8.64/4.81 ! [B: int,Q4: int,R5: int,Q2: int,R3: int] :
% 8.64/4.81 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R5 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 8.64/4.81 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 8.64/4.81 => ( ( ord_less_int @ R5 @ B )
% 8.64/4.81 => ( ( ord_less_int @ R3 @ B )
% 8.64/4.81 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3766_zdiv__mono2__neg__lemma,axiom,
% 8.64/4.81 ! [B: int,Q2: int,R3: int,B2: int,Q4: int,R5: int] :
% 8.64/4.81 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 )
% 8.64/4.81 = ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 8.64/4.81 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) @ zero_zero_int )
% 8.64/4.81 => ( ( ord_less_int @ R3 @ B )
% 8.64/4.81 => ( ( ord_less_eq_int @ zero_zero_int @ R5 )
% 8.64/4.81 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 8.64/4.81 => ( ( ord_less_eq_int @ B2 @ B )
% 8.64/4.81 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3767_zdiv__mono2__lemma,axiom,
% 8.64/4.81 ! [B: int,Q2: int,R3: int,B2: int,Q4: int,R5: int] :
% 8.64/4.81 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 )
% 8.64/4.81 = ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 8.64/4.81 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 8.64/4.81 => ( ( ord_less_int @ R5 @ B2 )
% 8.64/4.81 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 8.64/4.81 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 8.64/4.81 => ( ( ord_less_eq_int @ B2 @ B )
% 8.64/4.81 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3768_q__pos__lemma,axiom,
% 8.64/4.81 ! [B2: int,Q4: int,R5: int] :
% 8.64/4.81 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q4 ) @ R5 ) )
% 8.64/4.81 => ( ( ord_less_int @ R5 @ B2 )
% 8.64/4.81 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 8.64/4.81 => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3769_incr__mult__lemma,axiom,
% 8.64/4.81 ! [D: int,P2: int > $o,K2: int] :
% 8.64/4.81 ( ( ord_less_int @ zero_zero_int @ D )
% 8.64/4.81 => ( ! [X3: int] :
% 8.64/4.81 ( ( P2 @ X3 )
% 8.64/4.81 => ( P2 @ ( plus_plus_int @ X3 @ D ) ) )
% 8.64/4.81 => ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 8.64/4.81 => ! [X5: int] :
% 8.64/4.81 ( ( P2 @ X5 )
% 8.64/4.81 => ( P2 @ ( plus_plus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3770_ivl__disj__un__two__touch_I4_J,axiom,
% 8.64/4.81 ! [L: rat,M2: rat,U: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ L @ M2 )
% 8.64/4.81 => ( ( ord_less_eq_rat @ M2 @ U )
% 8.64/4.81 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M2 ) @ ( set_or633870826150836451st_rat @ M2 @ U ) )
% 8.64/4.81 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3771_ivl__disj__un__two__touch_I4_J,axiom,
% 8.64/4.81 ! [L: num,M2: num,U: num] :
% 8.64/4.81 ( ( ord_less_eq_num @ L @ M2 )
% 8.64/4.81 => ( ( ord_less_eq_num @ M2 @ U )
% 8.64/4.81 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M2 ) @ ( set_or7049704709247886629st_num @ M2 @ U ) )
% 8.64/4.81 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3772_ivl__disj__un__two__touch_I4_J,axiom,
% 8.64/4.81 ! [L: nat,M2: nat,U: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ L @ M2 )
% 8.64/4.81 => ( ( ord_less_eq_nat @ M2 @ U )
% 8.64/4.81 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M2 ) @ ( set_or1269000886237332187st_nat @ M2 @ U ) )
% 8.64/4.81 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3773_ivl__disj__un__two__touch_I4_J,axiom,
% 8.64/4.81 ! [L: int,M2: int,U: int] :
% 8.64/4.81 ( ( ord_less_eq_int @ L @ M2 )
% 8.64/4.81 => ( ( ord_less_eq_int @ M2 @ U )
% 8.64/4.81 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M2 ) @ ( set_or1266510415728281911st_int @ M2 @ U ) )
% 8.64/4.81 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3774_ivl__disj__un__two__touch_I4_J,axiom,
% 8.64/4.81 ! [L: real,M2: real,U: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ L @ M2 )
% 8.64/4.81 => ( ( ord_less_eq_real @ M2 @ U )
% 8.64/4.81 => ( ( sup_sup_set_real @ ( set_or1222579329274155063t_real @ L @ M2 ) @ ( set_or1222579329274155063t_real @ M2 @ U ) )
% 8.64/4.81 = ( set_or1222579329274155063t_real @ L @ U ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3775_int__distrib_I2_J,axiom,
% 8.64/4.81 ! [W2: int,Z1: int,Z22: int] :
% 8.64/4.81 ( ( times_times_int @ W2 @ ( plus_plus_int @ Z1 @ Z22 ) )
% 8.64/4.81 = ( plus_plus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3776_int__distrib_I1_J,axiom,
% 8.64/4.81 ! [Z1: int,Z22: int,W2: int] :
% 8.64/4.81 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W2 )
% 8.64/4.81 = ( plus_plus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3777_int__distrib_I3_J,axiom,
% 8.64/4.81 ! [Z1: int,Z22: int,W2: int] :
% 8.64/4.81 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W2 )
% 8.64/4.81 = ( minus_minus_int @ ( times_times_int @ Z1 @ W2 ) @ ( times_times_int @ Z22 @ W2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3778_int__distrib_I4_J,axiom,
% 8.64/4.81 ! [W2: int,Z1: int,Z22: int] :
% 8.64/4.81 ( ( times_times_int @ W2 @ ( minus_minus_int @ Z1 @ Z22 ) )
% 8.64/4.81 = ( minus_minus_int @ ( times_times_int @ W2 @ Z1 ) @ ( times_times_int @ W2 @ Z22 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3779_divide__divide__eq__left_H,axiom,
% 8.64/4.81 ! [A: complex,B: complex,C2: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C2 )
% 8.64/4.81 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C2 @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3780_divide__divide__eq__left_H,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C2 )
% 8.64/4.81 = ( divide_divide_real @ A @ ( times_times_real @ C2 @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3781_divide__divide__eq__left_H,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C2 )
% 8.64/4.81 = ( divide_divide_rat @ A @ ( times_times_rat @ C2 @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3782_divide__divide__times__eq,axiom,
% 8.64/4.81 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W2 ) @ ( times_times_complex @ Y @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3783_divide__divide__times__eq,axiom,
% 8.64/4.81 ! [X: real,Y: real,Z3: real,W2: real] :
% 8.64/4.81 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 8.64/4.81 = ( divide_divide_real @ ( times_times_real @ X @ W2 ) @ ( times_times_real @ Y @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3784_divide__divide__times__eq,axiom,
% 8.64/4.81 ! [X: rat,Y: rat,Z3: rat,W2: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z3 @ W2 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( times_times_rat @ X @ W2 ) @ ( times_times_rat @ Y @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3785_times__divide__times__eq,axiom,
% 8.64/4.81 ! [X: complex,Y: complex,Z3: complex,W2: complex] :
% 8.64/4.81 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z3 @ W2 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ Y @ W2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3786_times__divide__times__eq,axiom,
% 8.64/4.81 ! [X: real,Y: real,Z3: real,W2: real] :
% 8.64/4.81 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z3 @ W2 ) )
% 8.64/4.81 = ( divide_divide_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ Y @ W2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3787_times__divide__times__eq,axiom,
% 8.64/4.81 ! [X: rat,Y: rat,Z3: rat,W2: rat] :
% 8.64/4.81 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z3 @ W2 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ Y @ W2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3788_atLeastatMost__psubset__iff,axiom,
% 8.64/4.81 ! [A: set_nat,B: set_nat,C2: set_nat,D: set_nat] :
% 8.64/4.81 ( ( ord_less_set_set_nat @ ( set_or4548717258645045905et_nat @ A @ B ) @ ( set_or4548717258645045905et_nat @ C2 @ D ) )
% 8.64/4.81 = ( ( ~ ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_set_nat @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_set_nat @ B @ D )
% 8.64/4.81 & ( ( ord_less_set_nat @ C2 @ A )
% 8.64/4.81 | ( ord_less_set_nat @ B @ D ) ) ) )
% 8.64/4.81 & ( ord_less_eq_set_nat @ C2 @ D ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3789_atLeastatMost__psubset__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.64/4.81 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C2 @ D ) )
% 8.64/4.81 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_rat @ B @ D )
% 8.64/4.81 & ( ( ord_less_rat @ C2 @ A )
% 8.64/4.81 | ( ord_less_rat @ B @ D ) ) ) )
% 8.64/4.81 & ( ord_less_eq_rat @ C2 @ D ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3790_atLeastatMost__psubset__iff,axiom,
% 8.64/4.81 ! [A: num,B: num,C2: num,D: num] :
% 8.64/4.81 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C2 @ D ) )
% 8.64/4.81 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_num @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_num @ B @ D )
% 8.64/4.81 & ( ( ord_less_num @ C2 @ A )
% 8.64/4.81 | ( ord_less_num @ B @ D ) ) ) )
% 8.64/4.81 & ( ord_less_eq_num @ C2 @ D ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3791_atLeastatMost__psubset__iff,axiom,
% 8.64/4.81 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.64/4.81 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C2 @ D ) )
% 8.64/4.81 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_nat @ B @ D )
% 8.64/4.81 & ( ( ord_less_nat @ C2 @ A )
% 8.64/4.81 | ( ord_less_nat @ B @ D ) ) ) )
% 8.64/4.81 & ( ord_less_eq_nat @ C2 @ D ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3792_atLeastatMost__psubset__iff,axiom,
% 8.64/4.81 ! [A: int,B: int,C2: int,D: int] :
% 8.64/4.81 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C2 @ D ) )
% 8.64/4.81 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_int @ B @ D )
% 8.64/4.81 & ( ( ord_less_int @ C2 @ A )
% 8.64/4.81 | ( ord_less_int @ B @ D ) ) ) )
% 8.64/4.81 & ( ord_less_eq_int @ C2 @ D ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3793_atLeastatMost__psubset__iff,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real,D: real] :
% 8.64/4.81 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C2 @ D ) )
% 8.64/4.81 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 8.64/4.81 | ( ( ord_less_eq_real @ C2 @ A )
% 8.64/4.81 & ( ord_less_eq_real @ B @ D )
% 8.64/4.81 & ( ( ord_less_real @ C2 @ A )
% 8.64/4.81 | ( ord_less_real @ B @ D ) ) ) )
% 8.64/4.81 & ( ord_less_eq_real @ C2 @ D ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3794_infinite__Icc,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ B )
% 8.64/4.81 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3795_infinite__Icc,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ B )
% 8.64/4.81 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3796_atLeastAtMost__singleton_H,axiom,
% 8.64/4.81 ! [A: nat,B: nat] :
% 8.64/4.81 ( ( A = B )
% 8.64/4.81 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 8.64/4.81 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3797_atLeastAtMost__singleton_H,axiom,
% 8.64/4.81 ! [A: int,B: int] :
% 8.64/4.81 ( ( A = B )
% 8.64/4.81 => ( ( set_or1266510415728281911st_int @ A @ B )
% 8.64/4.81 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3798_atLeastAtMost__singleton_H,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( A = B )
% 8.64/4.81 => ( ( set_or1222579329274155063t_real @ A @ B )
% 8.64/4.81 = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3799_divide__right__mono__neg,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ A @ B )
% 8.64/4.81 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( divide_divide_real @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3800_divide__right__mono__neg,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.81 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( divide_divide_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3801_divide__nonpos__nonpos,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3802_divide__nonpos__nonpos,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3803_divide__nonpos__nonneg,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3804_divide__nonpos__nonneg,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3805_divide__nonneg__nonpos,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3806_divide__nonneg__nonpos,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3807_divide__nonneg__nonneg,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3808_divide__nonneg__nonneg,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3809_zero__le__divide__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 8.64/4.81 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 8.64/4.81 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3810_zero__le__divide__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 8.64/4.81 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 8.64/4.81 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3811_divide__right__mono,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ A @ B )
% 8.64/4.81 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3812_divide__right__mono,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.81 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3813_divide__le__0__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 8.64/4.81 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 8.64/4.81 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3814_divide__le__0__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 8.64/4.81 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 8.64/4.81 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3815_divide__strict__right__mono__neg,axiom,
% 8.64/4.81 ! [B: real,A: real,C2: real] :
% 8.64/4.81 ( ( ord_less_real @ B @ A )
% 8.64/4.81 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3816_divide__strict__right__mono__neg,axiom,
% 8.64/4.81 ! [B: rat,A: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_rat @ B @ A )
% 8.64/4.81 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3817_divide__strict__right__mono,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ B )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3818_divide__strict__right__mono,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ B )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3819_zero__less__divide__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_real @ zero_zero_real @ B ) )
% 8.64/4.81 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3820_zero__less__divide__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 8.64/4.81 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3821_divide__less__cancel,axiom,
% 8.64/4.81 ! [A: real,C2: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_real @ A @ B ) )
% 8.64/4.81 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ B @ A ) )
% 8.64/4.81 & ( C2 != zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3822_divide__less__cancel,axiom,
% 8.64/4.81 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_rat @ A @ B ) )
% 8.64/4.81 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ B @ A ) )
% 8.64/4.81 & ( C2 != zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3823_divide__less__0__iff,axiom,
% 8.64/4.81 ! [A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_real @ B @ zero_zero_real ) )
% 8.64/4.81 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3824_divide__less__0__iff,axiom,
% 8.64/4.81 ! [A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 8.64/4.81 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3825_divide__pos__pos,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3826_divide__pos__pos,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3827_divide__pos__neg,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3828_divide__pos__neg,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3829_divide__neg__pos,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_real @ X @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3830_divide__neg__pos,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_rat @ X @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3831_divide__neg__neg,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_real @ X @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3832_divide__neg__neg,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_rat @ X @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3833_all__nat__less,axiom,
% 8.64/4.81 ! [N: nat,P2: nat > $o] :
% 8.64/4.81 ( ( ! [M6: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ M6 @ N )
% 8.64/4.81 => ( P2 @ M6 ) ) )
% 8.64/4.81 = ( ! [X4: nat] :
% 8.64/4.81 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.81 => ( P2 @ X4 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3834_ex__nat__less,axiom,
% 8.64/4.81 ! [N: nat,P2: nat > $o] :
% 8.64/4.81 ( ( ? [M6: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ M6 @ N )
% 8.64/4.81 & ( P2 @ M6 ) ) )
% 8.64/4.81 = ( ? [X4: nat] :
% 8.64/4.81 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.81 & ( P2 @ X4 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3835_frac__eq__eq,axiom,
% 8.64/4.81 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 8.64/4.81 ( ( Y != zero_zero_complex )
% 8.64/4.81 => ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 8.64/4.81 = ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 8.64/4.81 = ( ( times_times_complex @ X @ Z3 )
% 8.64/4.81 = ( times_times_complex @ W2 @ Y ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3836_frac__eq__eq,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real,W2: real] :
% 8.64/4.81 ( ( Y != zero_zero_real )
% 8.64/4.81 => ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( ( divide_divide_real @ X @ Y )
% 8.64/4.81 = ( divide_divide_real @ W2 @ Z3 ) )
% 8.64/4.81 = ( ( times_times_real @ X @ Z3 )
% 8.64/4.81 = ( times_times_real @ W2 @ Y ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3837_frac__eq__eq,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 8.64/4.81 ( ( Y != zero_zero_rat )
% 8.64/4.81 => ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( ( divide_divide_rat @ X @ Y )
% 8.64/4.81 = ( divide_divide_rat @ W2 @ Z3 ) )
% 8.64/4.81 = ( ( times_times_rat @ X @ Z3 )
% 8.64/4.81 = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3838_divide__eq__eq,axiom,
% 8.64/4.81 ! [B: complex,C2: complex,A: complex] :
% 8.64/4.81 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 8.64/4.81 = A )
% 8.64/4.81 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_complex @ A @ C2 ) ) )
% 8.64/4.81 & ( ( C2 = zero_zero_complex )
% 8.64/4.81 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3839_divide__eq__eq,axiom,
% 8.64/4.81 ! [B: real,C2: real,A: real] :
% 8.64/4.81 ( ( ( divide_divide_real @ B @ C2 )
% 8.64/4.81 = A )
% 8.64/4.81 = ( ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_real @ A @ C2 ) ) )
% 8.64/4.81 & ( ( C2 = zero_zero_real )
% 8.64/4.81 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3840_divide__eq__eq,axiom,
% 8.64/4.81 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.81 ( ( ( divide_divide_rat @ B @ C2 )
% 8.64/4.81 = A )
% 8.64/4.81 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.81 & ( ( C2 = zero_zero_rat )
% 8.64/4.81 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3841_eq__divide__eq,axiom,
% 8.64/4.81 ! [A: complex,B: complex,C2: complex] :
% 8.64/4.81 ( ( A
% 8.64/4.81 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( times_times_complex @ A @ C2 )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( C2 = zero_zero_complex )
% 8.64/4.81 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3842_eq__divide__eq,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( A
% 8.64/4.81 = ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( times_times_real @ A @ C2 )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( C2 = zero_zero_real )
% 8.64/4.81 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3843_eq__divide__eq,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( A
% 8.64/4.81 = ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( times_times_rat @ A @ C2 )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( C2 = zero_zero_rat )
% 8.64/4.81 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3844_divide__eq__imp,axiom,
% 8.64/4.81 ! [C2: complex,B: complex,A: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( B
% 8.64/4.81 = ( times_times_complex @ A @ C2 ) )
% 8.64/4.81 => ( ( divide1717551699836669952omplex @ B @ C2 )
% 8.64/4.81 = A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3845_divide__eq__imp,axiom,
% 8.64/4.81 ! [C2: real,B: real,A: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( B
% 8.64/4.81 = ( times_times_real @ A @ C2 ) )
% 8.64/4.81 => ( ( divide_divide_real @ B @ C2 )
% 8.64/4.81 = A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3846_divide__eq__imp,axiom,
% 8.64/4.81 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( B
% 8.64/4.81 = ( times_times_rat @ A @ C2 ) )
% 8.64/4.81 => ( ( divide_divide_rat @ B @ C2 )
% 8.64/4.81 = A ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3847_eq__divide__imp,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( ( times_times_complex @ A @ C2 )
% 8.64/4.81 = B )
% 8.64/4.81 => ( A
% 8.64/4.81 = ( divide1717551699836669952omplex @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3848_eq__divide__imp,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( ( times_times_real @ A @ C2 )
% 8.64/4.81 = B )
% 8.64/4.81 => ( A
% 8.64/4.81 = ( divide_divide_real @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3849_eq__divide__imp,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( ( times_times_rat @ A @ C2 )
% 8.64/4.81 = B )
% 8.64/4.81 => ( A
% 8.64/4.81 = ( divide_divide_rat @ B @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3850_nonzero__divide__eq__eq,axiom,
% 8.64/4.81 ! [C2: complex,B: complex,A: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 8.64/4.81 = A )
% 8.64/4.81 = ( B
% 8.64/4.81 = ( times_times_complex @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3851_nonzero__divide__eq__eq,axiom,
% 8.64/4.81 ! [C2: real,B: real,A: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( ( divide_divide_real @ B @ C2 )
% 8.64/4.81 = A )
% 8.64/4.81 = ( B
% 8.64/4.81 = ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3852_nonzero__divide__eq__eq,axiom,
% 8.64/4.81 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( ( divide_divide_rat @ B @ C2 )
% 8.64/4.81 = A )
% 8.64/4.81 = ( B
% 8.64/4.81 = ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3853_nonzero__eq__divide__eq,axiom,
% 8.64/4.81 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( A
% 8.64/4.81 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.81 = ( ( times_times_complex @ A @ C2 )
% 8.64/4.81 = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3854_nonzero__eq__divide__eq,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( A
% 8.64/4.81 = ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( times_times_real @ A @ C2 )
% 8.64/4.81 = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3855_nonzero__eq__divide__eq,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( A
% 8.64/4.81 = ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( times_times_rat @ A @ C2 )
% 8.64/4.81 = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3856_right__inverse__eq,axiom,
% 8.64/4.81 ! [B: complex,A: complex] :
% 8.64/4.81 ( ( B != zero_zero_complex )
% 8.64/4.81 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.64/4.81 = one_one_complex )
% 8.64/4.81 = ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3857_right__inverse__eq,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( B != zero_zero_real )
% 8.64/4.81 => ( ( ( divide_divide_real @ A @ B )
% 8.64/4.81 = one_one_real )
% 8.64/4.81 = ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3858_right__inverse__eq,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( B != zero_zero_rat )
% 8.64/4.81 => ( ( ( divide_divide_rat @ A @ B )
% 8.64/4.81 = one_one_rat )
% 8.64/4.81 = ( A = B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3859_divide__numeral__1,axiom,
% 8.64/4.81 ! [A: complex] :
% 8.64/4.81 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3860_divide__numeral__1,axiom,
% 8.64/4.81 ! [A: real] :
% 8.64/4.81 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3861_divide__numeral__1,axiom,
% 8.64/4.81 ! [A: rat] :
% 8.64/4.81 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 8.64/4.81 = A ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3862_div__positive,axiom,
% 8.64/4.81 ! [B: nat,A: nat] :
% 8.64/4.81 ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.64/4.81 => ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.81 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3863_div__positive,axiom,
% 8.64/4.81 ! [B: int,A: int] :
% 8.64/4.81 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.81 => ( ( ord_less_eq_int @ B @ A )
% 8.64/4.81 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3864_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 8.64/4.81 ! [A: nat,B: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.64/4.81 => ( ( ord_less_nat @ A @ B )
% 8.64/4.81 => ( ( divide_divide_nat @ A @ B )
% 8.64/4.81 = zero_zero_nat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3865_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 8.64/4.81 ! [A: int,B: int] :
% 8.64/4.81 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.81 => ( ( ord_less_int @ A @ B )
% 8.64/4.81 => ( ( divide_divide_int @ A @ B )
% 8.64/4.81 = zero_zero_int ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3866_divide__nonpos__pos,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3867_divide__nonpos__pos,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3868_divide__nonpos__neg,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3869_divide__nonpos__neg,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3870_divide__nonneg__pos,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3871_divide__nonneg__pos,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3872_divide__nonneg__neg,axiom,
% 8.64/4.81 ! [X: real,Y: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_real @ Y @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3873_divide__nonneg__neg,axiom,
% 8.64/4.81 ! [X: rat,Y: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3874_divide__le__cancel,axiom,
% 8.64/4.81 ! [A: real,C2: real,B: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C2 ) @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_eq_real @ A @ B ) )
% 8.64/4.81 & ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3875_divide__le__cancel,axiom,
% 8.64/4.81 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_eq_rat @ A @ B ) )
% 8.64/4.81 & ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3876_frac__less2,axiom,
% 8.64/4.81 ! [X: real,Y: real,W2: real,Z3: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_eq_real @ X @ Y )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 8.64/4.81 => ( ( ord_less_real @ W2 @ Z3 )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3877_frac__less2,axiom,
% 8.64/4.81 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_eq_rat @ X @ Y )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 8.64/4.81 => ( ( ord_less_rat @ W2 @ Z3 )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3878_frac__less,axiom,
% 8.64/4.81 ! [X: real,Y: real,W2: real,Z3: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.81 => ( ( ord_less_real @ X @ Y )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 8.64/4.81 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3879_frac__less,axiom,
% 8.64/4.81 ! [X: rat,Y: rat,W2: rat,Z3: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.81 => ( ( ord_less_rat @ X @ Y )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 8.64/4.81 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3880_frac__le,axiom,
% 8.64/4.81 ! [Y: real,X: real,W2: real,Z3: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ( ord_less_eq_real @ X @ Y )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ W2 )
% 8.64/4.81 => ( ( ord_less_eq_real @ W2 @ Z3 )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z3 ) @ ( divide_divide_real @ Y @ W2 ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3881_frac__le,axiom,
% 8.64/4.81 ! [Y: rat,X: rat,W2: rat,Z3: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ( ord_less_eq_rat @ X @ Y )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 8.64/4.81 => ( ( ord_less_eq_rat @ W2 @ Z3 )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z3 ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3882_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 8.64/4.81 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.64/4.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3883_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 8.64/4.81 ! [C2: int,A: int,B: int] :
% 8.64/4.81 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.64/4.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.81 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3884_divide__less__eq,axiom,
% 8.64/4.81 ! [B: real,C2: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3885_divide__less__eq,axiom,
% 8.64/4.81 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3886_less__divide__eq,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3887_less__divide__eq,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3888_neg__divide__less__eq,axiom,
% 8.64/4.81 ! [C2: real,B: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3889_neg__divide__less__eq,axiom,
% 8.64/4.81 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3890_neg__less__divide__eq,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3891_neg__less__divide__eq,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3892_pos__divide__less__eq,axiom,
% 8.64/4.81 ! [C2: real,B: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3893_pos__divide__less__eq,axiom,
% 8.64/4.81 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3894_pos__less__divide__eq,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3895_pos__less__divide__eq,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3896_mult__imp__div__pos__less,axiom,
% 8.64/4.81 ! [Y: real,X: real,Z3: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ( ord_less_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3897_mult__imp__div__pos__less,axiom,
% 8.64/4.81 ! [Y: rat,X: rat,Z3: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3898_mult__imp__less__div__pos,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ( ord_less_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 8.64/4.81 => ( ord_less_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3899_mult__imp__less__div__pos,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ( ord_less_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 8.64/4.81 => ( ord_less_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3900_divide__strict__left__mono,axiom,
% 8.64/4.81 ! [B: real,A: real,C2: real] :
% 8.64/4.81 ( ( ord_less_real @ B @ A )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3901_divide__strict__left__mono,axiom,
% 8.64/4.81 ! [B: rat,A: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_rat @ B @ A )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3902_divide__strict__left__mono__neg,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_real @ A @ B )
% 8.64/4.81 => ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.64/4.81 => ( ord_less_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3903_divide__strict__left__mono__neg,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_rat @ A @ B )
% 8.64/4.81 => ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.64/4.81 => ( ord_less_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3904_less__divide__eq__1,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_real @ A @ B ) )
% 8.64/4.81 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_real @ B @ A ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3905_less__divide__eq__1,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_rat @ A @ B ) )
% 8.64/4.81 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3906_divide__less__eq__1,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_real @ B @ A ) )
% 8.64/4.81 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_real @ A @ B ) )
% 8.64/4.81 | ( A = zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3907_divide__less__eq__1,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_rat @ B @ A ) )
% 8.64/4.81 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_rat @ A @ B ) )
% 8.64/4.81 | ( A = zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3908_divide__eq__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [B: complex,C2: complex,W2: num] :
% 8.64/4.81 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 8.64/4.81 = ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C2 ) ) )
% 8.64/4.81 & ( ( C2 = zero_zero_complex )
% 8.64/4.81 => ( ( numera6690914467698888265omplex @ W2 )
% 8.64/4.81 = zero_zero_complex ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3909_divide__eq__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [B: real,C2: real,W2: num] :
% 8.64/4.81 ( ( ( divide_divide_real @ B @ C2 )
% 8.64/4.81 = ( numeral_numeral_real @ W2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 8.64/4.81 & ( ( C2 = zero_zero_real )
% 8.64/4.81 => ( ( numeral_numeral_real @ W2 )
% 8.64/4.81 = zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3910_divide__eq__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [B: rat,C2: rat,W2: num] :
% 8.64/4.81 ( ( ( divide_divide_rat @ B @ C2 )
% 8.64/4.81 = ( numeral_numeral_rat @ W2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( B
% 8.64/4.81 = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 8.64/4.81 & ( ( C2 = zero_zero_rat )
% 8.64/4.81 => ( ( numeral_numeral_rat @ W2 )
% 8.64/4.81 = zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3911_eq__divide__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [W2: num,B: complex,C2: complex] :
% 8.64/4.81 ( ( ( numera6690914467698888265omplex @ W2 )
% 8.64/4.81 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.81 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ C2 )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( C2 = zero_zero_complex )
% 8.64/4.81 => ( ( numera6690914467698888265omplex @ W2 )
% 8.64/4.81 = zero_zero_complex ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3912_eq__divide__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [W2: num,B: real,C2: real] :
% 8.64/4.81 ( ( ( numeral_numeral_real @ W2 )
% 8.64/4.81 = ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_real )
% 8.64/4.81 => ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( C2 = zero_zero_real )
% 8.64/4.81 => ( ( numeral_numeral_real @ W2 )
% 8.64/4.81 = zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3913_eq__divide__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [W2: num,B: rat,C2: rat] :
% 8.64/4.81 ( ( ( numeral_numeral_rat @ W2 )
% 8.64/4.81 = ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.81 => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( C2 = zero_zero_rat )
% 8.64/4.81 => ( ( numeral_numeral_rat @ W2 )
% 8.64/4.81 = zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3914_add__divide__eq__if__simps_I2_J,axiom,
% 8.64/4.81 ! [Z3: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3915_add__divide__eq__if__simps_I2_J,axiom,
% 8.64/4.81 ! [Z3: real,A: real,B: real] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 8.64/4.81 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3916_add__divide__eq__if__simps_I2_J,axiom,
% 8.64/4.81 ! [Z3: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 8.64/4.81 = B ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 8.64/4.81 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3917_add__divide__eq__if__simps_I1_J,axiom,
% 8.64/4.81 ! [Z3: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 8.64/4.81 = A ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3918_add__divide__eq__if__simps_I1_J,axiom,
% 8.64/4.81 ! [Z3: real,A: real,B: real] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 8.64/4.81 = A ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 8.64/4.81 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3919_add__divide__eq__if__simps_I1_J,axiom,
% 8.64/4.81 ! [Z3: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 8.64/4.81 = A ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3920_add__frac__eq,axiom,
% 8.64/4.81 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 8.64/4.81 ( ( Y != zero_zero_complex )
% 8.64/4.81 => ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3921_add__frac__eq,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real,W2: real] :
% 8.64/4.81 ( ( Y != zero_zero_real )
% 8.64/4.81 => ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 8.64/4.81 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3922_add__frac__eq,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 8.64/4.81 ( ( Y != zero_zero_rat )
% 8.64/4.81 => ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3923_add__frac__num,axiom,
% 8.64/4.81 ! [Y: complex,X: complex,Z3: complex] :
% 8.64/4.81 ( ( Y != zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z3 )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3924_add__frac__num,axiom,
% 8.64/4.81 ! [Y: real,X: real,Z3: real] :
% 8.64/4.81 ( ( Y != zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z3 )
% 8.64/4.81 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3925_add__frac__num,axiom,
% 8.64/4.81 ! [Y: rat,X: rat,Z3: rat] :
% 8.64/4.81 ( ( Y != zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 )
% 8.64/4.81 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3926_add__num__frac,axiom,
% 8.64/4.81 ! [Y: complex,Z3: complex,X: complex] :
% 8.64/4.81 ( ( Y != zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z3 @ Y ) ) @ Y ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3927_add__num__frac,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real] :
% 8.64/4.81 ( ( Y != zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ Z3 @ ( divide_divide_real @ X @ Y ) )
% 8.64/4.81 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z3 @ Y ) ) @ Y ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3928_add__num__frac,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat] :
% 8.64/4.81 ( ( Y != zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) )
% 8.64/4.81 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z3 @ Y ) ) @ Y ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3929_add__divide__eq__iff,axiom,
% 8.64/4.81 ! [Z3: complex,X: complex,Y: complex] :
% 8.64/4.81 ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3930_add__divide__eq__iff,axiom,
% 8.64/4.81 ! [Z3: real,X: real,Y: real] :
% 8.64/4.81 ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 8.64/4.81 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3931_add__divide__eq__iff,axiom,
% 8.64/4.81 ! [Z3: rat,X: rat,Y: rat] :
% 8.64/4.81 ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z3 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3932_divide__add__eq__iff,axiom,
% 8.64/4.81 ! [Z3: complex,X: complex,Y: complex] :
% 8.64/4.81 ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3933_divide__add__eq__iff,axiom,
% 8.64/4.81 ! [Z3: real,X: real,Y: real] :
% 8.64/4.81 ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 8.64/4.81 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3934_divide__add__eq__iff,axiom,
% 8.64/4.81 ! [Z3: rat,X: rat,Y: rat] :
% 8.64/4.81 ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z3 ) @ Y )
% 8.64/4.81 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3935_add__divide__eq__if__simps_I4_J,axiom,
% 8.64/4.81 ! [Z3: complex,A: complex,B: complex] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_complex )
% 8.64/4.81 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 8.64/4.81 = A ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z3 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3936_add__divide__eq__if__simps_I4_J,axiom,
% 8.64/4.81 ! [Z3: real,A: real,B: real] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_real )
% 8.64/4.81 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 8.64/4.81 = A ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z3 ) )
% 8.64/4.81 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3937_add__divide__eq__if__simps_I4_J,axiom,
% 8.64/4.81 ! [Z3: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ( Z3 = zero_zero_rat )
% 8.64/4.81 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 8.64/4.81 = A ) )
% 8.64/4.81 & ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z3 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z3 ) @ B ) @ Z3 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3938_diff__frac__eq,axiom,
% 8.64/4.81 ! [Y: complex,Z3: complex,X: complex,W2: complex] :
% 8.64/4.81 ( ( Y != zero_zero_complex )
% 8.64/4.81 => ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W2 @ Z3 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ ( times_times_complex @ W2 @ Y ) ) @ ( times_times_complex @ Y @ Z3 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3939_diff__frac__eq,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real,W2: real] :
% 8.64/4.81 ( ( Y != zero_zero_real )
% 8.64/4.81 => ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 8.64/4.81 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3940_diff__frac__eq,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 8.64/4.81 ( ( Y != zero_zero_rat )
% 8.64/4.81 => ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3941_diff__divide__eq__iff,axiom,
% 8.64/4.81 ! [Z3: complex,X: complex,Y: complex] :
% 8.64/4.81 ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z3 ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3942_diff__divide__eq__iff,axiom,
% 8.64/4.81 ! [Z3: real,X: real,Y: real] :
% 8.64/4.81 ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z3 ) )
% 8.64/4.81 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3943_diff__divide__eq__iff,axiom,
% 8.64/4.81 ! [Z3: rat,X: rat,Y: rat] :
% 8.64/4.81 ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z3 ) )
% 8.64/4.81 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3944_divide__diff__eq__iff,axiom,
% 8.64/4.81 ! [Z3: complex,X: complex,Y: complex] :
% 8.64/4.81 ( ( Z3 != zero_zero_complex )
% 8.64/4.81 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z3 ) @ Y )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3945_divide__diff__eq__iff,axiom,
% 8.64/4.81 ! [Z3: real,X: real,Y: real] :
% 8.64/4.81 ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z3 ) @ Y )
% 8.64/4.81 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3946_divide__diff__eq__iff,axiom,
% 8.64/4.81 ! [Z3: rat,X: rat,Y: rat] :
% 8.64/4.81 ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z3 ) @ Y )
% 8.64/4.81 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3947_card__Un__le,axiom,
% 8.64/4.81 ! [A4: set_complex,B5: set_complex] : ( ord_less_eq_nat @ ( finite_card_complex @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_complex @ A4 ) @ ( finite_card_complex @ B5 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3948_card__Un__le,axiom,
% 8.64/4.81 ! [A4: set_int,B5: set_int] : ( ord_less_eq_nat @ ( finite_card_int @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_int @ A4 ) @ ( finite_card_int @ B5 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3949_card__Un__le,axiom,
% 8.64/4.81 ! [A4: set_list_nat,B5: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A4 ) @ ( finite_card_list_nat @ B5 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3950_card__Un__le,axiom,
% 8.64/4.81 ! [A4: set_set_nat,B5: set_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_set_nat @ A4 ) @ ( finite_card_set_nat @ B5 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3951_card__Un__le,axiom,
% 8.64/4.81 ! [A4: set_nat,B5: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A4 ) @ ( finite_card_nat @ B5 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3952_atLeast0__atMost__Suc,axiom,
% 8.64/4.81 ! [N: nat] :
% 8.64/4.81 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.64/4.81 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3953_nat__mult__div__cancel1,axiom,
% 8.64/4.81 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.81 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.81 => ( ( divide_divide_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.64/4.81 = ( divide_divide_nat @ M2 @ N ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3954_Icc__eq__insert__lb__nat,axiom,
% 8.64/4.81 ! [M2: nat,N: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.81 => ( ( set_or1269000886237332187st_nat @ M2 @ N )
% 8.64/4.81 = ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3955_atLeastAtMostSuc__conv,axiom,
% 8.64/4.81 ! [M2: nat,N: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.81 => ( ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) )
% 8.64/4.81 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3956_atLeastAtMost__insertL,axiom,
% 8.64/4.81 ! [M2: nat,N: nat] :
% 8.64/4.81 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.81 => ( ( insert_nat @ M2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 8.64/4.81 = ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3957_subset__eq__atLeast0__atMost__finite,axiom,
% 8.64/4.81 ! [N6: set_nat,N: nat] :
% 8.64/4.81 ( ( ord_less_eq_set_nat @ N6 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.81 => ( finite_finite_nat @ N6 ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3958_divide__le__eq,axiom,
% 8.64/4.81 ! [B: real,C2: real,A: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3959_divide__le__eq,axiom,
% 8.64/4.81 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3960_le__divide__eq,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3961_le__divide__eq,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3962_divide__left__mono,axiom,
% 8.64/4.81 ! [B: real,A: real,C2: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ B @ A )
% 8.64/4.81 => ( ( ord_less_eq_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3963_divide__left__mono,axiom,
% 8.64/4.81 ! [B: rat,A: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.81 => ( ( ord_less_eq_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3964_neg__divide__le__eq,axiom,
% 8.64/4.81 ! [C2: real,B: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3965_neg__divide__le__eq,axiom,
% 8.64/4.81 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3966_neg__le__divide__eq,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3967_neg__le__divide__eq,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3968_pos__divide__le__eq,axiom,
% 8.64/4.81 ! [C2: real,B: real,A: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3969_pos__divide__le__eq,axiom,
% 8.64/4.81 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ A )
% 8.64/4.81 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3970_pos__le__divide__eq,axiom,
% 8.64/4.81 ! [C2: real,A: real,B: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3971_pos__le__divide__eq,axiom,
% 8.64/4.81 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3972_mult__imp__div__pos__le,axiom,
% 8.64/4.81 ! [Y: real,X: real,Z3: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z3 @ Y ) )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3973_mult__imp__div__pos__le,axiom,
% 8.64/4.81 ! [Y: rat,X: rat,Z3: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z3 @ Y ) )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z3 ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3974_mult__imp__le__div__pos,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real] :
% 8.64/4.81 ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.81 => ( ( ord_less_eq_real @ ( times_times_real @ Z3 @ Y ) @ X )
% 8.64/4.81 => ( ord_less_eq_real @ Z3 @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3975_mult__imp__le__div__pos,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat] :
% 8.64/4.81 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.81 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z3 @ Y ) @ X )
% 8.64/4.81 => ( ord_less_eq_rat @ Z3 @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3976_divide__left__mono__neg,axiom,
% 8.64/4.81 ! [A: real,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ A @ B )
% 8.64/4.81 => ( ( ord_less_eq_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 8.64/4.81 => ( ord_less_eq_real @ ( divide_divide_real @ C2 @ A ) @ ( divide_divide_real @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3977_divide__left__mono__neg,axiom,
% 8.64/4.81 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.81 => ( ( ord_less_eq_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 8.64/4.81 => ( ord_less_eq_rat @ ( divide_divide_rat @ C2 @ A ) @ ( divide_divide_rat @ C2 @ B ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3978_divide__le__eq__1,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_eq_real @ B @ A ) )
% 8.64/4.81 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_eq_real @ A @ B ) )
% 8.64/4.81 | ( A = zero_zero_real ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3979_divide__le__eq__1,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_eq_rat @ B @ A ) )
% 8.64/4.81 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_eq_rat @ A @ B ) )
% 8.64/4.81 | ( A = zero_zero_rat ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3980_le__divide__eq__1,axiom,
% 8.64/4.81 ! [B: real,A: real] :
% 8.64/4.81 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.81 & ( ord_less_eq_real @ A @ B ) )
% 8.64/4.81 | ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.81 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3981_le__divide__eq__1,axiom,
% 8.64/4.81 ! [B: rat,A: rat] :
% 8.64/4.81 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.81 & ( ord_less_eq_rat @ A @ B ) )
% 8.64/4.81 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.81 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3982_divide__less__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [B: real,C2: real,W2: num] :
% 8.64/4.81 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3983_divide__less__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [B: rat,C2: rat,W2: num] :
% 8.64/4.81 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3984_less__divide__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [W2: num,B: real,C2: real] :
% 8.64/4.81 ( ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.81 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.81 => ( ord_less_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3985_less__divide__eq__numeral_I1_J,axiom,
% 8.64/4.81 ! [W2: num,B: rat,C2: rat] :
% 8.64/4.81 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.81 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.81 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 8.64/4.81 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.81 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3986_frac__le__eq,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real,W2: real] :
% 8.64/4.81 ( ( Y != zero_zero_real )
% 8.64/4.81 => ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 8.64/4.81 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3987_frac__le__eq,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 8.64/4.81 ( ( Y != zero_zero_rat )
% 8.64/4.81 => ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 8.64/4.81 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3988_frac__less__eq,axiom,
% 8.64/4.81 ! [Y: real,Z3: real,X: real,W2: real] :
% 8.64/4.81 ( ( Y != zero_zero_real )
% 8.64/4.81 => ( ( Z3 != zero_zero_real )
% 8.64/4.81 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W2 @ Z3 ) )
% 8.64/4.81 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z3 ) @ ( times_times_real @ W2 @ Y ) ) @ ( times_times_real @ Y @ Z3 ) ) @ zero_zero_real ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3989_frac__less__eq,axiom,
% 8.64/4.81 ! [Y: rat,Z3: rat,X: rat,W2: rat] :
% 8.64/4.81 ( ( Y != zero_zero_rat )
% 8.64/4.81 => ( ( Z3 != zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z3 ) )
% 8.64/4.81 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z3 ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z3 ) ) @ zero_zero_rat ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3990_power__diff,axiom,
% 8.64/4.81 ! [A: complex,N: nat,M2: nat] :
% 8.64/4.81 ( ( A != zero_zero_complex )
% 8.64/4.81 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.81 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.81 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3991_power__diff,axiom,
% 8.64/4.81 ! [A: real,N: nat,M2: nat] :
% 8.64/4.81 ( ( A != zero_zero_real )
% 8.64/4.81 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.81 => ( ( power_power_real @ A @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.81 = ( divide_divide_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3992_power__diff,axiom,
% 8.64/4.81 ! [A: rat,N: nat,M2: nat] :
% 8.64/4.81 ( ( A != zero_zero_rat )
% 8.64/4.81 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.81 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.81 = ( divide_divide_rat @ ( power_power_rat @ A @ M2 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 8.64/4.81
% 8.64/4.81 thf(fact_3993_power__diff,axiom,
% 8.64/4.81 ! [A: nat,N: nat,M2: nat] :
% 8.64/4.81 ( ( A != zero_zero_nat )
% 8.64/4.82 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.82 = ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_3994_power__diff,axiom,
% 8.64/4.82 ! [A: int,N: nat,M2: nat] :
% 8.64/4.82 ( ( A != zero_zero_int )
% 8.64/4.82 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.82 = ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_3995_div__geq,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ~ ( ord_less_nat @ M2 @ N )
% 8.64/4.82 => ( ( divide_divide_nat @ M2 @ N )
% 8.64/4.82 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_3996_four__x__squared,axiom,
% 8.64/4.82 ! [X: real] :
% 8.64/4.82 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.82 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_3997_L2__set__mult__ineq__lemma,axiom,
% 8.64/4.82 ! [A: real,C2: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C2 ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_3998_divide__le__eq__numeral_I1_J,axiom,
% 8.64/4.82 ! [B: real,C2: real,W2: num] :
% 8.64/4.82 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.82 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.82 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 8.64/4.82 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.82 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.82 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 8.64/4.82 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.82 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_3999_divide__le__eq__numeral_I1_J,axiom,
% 8.64/4.82 ! [B: rat,C2: rat,W2: num] :
% 8.64/4.82 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.82 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.82 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 8.64/4.82 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.82 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.82 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 8.64/4.82 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.82 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4000_le__divide__eq__numeral_I1_J,axiom,
% 8.64/4.82 ! [W2: num,B: real,C2: real] :
% 8.64/4.82 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.82 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.82 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) @ B ) )
% 8.64/4.82 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.82 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.82 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ C2 ) ) )
% 8.64/4.82 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.82 => ( ord_less_eq_real @ ( numeral_numeral_real @ W2 ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4001_le__divide__eq__numeral_I1_J,axiom,
% 8.64/4.82 ! [W2: num,B: rat,C2: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.82 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.82 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) @ B ) )
% 8.64/4.82 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.82 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.82 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C2 ) ) )
% 8.64/4.82 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.82 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4002_half__gt__zero,axiom,
% 8.64/4.82 ! [A: real] :
% 8.64/4.82 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.82 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4003_half__gt__zero,axiom,
% 8.64/4.82 ! [A: rat] :
% 8.64/4.82 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.82 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4004_half__gt__zero__iff,axiom,
% 8.64/4.82 ! [A: real] :
% 8.64/4.82 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.82 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4005_half__gt__zero__iff,axiom,
% 8.64/4.82 ! [A: rat] :
% 8.64/4.82 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 8.64/4.82 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4006_scaling__mono,axiom,
% 8.64/4.82 ! [U: real,V2: real,R3: real,S2: real] :
% 8.64/4.82 ( ( ord_less_eq_real @ U @ V2 )
% 8.64/4.82 => ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 8.64/4.82 => ( ( ord_less_eq_real @ R3 @ S2 )
% 8.64/4.82 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R3 @ ( minus_minus_real @ V2 @ U ) ) @ S2 ) ) @ V2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4007_scaling__mono,axiom,
% 8.64/4.82 ! [U: rat,V2: rat,R3: rat,S2: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ U @ V2 )
% 8.64/4.82 => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 8.64/4.82 => ( ( ord_less_eq_rat @ R3 @ S2 )
% 8.64/4.82 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V2 @ U ) ) @ S2 ) ) @ V2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4008_nat__approx__posE,axiom,
% 8.64/4.82 ! [E: rat] :
% 8.64/4.82 ( ( ord_less_rat @ zero_zero_rat @ E )
% 8.64/4.82 => ~ ! [N3: nat] :
% 8.64/4.82 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4009_nat__approx__posE,axiom,
% 8.64/4.82 ! [E: real] :
% 8.64/4.82 ( ( ord_less_real @ zero_zero_real @ E )
% 8.64/4.82 => ~ ! [N3: nat] :
% 8.64/4.82 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4010_inverse__of__nat__le,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( N != zero_zero_nat )
% 8.64/4.82 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4011_inverse__of__nat__le,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( N != zero_zero_nat )
% 8.64/4.82 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4012_triangle__def,axiom,
% 8.64/4.82 ( nat_triangle
% 8.64/4.82 = ( ^ [N4: nat] : ( divide_divide_nat @ ( times_times_nat @ N4 @ ( suc @ N4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4013_arith__geo__mean,axiom,
% 8.64/4.82 ! [U: real,X: real,Y: real] :
% 8.64/4.82 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.82 = ( times_times_real @ X @ Y ) )
% 8.64/4.82 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.82 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.82 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4014_arith__geo__mean,axiom,
% 8.64/4.82 ! [U: rat,X: rat,Y: rat] :
% 8.64/4.82 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.82 = ( times_times_rat @ X @ Y ) )
% 8.64/4.82 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.82 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.82 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4015_double__not__eq__Suc__double,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 8.64/4.82 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4016_Suc__double__not__eq__double,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.82 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4017_exp__add__not__zero__imp__right,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.82 != zero_zero_nat )
% 8.64/4.82 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.82 != zero_zero_nat ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4018_exp__add__not__zero__imp__right,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.82 != zero_zero_int )
% 8.64/4.82 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.64/4.82 != zero_zero_int ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4019_one__div__two__eq__zero,axiom,
% 8.64/4.82 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.82 = zero_z3403309356797280102nteger ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4020_one__div__two__eq__zero,axiom,
% 8.64/4.82 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.82 = zero_zero_nat ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4021_one__div__two__eq__zero,axiom,
% 8.64/4.82 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.82 = zero_zero_int ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4022_div2__Suc__Suc,axiom,
% 8.64/4.82 ! [M2: nat] :
% 8.64/4.82 ( ( divide_divide_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.82 = ( suc @ ( divide_divide_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4023_insert_H__correct,axiom,
% 8.64/4.82 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.64/4.82 ( ( vEBT_invar_vebt @ T @ N )
% 8.64/4.82 => ( ( vEBT_set_vebt @ ( vEBT_VEBT_insert @ T @ X ) )
% 8.64/4.82 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ ( vEBT_set_vebt @ T ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4024_div__mult__self__is__m,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ( divide_divide_nat @ ( times_times_nat @ M2 @ N ) @ N )
% 8.64/4.82 = M2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4025_div__mult__self1__is__m,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M2 ) @ N )
% 8.64/4.82 = M2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4026_div__mult__self1,axiom,
% 8.64/4.82 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.82 ( ( B != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 8.64/4.82 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4027_div__mult__self1,axiom,
% 8.64/4.82 ! [B: int,A: int,C2: int] :
% 8.64/4.82 ( ( B != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 8.64/4.82 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4028_div__mult__self2,axiom,
% 8.64/4.82 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.82 ( ( B != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 8.64/4.82 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4029_div__mult__self2,axiom,
% 8.64/4.82 ! [B: int,A: int,C2: int] :
% 8.64/4.82 ( ( B != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 8.64/4.82 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4030_div__mult__self3,axiom,
% 8.64/4.82 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.82 ( ( B != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 8.64/4.82 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4031_div__mult__self3,axiom,
% 8.64/4.82 ! [B: int,C2: int,A: int] :
% 8.64/4.82 ( ( B != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 8.64/4.82 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4032_zdiv__numeral__Bit0,axiom,
% 8.64/4.82 ! [V2: num,W2: num] :
% 8.64/4.82 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 8.64/4.82 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4033_real__divide__square__eq,axiom,
% 8.64/4.82 ! [R3: real,A: real] :
% 8.64/4.82 ( ( divide_divide_real @ ( times_times_real @ R3 @ A ) @ ( times_times_real @ R3 @ R3 ) )
% 8.64/4.82 = ( divide_divide_real @ A @ R3 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4034_div__mult__mult1__if,axiom,
% 8.64/4.82 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.82 ( ( ( C2 = zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 8.64/4.82 = zero_zero_nat ) )
% 8.64/4.82 & ( ( C2 != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 8.64/4.82 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4035_div__mult__mult1__if,axiom,
% 8.64/4.82 ! [C2: int,A: int,B: int] :
% 8.64/4.82 ( ( ( C2 = zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.64/4.82 = zero_zero_int ) )
% 8.64/4.82 & ( ( C2 != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.64/4.82 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4036_div__mult__mult2,axiom,
% 8.64/4.82 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.82 ( ( C2 != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.82 = ( divide_divide_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4037_div__mult__mult2,axiom,
% 8.64/4.82 ! [C2: int,A: int,B: int] :
% 8.64/4.82 ( ( C2 != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.64/4.82 = ( divide_divide_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4038_div__mult__mult1,axiom,
% 8.64/4.82 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.82 ( ( C2 != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) )
% 8.64/4.82 = ( divide_divide_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4039_div__mult__mult1,axiom,
% 8.64/4.82 ! [C2: int,A: int,B: int] :
% 8.64/4.82 ( ( C2 != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.64/4.82 = ( divide_divide_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4040_div__by__Suc__0,axiom,
% 8.64/4.82 ! [M2: nat] :
% 8.64/4.82 ( ( divide_divide_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 8.64/4.82 = M2 ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4041_div__less,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ M2 @ N )
% 8.64/4.82 => ( ( divide_divide_nat @ M2 @ N )
% 8.64/4.82 = zero_zero_nat ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4042_div__mult__self4,axiom,
% 8.64/4.82 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.82 ( ( B != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 8.64/4.82 = ( plus_plus_nat @ C2 @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4043_div__mult__self4,axiom,
% 8.64/4.82 ! [B: int,C2: int,A: int] :
% 8.64/4.82 ( ( B != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 8.64/4.82 = ( plus_plus_int @ C2 @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4044_zdiv__zmult2__eq,axiom,
% 8.64/4.82 ! [C2: int,A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.64/4.82 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.82 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4045_div__neg__pos__less0,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_int @ A @ zero_zero_int )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.82 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4046_neg__imp__zdiv__neg__iff,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( ord_less_int @ B @ zero_zero_int )
% 8.64/4.82 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 8.64/4.82 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4047_pos__imp__zdiv__neg__iff,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.82 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 8.64/4.82 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4048_zdiv__int,axiom,
% 8.64/4.82 ! [A: nat,B: nat] :
% 8.64/4.82 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 8.64/4.82 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4049_atLeastAtMostPlus1__int__conv,axiom,
% 8.64/4.82 ! [M2: int,N: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 8.64/4.82 => ( ( set_or1266510415728281911st_int @ M2 @ ( plus_plus_int @ one_one_int @ N ) )
% 8.64/4.82 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M2 @ N ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4050_nonneg1__imp__zdiv__pos__iff,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.64/4.82 = ( ( ord_less_eq_int @ B @ A )
% 8.64/4.82 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4051_pos__imp__zdiv__nonneg__iff,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.82 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.64/4.82 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4052_neg__imp__zdiv__nonneg__iff,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( ord_less_int @ B @ zero_zero_int )
% 8.64/4.82 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 8.64/4.82 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4053_pos__imp__zdiv__pos__iff,axiom,
% 8.64/4.82 ! [K2: int,I2: int] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K2 ) )
% 8.64/4.82 = ( ord_less_eq_int @ K2 @ I2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4054_div__nonpos__pos__le0,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.82 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4055_div__nonneg__neg__le0,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.82 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.64/4.82 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4056_div__positive__int,axiom,
% 8.64/4.82 ! [L: int,K2: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ L @ K2 )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ L )
% 8.64/4.82 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4057_div__int__pos__iff,axiom,
% 8.64/4.82 ! [K2: int,L: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K2 @ L ) )
% 8.64/4.82 = ( ( K2 = zero_zero_int )
% 8.64/4.82 | ( L = zero_zero_int )
% 8.64/4.82 | ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 8.64/4.82 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 8.64/4.82 | ( ( ord_less_int @ K2 @ zero_zero_int )
% 8.64/4.82 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4058_zdiv__mono2__neg,axiom,
% 8.64/4.82 ! [A: int,B2: int,B: int] :
% 8.64/4.82 ( ( ord_less_int @ A @ zero_zero_int )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 8.64/4.82 => ( ( ord_less_eq_int @ B2 @ B )
% 8.64/4.82 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4059_zdiv__mono1__neg,axiom,
% 8.64/4.82 ! [A: int,A2: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ A2 )
% 8.64/4.82 => ( ( ord_less_int @ B @ zero_zero_int )
% 8.64/4.82 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4060_zdiv__eq__0__iff,axiom,
% 8.64/4.82 ! [I2: int,K2: int] :
% 8.64/4.82 ( ( ( divide_divide_int @ I2 @ K2 )
% 8.64/4.82 = zero_zero_int )
% 8.64/4.82 = ( ( K2 = zero_zero_int )
% 8.64/4.82 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 8.64/4.82 & ( ord_less_int @ I2 @ K2 ) )
% 8.64/4.82 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 8.64/4.82 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4061_zdiv__mono2,axiom,
% 8.64/4.82 ! [A: int,B2: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 8.64/4.82 => ( ( ord_less_eq_int @ B2 @ B )
% 8.64/4.82 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4062_zdiv__mono1,axiom,
% 8.64/4.82 ! [A: int,A2: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ A2 )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.82 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4063_int__div__less__self,axiom,
% 8.64/4.82 ! [X: int,K2: int] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ X )
% 8.64/4.82 => ( ( ord_less_int @ one_one_int @ K2 )
% 8.64/4.82 => ( ord_less_int @ ( divide_divide_int @ X @ K2 ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4064_periodic__finite__ex,axiom,
% 8.64/4.82 ! [D: int,P2: int > $o] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ D )
% 8.64/4.82 => ( ! [X3: int,K: int] :
% 8.64/4.82 ( ( P2 @ X3 )
% 8.64/4.82 = ( P2 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D ) ) ) )
% 8.64/4.82 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 8.64/4.82 = ( ? [X4: int] :
% 8.64/4.82 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 8.64/4.82 & ( P2 @ X4 ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4065_split__zdiv,axiom,
% 8.64/4.82 ! [P2: int > $o,N: int,K2: int] :
% 8.64/4.82 ( ( P2 @ ( divide_divide_int @ N @ K2 ) )
% 8.64/4.82 = ( ( ( K2 = zero_zero_int )
% 8.64/4.82 => ( P2 @ zero_zero_int ) )
% 8.64/4.82 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.82 => ! [I: int,J: int] :
% 8.64/4.82 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 8.64/4.82 & ( ord_less_int @ J @ K2 )
% 8.64/4.82 & ( N
% 8.64/4.82 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 8.64/4.82 => ( P2 @ I ) ) )
% 8.64/4.82 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 8.64/4.82 => ! [I: int,J: int] :
% 8.64/4.82 ( ( ( ord_less_int @ K2 @ J )
% 8.64/4.82 & ( ord_less_eq_int @ J @ zero_zero_int )
% 8.64/4.82 & ( N
% 8.64/4.82 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 8.64/4.82 => ( P2 @ I ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4066_int__div__neg__eq,axiom,
% 8.64/4.82 ! [A: int,B: int,Q2: int,R3: int] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 8.64/4.82 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 8.64/4.82 => ( ( ord_less_int @ B @ R3 )
% 8.64/4.82 => ( ( divide_divide_int @ A @ B )
% 8.64/4.82 = Q2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4067_int__div__pos__eq,axiom,
% 8.64/4.82 ! [A: int,B: int,Q2: int,R3: int] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 8.64/4.82 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 8.64/4.82 => ( ( ord_less_int @ R3 @ B )
% 8.64/4.82 => ( ( divide_divide_int @ A @ B )
% 8.64/4.82 = Q2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4068_cpmi,axiom,
% 8.64/4.82 ! [D3: int,P2: int > $o,P6: int > $o,B5: set_int] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.64/4.82 => ( ? [Z5: int] :
% 8.64/4.82 ! [X3: int] :
% 8.64/4.82 ( ( ord_less_int @ X3 @ Z5 )
% 8.64/4.82 => ( ( P2 @ X3 )
% 8.64/4.82 = ( P6 @ X3 ) ) )
% 8.64/4.82 => ( ! [X3: int] :
% 8.64/4.82 ( ! [Xa: int] :
% 8.64/4.82 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.64/4.82 => ! [Xb2: int] :
% 8.64/4.82 ( ( member_int @ Xb2 @ B5 )
% 8.64/4.82 => ( X3
% 8.64/4.82 != ( plus_plus_int @ Xb2 @ Xa ) ) ) )
% 8.64/4.82 => ( ( P2 @ X3 )
% 8.64/4.82 => ( P2 @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 8.64/4.82 => ( ! [X3: int,K: int] :
% 8.64/4.82 ( ( P6 @ X3 )
% 8.64/4.82 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 8.64/4.82 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 8.64/4.82 = ( ? [X4: int] :
% 8.64/4.82 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.64/4.82 & ( P6 @ X4 ) )
% 8.64/4.82 | ? [X4: int] :
% 8.64/4.82 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.64/4.82 & ? [Y4: int] :
% 8.64/4.82 ( ( member_int @ Y4 @ B5 )
% 8.64/4.82 & ( P2 @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4069_cppi,axiom,
% 8.64/4.82 ! [D3: int,P2: int > $o,P6: int > $o,A4: set_int] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ D3 )
% 8.64/4.82 => ( ? [Z5: int] :
% 8.64/4.82 ! [X3: int] :
% 8.64/4.82 ( ( ord_less_int @ Z5 @ X3 )
% 8.64/4.82 => ( ( P2 @ X3 )
% 8.64/4.82 = ( P6 @ X3 ) ) )
% 8.64/4.82 => ( ! [X3: int] :
% 8.64/4.82 ( ! [Xa: int] :
% 8.64/4.82 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.64/4.82 => ! [Xb2: int] :
% 8.64/4.82 ( ( member_int @ Xb2 @ A4 )
% 8.64/4.82 => ( X3
% 8.64/4.82 != ( minus_minus_int @ Xb2 @ Xa ) ) ) )
% 8.64/4.82 => ( ( P2 @ X3 )
% 8.64/4.82 => ( P2 @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 8.64/4.82 => ( ! [X3: int,K: int] :
% 8.64/4.82 ( ( P6 @ X3 )
% 8.64/4.82 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K @ D3 ) ) ) )
% 8.64/4.82 => ( ( ? [X7: int] : ( P2 @ X7 ) )
% 8.64/4.82 = ( ? [X4: int] :
% 8.64/4.82 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.64/4.82 & ( P6 @ X4 ) )
% 8.64/4.82 | ? [X4: int] :
% 8.64/4.82 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 8.64/4.82 & ? [Y4: int] :
% 8.64/4.82 ( ( member_int @ Y4 @ A4 )
% 8.64/4.82 & ( P2 @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4070_int__power__div__base,axiom,
% 8.64/4.82 ! [M2: nat,K2: int] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.82 => ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.82 => ( ( divide_divide_int @ ( power_power_int @ K2 @ M2 ) @ K2 )
% 8.64/4.82 = ( power_power_int @ K2 @ ( minus_minus_nat @ M2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4071_div__pos__geq,axiom,
% 8.64/4.82 ! [L: int,K2: int] :
% 8.64/4.82 ( ( ord_less_int @ zero_zero_int @ L )
% 8.64/4.82 => ( ( ord_less_eq_int @ L @ K2 )
% 8.64/4.82 => ( ( divide_divide_int @ K2 @ L )
% 8.64/4.82 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K2 @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4072_div__le__dividend,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4073_div__le__mono,axiom,
% 8.64/4.82 ! [M2: nat,N: nat,K2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.82 => ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ K2 ) @ ( divide_divide_nat @ N @ K2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4074_div__mult2__eq,axiom,
% 8.64/4.82 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.82 ( ( divide_divide_nat @ M2 @ ( times_times_nat @ N @ Q2 ) )
% 8.64/4.82 = ( divide_divide_nat @ ( divide_divide_nat @ M2 @ N ) @ Q2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4075_pos__zdiv__mult__2,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.64/4.82 = ( divide_divide_int @ B @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4076_neg__zdiv__mult__2,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.64/4.82 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4077_div__mult2__eq_H,axiom,
% 8.64/4.82 ! [A: int,M2: nat,N: nat] :
% 8.64/4.82 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.82 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4078_div__mult2__eq_H,axiom,
% 8.64/4.82 ! [A: nat,M2: nat,N: nat] :
% 8.64/4.82 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 8.64/4.82 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4079_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( ( divide_divide_nat @ M2 @ N )
% 8.64/4.82 = zero_zero_nat )
% 8.64/4.82 = ( ( ord_less_nat @ M2 @ N )
% 8.64/4.82 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4080_Suc__div__le__mono,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M2 @ N ) @ ( divide_divide_nat @ ( suc @ M2 ) @ N ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4081_less__mult__imp__div__less,axiom,
% 8.64/4.82 ! [M2: nat,I2: nat,N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ M2 @ ( times_times_nat @ I2 @ N ) )
% 8.64/4.82 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ I2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4082_times__div__less__eq__dividend,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) @ M2 ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4083_div__times__less__eq__dividend,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) @ M2 ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4084_div__mult2__numeral__eq,axiom,
% 8.64/4.82 ! [A: nat,K2: num,L: num] :
% 8.64/4.82 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K2 ) ) @ ( numeral_numeral_nat @ L ) )
% 8.64/4.82 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K2 @ L ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4085_div__mult2__numeral__eq,axiom,
% 8.64/4.82 ! [A: int,K2: num,L: num] :
% 8.64/4.82 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ L ) )
% 8.64/4.82 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K2 @ L ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4086_div__add__self1,axiom,
% 8.64/4.82 ! [B: code_integer,A: code_integer] :
% 8.64/4.82 ( ( B != zero_z3403309356797280102nteger )
% 8.64/4.82 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 8.64/4.82 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4087_div__add__self1,axiom,
% 8.64/4.82 ! [B: nat,A: nat] :
% 8.64/4.82 ( ( B != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 8.64/4.82 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4088_div__add__self1,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( B != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 8.64/4.82 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4089_div__add__self2,axiom,
% 8.64/4.82 ! [B: code_integer,A: code_integer] :
% 8.64/4.82 ( ( B != zero_z3403309356797280102nteger )
% 8.64/4.82 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 8.64/4.82 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4090_div__add__self2,axiom,
% 8.64/4.82 ! [B: nat,A: nat] :
% 8.64/4.82 ( ( B != zero_zero_nat )
% 8.64/4.82 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 8.64/4.82 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4091_div__add__self2,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( B != zero_zero_int )
% 8.64/4.82 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 8.64/4.82 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4092_div__le__mono2,axiom,
% 8.64/4.82 ! [M2: nat,N: nat,K2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.82 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.82 => ( ord_less_eq_nat @ ( divide_divide_nat @ K2 @ N ) @ ( divide_divide_nat @ K2 @ M2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4093_div__greater__zero__iff,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M2 @ N ) )
% 8.64/4.82 = ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4094_div__less__iff__less__mult,axiom,
% 8.64/4.82 ! [Q2: nat,M2: nat,N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 8.64/4.82 => ( ( ord_less_nat @ ( divide_divide_nat @ M2 @ Q2 ) @ N )
% 8.64/4.82 = ( ord_less_nat @ M2 @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4095_div__less__dividend,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ one_one_nat @ N )
% 8.64/4.82 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.82 => ( ord_less_nat @ ( divide_divide_nat @ M2 @ N ) @ M2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4096_div__eq__dividend__iff,axiom,
% 8.64/4.82 ! [M2: nat,N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.82 => ( ( ( divide_divide_nat @ M2 @ N )
% 8.64/4.82 = M2 )
% 8.64/4.82 = ( N = one_one_nat ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4097_div__if,axiom,
% 8.64/4.82 ( divide_divide_nat
% 8.64/4.82 = ( ^ [M6: nat,N4: nat] :
% 8.64/4.82 ( if_nat
% 8.64/4.82 @ ( ( ord_less_nat @ M6 @ N4 )
% 8.64/4.82 | ( N4 = zero_zero_nat ) )
% 8.64/4.82 @ zero_zero_nat
% 8.64/4.82 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4098_div__nat__eqI,axiom,
% 8.64/4.82 ! [N: nat,Q2: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M2 )
% 8.64/4.82 => ( ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 8.64/4.82 => ( ( divide_divide_nat @ M2 @ N )
% 8.64/4.82 = Q2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4099_less__eq__div__iff__mult__less__eq,axiom,
% 8.64/4.82 ! [Q2: nat,M2: nat,N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 8.64/4.82 => ( ( ord_less_eq_nat @ M2 @ ( divide_divide_nat @ N @ Q2 ) )
% 8.64/4.82 = ( ord_less_eq_nat @ ( times_times_nat @ M2 @ Q2 ) @ N ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4100_dividend__less__times__div,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4101_dividend__less__div__times,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ord_less_nat @ M2 @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M2 @ N ) @ N ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4102_split__div,axiom,
% 8.64/4.82 ! [P2: nat > $o,M2: nat,N: nat] :
% 8.64/4.82 ( ( P2 @ ( divide_divide_nat @ M2 @ N ) )
% 8.64/4.82 = ( ( ( N = zero_zero_nat )
% 8.64/4.82 => ( P2 @ zero_zero_nat ) )
% 8.64/4.82 & ( ( N != zero_zero_nat )
% 8.64/4.82 => ! [I: nat,J: nat] :
% 8.64/4.82 ( ( ord_less_nat @ J @ N )
% 8.64/4.82 => ( ( M2
% 8.64/4.82 = ( plus_plus_nat @ ( times_times_nat @ N @ I ) @ J ) )
% 8.64/4.82 => ( P2 @ I ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4103_power__diff__power__eq,axiom,
% 8.64/4.82 ! [A: code_integer,N: nat,M2: nat] :
% 8.64/4.82 ( ( A != zero_z3403309356797280102nteger )
% 8.64/4.82 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.64/4.82 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 8.64/4.82 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M2 ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 8.64/4.82 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4104_power__diff__power__eq,axiom,
% 8.64/4.82 ! [A: nat,N: nat,M2: nat] :
% 8.64/4.82 ( ( A != zero_zero_nat )
% 8.64/4.82 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 8.64/4.82 = ( power_power_nat @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 8.64/4.82 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) )
% 8.64/4.82 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4105_power__diff__power__eq,axiom,
% 8.64/4.82 ! [A: int,N: nat,M2: nat] :
% 8.64/4.82 ( ( A != zero_zero_int )
% 8.64/4.82 => ( ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 8.64/4.82 = ( power_power_int @ A @ ( minus_minus_nat @ M2 @ N ) ) ) )
% 8.64/4.82 & ( ~ ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( divide_divide_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) )
% 8.64/4.82 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4106_le__div__geq,axiom,
% 8.64/4.82 ! [N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.82 => ( ( divide_divide_nat @ M2 @ N )
% 8.64/4.82 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4107_split__div_H,axiom,
% 8.64/4.82 ! [P2: nat > $o,M2: nat,N: nat] :
% 8.64/4.82 ( ( P2 @ ( divide_divide_nat @ M2 @ N ) )
% 8.64/4.82 = ( ( ( N = zero_zero_nat )
% 8.64/4.82 & ( P2 @ zero_zero_nat ) )
% 8.64/4.82 | ? [Q5: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M2 )
% 8.64/4.82 & ( ord_less_nat @ M2 @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 8.64/4.82 & ( P2 @ Q5 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4108_div__2__gt__zero,axiom,
% 8.64/4.82 ! [N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.82 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4109_Suc__n__div__2__gt__zero,axiom,
% 8.64/4.82 ! [N: nat] :
% 8.64/4.82 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4110_linear__plus__1__le__power,axiom,
% 8.64/4.82 ! [X: real,N: nat] :
% 8.64/4.82 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.82 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4111_succ__list__to__short,axiom,
% 8.64/4.82 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.82 => ( ( ord_less_eq_nat @ Mi @ X )
% 8.64/4.82 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.82 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.82 = none_nat ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4112_pred__list__to__short,axiom,
% 8.64/4.82 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.82 => ( ( ord_less_eq_nat @ X @ Ma )
% 8.64/4.82 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.82 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.82 = none_nat ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4113_set__bit__0,axiom,
% 8.64/4.82 ! [A: code_integer] :
% 8.64/4.82 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 8.64/4.82 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4114_set__bit__0,axiom,
% 8.64/4.82 ! [A: nat] :
% 8.64/4.82 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 8.64/4.82 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4115_set__bit__0,axiom,
% 8.64/4.82 ! [A: int] :
% 8.64/4.82 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 8.64/4.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4116_case4_I11_J,axiom,
% 8.64/4.82 ( ( mi != ma )
% 8.64/4.82 => ! [I4: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 8.64/4.82 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 8.64/4.82 = I4 )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 8.64/4.82 & ! [X5: nat] :
% 8.64/4.82 ( ( ( ( vEBT_VEBT_high @ X5 @ na )
% 8.64/4.82 = I4 )
% 8.64/4.82 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ na ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ mi @ X5 )
% 8.64/4.82 & ( ord_less_eq_nat @ X5 @ ma ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4117_enat__ord__number_I1_J,axiom,
% 8.64/4.82 ! [M2: num,N: num] :
% 8.64/4.82 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( numera1916890842035813515d_enat @ N ) )
% 8.64/4.82 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4118_le__sup__iff,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z3 )
% 8.64/4.82 = ( ( ord_less_eq_set_nat @ X @ Z3 )
% 8.64/4.82 & ( ord_less_eq_set_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4119_le__sup__iff,axiom,
% 8.64/4.82 ! [X: rat,Y: rat,Z3: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z3 )
% 8.64/4.82 = ( ( ord_less_eq_rat @ X @ Z3 )
% 8.64/4.82 & ( ord_less_eq_rat @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4120_le__sup__iff,axiom,
% 8.64/4.82 ! [X: nat,Y: nat,Z3: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z3 )
% 8.64/4.82 = ( ( ord_less_eq_nat @ X @ Z3 )
% 8.64/4.82 & ( ord_less_eq_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4121_le__sup__iff,axiom,
% 8.64/4.82 ! [X: int,Y: int,Z3: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z3 )
% 8.64/4.82 = ( ( ord_less_eq_int @ X @ Z3 )
% 8.64/4.82 & ( ord_less_eq_int @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4122_sup_Obounded__iff,axiom,
% 8.64/4.82 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 8.64/4.82 = ( ( ord_less_eq_set_nat @ B @ A )
% 8.64/4.82 & ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4123_sup_Obounded__iff,axiom,
% 8.64/4.82 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 8.64/4.82 = ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.82 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4124_sup_Obounded__iff,axiom,
% 8.64/4.82 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 8.64/4.82 = ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.82 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4125_sup_Obounded__iff,axiom,
% 8.64/4.82 ! [B: int,C2: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 8.64/4.82 = ( ( ord_less_eq_int @ B @ A )
% 8.64/4.82 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4126_bit__split__inv,axiom,
% 8.64/4.82 ! [X: nat,D: nat] :
% 8.64/4.82 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 8.64/4.82 = X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4127_finite__atLeastAtMost__int,axiom,
% 8.64/4.82 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4128_high__def,axiom,
% 8.64/4.82 ( vEBT_VEBT_high
% 8.64/4.82 = ( ^ [X4: nat,N4: nat] : ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4129_high__bound__aux,axiom,
% 8.64/4.82 ! [Ma: nat,N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 8.64/4.82 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4130_high__inv,axiom,
% 8.64/4.82 ! [X: nat,N: nat,Y: nat] :
% 8.64/4.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.82 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4131_low__inv,axiom,
% 8.64/4.82 ! [X: nat,N: nat,Y: nat] :
% 8.64/4.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.82 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4132_le__inf__iff,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) )
% 8.64/4.82 = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 8.64/4.82 & ( ord_le3146513528884898305at_nat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4133_le__inf__iff,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) )
% 8.64/4.82 = ( ( ord_less_eq_set_nat @ X @ Y )
% 8.64/4.82 & ( ord_less_eq_set_nat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4134_le__inf__iff,axiom,
% 8.64/4.82 ! [X: rat,Y: rat,Z3: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) )
% 8.64/4.82 = ( ( ord_less_eq_rat @ X @ Y )
% 8.64/4.82 & ( ord_less_eq_rat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4135_le__inf__iff,axiom,
% 8.64/4.82 ! [X: nat,Y: nat,Z3: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) )
% 8.64/4.82 = ( ( ord_less_eq_nat @ X @ Y )
% 8.64/4.82 & ( ord_less_eq_nat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4136_le__inf__iff,axiom,
% 8.64/4.82 ! [X: int,Y: int,Z3: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) )
% 8.64/4.82 = ( ( ord_less_eq_int @ X @ Y )
% 8.64/4.82 & ( ord_less_eq_int @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4137_inf_Obounded__iff,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 8.64/4.82 = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 8.64/4.82 & ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4138_inf_Obounded__iff,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 8.64/4.82 = ( ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.82 & ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4139_inf_Obounded__iff,axiom,
% 8.64/4.82 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 8.64/4.82 = ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.82 & ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4140_inf_Obounded__iff,axiom,
% 8.64/4.82 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 8.64/4.82 = ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.82 & ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4141_inf_Obounded__iff,axiom,
% 8.64/4.82 ! [A: int,B: int,C2: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 8.64/4.82 = ( ( ord_less_eq_int @ A @ B )
% 8.64/4.82 & ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4142_both__member__options__ding,axiom,
% 8.64/4.82 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 8.64/4.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 8.64/4.82 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.64/4.82 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4143_both__member__options__from__complete__tree__to__child,axiom,
% 8.64/4.82 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 8.64/4.82 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.82 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.82 | ( X = Mi )
% 8.64/4.82 | ( X = Ma ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4144_member__inv,axiom,
% 8.64/4.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.64/4.82 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.82 & ( ( X = Mi )
% 8.64/4.82 | ( X = Ma )
% 8.64/4.82 | ( ( ord_less_nat @ X @ Ma )
% 8.64/4.82 & ( ord_less_nat @ Mi @ X )
% 8.64/4.82 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.82 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4145_both__member__options__from__chilf__to__complete__tree,axiom,
% 8.64/4.82 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 8.64/4.82 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.82 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 8.64/4.82 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4146_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 8.64/4.82 ! [X: nat,N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.82 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4147_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 8.64/4.82 ! [X: nat,N: nat,M2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M2 ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.82 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.82 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4148_inf__sup__ord_I2_J,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4149_inf__sup__ord_I2_J,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4150_inf__sup__ord_I2_J,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4151_inf__sup__ord_I2_J,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4152_inf__sup__ord_I2_J,axiom,
% 8.64/4.82 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4153_inf__sup__ord_I1_J,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4154_inf__sup__ord_I1_J,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4155_inf__sup__ord_I1_J,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4156_inf__sup__ord_I1_J,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4157_inf__sup__ord_I1_J,axiom,
% 8.64/4.82 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4158_inf__le1,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4159_inf__le1,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4160_inf__le1,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4161_inf__le1,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4162_inf__le1,axiom,
% 8.64/4.82 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4163_inf__le2,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4164_inf__le2,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4165_inf__le2,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4166_inf__le2,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4167_inf__le2,axiom,
% 8.64/4.82 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4168_le__infE,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 8.64/4.82 => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 8.64/4.82 => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4169_le__infE,axiom,
% 8.64/4.82 ! [X: set_nat,A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 8.64/4.82 => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4170_le__infE,axiom,
% 8.64/4.82 ! [X: rat,A: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_rat @ X @ A )
% 8.64/4.82 => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4171_le__infE,axiom,
% 8.64/4.82 ! [X: nat,A: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_nat @ X @ A )
% 8.64/4.82 => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4172_le__infE,axiom,
% 8.64/4.82 ! [X: int,A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_int @ X @ A )
% 8.64/4.82 => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4173_le__infI,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ X @ A )
% 8.64/4.82 => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4174_le__infI,axiom,
% 8.64/4.82 ! [X: set_nat,A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ A )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ X @ B )
% 8.64/4.82 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4175_le__infI,axiom,
% 8.64/4.82 ! [X: rat,A: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ A )
% 8.64/4.82 => ( ( ord_less_eq_rat @ X @ B )
% 8.64/4.82 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4176_le__infI,axiom,
% 8.64/4.82 ! [X: nat,A: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ A )
% 8.64/4.82 => ( ( ord_less_eq_nat @ X @ B )
% 8.64/4.82 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4177_le__infI,axiom,
% 8.64/4.82 ! [X: int,A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ A )
% 8.64/4.82 => ( ( ord_less_eq_int @ X @ B )
% 8.64/4.82 => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4178_inf__mono,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 8.64/4.82 => ( ( ord_le3146513528884898305at_nat @ B @ D )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4179_inf__mono,axiom,
% 8.64/4.82 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ B @ D )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4180_inf__mono,axiom,
% 8.64/4.82 ! [A: rat,C2: rat,B: rat,D: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_rat @ B @ D )
% 8.64/4.82 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4181_inf__mono,axiom,
% 8.64/4.82 ! [A: nat,C2: nat,B: nat,D: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_nat @ B @ D )
% 8.64/4.82 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4182_inf__mono,axiom,
% 8.64/4.82 ! [A: int,C2: int,B: int,D: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_int @ B @ D )
% 8.64/4.82 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4183_le__infI1,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ X )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4184_le__infI1,axiom,
% 8.64/4.82 ! [A: set_nat,X: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ X )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4185_le__infI1,axiom,
% 8.64/4.82 ! [A: rat,X: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ X )
% 8.64/4.82 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4186_le__infI1,axiom,
% 8.64/4.82 ! [A: nat,X: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ X )
% 8.64/4.82 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4187_le__infI1,axiom,
% 8.64/4.82 ! [A: int,X: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ X )
% 8.64/4.82 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4188_le__infI2,axiom,
% 8.64/4.82 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ B @ X )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4189_le__infI2,axiom,
% 8.64/4.82 ! [B: set_nat,X: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ B @ X )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4190_le__infI2,axiom,
% 8.64/4.82 ! [B: rat,X: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ B @ X )
% 8.64/4.82 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4191_le__infI2,axiom,
% 8.64/4.82 ! [B: nat,X: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ B @ X )
% 8.64/4.82 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4192_le__infI2,axiom,
% 8.64/4.82 ! [B: int,X: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ B @ X )
% 8.64/4.82 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4193_inf_OorderE,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4194_inf_OorderE,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4195_inf_OorderE,axiom,
% 8.64/4.82 ! [A: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( inf_inf_rat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4196_inf_OorderE,axiom,
% 8.64/4.82 ! [A: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( inf_inf_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4197_inf_OorderE,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ B )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( inf_inf_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4198_inf_OorderI,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4199_inf_OorderI,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( inf_inf_set_nat @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4200_inf_OorderI,axiom,
% 8.64/4.82 ! [A: rat,B: rat] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( inf_inf_rat @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4201_inf_OorderI,axiom,
% 8.64/4.82 ! [A: nat,B: nat] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( inf_inf_nat @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_nat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4202_inf_OorderI,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( inf_inf_int @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_int @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4203_inf__unique,axiom,
% 8.64/4.82 ! [F2: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 8.64/4.82 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 8.64/4.82 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ X3 @ Y3 )
% 8.64/4.82 => ( ( ord_le3146513528884898305at_nat @ X3 @ Z )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 8.64/4.82 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4204_inf__unique,axiom,
% 8.64/4.82 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 8.64/4.82 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 8.64/4.82 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 8.64/4.82 => ( ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ X3 @ Z )
% 8.64/4.82 => ( ord_less_eq_set_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 8.64/4.82 => ( ( inf_inf_set_nat @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4205_inf__unique,axiom,
% 8.64/4.82 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 8.64/4.82 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 8.64/4.82 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 8.64/4.82 => ( ! [X3: rat,Y3: rat,Z: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 8.64/4.82 => ( ( ord_less_eq_rat @ X3 @ Z )
% 8.64/4.82 => ( ord_less_eq_rat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 8.64/4.82 => ( ( inf_inf_rat @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4206_inf__unique,axiom,
% 8.64/4.82 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 8.64/4.82 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ X3 )
% 8.64/4.82 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 8.64/4.82 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 8.64/4.82 => ( ( ord_less_eq_nat @ X3 @ Z )
% 8.64/4.82 => ( ord_less_eq_nat @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 8.64/4.82 => ( ( inf_inf_nat @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4207_inf__unique,axiom,
% 8.64/4.82 ! [F2: int > int > int,X: int,Y: int] :
% 8.64/4.82 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ X3 )
% 8.64/4.82 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F2 @ X3 @ Y3 ) @ Y3 )
% 8.64/4.82 => ( ! [X3: int,Y3: int,Z: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X3 @ Y3 )
% 8.64/4.82 => ( ( ord_less_eq_int @ X3 @ Z )
% 8.64/4.82 => ( ord_less_eq_int @ X3 @ ( F2 @ Y3 @ Z ) ) ) )
% 8.64/4.82 => ( ( inf_inf_int @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4208_le__iff__inf,axiom,
% 8.64/4.82 ( ord_le3146513528884898305at_nat
% 8.64/4.82 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( inf_in2572325071724192079at_nat @ X4 @ Y4 )
% 8.64/4.82 = X4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4209_le__iff__inf,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [X4: set_nat,Y4: set_nat] :
% 8.64/4.82 ( ( inf_inf_set_nat @ X4 @ Y4 )
% 8.64/4.82 = X4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4210_le__iff__inf,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [X4: rat,Y4: rat] :
% 8.64/4.82 ( ( inf_inf_rat @ X4 @ Y4 )
% 8.64/4.82 = X4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4211_le__iff__inf,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [X4: nat,Y4: nat] :
% 8.64/4.82 ( ( inf_inf_nat @ X4 @ Y4 )
% 8.64/4.82 = X4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4212_le__iff__inf,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [X4: int,Y4: int] :
% 8.64/4.82 ( ( inf_inf_int @ X4 @ Y4 )
% 8.64/4.82 = X4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4213_inf_Oabsorb1,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 8.64/4.82 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4214_inf_Oabsorb1,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.82 => ( ( inf_inf_set_nat @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4215_inf_Oabsorb1,axiom,
% 8.64/4.82 ! [A: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.82 => ( ( inf_inf_rat @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4216_inf_Oabsorb1,axiom,
% 8.64/4.82 ! [A: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.82 => ( ( inf_inf_nat @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4217_inf_Oabsorb1,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ B )
% 8.64/4.82 => ( ( inf_inf_int @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4218_inf_Oabsorb2,axiom,
% 8.64/4.82 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ B @ A )
% 8.64/4.82 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4219_inf_Oabsorb2,axiom,
% 8.64/4.82 ! [B: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ B @ A )
% 8.64/4.82 => ( ( inf_inf_set_nat @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4220_inf_Oabsorb2,axiom,
% 8.64/4.82 ! [B: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.82 => ( ( inf_inf_rat @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4221_inf_Oabsorb2,axiom,
% 8.64/4.82 ! [B: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.82 => ( ( inf_inf_nat @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4222_inf_Oabsorb2,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ B @ A )
% 8.64/4.82 => ( ( inf_inf_int @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4223_inf__absorb1,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 8.64/4.82 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4224_inf__absorb1,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.64/4.82 => ( ( inf_inf_set_nat @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4225_inf__absorb1,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ Y )
% 8.64/4.82 => ( ( inf_inf_rat @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4226_inf__absorb1,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ Y )
% 8.64/4.82 => ( ( inf_inf_nat @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4227_inf__absorb1,axiom,
% 8.64/4.82 ! [X: int,Y: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ Y )
% 8.64/4.82 => ( ( inf_inf_int @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4228_inf__absorb2,axiom,
% 8.64/4.82 ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 8.64/4.82 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4229_inf__absorb2,axiom,
% 8.64/4.82 ! [Y: set_nat,X: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ Y @ X )
% 8.64/4.82 => ( ( inf_inf_set_nat @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4230_inf__absorb2,axiom,
% 8.64/4.82 ! [Y: rat,X: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ Y @ X )
% 8.64/4.82 => ( ( inf_inf_rat @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4231_inf__absorb2,axiom,
% 8.64/4.82 ! [Y: nat,X: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ Y @ X )
% 8.64/4.82 => ( ( inf_inf_nat @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4232_inf__absorb2,axiom,
% 8.64/4.82 ! [Y: int,X: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ Y @ X )
% 8.64/4.82 => ( ( inf_inf_int @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4233_inf_OboundedE,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) )
% 8.64/4.82 => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 8.64/4.82 => ~ ( ord_le3146513528884898305at_nat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4234_inf_OboundedE,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.82 => ~ ( ord_less_eq_set_nat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4235_inf_OboundedE,axiom,
% 8.64/4.82 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.82 => ~ ( ord_less_eq_rat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4236_inf_OboundedE,axiom,
% 8.64/4.82 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.82 => ~ ( ord_less_eq_nat @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4237_inf_OboundedE,axiom,
% 8.64/4.82 ! [A: int,B: int,C2: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) )
% 8.64/4.82 => ~ ( ( ord_less_eq_int @ A @ B )
% 8.64/4.82 => ~ ( ord_less_eq_int @ A @ C2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4238_inf_OboundedI,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 8.64/4.82 => ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4239_inf_OboundedI,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat,C2: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4240_inf_OboundedI,axiom,
% 8.64/4.82 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.82 => ( ( ord_less_eq_rat @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4241_inf_OboundedI,axiom,
% 8.64/4.82 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.82 => ( ( ord_less_eq_nat @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4242_inf_OboundedI,axiom,
% 8.64/4.82 ! [A: int,B: int,C2: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ B )
% 8.64/4.82 => ( ( ord_less_eq_int @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4243_inf__greatest,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 8.64/4.82 => ( ( ord_le3146513528884898305at_nat @ X @ Z3 )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4244_inf__greatest,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ X @ Z3 )
% 8.64/4.82 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4245_inf__greatest,axiom,
% 8.64/4.82 ! [X: rat,Y: rat,Z3: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ Y )
% 8.64/4.82 => ( ( ord_less_eq_rat @ X @ Z3 )
% 8.64/4.82 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4246_inf__greatest,axiom,
% 8.64/4.82 ! [X: nat,Y: nat,Z3: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ Y )
% 8.64/4.82 => ( ( ord_less_eq_nat @ X @ Z3 )
% 8.64/4.82 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4247_inf__greatest,axiom,
% 8.64/4.82 ! [X: int,Y: int,Z3: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ Y )
% 8.64/4.82 => ( ( ord_less_eq_int @ X @ Z3 )
% 8.64/4.82 => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4248_inf_Oorder__iff,axiom,
% 8.64/4.82 ( ord_le3146513528884898305at_nat
% 8.64/4.82 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( inf_in2572325071724192079at_nat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4249_inf_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( inf_inf_set_nat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4250_inf_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [A5: rat,B4: rat] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( inf_inf_rat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4251_inf_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [A5: nat,B4: nat] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( inf_inf_nat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4252_inf_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [A5: int,B4: int] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( inf_inf_int @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4253_inf_Ocobounded1,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4254_inf_Ocobounded1,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4255_inf_Ocobounded1,axiom,
% 8.64/4.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4256_inf_Ocobounded1,axiom,
% 8.64/4.82 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4257_inf_Ocobounded1,axiom,
% 8.64/4.82 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4258_inf_Ocobounded2,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4259_inf_Ocobounded2,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4260_inf_Ocobounded2,axiom,
% 8.64/4.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4261_inf_Ocobounded2,axiom,
% 8.64/4.82 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4262_inf_Ocobounded2,axiom,
% 8.64/4.82 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4263_inf_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_le3146513528884898305at_nat
% 8.64/4.82 = ( ^ [A5: set_Pr1261947904930325089at_nat,B4: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4264_inf_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.64/4.82 ( ( inf_inf_set_nat @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4265_inf_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [A5: rat,B4: rat] :
% 8.64/4.82 ( ( inf_inf_rat @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4266_inf_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [A5: nat,B4: nat] :
% 8.64/4.82 ( ( inf_inf_nat @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4267_inf_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [A5: int,B4: int] :
% 8.64/4.82 ( ( inf_inf_int @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4268_inf_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_le3146513528884898305at_nat
% 8.64/4.82 = ( ^ [B4: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( inf_in2572325071724192079at_nat @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4269_inf_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [B4: set_nat,A5: set_nat] :
% 8.64/4.82 ( ( inf_inf_set_nat @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4270_inf_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [B4: rat,A5: rat] :
% 8.64/4.82 ( ( inf_inf_rat @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4271_inf_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [B4: nat,A5: nat] :
% 8.64/4.82 ( ( inf_inf_nat @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4272_inf_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [B4: int,A5: int] :
% 8.64/4.82 ( ( inf_inf_int @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4273_inf_OcoboundedI1,axiom,
% 8.64/4.82 ! [A: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ A @ C2 )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4274_inf_OcoboundedI1,axiom,
% 8.64/4.82 ! [A: set_nat,C2: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4275_inf_OcoboundedI1,axiom,
% 8.64/4.82 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4276_inf_OcoboundedI1,axiom,
% 8.64/4.82 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4277_inf_OcoboundedI1,axiom,
% 8.64/4.82 ! [A: int,C2: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ C2 )
% 8.64/4.82 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4278_inf_OcoboundedI2,axiom,
% 8.64/4.82 ! [B: set_Pr1261947904930325089at_nat,C2: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( ord_le3146513528884898305at_nat @ B @ C2 )
% 8.64/4.82 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4279_inf_OcoboundedI2,axiom,
% 8.64/4.82 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ B @ C2 )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4280_inf_OcoboundedI2,axiom,
% 8.64/4.82 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ B @ C2 )
% 8.64/4.82 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4281_inf_OcoboundedI2,axiom,
% 8.64/4.82 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ B @ C2 )
% 8.64/4.82 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4282_inf_OcoboundedI2,axiom,
% 8.64/4.82 ! [B: int,C2: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ B @ C2 )
% 8.64/4.82 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4283_sup_OcoboundedI2,axiom,
% 8.64/4.82 ! [C2: set_nat,B: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ C2 @ B )
% 8.64/4.82 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4284_sup_OcoboundedI2,axiom,
% 8.64/4.82 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ C2 @ B )
% 8.64/4.82 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4285_sup_OcoboundedI2,axiom,
% 8.64/4.82 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ C2 @ B )
% 8.64/4.82 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4286_sup_OcoboundedI2,axiom,
% 8.64/4.82 ! [C2: int,B: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ C2 @ B )
% 8.64/4.82 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4287_sup_OcoboundedI1,axiom,
% 8.64/4.82 ! [C2: set_nat,A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_set_nat @ C2 @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4288_sup_OcoboundedI1,axiom,
% 8.64/4.82 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_rat @ C2 @ ( sup_sup_rat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4289_sup_OcoboundedI1,axiom,
% 8.64/4.82 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_nat @ C2 @ ( sup_sup_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4290_sup_OcoboundedI1,axiom,
% 8.64/4.82 ! [C2: int,A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_int @ C2 @ ( sup_sup_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4291_sup_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [A5: set_nat,B4: set_nat] :
% 8.64/4.82 ( ( sup_sup_set_nat @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4292_sup_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [A5: rat,B4: rat] :
% 8.64/4.82 ( ( sup_sup_rat @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4293_sup_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [A5: nat,B4: nat] :
% 8.64/4.82 ( ( sup_sup_nat @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4294_sup_Oabsorb__iff2,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [A5: int,B4: int] :
% 8.64/4.82 ( ( sup_sup_int @ A5 @ B4 )
% 8.64/4.82 = B4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4295_sup_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [B4: set_nat,A5: set_nat] :
% 8.64/4.82 ( ( sup_sup_set_nat @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4296_sup_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [B4: rat,A5: rat] :
% 8.64/4.82 ( ( sup_sup_rat @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4297_sup_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [B4: nat,A5: nat] :
% 8.64/4.82 ( ( sup_sup_nat @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4298_sup_Oabsorb__iff1,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [B4: int,A5: int] :
% 8.64/4.82 ( ( sup_sup_int @ A5 @ B4 )
% 8.64/4.82 = A5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4299_sup_Ocobounded2,axiom,
% 8.64/4.82 ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4300_sup_Ocobounded2,axiom,
% 8.64/4.82 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4301_sup_Ocobounded2,axiom,
% 8.64/4.82 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4302_sup_Ocobounded2,axiom,
% 8.64/4.82 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4303_sup_Ocobounded1,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4304_sup_Ocobounded1,axiom,
% 8.64/4.82 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4305_sup_Ocobounded1,axiom,
% 8.64/4.82 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4306_sup_Ocobounded1,axiom,
% 8.64/4.82 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4307_sup_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [B4: set_nat,A5: set_nat] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( sup_sup_set_nat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4308_sup_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [B4: rat,A5: rat] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( sup_sup_rat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4309_sup_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [B4: nat,A5: nat] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( sup_sup_nat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4310_sup_Oorder__iff,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [B4: int,A5: int] :
% 8.64/4.82 ( A5
% 8.64/4.82 = ( sup_sup_int @ A5 @ B4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4311_sup_OboundedI,axiom,
% 8.64/4.82 ! [B: set_nat,A: set_nat,C2: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ B @ A )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4312_sup_OboundedI,axiom,
% 8.64/4.82 ! [B: rat,A: rat,C2: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.82 => ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4313_sup_OboundedI,axiom,
% 8.64/4.82 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.82 => ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4314_sup_OboundedI,axiom,
% 8.64/4.82 ! [B: int,A: int,C2: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ B @ A )
% 8.64/4.82 => ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.82 => ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4315_sup_OboundedE,axiom,
% 8.64/4.82 ! [B: set_nat,C2: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C2 ) @ A )
% 8.64/4.82 => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 8.64/4.82 => ~ ( ord_less_eq_set_nat @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4316_sup_OboundedE,axiom,
% 8.64/4.82 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C2 ) @ A )
% 8.64/4.82 => ~ ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.82 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4317_sup_OboundedE,axiom,
% 8.64/4.82 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C2 ) @ A )
% 8.64/4.82 => ~ ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.82 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4318_sup_OboundedE,axiom,
% 8.64/4.82 ! [B: int,C2: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C2 ) @ A )
% 8.64/4.82 => ~ ( ( ord_less_eq_int @ B @ A )
% 8.64/4.82 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4319_sup__absorb2,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.64/4.82 => ( ( sup_sup_set_nat @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4320_sup__absorb2,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ Y )
% 8.64/4.82 => ( ( sup_sup_rat @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4321_sup__absorb2,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ Y )
% 8.64/4.82 => ( ( sup_sup_nat @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4322_sup__absorb2,axiom,
% 8.64/4.82 ! [X: int,Y: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ Y )
% 8.64/4.82 => ( ( sup_sup_int @ X @ Y )
% 8.64/4.82 = Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4323_sup__absorb1,axiom,
% 8.64/4.82 ! [Y: set_nat,X: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ Y @ X )
% 8.64/4.82 => ( ( sup_sup_set_nat @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4324_sup__absorb1,axiom,
% 8.64/4.82 ! [Y: rat,X: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ Y @ X )
% 8.64/4.82 => ( ( sup_sup_rat @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4325_sup__absorb1,axiom,
% 8.64/4.82 ! [Y: nat,X: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ Y @ X )
% 8.64/4.82 => ( ( sup_sup_nat @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4326_sup__absorb1,axiom,
% 8.64/4.82 ! [Y: int,X: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ Y @ X )
% 8.64/4.82 => ( ( sup_sup_int @ X @ Y )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4327_sup_Oabsorb2,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ B )
% 8.64/4.82 => ( ( sup_sup_set_nat @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4328_sup_Oabsorb2,axiom,
% 8.64/4.82 ! [A: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.82 => ( ( sup_sup_rat @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4329_sup_Oabsorb2,axiom,
% 8.64/4.82 ! [A: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.82 => ( ( sup_sup_nat @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4330_sup_Oabsorb2,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ B )
% 8.64/4.82 => ( ( sup_sup_int @ A @ B )
% 8.64/4.82 = B ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4331_sup_Oabsorb1,axiom,
% 8.64/4.82 ! [B: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ B @ A )
% 8.64/4.82 => ( ( sup_sup_set_nat @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4332_sup_Oabsorb1,axiom,
% 8.64/4.82 ! [B: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.82 => ( ( sup_sup_rat @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4333_sup_Oabsorb1,axiom,
% 8.64/4.82 ! [B: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.82 => ( ( sup_sup_nat @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4334_sup_Oabsorb1,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ B @ A )
% 8.64/4.82 => ( ( sup_sup_int @ A @ B )
% 8.64/4.82 = A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4335_sup__unique,axiom,
% 8.64/4.82 ! [F2: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 8.64/4.82 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: set_nat,Y3: set_nat,Z: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ Z @ X3 )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 8.64/4.82 => ( ( sup_sup_set_nat @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4336_sup__unique,axiom,
% 8.64/4.82 ! [F2: rat > rat > rat,X: rat,Y: rat] :
% 8.64/4.82 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: rat,Y3: rat,Z: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ Y3 @ X3 )
% 8.64/4.82 => ( ( ord_less_eq_rat @ Z @ X3 )
% 8.64/4.82 => ( ord_less_eq_rat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 8.64/4.82 => ( ( sup_sup_rat @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4337_sup__unique,axiom,
% 8.64/4.82 ! [F2: nat > nat > nat,X: nat,Y: nat] :
% 8.64/4.82 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ X3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: nat,Y3: nat,Z: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 8.64/4.82 => ( ( ord_less_eq_nat @ Z @ X3 )
% 8.64/4.82 => ( ord_less_eq_nat @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 8.64/4.82 => ( ( sup_sup_nat @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4338_sup__unique,axiom,
% 8.64/4.82 ! [F2: int > int > int,X: int,Y: int] :
% 8.64/4.82 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ X3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ Y3 @ ( F2 @ X3 @ Y3 ) )
% 8.64/4.82 => ( ! [X3: int,Y3: int,Z: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ Y3 @ X3 )
% 8.64/4.82 => ( ( ord_less_eq_int @ Z @ X3 )
% 8.64/4.82 => ( ord_less_eq_int @ ( F2 @ Y3 @ Z ) @ X3 ) ) )
% 8.64/4.82 => ( ( sup_sup_int @ X @ Y )
% 8.64/4.82 = ( F2 @ X @ Y ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4339_sup_OorderI,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( sup_sup_set_nat @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4340_sup_OorderI,axiom,
% 8.64/4.82 ! [A: rat,B: rat] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( sup_sup_rat @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_rat @ B @ A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4341_sup_OorderI,axiom,
% 8.64/4.82 ! [A: nat,B: nat] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( sup_sup_nat @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_nat @ B @ A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4342_sup_OorderI,axiom,
% 8.64/4.82 ! [A: int,B: int] :
% 8.64/4.82 ( ( A
% 8.64/4.82 = ( sup_sup_int @ A @ B ) )
% 8.64/4.82 => ( ord_less_eq_int @ B @ A ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4343_sup_OorderE,axiom,
% 8.64/4.82 ! [B: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ B @ A )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4344_sup_OorderE,axiom,
% 8.64/4.82 ! [B: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( sup_sup_rat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4345_sup_OorderE,axiom,
% 8.64/4.82 ! [B: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( sup_sup_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4346_sup_OorderE,axiom,
% 8.64/4.82 ! [B: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ B @ A )
% 8.64/4.82 => ( A
% 8.64/4.82 = ( sup_sup_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4347_le__iff__sup,axiom,
% 8.64/4.82 ( ord_less_eq_set_nat
% 8.64/4.82 = ( ^ [X4: set_nat,Y4: set_nat] :
% 8.64/4.82 ( ( sup_sup_set_nat @ X4 @ Y4 )
% 8.64/4.82 = Y4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4348_le__iff__sup,axiom,
% 8.64/4.82 ( ord_less_eq_rat
% 8.64/4.82 = ( ^ [X4: rat,Y4: rat] :
% 8.64/4.82 ( ( sup_sup_rat @ X4 @ Y4 )
% 8.64/4.82 = Y4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4349_le__iff__sup,axiom,
% 8.64/4.82 ( ord_less_eq_nat
% 8.64/4.82 = ( ^ [X4: nat,Y4: nat] :
% 8.64/4.82 ( ( sup_sup_nat @ X4 @ Y4 )
% 8.64/4.82 = Y4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4350_le__iff__sup,axiom,
% 8.64/4.82 ( ord_less_eq_int
% 8.64/4.82 = ( ^ [X4: int,Y4: int] :
% 8.64/4.82 ( ( sup_sup_int @ X4 @ Y4 )
% 8.64/4.82 = Y4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4351_sup__least,axiom,
% 8.64/4.82 ! [Y: set_nat,X: set_nat,Z3: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ Y @ X )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ Z3 @ X )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z3 ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4352_sup__least,axiom,
% 8.64/4.82 ! [Y: rat,X: rat,Z3: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ Y @ X )
% 8.64/4.82 => ( ( ord_less_eq_rat @ Z3 @ X )
% 8.64/4.82 => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z3 ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4353_sup__least,axiom,
% 8.64/4.82 ! [Y: nat,X: nat,Z3: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ Y @ X )
% 8.64/4.82 => ( ( ord_less_eq_nat @ Z3 @ X )
% 8.64/4.82 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z3 ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4354_sup__least,axiom,
% 8.64/4.82 ! [Y: int,X: int,Z3: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ Y @ X )
% 8.64/4.82 => ( ( ord_less_eq_int @ Z3 @ X )
% 8.64/4.82 => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z3 ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4355_sup__mono,axiom,
% 8.64/4.82 ! [A: set_nat,C2: set_nat,B: set_nat,D: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ B @ D )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4356_sup__mono,axiom,
% 8.64/4.82 ! [A: rat,C2: rat,B: rat,D: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_rat @ B @ D )
% 8.64/4.82 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4357_sup__mono,axiom,
% 8.64/4.82 ! [A: nat,C2: nat,B: nat,D: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_nat @ B @ D )
% 8.64/4.82 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4358_sup__mono,axiom,
% 8.64/4.82 ! [A: int,C2: int,B: int,D: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ C2 )
% 8.64/4.82 => ( ( ord_less_eq_int @ B @ D )
% 8.64/4.82 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C2 @ D ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4359_sup_Omono,axiom,
% 8.64/4.82 ! [C2: set_nat,A: set_nat,D: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ C2 @ A )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ D @ B )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C2 @ D ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4360_sup_Omono,axiom,
% 8.64/4.82 ! [C2: rat,A: rat,D: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.82 => ( ( ord_less_eq_rat @ D @ B )
% 8.64/4.82 => ( ord_less_eq_rat @ ( sup_sup_rat @ C2 @ D ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4361_sup_Omono,axiom,
% 8.64/4.82 ! [C2: nat,A: nat,D: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.82 => ( ( ord_less_eq_nat @ D @ B )
% 8.64/4.82 => ( ord_less_eq_nat @ ( sup_sup_nat @ C2 @ D ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4362_sup_Omono,axiom,
% 8.64/4.82 ! [C2: int,A: int,D: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.82 => ( ( ord_less_eq_int @ D @ B )
% 8.64/4.82 => ( ord_less_eq_int @ ( sup_sup_int @ C2 @ D ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4363_le__supI2,axiom,
% 8.64/4.82 ! [X: set_nat,B: set_nat,A: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ B )
% 8.64/4.82 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4364_le__supI2,axiom,
% 8.64/4.82 ! [X: rat,B: rat,A: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ B )
% 8.64/4.82 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4365_le__supI2,axiom,
% 8.64/4.82 ! [X: nat,B: nat,A: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ B )
% 8.64/4.82 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4366_le__supI2,axiom,
% 8.64/4.82 ! [X: int,B: int,A: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ B )
% 8.64/4.82 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4367_le__supI1,axiom,
% 8.64/4.82 ! [X: set_nat,A: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ X @ A )
% 8.64/4.82 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4368_le__supI1,axiom,
% 8.64/4.82 ! [X: rat,A: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ X @ A )
% 8.64/4.82 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4369_le__supI1,axiom,
% 8.64/4.82 ! [X: nat,A: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ X @ A )
% 8.64/4.82 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4370_le__supI1,axiom,
% 8.64/4.82 ! [X: int,A: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ X @ A )
% 8.64/4.82 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4371_sup__ge2,axiom,
% 8.64/4.82 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4372_sup__ge2,axiom,
% 8.64/4.82 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4373_sup__ge2,axiom,
% 8.64/4.82 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4374_sup__ge2,axiom,
% 8.64/4.82 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4375_sup__ge1,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4376_sup__ge1,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4377_sup__ge1,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4378_sup__ge1,axiom,
% 8.64/4.82 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4379_le__supI,axiom,
% 8.64/4.82 ! [A: set_nat,X: set_nat,B: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ A @ X )
% 8.64/4.82 => ( ( ord_less_eq_set_nat @ B @ X )
% 8.64/4.82 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4380_le__supI,axiom,
% 8.64/4.82 ! [A: rat,X: rat,B: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ A @ X )
% 8.64/4.82 => ( ( ord_less_eq_rat @ B @ X )
% 8.64/4.82 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4381_le__supI,axiom,
% 8.64/4.82 ! [A: nat,X: nat,B: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ A @ X )
% 8.64/4.82 => ( ( ord_less_eq_nat @ B @ X )
% 8.64/4.82 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4382_le__supI,axiom,
% 8.64/4.82 ! [A: int,X: int,B: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ A @ X )
% 8.64/4.82 => ( ( ord_less_eq_int @ B @ X )
% 8.64/4.82 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4383_le__supE,axiom,
% 8.64/4.82 ! [A: set_nat,B: set_nat,X: set_nat] :
% 8.64/4.82 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 8.64/4.82 => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 8.64/4.82 => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4384_le__supE,axiom,
% 8.64/4.82 ! [A: rat,B: rat,X: rat] :
% 8.64/4.82 ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 8.64/4.82 => ~ ( ( ord_less_eq_rat @ A @ X )
% 8.64/4.82 => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4385_le__supE,axiom,
% 8.64/4.82 ! [A: nat,B: nat,X: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 8.64/4.82 => ~ ( ( ord_less_eq_nat @ A @ X )
% 8.64/4.82 => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4386_le__supE,axiom,
% 8.64/4.82 ! [A: int,B: int,X: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 8.64/4.82 => ~ ( ( ord_less_eq_int @ A @ X )
% 8.64/4.82 => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4387_inf__sup__ord_I3_J,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4388_inf__sup__ord_I3_J,axiom,
% 8.64/4.82 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4389_inf__sup__ord_I3_J,axiom,
% 8.64/4.82 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4390_inf__sup__ord_I3_J,axiom,
% 8.64/4.82 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4391_inf__sup__ord_I4_J,axiom,
% 8.64/4.82 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4392_inf__sup__ord_I4_J,axiom,
% 8.64/4.82 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4393_inf__sup__ord_I4_J,axiom,
% 8.64/4.82 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4394_inf__sup__ord_I4_J,axiom,
% 8.64/4.82 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4395_invar__vebt_Ointros_I4_J,axiom,
% 8.64/4.82 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 8.64/4.82 ( ! [X3: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X3 @ N ) )
% 8.64/4.82 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 8.64/4.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.82 => ( ( M2 = N )
% 8.64/4.82 => ( ( Deg
% 8.64/4.82 = ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.82 => ( ! [I3: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.82 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 8.64/4.82 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 8.64/4.82 => ( ( ( Mi = Ma )
% 8.64/4.82 => ! [X3: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.82 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 8.64/4.82 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 8.64/4.82 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.64/4.82 => ( ( ( Mi != Ma )
% 8.64/4.82 => ! [I3: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.82 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 8.64/4.82 = I3 )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 8.64/4.82 & ! [X3: nat] :
% 8.64/4.82 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 8.64/4.82 = I3 )
% 8.64/4.82 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ Mi @ X3 )
% 8.64/4.82 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4396_invar__vebt_Ointros_I5_J,axiom,
% 8.64/4.82 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M2: nat,Deg: nat,Mi: nat,Ma: nat] :
% 8.64/4.82 ( ! [X3: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X3 @ N ) )
% 8.64/4.82 => ( ( vEBT_invar_vebt @ Summary @ M2 )
% 8.64/4.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.82 => ( ( M2
% 8.64/4.82 = ( suc @ N ) )
% 8.64/4.82 => ( ( Deg
% 8.64/4.82 = ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.82 => ( ! [I3: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.82 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X7 ) )
% 8.64/4.82 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 8.64/4.82 => ( ( ( Mi = Ma )
% 8.64/4.82 => ! [X3: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.82 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X_12 ) ) )
% 8.64/4.82 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 8.64/4.82 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.64/4.82 => ( ( ( Mi != Ma )
% 8.64/4.82 => ! [I3: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.82 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 8.64/4.82 = I3 )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 8.64/4.82 & ! [X3: nat] :
% 8.64/4.82 ( ( ( ( vEBT_VEBT_high @ X3 @ N )
% 8.64/4.82 = I3 )
% 8.64/4.82 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ ( vEBT_VEBT_low @ X3 @ N ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ Mi @ X3 )
% 8.64/4.82 & ( ord_less_eq_nat @ X3 @ Ma ) ) ) ) ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4397_invar__vebt_Ocases,axiom,
% 8.64/4.82 ! [A12: vEBT_VEBT,A23: nat] :
% 8.64/4.82 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 8.64/4.82 => ( ( ? [A3: $o,B3: $o] :
% 8.64/4.82 ( A12
% 8.64/4.82 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.82 => ( A23
% 8.64/4.82 != ( suc @ zero_zero_nat ) ) )
% 8.64/4.82 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat] :
% 8.64/4.82 ( ( A12
% 8.64/4.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.82 => ( ( A23 = Deg2 )
% 8.64/4.82 => ( ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 8.64/4.82 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 8.64/4.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( M = N3 )
% 8.64/4.82 => ( ( Deg2
% 8.64/4.82 = ( plus_plus_nat @ N3 @ M ) )
% 8.64/4.82 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 8.64/4.82 => ~ ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 8.64/4.82 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat] :
% 8.64/4.82 ( ( A12
% 8.64/4.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.82 => ( ( A23 = Deg2 )
% 8.64/4.82 => ( ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 8.64/4.82 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 8.64/4.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( M
% 8.64/4.82 = ( suc @ N3 ) )
% 8.64/4.82 => ( ( Deg2
% 8.64/4.82 = ( plus_plus_nat @ N3 @ M ) )
% 8.64/4.82 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_1 )
% 8.64/4.82 => ~ ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) ) ) ) ) ) ) ) )
% 8.64/4.82 => ( ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 8.64/4.82 ( ( A12
% 8.64/4.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.82 => ( ( A23 = Deg2 )
% 8.64/4.82 => ( ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 8.64/4.82 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 8.64/4.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( M = N3 )
% 8.64/4.82 => ( ( Deg2
% 8.64/4.82 = ( plus_plus_nat @ N3 @ M ) )
% 8.64/4.82 => ( ! [I4: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X7 ) )
% 8.64/4.82 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 8.64/4.82 => ( ( ( Mi2 = Ma2 )
% 8.64/4.82 => ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 8.64/4.82 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 8.64/4.82 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.82 => ~ ( ( Mi2 != Ma2 )
% 8.64/4.82 => ! [I4: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 8.64/4.82 = I4 )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 8.64/4.82 & ! [X5: nat] :
% 8.64/4.82 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 8.64/4.82 = I4 )
% 8.64/4.82 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ Mi2 @ X5 )
% 8.64/4.82 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.82 => ~ ! [TreeList: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 8.64/4.82 ( ( A12
% 8.64/4.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.82 => ( ( A23 = Deg2 )
% 8.64/4.82 => ( ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X5 @ N3 ) )
% 8.64/4.82 => ( ( vEBT_invar_vebt @ Summary2 @ M )
% 8.64/4.82 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( M
% 8.64/4.82 = ( suc @ N3 ) )
% 8.64/4.82 => ( ( Deg2
% 8.64/4.82 = ( plus_plus_nat @ N3 @ M ) )
% 8.64/4.82 => ( ! [I4: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ X7 ) )
% 8.64/4.82 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I4 ) ) )
% 8.64/4.82 => ( ( ( Mi2 = Ma2 )
% 8.64/4.82 => ! [X5: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.82 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_1 ) ) )
% 8.64/4.82 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 8.64/4.82 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.82 => ~ ( ( Mi2 != Ma2 )
% 8.64/4.82 => ! [I4: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 8.64/4.82 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 8.64/4.82 = I4 )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 8.64/4.82 & ! [X5: nat] :
% 8.64/4.82 ( ( ( ( vEBT_VEBT_high @ X5 @ N3 )
% 8.64/4.82 = I4 )
% 8.64/4.82 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N3 ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ Mi2 @ X5 )
% 8.64/4.82 & ( ord_less_eq_nat @ X5 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4398_invar__vebt_Osimps,axiom,
% 8.64/4.82 ( vEBT_invar_vebt
% 8.64/4.82 = ( ^ [A13: vEBT_VEBT,A24: nat] :
% 8.64/4.82 ( ( ? [A5: $o,B4: $o] :
% 8.64/4.82 ( A13
% 8.64/4.82 = ( vEBT_Leaf @ A5 @ B4 ) )
% 8.64/4.82 & ( A24
% 8.64/4.82 = ( suc @ zero_zero_nat ) ) )
% 8.64/4.82 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT] :
% 8.64/4.82 ( ( A13
% 8.64/4.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary4 ) )
% 8.64/4.82 & ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 8.64/4.82 & ( vEBT_invar_vebt @ Summary4 @ N4 )
% 8.64/4.82 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 8.64/4.82 & ( A24
% 8.64/4.82 = ( plus_plus_nat @ N4 @ N4 ) )
% 8.64/4.82 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X7 )
% 8.64/4.82 & ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.82 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT] :
% 8.64/4.82 ( ( A13
% 8.64/4.82 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A24 @ TreeList4 @ Summary4 ) )
% 8.64/4.82 & ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 8.64/4.82 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N4 ) )
% 8.64/4.82 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 8.64/4.82 & ( A24
% 8.64/4.82 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 8.64/4.82 & ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary4 @ X7 )
% 8.64/4.82 & ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.82 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 8.64/4.82 ( ( A13
% 8.64/4.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary4 ) )
% 8.64/4.82 & ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 8.64/4.82 & ( vEBT_invar_vebt @ Summary4 @ N4 )
% 8.64/4.82 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 8.64/4.82 & ( A24
% 8.64/4.82 = ( plus_plus_nat @ N4 @ N4 ) )
% 8.64/4.82 & ! [I: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 8.64/4.82 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ X7 ) )
% 8.64/4.82 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I ) ) )
% 8.64/4.82 & ( ( Mi3 = Ma3 )
% 8.64/4.82 => ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.82 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.82 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 8.64/4.82 & ( ( Mi3 != Ma3 )
% 8.64/4.82 => ! [I: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) )
% 8.64/4.82 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 8.64/4.82 = I )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 8.64/4.82 & ! [X4: nat] :
% 8.64/4.82 ( ( ( ( vEBT_VEBT_high @ X4 @ N4 )
% 8.64/4.82 = I )
% 8.64/4.82 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.82 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) )
% 8.64/4.82 | ? [TreeList4: list_VEBT_VEBT,N4: nat,Summary4: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 8.64/4.82 ( ( A13
% 8.64/4.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A24 @ TreeList4 @ Summary4 ) )
% 8.64/4.82 & ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ( vEBT_invar_vebt @ X4 @ N4 ) )
% 8.64/4.82 & ( vEBT_invar_vebt @ Summary4 @ ( suc @ N4 ) )
% 8.64/4.82 & ( ( size_s6755466524823107622T_VEBT @ TreeList4 )
% 8.64/4.82 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 8.64/4.82 & ( A24
% 8.64/4.82 = ( plus_plus_nat @ N4 @ ( suc @ N4 ) ) )
% 8.64/4.82 & ! [I: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 8.64/4.82 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ X7 ) )
% 8.64/4.82 = ( vEBT_V8194947554948674370ptions @ Summary4 @ I ) ) )
% 8.64/4.82 & ( ( Mi3 = Ma3 )
% 8.64/4.82 => ! [X4: vEBT_VEBT] :
% 8.64/4.82 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList4 ) )
% 8.64/4.82 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.82 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.82 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A24 ) )
% 8.64/4.82 & ( ( Mi3 != Ma3 )
% 8.64/4.82 => ! [I: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) )
% 8.64/4.82 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N4 )
% 8.64/4.82 = I )
% 8.64/4.82 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N4 ) ) )
% 8.64/4.82 & ! [X4: nat] :
% 8.64/4.82 ( ( ( ( vEBT_VEBT_high @ X4 @ N4 )
% 8.64/4.82 = I )
% 8.64/4.82 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ I ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) )
% 8.64/4.82 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.82 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4399_distrib__inf__le,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4400_distrib__inf__le,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z3 ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4401_distrib__inf__le,axiom,
% 8.64/4.82 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z3 ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4402_distrib__inf__le,axiom,
% 8.64/4.82 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z3 ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4403_distrib__inf__le,axiom,
% 8.64/4.82 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z3 ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4404_distrib__sup__le,axiom,
% 8.64/4.82 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z3 ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4405_distrib__sup__le,axiom,
% 8.64/4.82 ! [X: set_nat,Y: set_nat,Z3: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z3 ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4406_distrib__sup__le,axiom,
% 8.64/4.82 ! [X: rat,Y: rat,Z3: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z3 ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4407_distrib__sup__le,axiom,
% 8.64/4.82 ! [X: nat,Y: nat,Z3: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z3 ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4408_distrib__sup__le,axiom,
% 8.64/4.82 ! [X: int,Y: int,Z3: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z3 ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z3 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4409_in__children__def,axiom,
% 8.64/4.82 ( vEBT_V5917875025757280293ildren
% 8.64/4.82 = ( ^ [N4: nat,TreeList4: list_VEBT_VEBT,X4: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList4 @ ( vEBT_VEBT_high @ X4 @ N4 ) ) @ ( vEBT_VEBT_low @ X4 @ N4 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4410_nested__mint,axiom,
% 8.64/4.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va3: nat] :
% 8.64/4.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 8.64/4.82 => ( ( N
% 8.64/4.82 = ( suc @ ( suc @ Va3 ) ) )
% 8.64/4.82 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 8.64/4.82 => ( ( Ma != Mi )
% 8.64/4.82 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4411_summaxma,axiom,
% 8.64/4.82 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.82 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 8.64/4.82 => ( ( Mi != Ma )
% 8.64/4.82 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 8.64/4.82 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4412_set__encode__insert,axiom,
% 8.64/4.82 ! [A4: set_nat,N: nat] :
% 8.64/4.82 ( ( finite_finite_nat @ A4 )
% 8.64/4.82 => ( ~ ( member_nat @ N @ A4 )
% 8.64/4.82 => ( ( nat_set_encode @ ( insert_nat @ N @ A4 ) )
% 8.64/4.82 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A4 ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4413_unset__bit__0,axiom,
% 8.64/4.82 ! [A: nat] :
% 8.64/4.82 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 8.64/4.82 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4414_unset__bit__0,axiom,
% 8.64/4.82 ! [A: int] :
% 8.64/4.82 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 8.64/4.82 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4415_del__x__mi__lets__in__not__minNull,axiom,
% 8.64/4.82 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 8.64/4.82 ( ( ( X = Mi )
% 8.64/4.82 & ( ord_less_nat @ X @ Ma ) )
% 8.64/4.82 => ( ( Mi != Ma )
% 8.64/4.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.82 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.82 = H )
% 8.64/4.82 => ( ( Xn
% 8.64/4.82 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.64/4.82 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.82 = L )
% 8.64/4.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.82 => ( ( Newnode
% 8.64/4.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.82 => ( ( Newlist
% 8.64/4.82 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 8.64/4.82 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4416_del__x__not__mi__newnode__not__nil,axiom,
% 8.64/4.82 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.82 ( ( ( ord_less_nat @ Mi @ X )
% 8.64/4.82 & ( ord_less_eq_nat @ X @ Ma ) )
% 8.64/4.82 => ( ( Mi != Ma )
% 8.64/4.82 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.82 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.82 = H )
% 8.64/4.82 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.82 = L )
% 8.64/4.82 => ( ( Newnode
% 8.64/4.82 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.82 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.82 => ( ( Newlist
% 8.64/4.82 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 8.64/4.82 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.82 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.82 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4417_neg__eucl__rel__int__mult__2,axiom,
% 8.64/4.82 ! [B: int,A: int,Q2: int,R3: int] :
% 8.64/4.82 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 8.64/4.82 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.82 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4418_length__list__update,axiom,
% 8.64/4.82 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 8.64/4.82 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) )
% 8.64/4.82 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4419_length__list__update,axiom,
% 8.64/4.82 ! [Xs2: list_o,I2: nat,X: $o] :
% 8.64/4.82 ( ( size_size_list_o @ ( list_update_o @ Xs2 @ I2 @ X ) )
% 8.64/4.82 = ( size_size_list_o @ Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4420_length__list__update,axiom,
% 8.64/4.82 ! [Xs2: list_nat,I2: nat,X: nat] :
% 8.64/4.82 ( ( size_size_list_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) )
% 8.64/4.82 = ( size_size_list_nat @ Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4421_length__list__update,axiom,
% 8.64/4.82 ! [Xs2: list_int,I2: nat,X: int] :
% 8.64/4.82 ( ( size_size_list_int @ ( list_update_int @ Xs2 @ I2 @ X ) )
% 8.64/4.82 = ( size_size_list_int @ Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4422_option_Ocollapse,axiom,
% 8.64/4.82 ! [Option: option4927543243414619207at_nat] :
% 8.64/4.82 ( ( Option != none_P5556105721700978146at_nat )
% 8.64/4.82 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 8.64/4.82 = Option ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4423_option_Ocollapse,axiom,
% 8.64/4.82 ! [Option: option_nat] :
% 8.64/4.82 ( ( Option != none_nat )
% 8.64/4.82 => ( ( some_nat @ ( the_nat @ Option ) )
% 8.64/4.82 = Option ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4424_option_Ocollapse,axiom,
% 8.64/4.82 ! [Option: option_num] :
% 8.64/4.82 ( ( Option != none_num )
% 8.64/4.82 => ( ( some_num @ ( the_num @ Option ) )
% 8.64/4.82 = Option ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4425_list__update__beyond,axiom,
% 8.64/4.82 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ I2 )
% 8.64/4.82 => ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 8.64/4.82 = Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4426_list__update__beyond,axiom,
% 8.64/4.82 ! [Xs2: list_o,I2: nat,X: $o] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ I2 )
% 8.64/4.82 => ( ( list_update_o @ Xs2 @ I2 @ X )
% 8.64/4.82 = Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4427_list__update__beyond,axiom,
% 8.64/4.82 ! [Xs2: list_nat,I2: nat,X: nat] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ I2 )
% 8.64/4.82 => ( ( list_update_nat @ Xs2 @ I2 @ X )
% 8.64/4.82 = Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4428_list__update__beyond,axiom,
% 8.64/4.82 ! [Xs2: list_int,I2: nat,X: int] :
% 8.64/4.82 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ I2 )
% 8.64/4.82 => ( ( list_update_int @ Xs2 @ I2 @ X )
% 8.64/4.82 = Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4429_set__encode__empty,axiom,
% 8.64/4.82 ( ( nat_set_encode @ bot_bot_set_nat )
% 8.64/4.82 = zero_zero_nat ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4430_nth__list__update__eq,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.82 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ I2 )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4431_nth__list__update__eq,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_o,X: $o] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.82 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ I2 )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4432_nth__list__update__eq,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_nat,X: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.82 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ I2 )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4433_nth__list__update__eq,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_int,X: int] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.82 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ I2 )
% 8.64/4.82 = X ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4434_set__swap,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.82 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.82 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) @ J2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 8.64/4.82 = ( set_VEBT_VEBT2 @ Xs2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4435_set__swap,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_o,J2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.82 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.82 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J2 ) ) @ J2 @ ( nth_o @ Xs2 @ I2 ) ) )
% 8.64/4.82 = ( set_o2 @ Xs2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4436_set__swap,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_nat,J2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.82 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.82 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J2 ) ) @ J2 @ ( nth_nat @ Xs2 @ I2 ) ) )
% 8.64/4.82 = ( set_nat2 @ Xs2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4437_set__swap,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_int,J2: nat] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.82 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.82 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J2 ) ) @ J2 @ ( nth_int @ Xs2 @ I2 ) ) )
% 8.64/4.82 = ( set_int2 @ Xs2 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4438_unique__quotient,axiom,
% 8.64/4.82 ! [A: int,B: int,Q2: int,R3: int,Q4: int,R5: int] :
% 8.64/4.82 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.82 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R5 ) )
% 8.64/4.82 => ( Q2 = Q4 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4439_unique__remainder,axiom,
% 8.64/4.82 ! [A: int,B: int,Q2: int,R3: int,Q4: int,R5: int] :
% 8.64/4.82 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.82 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R5 ) )
% 8.64/4.82 => ( R3 = R5 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4440_zip__update,axiom,
% 8.64/4.82 ! [Xs2: list_VEBT_VEBT,I2: nat,X: vEBT_VEBT,Ys: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 8.64/4.82 ( ( zip_VE537291747668921783T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ ( list_u1324408373059187874T_VEBT @ Ys @ I2 @ Y ) )
% 8.64/4.82 = ( list_u6961636818849549845T_VEBT @ ( zip_VE537291747668921783T_VEBT @ Xs2 @ Ys ) @ I2 @ ( produc537772716801021591T_VEBT @ X @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4441_zip__update,axiom,
% 8.64/4.82 ! [Xs2: list_Code_integer,I2: nat,X: code_integer,Ys: list_Code_integer,Y: code_integer] :
% 8.64/4.82 ( ( zip_Co3543743374963494515nteger @ ( list_u5447711078246177391nteger @ Xs2 @ I2 @ X ) @ ( list_u5447711078246177391nteger @ Ys @ I2 @ Y ) )
% 8.64/4.82 = ( list_u2254550707601501961nteger @ ( zip_Co3543743374963494515nteger @ Xs2 @ Ys ) @ I2 @ ( produc1086072967326762835nteger @ X @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4442_zip__update,axiom,
% 8.64/4.82 ! [Xs2: list_P6011104703257516679at_nat,I2: nat,X: product_prod_nat_nat,Ys: list_P6011104703257516679at_nat,Y: product_prod_nat_nat] :
% 8.64/4.82 ( ( zip_Pr4664179122662387191at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ I2 @ X ) @ ( list_u6180841689913720943at_nat @ Ys @ I2 @ Y ) )
% 8.64/4.82 = ( list_u5003261594476800725at_nat @ ( zip_Pr4664179122662387191at_nat @ Xs2 @ Ys ) @ I2 @ ( produc6161850002892822231at_nat @ X @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4443_zip__update,axiom,
% 8.64/4.82 ! [Xs2: list_s1210847774152347623at_nat,I2: nat,X: set_Pr1261947904930325089at_nat,Ys: list_s1210847774152347623at_nat,Y: set_Pr1261947904930325089at_nat] :
% 8.64/4.82 ( ( zip_se5600341670672612855at_nat @ ( list_u8444657558853818831at_nat @ Xs2 @ I2 @ X ) @ ( list_u8444657558853818831at_nat @ Ys @ I2 @ Y ) )
% 8.64/4.82 = ( list_u4696772448584712917at_nat @ ( zip_se5600341670672612855at_nat @ Xs2 @ Ys ) @ I2 @ ( produc2922128104949294807at_nat @ X @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4444_zip__update,axiom,
% 8.64/4.82 ! [Xs2: list_nat,I2: nat,X: nat,Ys: list_nat,Y: nat] :
% 8.64/4.82 ( ( zip_nat_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ ( list_update_nat @ Ys @ I2 @ Y ) )
% 8.64/4.82 = ( list_u6180841689913720943at_nat @ ( zip_nat_nat @ Xs2 @ Ys ) @ I2 @ ( product_Pair_nat_nat @ X @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4445_zip__update,axiom,
% 8.64/4.82 ! [Xs2: list_int,I2: nat,X: int,Ys: list_int,Y: int] :
% 8.64/4.82 ( ( zip_int_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ ( list_update_int @ Ys @ I2 @ Y ) )
% 8.64/4.82 = ( list_u3002344382305578791nt_int @ ( zip_int_int @ Xs2 @ Ys ) @ I2 @ ( product_Pair_int_int @ X @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4446_option_Osel,axiom,
% 8.64/4.82 ! [X2: product_prod_nat_nat] :
% 8.64/4.82 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X2 ) )
% 8.64/4.82 = X2 ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4447_option_Osel,axiom,
% 8.64/4.82 ! [X2: nat] :
% 8.64/4.82 ( ( the_nat @ ( some_nat @ X2 ) )
% 8.64/4.82 = X2 ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4448_option_Osel,axiom,
% 8.64/4.82 ! [X2: num] :
% 8.64/4.82 ( ( the_num @ ( some_num @ X2 ) )
% 8.64/4.82 = X2 ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4449_option_Oexpand,axiom,
% 8.64/4.82 ! [Option: option_nat,Option2: option_nat] :
% 8.64/4.82 ( ( ( Option = none_nat )
% 8.64/4.82 = ( Option2 = none_nat ) )
% 8.64/4.82 => ( ( ( Option != none_nat )
% 8.64/4.82 => ( ( Option2 != none_nat )
% 8.64/4.82 => ( ( the_nat @ Option )
% 8.64/4.82 = ( the_nat @ Option2 ) ) ) )
% 8.64/4.82 => ( Option = Option2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4450_option_Oexpand,axiom,
% 8.64/4.82 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 8.64/4.82 ( ( ( Option = none_P5556105721700978146at_nat )
% 8.64/4.82 = ( Option2 = none_P5556105721700978146at_nat ) )
% 8.64/4.82 => ( ( ( Option != none_P5556105721700978146at_nat )
% 8.64/4.82 => ( ( Option2 != none_P5556105721700978146at_nat )
% 8.64/4.82 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 8.64/4.82 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 8.64/4.82 => ( Option = Option2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4451_option_Oexpand,axiom,
% 8.64/4.82 ! [Option: option_num,Option2: option_num] :
% 8.64/4.82 ( ( ( Option = none_num )
% 8.64/4.82 = ( Option2 = none_num ) )
% 8.64/4.82 => ( ( ( Option != none_num )
% 8.64/4.82 => ( ( Option2 != none_num )
% 8.64/4.82 => ( ( the_num @ Option )
% 8.64/4.82 = ( the_num @ Option2 ) ) ) )
% 8.64/4.82 => ( Option = Option2 ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4452_eucl__rel__int__by0,axiom,
% 8.64/4.82 ! [K2: int] : ( eucl_rel_int @ K2 @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4453_div__int__unique,axiom,
% 8.64/4.82 ! [K2: int,L: int,Q2: int,R3: int] :
% 8.64/4.82 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.82 => ( ( divide_divide_int @ K2 @ L )
% 8.64/4.82 = Q2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4454_list__update__code_I3_J,axiom,
% 8.64/4.82 ! [X: nat,Xs2: list_nat,I2: nat,Y: nat] :
% 8.64/4.82 ( ( list_update_nat @ ( cons_nat @ X @ Xs2 ) @ ( suc @ I2 ) @ Y )
% 8.64/4.82 = ( cons_nat @ X @ ( list_update_nat @ Xs2 @ I2 @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4455_list__update__code_I3_J,axiom,
% 8.64/4.82 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,I2: nat,Y: vEBT_VEBT] :
% 8.64/4.82 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ ( suc @ I2 ) @ Y )
% 8.64/4.82 = ( cons_VEBT_VEBT @ X @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ Y ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4456_list__update__code_I2_J,axiom,
% 8.64/4.82 ! [X: nat,Xs2: list_nat,Y: nat] :
% 8.64/4.82 ( ( list_update_nat @ ( cons_nat @ X @ Xs2 ) @ zero_zero_nat @ Y )
% 8.64/4.82 = ( cons_nat @ Y @ Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4457_list__update__code_I2_J,axiom,
% 8.64/4.82 ! [X: vEBT_VEBT,Xs2: list_VEBT_VEBT,Y: vEBT_VEBT] :
% 8.64/4.82 ( ( list_u1324408373059187874T_VEBT @ ( cons_VEBT_VEBT @ X @ Xs2 ) @ zero_zero_nat @ Y )
% 8.64/4.82 = ( cons_VEBT_VEBT @ Y @ Xs2 ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4458_set__encode__eq,axiom,
% 8.64/4.82 ! [A4: set_nat,B5: set_nat] :
% 8.64/4.82 ( ( finite_finite_nat @ A4 )
% 8.64/4.82 => ( ( finite_finite_nat @ B5 )
% 8.64/4.82 => ( ( ( nat_set_encode @ A4 )
% 8.64/4.82 = ( nat_set_encode @ B5 ) )
% 8.64/4.82 = ( A4 = B5 ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4459_option_Oexhaust__sel,axiom,
% 8.64/4.82 ! [Option: option4927543243414619207at_nat] :
% 8.64/4.82 ( ( Option != none_P5556105721700978146at_nat )
% 8.64/4.82 => ( Option
% 8.64/4.82 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4460_option_Oexhaust__sel,axiom,
% 8.64/4.82 ! [Option: option_nat] :
% 8.64/4.82 ( ( Option != none_nat )
% 8.64/4.82 => ( Option
% 8.64/4.82 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4461_option_Oexhaust__sel,axiom,
% 8.64/4.82 ! [Option: option_num] :
% 8.64/4.82 ( ( Option != none_num )
% 8.64/4.82 => ( Option
% 8.64/4.82 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4462_eucl__rel__int__dividesI,axiom,
% 8.64/4.82 ! [L: int,K2: int,Q2: int] :
% 8.64/4.82 ( ( L != zero_zero_int )
% 8.64/4.82 => ( ( K2
% 8.64/4.82 = ( times_times_int @ Q2 @ L ) )
% 8.64/4.82 => ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4463_set__update__memI,axiom,
% 8.64/4.82 ! [N: nat,Xs2: list_complex,X: complex] :
% 8.64/4.82 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.64/4.82 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs2 @ N @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4464_set__update__memI,axiom,
% 8.64/4.82 ! [N: nat,Xs2: list_real,X: real] :
% 8.64/4.82 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 8.64/4.82 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4465_set__update__memI,axiom,
% 8.64/4.82 ! [N: nat,Xs2: list_set_nat,X: set_nat] :
% 8.64/4.82 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.64/4.82 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs2 @ N @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4466_set__update__memI,axiom,
% 8.64/4.82 ! [N: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.64/4.82 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.82 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4467_set__update__memI,axiom,
% 8.64/4.82 ! [N: nat,Xs2: list_o,X: $o] :
% 8.64/4.82 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.82 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4468_set__update__memI,axiom,
% 8.64/4.82 ! [N: nat,Xs2: list_nat,X: nat] :
% 8.64/4.82 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.82 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4469_set__update__memI,axiom,
% 8.64/4.82 ! [N: nat,Xs2: list_int,X: int] :
% 8.64/4.82 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.82 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4470_list__update__same__conv,axiom,
% 8.64/4.82 ! [I2: nat,Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.64/4.82 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.82 => ( ( ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X )
% 8.64/4.82 = Xs2 )
% 8.64/4.82 = ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 8.64/4.82 = X ) ) ) ).
% 8.64/4.82
% 8.64/4.82 thf(fact_4471_list__update__same__conv,axiom,
% 8.64/4.83 ! [I2: nat,Xs2: list_o,X: $o] :
% 8.64/4.83 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.83 => ( ( ( list_update_o @ Xs2 @ I2 @ X )
% 8.64/4.83 = Xs2 )
% 8.64/4.83 = ( ( nth_o @ Xs2 @ I2 )
% 8.64/4.83 = X ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4472_list__update__same__conv,axiom,
% 8.64/4.83 ! [I2: nat,Xs2: list_nat,X: nat] :
% 8.64/4.83 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.83 => ( ( ( list_update_nat @ Xs2 @ I2 @ X )
% 8.64/4.83 = Xs2 )
% 8.64/4.83 = ( ( nth_nat @ Xs2 @ I2 )
% 8.64/4.83 = X ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4473_list__update__same__conv,axiom,
% 8.64/4.83 ! [I2: nat,Xs2: list_int,X: int] :
% 8.64/4.83 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.83 => ( ( ( list_update_int @ Xs2 @ I2 @ X )
% 8.64/4.83 = Xs2 )
% 8.64/4.83 = ( ( nth_int @ Xs2 @ I2 )
% 8.64/4.83 = X ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4474_nth__list__update,axiom,
% 8.64/4.83 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat,X: vEBT_VEBT] :
% 8.64/4.83 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.83 => ( ( ( I2 = J2 )
% 8.64/4.83 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J2 )
% 8.64/4.83 = X ) )
% 8.64/4.83 & ( ( I2 != J2 )
% 8.64/4.83 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ X ) @ J2 )
% 8.64/4.83 = ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4475_nth__list__update,axiom,
% 8.64/4.83 ! [I2: nat,Xs2: list_o,X: $o,J2: nat] :
% 8.64/4.83 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.83 => ( ( nth_o @ ( list_update_o @ Xs2 @ I2 @ X ) @ J2 )
% 8.64/4.83 = ( ( ( I2 = J2 )
% 8.64/4.83 => X )
% 8.64/4.83 & ( ( I2 != J2 )
% 8.64/4.83 => ( nth_o @ Xs2 @ J2 ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4476_nth__list__update,axiom,
% 8.64/4.83 ! [I2: nat,Xs2: list_nat,J2: nat,X: nat] :
% 8.64/4.83 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.83 => ( ( ( I2 = J2 )
% 8.64/4.83 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J2 )
% 8.64/4.83 = X ) )
% 8.64/4.83 & ( ( I2 != J2 )
% 8.64/4.83 => ( ( nth_nat @ ( list_update_nat @ Xs2 @ I2 @ X ) @ J2 )
% 8.64/4.83 = ( nth_nat @ Xs2 @ J2 ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4477_nth__list__update,axiom,
% 8.64/4.83 ! [I2: nat,Xs2: list_int,J2: nat,X: int] :
% 8.64/4.83 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.83 => ( ( ( I2 = J2 )
% 8.64/4.83 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J2 )
% 8.64/4.83 = X ) )
% 8.64/4.83 & ( ( I2 != J2 )
% 8.64/4.83 => ( ( nth_int @ ( list_update_int @ Xs2 @ I2 @ X ) @ J2 )
% 8.64/4.83 = ( nth_int @ Xs2 @ J2 ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4478_set__encode__inf,axiom,
% 8.64/4.83 ! [A4: set_nat] :
% 8.64/4.83 ( ~ ( finite_finite_nat @ A4 )
% 8.64/4.83 => ( ( nat_set_encode @ A4 )
% 8.64/4.83 = zero_zero_nat ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4479_eucl__rel__int__iff,axiom,
% 8.64/4.83 ! [K2: int,L: int,Q2: int,R3: int] :
% 8.64/4.83 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.83 = ( ( K2
% 8.64/4.83 = ( plus_plus_int @ ( times_times_int @ L @ Q2 ) @ R3 ) )
% 8.64/4.83 & ( ( ord_less_int @ zero_zero_int @ L )
% 8.64/4.83 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 8.64/4.83 & ( ord_less_int @ R3 @ L ) ) )
% 8.64/4.83 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 8.64/4.83 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 8.64/4.83 => ( ( ord_less_int @ L @ R3 )
% 8.64/4.83 & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 8.64/4.83 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 8.64/4.83 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4480_pos__eucl__rel__int__mult__2,axiom,
% 8.64/4.83 ! [B: int,A: int,Q2: int,R3: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.64/4.83 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.83 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4481_insert__simp__excp,axiom,
% 8.64/4.83 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( ord_less_nat @ X @ Mi )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( X != Ma )
% 8.64/4.83 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4482_insert__simp__norm,axiom,
% 8.64/4.83 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( ord_less_nat @ Mi @ X )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( X != Ma )
% 8.64/4.83 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4483_pred__less__length__list,axiom,
% 8.64/4.83 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ord_less_eq_nat @ X @ Ma )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4484_pred__lesseq__max,axiom,
% 8.64/4.83 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ord_less_eq_nat @ X @ Ma )
% 8.64/4.83 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4485_succ__greatereq__min,axiom,
% 8.64/4.83 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ord_less_eq_nat @ Mi @ X )
% 8.64/4.83 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ none_nat
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4486_succ__less__length__list,axiom,
% 8.64/4.83 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ord_less_eq_nat @ Mi @ X )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ none_nat
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4487_del__in__range,axiom,
% 8.64/4.83 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ( ord_less_eq_nat @ Mi @ X )
% 8.64/4.83 & ( ord_less_eq_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( X = Mi )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 = Ma ) )
% 8.64/4.83 & ( ( X != Mi )
% 8.64/4.83 => ( X = Ma ) ) )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( X = Mi )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 = Ma ) )
% 8.64/4.83 & ( ( X != Mi )
% 8.64/4.83 => ( X = Ma ) ) )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ Summary ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4488_del__x__mi,axiom,
% 8.64/4.83 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat] :
% 8.64/4.83 ( ( ( X = Mi )
% 8.64/4.83 & ( ord_less_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = H )
% 8.64/4.83 => ( ( Xn
% 8.64/4.83 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.64/4.83 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = L )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ Xn
% 8.64/4.83 @ ( if_nat @ ( Xn = Ma )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ Xn
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4489_set__vebt_H__def,axiom,
% 8.64/4.83 ( vEBT_VEBT_set_vebt
% 8.64/4.83 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4490_pred__empty,axiom,
% 8.64/4.83 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.64/4.83 ( ( vEBT_invar_vebt @ T @ N )
% 8.64/4.83 => ( ( ( vEBT_vebt_pred @ T @ X )
% 8.64/4.83 = none_nat )
% 8.64/4.83 = ( ( collect_nat
% 8.64/4.83 @ ^ [Y4: nat] :
% 8.64/4.83 ( ( vEBT_vebt_member @ T @ Y4 )
% 8.64/4.83 & ( ord_less_nat @ Y4 @ X ) ) )
% 8.64/4.83 = bot_bot_set_nat ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4491_succ__empty,axiom,
% 8.64/4.83 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 8.64/4.83 ( ( vEBT_invar_vebt @ T @ N )
% 8.64/4.83 => ( ( ( vEBT_vebt_succ @ T @ X )
% 8.64/4.83 = none_nat )
% 8.64/4.83 = ( ( collect_nat
% 8.64/4.83 @ ^ [Y4: nat] :
% 8.64/4.83 ( ( vEBT_vebt_member @ T @ Y4 )
% 8.64/4.83 & ( ord_less_nat @ X @ Y4 ) ) )
% 8.64/4.83 = bot_bot_set_nat ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4492_max_Obounded__iff,axiom,
% 8.64/4.83 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 8.64/4.83 = ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.83 & ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4493_max_Obounded__iff,axiom,
% 8.64/4.83 ! [B: num,C2: num,A: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 8.64/4.83 = ( ( ord_less_eq_num @ B @ A )
% 8.64/4.83 & ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4494_max_Obounded__iff,axiom,
% 8.64/4.83 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 8.64/4.83 = ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.83 & ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4495_max_Obounded__iff,axiom,
% 8.64/4.83 ! [B: int,C2: int,A: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 8.64/4.83 = ( ( ord_less_eq_int @ B @ A )
% 8.64/4.83 & ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4496_max_Oabsorb2,axiom,
% 8.64/4.83 ! [A: rat,B: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.83 => ( ( ord_max_rat @ A @ B )
% 8.64/4.83 = B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4497_max_Oabsorb2,axiom,
% 8.64/4.83 ! [A: num,B: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ A @ B )
% 8.64/4.83 => ( ( ord_max_num @ A @ B )
% 8.64/4.83 = B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4498_max_Oabsorb2,axiom,
% 8.64/4.83 ! [A: nat,B: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.83 => ( ( ord_max_nat @ A @ B )
% 8.64/4.83 = B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4499_max_Oabsorb2,axiom,
% 8.64/4.83 ! [A: int,B: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ A @ B )
% 8.64/4.83 => ( ( ord_max_int @ A @ B )
% 8.64/4.83 = B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4500_max_Oabsorb1,axiom,
% 8.64/4.83 ! [B: rat,A: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.83 => ( ( ord_max_rat @ A @ B )
% 8.64/4.83 = A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4501_max_Oabsorb1,axiom,
% 8.64/4.83 ! [B: num,A: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ B @ A )
% 8.64/4.83 => ( ( ord_max_num @ A @ B )
% 8.64/4.83 = A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4502_max_Oabsorb1,axiom,
% 8.64/4.83 ! [B: nat,A: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.83 => ( ( ord_max_nat @ A @ B )
% 8.64/4.83 = A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4503_max_Oabsorb1,axiom,
% 8.64/4.83 ! [B: int,A: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ B @ A )
% 8.64/4.83 => ( ( ord_max_int @ A @ B )
% 8.64/4.83 = A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4504_max__bot,axiom,
% 8.64/4.83 ! [X: set_nat] :
% 8.64/4.83 ( ( ord_max_set_nat @ bot_bot_set_nat @ X )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4505_max__bot,axiom,
% 8.64/4.83 ! [X: set_int] :
% 8.64/4.83 ( ( ord_max_set_int @ bot_bot_set_int @ X )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4506_max__bot,axiom,
% 8.64/4.83 ! [X: set_real] :
% 8.64/4.83 ( ( ord_max_set_real @ bot_bot_set_real @ X )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4507_max__bot,axiom,
% 8.64/4.83 ! [X: nat] :
% 8.64/4.83 ( ( ord_max_nat @ bot_bot_nat @ X )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4508_max__bot2,axiom,
% 8.64/4.83 ! [X: set_nat] :
% 8.64/4.83 ( ( ord_max_set_nat @ X @ bot_bot_set_nat )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4509_max__bot2,axiom,
% 8.64/4.83 ! [X: set_int] :
% 8.64/4.83 ( ( ord_max_set_int @ X @ bot_bot_set_int )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4510_max__bot2,axiom,
% 8.64/4.83 ! [X: set_real] :
% 8.64/4.83 ( ( ord_max_set_real @ X @ bot_bot_set_real )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4511_max__bot2,axiom,
% 8.64/4.83 ! [X: nat] :
% 8.64/4.83 ( ( ord_max_nat @ X @ bot_bot_nat )
% 8.64/4.83 = X ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4512_max__Suc__Suc,axiom,
% 8.64/4.83 ! [M2: nat,N: nat] :
% 8.64/4.83 ( ( ord_max_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 8.64/4.83 = ( suc @ ( ord_max_nat @ M2 @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4513_max__nat_Oeq__neutr__iff,axiom,
% 8.64/4.83 ! [A: nat,B: nat] :
% 8.64/4.83 ( ( ( ord_max_nat @ A @ B )
% 8.64/4.83 = zero_zero_nat )
% 8.64/4.83 = ( ( A = zero_zero_nat )
% 8.64/4.83 & ( B = zero_zero_nat ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4514_max__nat_Oleft__neutral,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( ord_max_nat @ zero_zero_nat @ A )
% 8.64/4.83 = A ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4515_max__nat_Oneutr__eq__iff,axiom,
% 8.64/4.83 ! [A: nat,B: nat] :
% 8.64/4.83 ( ( zero_zero_nat
% 8.64/4.83 = ( ord_max_nat @ A @ B ) )
% 8.64/4.83 = ( ( A = zero_zero_nat )
% 8.64/4.83 & ( B = zero_zero_nat ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4516_max__nat_Oright__neutral,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( ord_max_nat @ A @ zero_zero_nat )
% 8.64/4.83 = A ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4517_max__0L,axiom,
% 8.64/4.83 ! [N: nat] :
% 8.64/4.83 ( ( ord_max_nat @ zero_zero_nat @ N )
% 8.64/4.83 = N ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4518_max__0R,axiom,
% 8.64/4.83 ! [N: nat] :
% 8.64/4.83 ( ( ord_max_nat @ N @ zero_zero_nat )
% 8.64/4.83 = N ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4519_finite__Collect__le__nat,axiom,
% 8.64/4.83 ! [K2: nat] :
% 8.64/4.83 ( finite_finite_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [N4: nat] : ( ord_less_eq_nat @ N4 @ K2 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4520_max__number__of_I1_J,axiom,
% 8.64/4.83 ! [U: num,V2: num] :
% 8.64/4.83 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 8.64/4.83 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 8.64/4.83 = ( numera1916890842035813515d_enat @ V2 ) ) )
% 8.64/4.83 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 8.64/4.83 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V2 ) )
% 8.64/4.83 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4521_max__number__of_I1_J,axiom,
% 8.64/4.83 ! [U: num,V2: num] :
% 8.64/4.83 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.83 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.83 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_real @ U ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4522_max__number__of_I1_J,axiom,
% 8.64/4.83 ! [U: num,V2: num] :
% 8.64/4.83 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.83 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.83 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4523_max__number__of_I1_J,axiom,
% 8.64/4.83 ! [U: num,V2: num] :
% 8.64/4.83 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 8.64/4.83 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_nat @ V2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 8.64/4.83 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4524_max__number__of_I1_J,axiom,
% 8.64/4.83 ! [U: num,V2: num] :
% 8.64/4.83 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.83 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.83 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.83 = ( numeral_numeral_int @ U ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4525_max__0__1_I3_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 8.64/4.83 = ( numeral_numeral_rat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4526_max__0__1_I3_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 8.64/4.83 = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4527_max__0__1_I3_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 8.64/4.83 = ( numeral_numeral_real @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4528_max__0__1_I3_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 8.64/4.83 = ( numeral_numeral_nat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4529_max__0__1_I3_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 8.64/4.83 = ( numeral_numeral_int @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4530_max__0__1_I4_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 8.64/4.83 = ( numeral_numeral_rat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4531_max__0__1_I4_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 8.64/4.83 = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4532_max__0__1_I4_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 8.64/4.83 = ( numeral_numeral_real @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4533_max__0__1_I4_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 8.64/4.83 = ( numeral_numeral_nat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4534_max__0__1_I4_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 8.64/4.83 = ( numeral_numeral_int @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4535_max__0__1_I2_J,axiom,
% 8.64/4.83 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 8.64/4.83 = one_one_Code_integer ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4536_max__0__1_I2_J,axiom,
% 8.64/4.83 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 8.64/4.83 = one_one_real ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4537_max__0__1_I2_J,axiom,
% 8.64/4.83 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 8.64/4.83 = one_one_rat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4538_max__0__1_I2_J,axiom,
% 8.64/4.83 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 8.64/4.83 = one_one_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4539_max__0__1_I2_J,axiom,
% 8.64/4.83 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 8.64/4.83 = one_one_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4540_max__0__1_I1_J,axiom,
% 8.64/4.83 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 8.64/4.83 = one_one_Code_integer ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4541_max__0__1_I1_J,axiom,
% 8.64/4.83 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 8.64/4.83 = one_one_real ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4542_max__0__1_I1_J,axiom,
% 8.64/4.83 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 8.64/4.83 = one_one_rat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4543_max__0__1_I1_J,axiom,
% 8.64/4.83 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 8.64/4.83 = one_one_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4544_max__0__1_I1_J,axiom,
% 8.64/4.83 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 8.64/4.83 = one_one_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4545_max__0__1_I5_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 8.64/4.83 = ( numera6620942414471956472nteger @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4546_max__0__1_I5_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 8.64/4.83 = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4547_max__0__1_I5_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 8.64/4.83 = ( numeral_numeral_real @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4548_max__0__1_I5_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 8.64/4.83 = ( numeral_numeral_nat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4549_max__0__1_I5_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 8.64/4.83 = ( numeral_numeral_int @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4550_max__0__1_I6_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 8.64/4.83 = ( numera6620942414471956472nteger @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4551_max__0__1_I6_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 8.64/4.83 = ( numera1916890842035813515d_enat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4552_max__0__1_I6_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 8.64/4.83 = ( numeral_numeral_real @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4553_max__0__1_I6_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 8.64/4.83 = ( numeral_numeral_nat @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4554_max__0__1_I6_J,axiom,
% 8.64/4.83 ! [X: num] :
% 8.64/4.83 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 8.64/4.83 = ( numeral_numeral_int @ X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4555_card__Collect__le__nat,axiom,
% 8.64/4.83 ! [N: nat] :
% 8.64/4.83 ( ( finite_card_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [I: nat] : ( ord_less_eq_nat @ I @ N ) ) )
% 8.64/4.83 = ( suc @ N ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4556_del__x__not__mia,axiom,
% 8.64/4.83 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ( ord_less_nat @ Mi @ X )
% 8.64/4.83 & ( ord_less_eq_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = H )
% 8.64/4.83 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = L )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ Mi
% 8.64/4.83 @ ( if_nat @ ( X = Ma )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ Mi
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ H ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4557_del__x__not__mi__new__node__nil,axiom,
% 8.64/4.83 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 8.64/4.83 ( ( ( ord_less_nat @ Mi @ X )
% 8.64/4.83 & ( ord_less_eq_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = H )
% 8.64/4.83 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = L )
% 8.64/4.83 => ( ( Newnode
% 8.64/4.83 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 => ( ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.83 => ( ( Sn
% 8.64/4.83 = ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 => ( ( Newlist
% 8.64/4.83 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ Mi
% 8.64/4.83 @ ( if_nat @ ( X = Ma )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ Sn )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ Mi
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ Newlist
% 8.64/4.83 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4558_del__x__not__mi,axiom,
% 8.64/4.83 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H: nat,L: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ( ord_less_nat @ Mi @ X )
% 8.64/4.83 & ( ord_less_eq_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = H )
% 8.64/4.83 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = L )
% 8.64/4.83 => ( ( Newnode
% 8.64/4.83 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 => ( ( Newlist
% 8.64/4.83 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ Mi
% 8.64/4.83 @ ( if_nat @ ( X = Ma )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ Mi
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ Newlist
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 8.64/4.83 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4559_del__x__mia,axiom,
% 8.64/4.83 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ( X = Mi )
% 8.64/4.83 & ( ord_less_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 = Ma )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 = Ma )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ Summary ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4560_del__x__mi__lets__in__minNull,axiom,
% 8.64/4.83 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 8.64/4.83 ( ( ( X = Mi )
% 8.64/4.83 & ( ord_less_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = H )
% 8.64/4.83 => ( ( Xn
% 8.64/4.83 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.64/4.83 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = L )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( Newnode
% 8.64/4.83 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 => ( ( Newlist
% 8.64/4.83 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 8.64/4.83 => ( ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.83 => ( ( Sn
% 8.64/4.83 = ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ Xn
% 8.64/4.83 @ ( if_nat @ ( Xn = Ma )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ Sn )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ Xn
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ Newlist
% 8.64/4.83 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4561_del__x__mi__lets__in,axiom,
% 8.64/4.83 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 8.64/4.83 ( ( ( X = Mi )
% 8.64/4.83 & ( ord_less_nat @ X @ Ma ) )
% 8.64/4.83 => ( ( Mi != Ma )
% 8.64/4.83 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 8.64/4.83 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = H )
% 8.64/4.83 => ( ( Xn
% 8.64/4.83 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 8.64/4.83 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.83 = L )
% 8.64/4.83 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( ( Newnode
% 8.64/4.83 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H ) @ L ) )
% 8.64/4.83 => ( ( Newlist
% 8.64/4.83 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H @ Newnode ) )
% 8.64/4.83 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ Xn
% 8.64/4.83 @ ( if_nat @ ( Xn = Ma )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ Xn
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ Deg
% 8.64/4.83 @ Newlist
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary @ H ) ) ) )
% 8.64/4.83 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4562_of__nat__max,axiom,
% 8.64/4.83 ! [X: nat,Y: nat] :
% 8.64/4.83 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 8.64/4.83 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4563_of__nat__max,axiom,
% 8.64/4.83 ! [X: nat,Y: nat] :
% 8.64/4.83 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 8.64/4.83 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4564_of__nat__max,axiom,
% 8.64/4.83 ! [X: nat,Y: nat] :
% 8.64/4.83 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 8.64/4.83 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4565_max__def__raw,axiom,
% 8.64/4.83 ( ord_max_set_nat
% 8.64/4.83 = ( ^ [A5: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4566_max__def__raw,axiom,
% 8.64/4.83 ( ord_max_rat
% 8.64/4.83 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4567_max__def__raw,axiom,
% 8.64/4.83 ( ord_max_num
% 8.64/4.83 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4568_max__def__raw,axiom,
% 8.64/4.83 ( ord_max_nat
% 8.64/4.83 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4569_max__def__raw,axiom,
% 8.64/4.83 ( ord_max_int
% 8.64/4.83 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4570_sup__nat__def,axiom,
% 8.64/4.83 sup_sup_nat = ord_max_nat ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4571_lambda__zero,axiom,
% 8.64/4.83 ( ( ^ [H2: complex] : zero_zero_complex )
% 8.64/4.83 = ( times_times_complex @ zero_zero_complex ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4572_lambda__zero,axiom,
% 8.64/4.83 ( ( ^ [H2: real] : zero_zero_real )
% 8.64/4.83 = ( times_times_real @ zero_zero_real ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4573_lambda__zero,axiom,
% 8.64/4.83 ( ( ^ [H2: rat] : zero_zero_rat )
% 8.64/4.83 = ( times_times_rat @ zero_zero_rat ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4574_lambda__zero,axiom,
% 8.64/4.83 ( ( ^ [H2: nat] : zero_zero_nat )
% 8.64/4.83 = ( times_times_nat @ zero_zero_nat ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4575_lambda__zero,axiom,
% 8.64/4.83 ( ( ^ [H2: int] : zero_zero_int )
% 8.64/4.83 = ( times_times_int @ zero_zero_int ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4576_lambda__one,axiom,
% 8.64/4.83 ( ( ^ [X4: code_integer] : X4 )
% 8.64/4.83 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4577_lambda__one,axiom,
% 8.64/4.83 ( ( ^ [X4: complex] : X4 )
% 8.64/4.83 = ( times_times_complex @ one_one_complex ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4578_lambda__one,axiom,
% 8.64/4.83 ( ( ^ [X4: real] : X4 )
% 8.64/4.83 = ( times_times_real @ one_one_real ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4579_lambda__one,axiom,
% 8.64/4.83 ( ( ^ [X4: rat] : X4 )
% 8.64/4.83 = ( times_times_rat @ one_one_rat ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4580_lambda__one,axiom,
% 8.64/4.83 ( ( ^ [X4: nat] : X4 )
% 8.64/4.83 = ( times_times_nat @ one_one_nat ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4581_lambda__one,axiom,
% 8.64/4.83 ( ( ^ [X4: int] : X4 )
% 8.64/4.83 = ( times_times_int @ one_one_int ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4582_finite__M__bounded__by__nat,axiom,
% 8.64/4.83 ! [P2: nat > $o,I2: nat] :
% 8.64/4.83 ( finite_finite_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [K3: nat] :
% 8.64/4.83 ( ( P2 @ K3 )
% 8.64/4.83 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4583_finite__less__ub,axiom,
% 8.64/4.83 ! [F2: nat > nat,U: nat] :
% 8.64/4.83 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F2 @ N3 ) )
% 8.64/4.83 => ( finite_finite_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [N4: nat] : ( ord_less_eq_nat @ ( F2 @ N4 ) @ U ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4584_max_Omono,axiom,
% 8.64/4.83 ! [C2: rat,A: rat,D: rat,B: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.83 => ( ( ord_less_eq_rat @ D @ B )
% 8.64/4.83 => ( ord_less_eq_rat @ ( ord_max_rat @ C2 @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4585_max_Omono,axiom,
% 8.64/4.83 ! [C2: num,A: num,D: num,B: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ C2 @ A )
% 8.64/4.83 => ( ( ord_less_eq_num @ D @ B )
% 8.64/4.83 => ( ord_less_eq_num @ ( ord_max_num @ C2 @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4586_max_Omono,axiom,
% 8.64/4.83 ! [C2: nat,A: nat,D: nat,B: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.83 => ( ( ord_less_eq_nat @ D @ B )
% 8.64/4.83 => ( ord_less_eq_nat @ ( ord_max_nat @ C2 @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4587_max_Omono,axiom,
% 8.64/4.83 ! [C2: int,A: int,D: int,B: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.83 => ( ( ord_less_eq_int @ D @ B )
% 8.64/4.83 => ( ord_less_eq_int @ ( ord_max_int @ C2 @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4588_max_OorderE,axiom,
% 8.64/4.83 ! [B: rat,A: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.83 => ( A
% 8.64/4.83 = ( ord_max_rat @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4589_max_OorderE,axiom,
% 8.64/4.83 ! [B: num,A: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ B @ A )
% 8.64/4.83 => ( A
% 8.64/4.83 = ( ord_max_num @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4590_max_OorderE,axiom,
% 8.64/4.83 ! [B: nat,A: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.83 => ( A
% 8.64/4.83 = ( ord_max_nat @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4591_max_OorderE,axiom,
% 8.64/4.83 ! [B: int,A: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ B @ A )
% 8.64/4.83 => ( A
% 8.64/4.83 = ( ord_max_int @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4592_max_OorderI,axiom,
% 8.64/4.83 ! [A: rat,B: rat] :
% 8.64/4.83 ( ( A
% 8.64/4.83 = ( ord_max_rat @ A @ B ) )
% 8.64/4.83 => ( ord_less_eq_rat @ B @ A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4593_max_OorderI,axiom,
% 8.64/4.83 ! [A: num,B: num] :
% 8.64/4.83 ( ( A
% 8.64/4.83 = ( ord_max_num @ A @ B ) )
% 8.64/4.83 => ( ord_less_eq_num @ B @ A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4594_max_OorderI,axiom,
% 8.64/4.83 ! [A: nat,B: nat] :
% 8.64/4.83 ( ( A
% 8.64/4.83 = ( ord_max_nat @ A @ B ) )
% 8.64/4.83 => ( ord_less_eq_nat @ B @ A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4595_max_OorderI,axiom,
% 8.64/4.83 ! [A: int,B: int] :
% 8.64/4.83 ( ( A
% 8.64/4.83 = ( ord_max_int @ A @ B ) )
% 8.64/4.83 => ( ord_less_eq_int @ B @ A ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4596_max_OboundedE,axiom,
% 8.64/4.83 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A )
% 8.64/4.83 => ~ ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.83 => ~ ( ord_less_eq_rat @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4597_max_OboundedE,axiom,
% 8.64/4.83 ! [B: num,C2: num,A: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A )
% 8.64/4.83 => ~ ( ( ord_less_eq_num @ B @ A )
% 8.64/4.83 => ~ ( ord_less_eq_num @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4598_max_OboundedE,axiom,
% 8.64/4.83 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A )
% 8.64/4.83 => ~ ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.83 => ~ ( ord_less_eq_nat @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4599_max_OboundedE,axiom,
% 8.64/4.83 ! [B: int,C2: int,A: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A )
% 8.64/4.83 => ~ ( ( ord_less_eq_int @ B @ A )
% 8.64/4.83 => ~ ( ord_less_eq_int @ C2 @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4600_max_OboundedI,axiom,
% 8.64/4.83 ! [B: rat,A: rat,C2: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ B @ A )
% 8.64/4.83 => ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4601_max_OboundedI,axiom,
% 8.64/4.83 ! [B: num,A: num,C2: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ B @ A )
% 8.64/4.83 => ( ( ord_less_eq_num @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_num @ ( ord_max_num @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4602_max_OboundedI,axiom,
% 8.64/4.83 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ B @ A )
% 8.64/4.83 => ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4603_max_OboundedI,axiom,
% 8.64/4.83 ! [B: int,A: int,C2: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ B @ A )
% 8.64/4.83 => ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_int @ ( ord_max_int @ B @ C2 ) @ A ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4604_max_Oorder__iff,axiom,
% 8.64/4.83 ( ord_less_eq_rat
% 8.64/4.83 = ( ^ [B4: rat,A5: rat] :
% 8.64/4.83 ( A5
% 8.64/4.83 = ( ord_max_rat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4605_max_Oorder__iff,axiom,
% 8.64/4.83 ( ord_less_eq_num
% 8.64/4.83 = ( ^ [B4: num,A5: num] :
% 8.64/4.83 ( A5
% 8.64/4.83 = ( ord_max_num @ A5 @ B4 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4606_max_Oorder__iff,axiom,
% 8.64/4.83 ( ord_less_eq_nat
% 8.64/4.83 = ( ^ [B4: nat,A5: nat] :
% 8.64/4.83 ( A5
% 8.64/4.83 = ( ord_max_nat @ A5 @ B4 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4607_max_Oorder__iff,axiom,
% 8.64/4.83 ( ord_less_eq_int
% 8.64/4.83 = ( ^ [B4: int,A5: int] :
% 8.64/4.83 ( A5
% 8.64/4.83 = ( ord_max_int @ A5 @ B4 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4608_max_Ocobounded1,axiom,
% 8.64/4.83 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4609_max_Ocobounded1,axiom,
% 8.64/4.83 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4610_max_Ocobounded1,axiom,
% 8.64/4.83 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4611_max_Ocobounded1,axiom,
% 8.64/4.83 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4612_max_Ocobounded2,axiom,
% 8.64/4.83 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4613_max_Ocobounded2,axiom,
% 8.64/4.83 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4614_max_Ocobounded2,axiom,
% 8.64/4.83 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4615_max_Ocobounded2,axiom,
% 8.64/4.83 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4616_le__max__iff__disj,axiom,
% 8.64/4.83 ! [Z3: rat,X: rat,Y: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ Z3 @ ( ord_max_rat @ X @ Y ) )
% 8.64/4.83 = ( ( ord_less_eq_rat @ Z3 @ X )
% 8.64/4.83 | ( ord_less_eq_rat @ Z3 @ Y ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4617_le__max__iff__disj,axiom,
% 8.64/4.83 ! [Z3: num,X: num,Y: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ Z3 @ ( ord_max_num @ X @ Y ) )
% 8.64/4.83 = ( ( ord_less_eq_num @ Z3 @ X )
% 8.64/4.83 | ( ord_less_eq_num @ Z3 @ Y ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4618_le__max__iff__disj,axiom,
% 8.64/4.83 ! [Z3: nat,X: nat,Y: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ Z3 @ ( ord_max_nat @ X @ Y ) )
% 8.64/4.83 = ( ( ord_less_eq_nat @ Z3 @ X )
% 8.64/4.83 | ( ord_less_eq_nat @ Z3 @ Y ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4619_le__max__iff__disj,axiom,
% 8.64/4.83 ! [Z3: int,X: int,Y: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ Z3 @ ( ord_max_int @ X @ Y ) )
% 8.64/4.83 = ( ( ord_less_eq_int @ Z3 @ X )
% 8.64/4.83 | ( ord_less_eq_int @ Z3 @ Y ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4620_max_Oabsorb__iff1,axiom,
% 8.64/4.83 ( ord_less_eq_rat
% 8.64/4.83 = ( ^ [B4: rat,A5: rat] :
% 8.64/4.83 ( ( ord_max_rat @ A5 @ B4 )
% 8.64/4.83 = A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4621_max_Oabsorb__iff1,axiom,
% 8.64/4.83 ( ord_less_eq_num
% 8.64/4.83 = ( ^ [B4: num,A5: num] :
% 8.64/4.83 ( ( ord_max_num @ A5 @ B4 )
% 8.64/4.83 = A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4622_max_Oabsorb__iff1,axiom,
% 8.64/4.83 ( ord_less_eq_nat
% 8.64/4.83 = ( ^ [B4: nat,A5: nat] :
% 8.64/4.83 ( ( ord_max_nat @ A5 @ B4 )
% 8.64/4.83 = A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4623_max_Oabsorb__iff1,axiom,
% 8.64/4.83 ( ord_less_eq_int
% 8.64/4.83 = ( ^ [B4: int,A5: int] :
% 8.64/4.83 ( ( ord_max_int @ A5 @ B4 )
% 8.64/4.83 = A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4624_max_Oabsorb__iff2,axiom,
% 8.64/4.83 ( ord_less_eq_rat
% 8.64/4.83 = ( ^ [A5: rat,B4: rat] :
% 8.64/4.83 ( ( ord_max_rat @ A5 @ B4 )
% 8.64/4.83 = B4 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4625_max_Oabsorb__iff2,axiom,
% 8.64/4.83 ( ord_less_eq_num
% 8.64/4.83 = ( ^ [A5: num,B4: num] :
% 8.64/4.83 ( ( ord_max_num @ A5 @ B4 )
% 8.64/4.83 = B4 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4626_max_Oabsorb__iff2,axiom,
% 8.64/4.83 ( ord_less_eq_nat
% 8.64/4.83 = ( ^ [A5: nat,B4: nat] :
% 8.64/4.83 ( ( ord_max_nat @ A5 @ B4 )
% 8.64/4.83 = B4 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4627_max_Oabsorb__iff2,axiom,
% 8.64/4.83 ( ord_less_eq_int
% 8.64/4.83 = ( ^ [A5: int,B4: int] :
% 8.64/4.83 ( ( ord_max_int @ A5 @ B4 )
% 8.64/4.83 = B4 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4628_max_OcoboundedI1,axiom,
% 8.64/4.83 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4629_max_OcoboundedI1,axiom,
% 8.64/4.83 ! [C2: num,A: num,B: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4630_max_OcoboundedI1,axiom,
% 8.64/4.83 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4631_max_OcoboundedI1,axiom,
% 8.64/4.83 ! [C2: int,A: int,B: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ C2 @ A )
% 8.64/4.83 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4632_max_OcoboundedI2,axiom,
% 8.64/4.83 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ C2 @ B )
% 8.64/4.83 => ( ord_less_eq_rat @ C2 @ ( ord_max_rat @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4633_max_OcoboundedI2,axiom,
% 8.64/4.83 ! [C2: num,B: num,A: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ C2 @ B )
% 8.64/4.83 => ( ord_less_eq_num @ C2 @ ( ord_max_num @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4634_max_OcoboundedI2,axiom,
% 8.64/4.83 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ C2 @ B )
% 8.64/4.83 => ( ord_less_eq_nat @ C2 @ ( ord_max_nat @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4635_max_OcoboundedI2,axiom,
% 8.64/4.83 ! [C2: int,B: int,A: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ C2 @ B )
% 8.64/4.83 => ( ord_less_eq_int @ C2 @ ( ord_max_int @ A @ B ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4636_max__absorb2,axiom,
% 8.64/4.83 ! [X: set_nat,Y: set_nat] :
% 8.64/4.83 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.64/4.83 => ( ( ord_max_set_nat @ X @ Y )
% 8.64/4.83 = Y ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4637_max__absorb2,axiom,
% 8.64/4.83 ! [X: rat,Y: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ X @ Y )
% 8.64/4.83 => ( ( ord_max_rat @ X @ Y )
% 8.64/4.83 = Y ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4638_max__absorb2,axiom,
% 8.64/4.83 ! [X: num,Y: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ X @ Y )
% 8.64/4.83 => ( ( ord_max_num @ X @ Y )
% 8.64/4.83 = Y ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4639_max__absorb2,axiom,
% 8.64/4.83 ! [X: nat,Y: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ X @ Y )
% 8.64/4.83 => ( ( ord_max_nat @ X @ Y )
% 8.64/4.83 = Y ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4640_max__absorb2,axiom,
% 8.64/4.83 ! [X: int,Y: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ X @ Y )
% 8.64/4.83 => ( ( ord_max_int @ X @ Y )
% 8.64/4.83 = Y ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4641_max__absorb1,axiom,
% 8.64/4.83 ! [Y: set_nat,X: set_nat] :
% 8.64/4.83 ( ( ord_less_eq_set_nat @ Y @ X )
% 8.64/4.83 => ( ( ord_max_set_nat @ X @ Y )
% 8.64/4.83 = X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4642_max__absorb1,axiom,
% 8.64/4.83 ! [Y: rat,X: rat] :
% 8.64/4.83 ( ( ord_less_eq_rat @ Y @ X )
% 8.64/4.83 => ( ( ord_max_rat @ X @ Y )
% 8.64/4.83 = X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4643_max__absorb1,axiom,
% 8.64/4.83 ! [Y: num,X: num] :
% 8.64/4.83 ( ( ord_less_eq_num @ Y @ X )
% 8.64/4.83 => ( ( ord_max_num @ X @ Y )
% 8.64/4.83 = X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4644_max__absorb1,axiom,
% 8.64/4.83 ! [Y: nat,X: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ Y @ X )
% 8.64/4.83 => ( ( ord_max_nat @ X @ Y )
% 8.64/4.83 = X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4645_max__absorb1,axiom,
% 8.64/4.83 ! [Y: int,X: int] :
% 8.64/4.83 ( ( ord_less_eq_int @ Y @ X )
% 8.64/4.83 => ( ( ord_max_int @ X @ Y )
% 8.64/4.83 = X ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4646_max__def,axiom,
% 8.64/4.83 ( ord_max_set_nat
% 8.64/4.83 = ( ^ [A5: set_nat,B4: set_nat] : ( if_set_nat @ ( ord_less_eq_set_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4647_max__def,axiom,
% 8.64/4.83 ( ord_max_rat
% 8.64/4.83 = ( ^ [A5: rat,B4: rat] : ( if_rat @ ( ord_less_eq_rat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4648_max__def,axiom,
% 8.64/4.83 ( ord_max_num
% 8.64/4.83 = ( ^ [A5: num,B4: num] : ( if_num @ ( ord_less_eq_num @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4649_max__def,axiom,
% 8.64/4.83 ( ord_max_nat
% 8.64/4.83 = ( ^ [A5: nat,B4: nat] : ( if_nat @ ( ord_less_eq_nat @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4650_max__def,axiom,
% 8.64/4.83 ( ord_max_int
% 8.64/4.83 = ( ^ [A5: int,B4: int] : ( if_int @ ( ord_less_eq_int @ A5 @ B4 ) @ B4 @ A5 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4651_max__add__distrib__left,axiom,
% 8.64/4.83 ! [X: real,Y: real,Z3: real] :
% 8.64/4.83 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z3 )
% 8.64/4.83 = ( ord_max_real @ ( plus_plus_real @ X @ Z3 ) @ ( plus_plus_real @ Y @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4652_max__add__distrib__left,axiom,
% 8.64/4.83 ! [X: rat,Y: rat,Z3: rat] :
% 8.64/4.83 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 8.64/4.83 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z3 ) @ ( plus_plus_rat @ Y @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4653_max__add__distrib__left,axiom,
% 8.64/4.83 ! [X: nat,Y: nat,Z3: nat] :
% 8.64/4.83 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z3 )
% 8.64/4.83 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z3 ) @ ( plus_plus_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4654_max__add__distrib__left,axiom,
% 8.64/4.83 ! [X: int,Y: int,Z3: int] :
% 8.64/4.83 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 8.64/4.83 = ( ord_max_int @ ( plus_plus_int @ X @ Z3 ) @ ( plus_plus_int @ Y @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4655_max__add__distrib__right,axiom,
% 8.64/4.83 ! [X: real,Y: real,Z3: real] :
% 8.64/4.83 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z3 ) )
% 8.64/4.83 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4656_max__add__distrib__right,axiom,
% 8.64/4.83 ! [X: rat,Y: rat,Z3: rat] :
% 8.64/4.83 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z3 ) )
% 8.64/4.83 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4657_max__add__distrib__right,axiom,
% 8.64/4.83 ! [X: nat,Y: nat,Z3: nat] :
% 8.64/4.83 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z3 ) )
% 8.64/4.83 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4658_max__add__distrib__right,axiom,
% 8.64/4.83 ! [X: int,Y: int,Z3: int] :
% 8.64/4.83 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z3 ) )
% 8.64/4.83 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4659_max__diff__distrib__left,axiom,
% 8.64/4.83 ! [X: rat,Y: rat,Z3: rat] :
% 8.64/4.83 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z3 )
% 8.64/4.83 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z3 ) @ ( minus_minus_rat @ Y @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4660_max__diff__distrib__left,axiom,
% 8.64/4.83 ! [X: int,Y: int,Z3: int] :
% 8.64/4.83 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z3 )
% 8.64/4.83 = ( ord_max_int @ ( minus_minus_int @ X @ Z3 ) @ ( minus_minus_int @ Y @ Z3 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4661_nat__add__max__left,axiom,
% 8.64/4.83 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.83 ( ( plus_plus_nat @ ( ord_max_nat @ M2 @ N ) @ Q2 )
% 8.64/4.83 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4662_nat__add__max__right,axiom,
% 8.64/4.83 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.83 ( ( plus_plus_nat @ M2 @ ( ord_max_nat @ N @ Q2 ) )
% 8.64/4.83 = ( ord_max_nat @ ( plus_plus_nat @ M2 @ N ) @ ( plus_plus_nat @ M2 @ Q2 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4663_set__vebt__def,axiom,
% 8.64/4.83 ( vEBT_set_vebt
% 8.64/4.83 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4664_nat__mult__max__left,axiom,
% 8.64/4.83 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.83 ( ( times_times_nat @ ( ord_max_nat @ M2 @ N ) @ Q2 )
% 8.64/4.83 = ( ord_max_nat @ ( times_times_nat @ M2 @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4665_nat__mult__max__right,axiom,
% 8.64/4.83 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.83 ( ( times_times_nat @ M2 @ ( ord_max_nat @ N @ Q2 ) )
% 8.64/4.83 = ( ord_max_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q2 ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4666_numeral__code_I2_J,axiom,
% 8.64/4.83 ! [N: num] :
% 8.64/4.83 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 8.64/4.83 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4667_numeral__code_I2_J,axiom,
% 8.64/4.83 ! [N: num] :
% 8.64/4.83 ( ( numera1916890842035813515d_enat @ ( bit0 @ N ) )
% 8.64/4.83 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4668_numeral__code_I2_J,axiom,
% 8.64/4.83 ! [N: num] :
% 8.64/4.83 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 8.64/4.83 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4669_numeral__code_I2_J,axiom,
% 8.64/4.83 ! [N: num] :
% 8.64/4.83 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 8.64/4.83 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4670_numeral__code_I2_J,axiom,
% 8.64/4.83 ! [N: num] :
% 8.64/4.83 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 8.64/4.83 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4671_numeral__code_I2_J,axiom,
% 8.64/4.83 ! [N: num] :
% 8.64/4.83 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 8.64/4.83 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4672_nat__leq__as__int,axiom,
% 8.64/4.83 ( ord_less_eq_nat
% 8.64/4.83 = ( ^ [A5: nat,B4: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4673_power__numeral__even,axiom,
% 8.64/4.83 ! [Z3: complex,W2: num] :
% 8.64/4.83 ( ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 8.64/4.83 = ( times_times_complex @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4674_power__numeral__even,axiom,
% 8.64/4.83 ! [Z3: real,W2: num] :
% 8.64/4.83 ( ( power_power_real @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 8.64/4.83 = ( times_times_real @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4675_power__numeral__even,axiom,
% 8.64/4.83 ! [Z3: rat,W2: num] :
% 8.64/4.83 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 8.64/4.83 = ( times_times_rat @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4676_power__numeral__even,axiom,
% 8.64/4.83 ! [Z3: nat,W2: num] :
% 8.64/4.83 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 8.64/4.83 = ( times_times_nat @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4677_power__numeral__even,axiom,
% 8.64/4.83 ! [Z3: int,W2: num] :
% 8.64/4.83 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 8.64/4.83 = ( times_times_int @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4678_card__less,axiom,
% 8.64/4.83 ! [M5: set_nat,I2: nat] :
% 8.64/4.83 ( ( member_nat @ zero_zero_nat @ M5 )
% 8.64/4.83 => ( ( finite_card_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [K3: nat] :
% 8.64/4.83 ( ( member_nat @ K3 @ M5 )
% 8.64/4.83 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 8.64/4.83 != zero_zero_nat ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4679_card__less__Suc,axiom,
% 8.64/4.83 ! [M5: set_nat,I2: nat] :
% 8.64/4.83 ( ( member_nat @ zero_zero_nat @ M5 )
% 8.64/4.83 => ( ( suc
% 8.64/4.83 @ ( finite_card_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [K3: nat] :
% 8.64/4.83 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 8.64/4.83 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 8.64/4.83 = ( finite_card_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [K3: nat] :
% 8.64/4.83 ( ( member_nat @ K3 @ M5 )
% 8.64/4.83 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4680_card__less__Suc2,axiom,
% 8.64/4.83 ! [M5: set_nat,I2: nat] :
% 8.64/4.83 ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 8.64/4.83 => ( ( finite_card_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [K3: nat] :
% 8.64/4.83 ( ( member_nat @ ( suc @ K3 ) @ M5 )
% 8.64/4.83 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 8.64/4.83 = ( finite_card_nat
% 8.64/4.83 @ ( collect_nat
% 8.64/4.83 @ ^ [K3: nat] :
% 8.64/4.83 ( ( member_nat @ K3 @ M5 )
% 8.64/4.83 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4681_nat__minus__add__max,axiom,
% 8.64/4.83 ! [N: nat,M2: nat] :
% 8.64/4.83 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M2 ) @ M2 )
% 8.64/4.83 = ( ord_max_nat @ N @ M2 ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4682_finite__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_complex,N: nat] :
% 8.64/4.83 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.83 => ( finite8712137658972009173omplex
% 8.64/4.83 @ ( collect_list_complex
% 8.64/4.83 @ ^ [Xs: list_complex] :
% 8.64/4.83 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_s3451745648224563538omplex @ Xs )
% 8.64/4.83 = N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4683_finite__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_VEBT_VEBT,N: nat] :
% 8.64/4.83 ( ( finite5795047828879050333T_VEBT @ A4 )
% 8.64/4.83 => ( finite3004134309566078307T_VEBT
% 8.64/4.83 @ ( collec5608196760682091941T_VEBT
% 8.64/4.83 @ ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.83 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.64/4.83 = N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4684_finite__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_o,N: nat] :
% 8.64/4.83 ( ( finite_finite_o @ A4 )
% 8.64/4.83 => ( finite_finite_list_o
% 8.64/4.83 @ ( collect_list_o
% 8.64/4.83 @ ^ [Xs: list_o] :
% 8.64/4.83 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_size_list_o @ Xs )
% 8.64/4.83 = N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4685_finite__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_int,N: nat] :
% 8.64/4.83 ( ( finite_finite_int @ A4 )
% 8.64/4.83 => ( finite3922522038869484883st_int
% 8.64/4.83 @ ( collect_list_int
% 8.64/4.83 @ ^ [Xs: list_int] :
% 8.64/4.83 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_size_list_int @ Xs )
% 8.64/4.83 = N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4686_finite__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_nat,N: nat] :
% 8.64/4.83 ( ( finite_finite_nat @ A4 )
% 8.64/4.83 => ( finite8100373058378681591st_nat
% 8.64/4.83 @ ( collect_list_nat
% 8.64/4.83 @ ^ [Xs: list_nat] :
% 8.64/4.83 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_size_list_nat @ Xs )
% 8.64/4.83 = N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4687_card__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_list_nat,N: nat] :
% 8.64/4.83 ( ( finite8100373058378681591st_nat @ A4 )
% 8.64/4.83 => ( ( finite7325466520557071688st_nat
% 8.64/4.83 @ ( collec5989764272469232197st_nat
% 8.64/4.83 @ ^ [Xs: list_list_nat] :
% 8.64/4.83 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_s3023201423986296836st_nat @ Xs )
% 8.64/4.83 = N ) ) ) )
% 8.64/4.83 = ( power_power_nat @ ( finite_card_list_nat @ A4 ) @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4688_card__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_set_nat,N: nat] :
% 8.64/4.83 ( ( finite1152437895449049373et_nat @ A4 )
% 8.64/4.83 => ( ( finite5631907774883551598et_nat
% 8.64/4.83 @ ( collect_list_set_nat
% 8.64/4.83 @ ^ [Xs: list_set_nat] :
% 8.64/4.83 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_s3254054031482475050et_nat @ Xs )
% 8.64/4.83 = N ) ) ) )
% 8.64/4.83 = ( power_power_nat @ ( finite_card_set_nat @ A4 ) @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4689_card__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_complex,N: nat] :
% 8.64/4.83 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.83 => ( ( finite5120063068150530198omplex
% 8.64/4.83 @ ( collect_list_complex
% 8.64/4.83 @ ^ [Xs: list_complex] :
% 8.64/4.83 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_s3451745648224563538omplex @ Xs )
% 8.64/4.83 = N ) ) ) )
% 8.64/4.83 = ( power_power_nat @ ( finite_card_complex @ A4 ) @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4690_card__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_VEBT_VEBT,N: nat] :
% 8.64/4.83 ( ( finite5795047828879050333T_VEBT @ A4 )
% 8.64/4.83 => ( ( finite5915292604075114978T_VEBT
% 8.64/4.83 @ ( collec5608196760682091941T_VEBT
% 8.64/4.83 @ ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.83 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.64/4.83 = N ) ) ) )
% 8.64/4.83 = ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4691_card__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_o,N: nat] :
% 8.64/4.83 ( ( finite_finite_o @ A4 )
% 8.64/4.83 => ( ( finite_card_list_o
% 8.64/4.83 @ ( collect_list_o
% 8.64/4.83 @ ^ [Xs: list_o] :
% 8.64/4.83 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_size_list_o @ Xs )
% 8.64/4.83 = N ) ) ) )
% 8.64/4.83 = ( power_power_nat @ ( finite_card_o @ A4 ) @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4692_card__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_int,N: nat] :
% 8.64/4.83 ( ( finite_finite_int @ A4 )
% 8.64/4.83 => ( ( finite_card_list_int
% 8.64/4.83 @ ( collect_list_int
% 8.64/4.83 @ ^ [Xs: list_int] :
% 8.64/4.83 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_size_list_int @ Xs )
% 8.64/4.83 = N ) ) ) )
% 8.64/4.83 = ( power_power_nat @ ( finite_card_int @ A4 ) @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4693_card__lists__length__eq,axiom,
% 8.64/4.83 ! [A4: set_nat,N: nat] :
% 8.64/4.83 ( ( finite_finite_nat @ A4 )
% 8.64/4.83 => ( ( finite_card_list_nat
% 8.64/4.83 @ ( collect_list_nat
% 8.64/4.83 @ ^ [Xs: list_nat] :
% 8.64/4.83 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ( size_size_list_nat @ Xs )
% 8.64/4.83 = N ) ) ) )
% 8.64/4.83 = ( power_power_nat @ ( finite_card_nat @ A4 ) @ N ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4694_finite__lists__length__le,axiom,
% 8.64/4.83 ! [A4: set_complex,N: nat] :
% 8.64/4.83 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.83 => ( finite8712137658972009173omplex
% 8.64/4.83 @ ( collect_list_complex
% 8.64/4.83 @ ^ [Xs: list_complex] :
% 8.64/4.83 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4695_finite__lists__length__le,axiom,
% 8.64/4.83 ! [A4: set_VEBT_VEBT,N: nat] :
% 8.64/4.83 ( ( finite5795047828879050333T_VEBT @ A4 )
% 8.64/4.83 => ( finite3004134309566078307T_VEBT
% 8.64/4.83 @ ( collec5608196760682091941T_VEBT
% 8.64/4.83 @ ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.83 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4696_finite__lists__length__le,axiom,
% 8.64/4.83 ! [A4: set_o,N: nat] :
% 8.64/4.83 ( ( finite_finite_o @ A4 )
% 8.64/4.83 => ( finite_finite_list_o
% 8.64/4.83 @ ( collect_list_o
% 8.64/4.83 @ ^ [Xs: list_o] :
% 8.64/4.83 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4697_finite__lists__length__le,axiom,
% 8.64/4.83 ! [A4: set_int,N: nat] :
% 8.64/4.83 ( ( finite_finite_int @ A4 )
% 8.64/4.83 => ( finite3922522038869484883st_int
% 8.64/4.83 @ ( collect_list_int
% 8.64/4.83 @ ^ [Xs: list_int] :
% 8.64/4.83 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4698_finite__lists__length__le,axiom,
% 8.64/4.83 ! [A4: set_nat,N: nat] :
% 8.64/4.83 ( ( finite_finite_nat @ A4 )
% 8.64/4.83 => ( finite8100373058378681591st_nat
% 8.64/4.83 @ ( collect_list_nat
% 8.64/4.83 @ ^ [Xs: list_nat] :
% 8.64/4.83 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 8.64/4.83 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4699_vebt__insert_Osimps_I5_J,axiom,
% 8.64/4.83 ! [Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.64/4.83 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_VEBT_VEBT
% 8.64/4.83 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 & ~ ( ( X = Mi )
% 8.64/4.83 | ( X = Ma ) ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va3 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4700_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 8.64/4.83 ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList2: list_VEBT_VEBT,S2: vEBT_VEBT,X: nat] :
% 8.64/4.83 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList2 @ S2 ) @ X )
% 8.64/4.83 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4701_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 8.64/4.83 ! [V2: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X: nat] :
% 8.64/4.83 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList2 @ Vd2 ) @ X )
% 8.64/4.83 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4702_vebt__insert_Oelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.64/4.83 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 8.64/4.83 & ( ( Xa2 != one_one_nat )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) ) )
% 8.64/4.83 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) )
% 8.64/4.83 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) )
% 8.64/4.83 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( if_VEBT_VEBT
% 8.64/4.83 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 & ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 ) ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4703_vebt__member_Osimps_I5_J,axiom,
% 8.64/4.83 ! [Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 8.64/4.83 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( ( X != Mi )
% 8.64/4.83 => ( ( X != Ma )
% 8.64/4.83 => ( ~ ( ord_less_nat @ X @ Mi )
% 8.64/4.83 & ( ~ ( ord_less_nat @ X @ Mi )
% 8.64/4.83 => ( ~ ( ord_less_nat @ Ma @ X )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Ma @ X )
% 8.64/4.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4704_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 8.64/4.83 ! [Mi: nat,Ma: nat,V2: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 8.64/4.83 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V2 ) @ TreeList2 @ Vc ) @ X )
% 8.64/4.83 = ( ( X = Mi )
% 8.64/4.83 | ( X = Ma )
% 8.64/4.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4705_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.83 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => A3 )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => B3 )
% 8.64/4.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 8.64/4.83 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 8.64/4.83 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [S: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 8.64/4.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4706_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.83 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => A3 )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => B3 )
% 8.64/4.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 8.64/4.83 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [S: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 8.64/4.83 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4707_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.83 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => A3 )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => B3 )
% 8.64/4.83 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 8.64/4.83 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 8.64/4.83 => Y )
% 8.64/4.83 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [S: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4708_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.83 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat] :
% 8.64/4.83 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 8.64/4.83 => ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 ) ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Vc2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 8.64/4.83 => ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 )
% 8.64/4.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 8.64/4.83 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Vd: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 8.64/4.83 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4709_vebt__member_Oelims_I2_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.83 ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => A3 )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => B3 )
% 8.64/4.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Summary2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ~ ( ( Xa2 != Mi2 )
% 8.64/4.83 => ( ( Xa2 != Ma2 )
% 8.64/4.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4710_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.83 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.64/4.83 => ( ! [Uu2: $o,Uv2: $o] :
% 8.64/4.83 ( X
% 8.64/4.83 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.83 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat] :
% 8.64/4.83 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 8.64/4.83 => ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 ) ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Vc2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 8.64/4.83 => ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 )
% 8.64/4.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 8.64/4.83 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Vd: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 8.64/4.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4711_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.83 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.83 => Y )
% 8.64/4.83 => ( ( ? [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 8.64/4.83 => Y )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat] :
% 8.64/4.83 ( ? [Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 ) ) ) ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Vc2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 )
% 8.64/4.83 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) )
% 8.64/4.83 => ~ ! [V: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Vd: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4712_vebt__member_Oelims_I3_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.83 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => A3 )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => B3 )
% 8.64/4.83 & ( Xa2 = one_one_nat ) ) ) ) )
% 8.64/4.83 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.64/4.83 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 8.64/4.83 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Summary2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( ( Xa2 != Mi2 )
% 8.64/4.83 => ( ( Xa2 != Ma2 )
% 8.64/4.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4713_vebt__member_Oelims_I1_J,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.83 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => A3 )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => B3 )
% 8.64/4.83 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 8.64/4.83 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.64/4.83 => Y )
% 8.64/4.83 => ( ( ? [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 8.64/4.83 => Y )
% 8.64/4.83 => ( ( ? [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.64/4.83 => Y )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT] :
% 8.64/4.83 ( ? [Summary2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( ~ ( ( Xa2 != Mi2 )
% 8.64/4.83 => ( ( Xa2 != Ma2 )
% 8.64/4.83 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4714_vebt__pred_Osimps_I7_J,axiom,
% 8.64/4.83 ! [Ma: nat,X: nat,Mi: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ( ord_less_nat @ Ma @ X )
% 8.64/4.83 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( some_nat @ Ma ) ) )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Ma @ X )
% 8.64/4.83 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4715_vebt__succ_Osimps_I6_J,axiom,
% 8.64/4.83 ! [X: nat,Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ( ord_less_nat @ X @ Mi )
% 8.64/4.83 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( some_nat @ Mi ) ) )
% 8.64/4.83 & ( ~ ( ord_less_nat @ X @ Mi )
% 8.64/4.83 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ none_nat
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4716_vebt__delete_Osimps_I7_J,axiom,
% 8.64/4.83 ! [X: nat,Mi: nat,Ma: nat,Va3: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.83 ( ( ( ( ord_less_nat @ X @ Mi )
% 8.64/4.83 | ( ord_less_nat @ Ma @ X ) )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) )
% 8.64/4.83 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 8.64/4.83 | ( ord_less_nat @ Ma @ X ) )
% 8.64/4.83 => ( ( ( ( X = Mi )
% 8.64/4.83 & ( X = Ma ) )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) )
% 8.64/4.83 & ( ~ ( ( X = Mi )
% 8.64/4.83 & ( X = Ma ) )
% 8.64/4.83 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) @ X )
% 8.64/4.83 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 8.64/4.83 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( X = Mi )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 = Ma ) )
% 8.64/4.83 & ( ( X != Mi )
% 8.64/4.83 => ( X = Ma ) ) )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ ( suc @ ( suc @ Va3 ) )
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( X = Mi )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 8.64/4.83 = Ma ) )
% 8.64/4.83 & ( ( X != Mi )
% 8.64/4.83 => ( X = Ma ) ) )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma ) ) )
% 8.64/4.83 @ ( suc @ ( suc @ Va3 ) )
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ Summary ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va3 ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4717_vebt__delete_Oelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.64/4.83 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Leaf @ $false @ B3 ) ) ) )
% 8.64/4.83 => ( ! [A3: $o] :
% 8.64/4.83 ( ? [B3: $o] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ( Xa2
% 8.64/4.83 = ( suc @ zero_zero_nat ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Leaf @ A3 @ $false ) ) ) )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ? [N3: nat] :
% 8.64/4.83 ( Xa2
% 8.64/4.83 = ( suc @ ( suc @ N3 ) ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Leaf @ A3 @ B3 ) ) ) )
% 8.64/4.83 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 8.64/4.83 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.64/4.83 => ( ( ( ( Xa2 = Mi2 )
% 8.64/4.83 & ( Xa2 = Ma2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 8.64/4.83 & ( ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 & ( Xa2 = Ma2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( Xa2 = Mi2 )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.64/4.83 = Ma2 ) )
% 8.64/4.83 & ( ( Xa2 != Mi2 )
% 8.64/4.83 => ( Xa2 = Ma2 ) ) )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma2 ) ) )
% 8.64/4.83 @ ( suc @ ( suc @ Va ) )
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( Xa2 = Mi2 )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.64/4.83 = Ma2 ) )
% 8.64/4.83 & ( ( Xa2 != Mi2 )
% 8.64/4.83 => ( Xa2 = Ma2 ) ) )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma2 ) ) )
% 8.64/4.83 @ ( suc @ ( suc @ Va ) )
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ Summary2 ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4718_vebt__succ_Oelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.64/4.83 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ! [Uu2: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 8.64/4.83 => ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ~ ( ( B3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ one_one_nat ) ) )
% 8.64/4.83 & ( ~ B3
% 8.64/4.83 => ( Y = none_nat ) ) ) ) )
% 8.64/4.83 => ( ( ? [Uv2: $o,Uw: $o] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Leaf @ Uv2 @ Uw ) )
% 8.64/4.83 => ( ? [N3: nat] :
% 8.64/4.83 ( Xa2
% 8.64/4.83 = ( suc @ N3 ) )
% 8.64/4.83 => ( Y != none_nat ) ) )
% 8.64/4.83 => ( ( ? [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 8.64/4.83 => ( Y != none_nat ) )
% 8.64/4.83 => ( ( ? [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 8.64/4.83 => ( Y != none_nat ) )
% 8.64/4.83 => ( ( ? [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 8.64/4.83 => ( Y != none_nat ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ Mi2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ none_nat
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4719_vebt__pred_Oelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.64/4.83 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.83 => ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ( Y != none_nat ) ) )
% 8.64/4.83 => ( ! [A3: $o] :
% 8.64/4.83 ( ? [Uw: $o] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ Uw ) )
% 8.64/4.83 => ( ( Xa2
% 8.64/4.83 = ( suc @ zero_zero_nat ) )
% 8.64/4.83 => ~ ( ( A3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ zero_zero_nat ) ) )
% 8.64/4.83 & ( ~ A3
% 8.64/4.83 => ( Y = none_nat ) ) ) ) )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ? [Va: nat] :
% 8.64/4.83 ( Xa2
% 8.64/4.83 = ( suc @ ( suc @ Va ) ) )
% 8.64/4.83 => ~ ( ( B3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ one_one_nat ) ) )
% 8.64/4.83 & ( ~ B3
% 8.64/4.83 => ( ( A3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ zero_zero_nat ) ) )
% 8.64/4.83 & ( ~ A3
% 8.64/4.83 => ( Y = none_nat ) ) ) ) ) ) )
% 8.64/4.83 => ( ( ? [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) )
% 8.64/4.83 => ( Y != none_nat ) )
% 8.64/4.83 => ( ( ? [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 8.64/4.83 => ( Y != none_nat ) )
% 8.64/4.83 => ( ( ? [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 8.64/4.83 ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 8.64/4.83 => ( Y != none_nat ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ Ma2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4720_finite__nth__roots,axiom,
% 8.64/4.83 ! [N: nat,C2: complex] :
% 8.64/4.83 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.83 => ( finite3207457112153483333omplex
% 8.64/4.83 @ ( collect_complex
% 8.64/4.83 @ ^ [Z4: complex] :
% 8.64/4.83 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.83 = C2 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4721_card__roots__unity,axiom,
% 8.64/4.83 ! [N: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.83 => ( ord_less_eq_nat
% 8.64/4.83 @ ( finite_card_real
% 8.64/4.83 @ ( collect_real
% 8.64/4.83 @ ^ [Z4: real] :
% 8.64/4.83 ( ( power_power_real @ Z4 @ N )
% 8.64/4.83 = one_one_real ) ) )
% 8.64/4.83 @ N ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4722_card__roots__unity,axiom,
% 8.64/4.83 ! [N: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.83 => ( ord_less_eq_nat
% 8.64/4.83 @ ( finite_card_complex
% 8.64/4.83 @ ( collect_complex
% 8.64/4.83 @ ^ [Z4: complex] :
% 8.64/4.83 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.83 = one_one_complex ) ) )
% 8.64/4.83 @ N ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4723_finite__roots__unity,axiom,
% 8.64/4.83 ! [N: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.83 => ( finite_finite_real
% 8.64/4.83 @ ( collect_real
% 8.64/4.83 @ ^ [Z4: real] :
% 8.64/4.83 ( ( power_power_real @ Z4 @ N )
% 8.64/4.83 = one_one_real ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4724_finite__roots__unity,axiom,
% 8.64/4.83 ! [N: nat] :
% 8.64/4.83 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.83 => ( finite3207457112153483333omplex
% 8.64/4.83 @ ( collect_complex
% 8.64/4.83 @ ^ [Z4: complex] :
% 8.64/4.83 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.83 = one_one_complex ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4725_vebt__succ_Opelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.64/4.83 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.83 => ( ! [Uu2: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ Uu2 @ B3 ) )
% 8.64/4.83 => ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ( ( ( B3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ one_one_nat ) ) )
% 8.64/4.83 & ( ~ B3
% 8.64/4.83 => ( Y = none_nat ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 8.64/4.83 => ( ! [Uv2: $o,Uw: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ Uv2 @ Uw ) )
% 8.64/4.83 => ! [N3: nat] :
% 8.64/4.83 ( ( Xa2
% 8.64/4.83 = ( suc @ N3 ) )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw ) @ ( suc @ N3 ) ) ) ) ) )
% 8.64/4.83 => ( ! [Ux: nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [V: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc2 @ Vd ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Xa2 ) ) ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ Mi2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ none_nat
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4726_vebt__pred_Opelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 8.64/4.83 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.83 => ( ! [Uu2: $o,Uv2: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.83 => ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 8.64/4.83 => ( ! [A3: $o,Uw: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ Uw ) )
% 8.64/4.83 => ( ( Xa2
% 8.64/4.83 = ( suc @ zero_zero_nat ) )
% 8.64/4.83 => ( ( ( A3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ zero_zero_nat ) ) )
% 8.64/4.83 & ( ~ A3
% 8.64/4.83 => ( Y = none_nat ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ Uw ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ! [Va: nat] :
% 8.64/4.83 ( ( Xa2
% 8.64/4.83 = ( suc @ ( suc @ Va ) ) )
% 8.64/4.83 => ( ( ( B3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ one_one_nat ) ) )
% 8.64/4.83 & ( ~ B3
% 8.64/4.83 => ( ( A3
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ zero_zero_nat ) ) )
% 8.64/4.83 & ( ~ A3
% 8.64/4.83 => ( Y = none_nat ) ) ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ Va ) ) ) ) ) ) )
% 8.64/4.83 => ( ! [Uy: nat,Uz2: list_VEBT_VEBT,Va2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz2 @ Va2 ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) )
% 8.64/4.83 => ( ( Y = none_nat )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Xa2 ) ) ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( some_nat @ Ma2 ) ) )
% 8.64/4.83 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 != none_nat )
% 8.64/4.83 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( if_option_nat
% 8.64/4.83 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 8.64/4.83 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ none_nat ) ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4727_vebt__delete_Opelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.64/4.83 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Leaf @ $false @ B3 ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ zero_zero_nat ) ) ) ) )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ( Xa2
% 8.64/4.83 = ( suc @ zero_zero_nat ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ $false ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ! [N3: nat] :
% 8.64/4.83 ( ( Xa2
% 8.64/4.83 = ( suc @ ( suc @ N3 ) ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 8.64/4.83 => ( ! [Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst @ Smry ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [Mi2: nat,Ma2: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ Xa2 ) ) ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 8.64/4.83 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.83 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 8.64/4.83 => ( ( ( ( Xa2 = Mi2 )
% 8.64/4.83 & ( Xa2 = Ma2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 8.64/4.83 & ( ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 & ( Xa2 = Ma2 ) )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( Xa2 = Mi2 )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.64/4.83 = Ma2 ) )
% 8.64/4.83 & ( ( Xa2 != Mi2 )
% 8.64/4.83 => ( Xa2 = Ma2 ) ) )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 = none_nat )
% 8.64/4.83 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma2 ) ) )
% 8.64/4.83 @ ( suc @ ( suc @ Va ) )
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ ( vEBT_Node
% 8.64/4.83 @ ( some_P7363390416028606310at_nat
% 8.64/4.83 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 8.64/4.83 @ ( if_nat
% 8.64/4.83 @ ( ( ( Xa2 = Mi2 )
% 8.64/4.83 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 8.64/4.83 = Ma2 ) )
% 8.64/4.83 & ( ( Xa2 != Mi2 )
% 8.64/4.83 => ( Xa2 = Ma2 ) ) )
% 8.64/4.83 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 8.64/4.83 @ Ma2 ) ) )
% 8.64/4.83 @ ( suc @ ( suc @ Va ) )
% 8.64/4.83 @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.83 @ Summary2 ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) ) ) ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4728_vebt__insert_Opelims,axiom,
% 8.64/4.83 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.64/4.83 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 8.64/4.83 = Y )
% 8.64/4.83 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.83 => ( ! [A3: $o,B3: $o] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.83 => ( ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Leaf @ $true @ B3 ) ) )
% 8.64/4.83 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.83 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ $true ) ) )
% 8.64/4.83 & ( ( Xa2 != one_one_nat )
% 8.64/4.83 => ( Y
% 8.64/4.83 = ( vEBT_Leaf @ A3 @ B3 ) ) ) ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ Xa2 ) ) ) )
% 8.64/4.83 => ( ! [V: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 8.64/4.83 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.83 ( ( X
% 8.64/4.83 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.83 => ( ( Y
% 8.64/4.83 = ( if_VEBT_VEBT
% 8.64/4.83 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.83 & ~ ( ( Xa2 = Mi2 )
% 8.64/4.83 | ( Xa2 = Ma2 ) ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 8.64/4.83 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) ) )
% 8.64/4.83 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4729_low__def,axiom,
% 8.64/4.83 ( vEBT_VEBT_low
% 8.64/4.83 = ( ^ [X4: nat,N4: nat] : ( modulo_modulo_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4730_mod__0,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4731_mod__0,axiom,
% 8.64/4.83 ! [A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4732_mod__0,axiom,
% 8.64/4.83 ! [A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4733_mod__by__0,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 8.64/4.83 = A ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4734_mod__by__0,axiom,
% 8.64/4.83 ! [A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 8.64/4.83 = A ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4735_mod__by__0,axiom,
% 8.64/4.83 ! [A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ A @ zero_z2226904508553997617atural )
% 8.64/4.83 = A ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4736_mod__self,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ A @ A )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4737_mod__self,axiom,
% 8.64/4.83 ! [A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ A @ A )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4738_mod__self,axiom,
% 8.64/4.83 ! [A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ A @ A )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4739_bits__mod__0,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4740_bits__mod__0,axiom,
% 8.64/4.83 ! [A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4741_bits__mod__0,axiom,
% 8.64/4.83 ! [A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ zero_z2226904508553997617atural @ A )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4742_mod__mult__self2__is__0,axiom,
% 8.64/4.83 ! [A: nat,B: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4743_mod__mult__self2__is__0,axiom,
% 8.64/4.83 ! [A: int,B: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4744_mod__mult__self2__is__0,axiom,
% 8.64/4.83 ! [A: code_natural,B: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4745_mod__mult__self1__is__0,axiom,
% 8.64/4.83 ! [B: nat,A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4746_mod__mult__self1__is__0,axiom,
% 8.64/4.83 ! [B: int,A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4747_mod__mult__self1__is__0,axiom,
% 8.64/4.83 ! [B: code_natural,A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4748_mod__by__1,axiom,
% 8.64/4.83 ! [A: code_integer] :
% 8.64/4.83 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 8.64/4.83 = zero_z3403309356797280102nteger ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4749_mod__by__1,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4750_mod__by__1,axiom,
% 8.64/4.83 ! [A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ A @ one_one_int )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4751_mod__by__1,axiom,
% 8.64/4.83 ! [A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4752_bits__mod__by__1,axiom,
% 8.64/4.83 ! [A: code_integer] :
% 8.64/4.83 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 8.64/4.83 = zero_z3403309356797280102nteger ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4753_bits__mod__by__1,axiom,
% 8.64/4.83 ! [A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4754_bits__mod__by__1,axiom,
% 8.64/4.83 ! [A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ A @ one_one_int )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4755_bits__mod__by__1,axiom,
% 8.64/4.83 ! [A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ A @ one_one_Code_natural )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4756_mod__div__trivial,axiom,
% 8.64/4.83 ! [A: nat,B: nat] :
% 8.64/4.83 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4757_mod__div__trivial,axiom,
% 8.64/4.83 ! [A: int,B: int] :
% 8.64/4.83 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4758_mod__div__trivial,axiom,
% 8.64/4.83 ! [A: code_natural,B: code_natural] :
% 8.64/4.83 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4759_bits__mod__div__trivial,axiom,
% 8.64/4.83 ! [A: nat,B: nat] :
% 8.64/4.83 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4760_bits__mod__div__trivial,axiom,
% 8.64/4.83 ! [A: int,B: int] :
% 8.64/4.83 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 8.64/4.83 = zero_zero_int ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4761_bits__mod__div__trivial,axiom,
% 8.64/4.83 ! [A: code_natural,B: code_natural] :
% 8.64/4.83 ( ( divide5121882707175180666atural @ ( modulo8411746178871703098atural @ A @ B ) @ B )
% 8.64/4.83 = zero_z2226904508553997617atural ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4762_mod__mult__self1,axiom,
% 8.64/4.83 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C2 @ B ) ) @ B )
% 8.64/4.83 = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4763_mod__mult__self1,axiom,
% 8.64/4.83 ! [A: int,C2: int,B: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C2 @ B ) ) @ B )
% 8.64/4.83 = ( modulo_modulo_int @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4764_mod__mult__self1,axiom,
% 8.64/4.83 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C2 @ B ) ) @ B )
% 8.64/4.83 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4765_mod__mult__self2,axiom,
% 8.64/4.83 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C2 ) ) @ B )
% 8.64/4.83 = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4766_mod__mult__self2,axiom,
% 8.64/4.83 ! [A: int,B: int,C2: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C2 ) ) @ B )
% 8.64/4.83 = ( modulo_modulo_int @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4767_mod__mult__self2,axiom,
% 8.64/4.83 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C2 ) ) @ B )
% 8.64/4.83 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4768_mod__mult__self3,axiom,
% 8.64/4.83 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C2 @ B ) @ A ) @ B )
% 8.64/4.83 = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4769_mod__mult__self3,axiom,
% 8.64/4.83 ! [C2: int,B: int,A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C2 @ B ) @ A ) @ B )
% 8.64/4.83 = ( modulo_modulo_int @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4770_mod__mult__self3,axiom,
% 8.64/4.83 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C2 @ B ) @ A ) @ B )
% 8.64/4.83 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4771_mod__mult__self4,axiom,
% 8.64/4.83 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C2 ) @ A ) @ B )
% 8.64/4.83 = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4772_mod__mult__self4,axiom,
% 8.64/4.83 ! [B: int,C2: int,A: int] :
% 8.64/4.83 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C2 ) @ A ) @ B )
% 8.64/4.83 = ( modulo_modulo_int @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4773_mod__mult__self4,axiom,
% 8.64/4.83 ! [B: code_natural,C2: code_natural,A: code_natural] :
% 8.64/4.83 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C2 ) @ A ) @ B )
% 8.64/4.83 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4774_mod__by__Suc__0,axiom,
% 8.64/4.83 ! [M2: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 8.64/4.83 = zero_zero_nat ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4775_Suc__mod__mult__self4,axiom,
% 8.64/4.83 ! [N: nat,K2: nat,M2: nat] :
% 8.64/4.83 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K2 ) @ M2 ) ) @ N )
% 8.64/4.83 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 8.64/4.83
% 8.64/4.83 thf(fact_4776_Suc__mod__mult__self3,axiom,
% 8.64/4.83 ! [K2: nat,N: nat,M2: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K2 @ N ) @ M2 ) ) @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4777_Suc__mod__mult__self2,axiom,
% 8.64/4.84 ! [M2: nat,N: nat,K2: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ N @ K2 ) ) ) @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4778_Suc__mod__mult__self1,axiom,
% 8.64/4.84 ! [M2: nat,K2: nat,N: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M2 @ ( times_times_nat @ K2 @ N ) ) ) @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4779_mod2__Suc__Suc,axiom,
% 8.64/4.84 ! [M2: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 = ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4780_Suc__times__numeral__mod__eq,axiom,
% 8.64/4.84 ! [K2: num,N: nat] :
% 8.64/4.84 ( ( ( numeral_numeral_nat @ K2 )
% 8.64/4.84 != one_one_nat )
% 8.64/4.84 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K2 ) @ N ) ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.84 = one_one_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4781_not__mod__2__eq__0__eq__1,axiom,
% 8.64/4.84 ! [A: code_integer] :
% 8.64/4.84 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.84 != zero_z3403309356797280102nteger )
% 8.64/4.84 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.84 = one_one_Code_integer ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4782_not__mod__2__eq__0__eq__1,axiom,
% 8.64/4.84 ! [A: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 != zero_zero_nat )
% 8.64/4.84 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 = one_one_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4783_not__mod__2__eq__0__eq__1,axiom,
% 8.64/4.84 ! [A: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.84 != zero_zero_int )
% 8.64/4.84 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.84 = one_one_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4784_not__mod__2__eq__0__eq__1,axiom,
% 8.64/4.84 ! [A: code_natural] :
% 8.64/4.84 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.84 != zero_z2226904508553997617atural )
% 8.64/4.84 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.84 = one_one_Code_natural ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4785_not__mod__2__eq__1__eq__0,axiom,
% 8.64/4.84 ! [A: code_integer] :
% 8.64/4.84 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.84 != one_one_Code_integer )
% 8.64/4.84 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.84 = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4786_not__mod__2__eq__1__eq__0,axiom,
% 8.64/4.84 ! [A: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 != one_one_nat )
% 8.64/4.84 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4787_not__mod__2__eq__1__eq__0,axiom,
% 8.64/4.84 ! [A: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.84 != one_one_int )
% 8.64/4.84 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.84 = zero_zero_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4788_not__mod__2__eq__1__eq__0,axiom,
% 8.64/4.84 ! [A: code_natural] :
% 8.64/4.84 ( ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.84 != one_one_Code_natural )
% 8.64/4.84 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.84 = zero_z2226904508553997617atural ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4789_not__mod2__eq__Suc__0__eq__0,axiom,
% 8.64/4.84 ! [N: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 != ( suc @ zero_zero_nat ) )
% 8.64/4.84 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4790_add__self__mod__2,axiom,
% 8.64/4.84 ! [M2: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M2 @ M2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 = zero_zero_nat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4791_mod2__gr__0,axiom,
% 8.64/4.84 ! [M2: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.84 = ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 = one_one_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4792_mod__mult__eq,axiom,
% 8.64/4.84 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C2 ) @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4793_mod__mult__eq,axiom,
% 8.64/4.84 ! [A: int,C2: int,B: int] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C2 ) @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4794_mod__mult__eq,axiom,
% 8.64/4.84 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 8.64/4.84 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 8.64/4.84 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4795_mod__mult__cong,axiom,
% 8.64/4.84 ! [A: nat,C2: nat,A2: nat,B: nat,B2: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ A @ C2 )
% 8.64/4.84 = ( modulo_modulo_nat @ A2 @ C2 ) )
% 8.64/4.84 => ( ( ( modulo_modulo_nat @ B @ C2 )
% 8.64/4.84 = ( modulo_modulo_nat @ B2 @ C2 ) )
% 8.64/4.84 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4796_mod__mult__cong,axiom,
% 8.64/4.84 ! [A: int,C2: int,A2: int,B: int,B2: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ A @ C2 )
% 8.64/4.84 = ( modulo_modulo_int @ A2 @ C2 ) )
% 8.64/4.84 => ( ( ( modulo_modulo_int @ B @ C2 )
% 8.64/4.84 = ( modulo_modulo_int @ B2 @ C2 ) )
% 8.64/4.84 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4797_mod__mult__cong,axiom,
% 8.64/4.84 ! [A: code_natural,C2: code_natural,A2: code_natural,B: code_natural,B2: code_natural] :
% 8.64/4.84 ( ( ( modulo8411746178871703098atural @ A @ C2 )
% 8.64/4.84 = ( modulo8411746178871703098atural @ A2 @ C2 ) )
% 8.64/4.84 => ( ( ( modulo8411746178871703098atural @ B @ C2 )
% 8.64/4.84 = ( modulo8411746178871703098atural @ B2 @ C2 ) )
% 8.64/4.84 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 )
% 8.64/4.84 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A2 @ B2 ) @ C2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4798_mod__mult__mult2,axiom,
% 8.64/4.84 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.84 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4799_mod__mult__mult2,axiom,
% 8.64/4.84 ! [A: int,C2: int,B: int] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.64/4.84 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4800_mod__mult__mult2,axiom,
% 8.64/4.84 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 8.64/4.84 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ C2 ) @ ( times_2397367101498566445atural @ B @ C2 ) )
% 8.64/4.84 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4801_mult__mod__right,axiom,
% 8.64/4.84 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.84 ( ( times_times_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.84 = ( modulo_modulo_nat @ ( times_times_nat @ C2 @ A ) @ ( times_times_nat @ C2 @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4802_mult__mod__right,axiom,
% 8.64/4.84 ! [C2: int,A: int,B: int] :
% 8.64/4.84 ( ( times_times_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.84 = ( modulo_modulo_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4803_mult__mod__right,axiom,
% 8.64/4.84 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( times_2397367101498566445atural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.64/4.84 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ C2 @ A ) @ ( times_2397367101498566445atural @ C2 @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4804_mod__mult__left__eq,axiom,
% 8.64/4.84 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C2 ) @ B ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4805_mod__mult__left__eq,axiom,
% 8.64/4.84 ! [A: int,C2: int,B: int] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C2 ) @ B ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4806_mod__mult__left__eq,axiom,
% 8.64/4.84 ! [A: code_natural,C2: code_natural,B: code_natural] :
% 8.64/4.84 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C2 ) @ B ) @ C2 )
% 8.64/4.84 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4807_mod__mult__right__eq,axiom,
% 8.64/4.84 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4808_mod__mult__right__eq,axiom,
% 8.64/4.84 ! [A: int,B: int,C2: int] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 )
% 8.64/4.84 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4809_mod__mult__right__eq,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 8.64/4.84 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 )
% 8.64/4.84 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4810_mod__Suc__Suc__eq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ ( suc @ ( suc @ M2 ) ) @ N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4811_mod__Suc__eq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ ( suc @ M2 ) @ N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4812_mod__less__eq__dividend,axiom,
% 8.64/4.84 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ M2 ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4813_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.64/4.84 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4814_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.84 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4815_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.64/4.84 ! [B: nat,A: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.64/4.84 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4816_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 8.64/4.84 ! [B: int,A: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.84 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4817_mod__eq__self__iff__div__eq__0,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ A @ B )
% 8.64/4.84 = A )
% 8.64/4.84 = ( ( divide_divide_nat @ A @ B )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4818_mod__eq__self__iff__div__eq__0,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.84 = A )
% 8.64/4.84 = ( ( divide_divide_int @ A @ B )
% 8.64/4.84 = zero_zero_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4819_mod__eq__self__iff__div__eq__0,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( ( modulo8411746178871703098atural @ A @ B )
% 8.64/4.84 = A )
% 8.64/4.84 = ( ( divide5121882707175180666atural @ A @ B )
% 8.64/4.84 = zero_z2226904508553997617atural ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4820_cong__exp__iff__simps_I9_J,axiom,
% 8.64/4.84 ! [M2: num,Q2: num,N: num] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.84 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.64/4.84 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4821_cong__exp__iff__simps_I9_J,axiom,
% 8.64/4.84 ! [M2: num,Q2: num,N: num] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.84 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 8.64/4.84 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4822_cong__exp__iff__simps_I4_J,axiom,
% 8.64/4.84 ! [M2: num,N: num] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ one ) )
% 8.64/4.84 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4823_cong__exp__iff__simps_I4_J,axiom,
% 8.64/4.84 ! [M2: num,N: num] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ one ) )
% 8.64/4.84 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4824_mod__eqE,axiom,
% 8.64/4.84 ! [A: int,C2: int,B: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ A @ C2 )
% 8.64/4.84 = ( modulo_modulo_int @ B @ C2 ) )
% 8.64/4.84 => ~ ! [D5: int] :
% 8.64/4.84 ( B
% 8.64/4.84 != ( plus_plus_int @ A @ ( times_times_int @ C2 @ D5 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4825_mod__Suc,axiom,
% 8.64/4.84 ! [M2: nat,N: nat] :
% 8.64/4.84 ( ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 8.64/4.84 = N )
% 8.64/4.84 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 8.64/4.84 = zero_zero_nat ) )
% 8.64/4.84 & ( ( ( suc @ ( modulo_modulo_nat @ M2 @ N ) )
% 8.64/4.84 != N )
% 8.64/4.84 => ( ( modulo_modulo_nat @ ( suc @ M2 ) @ N )
% 8.64/4.84 = ( suc @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4826_mod__induct,axiom,
% 8.64/4.84 ! [P2: nat > $o,N: nat,P: nat,M2: nat] :
% 8.64/4.84 ( ( P2 @ N )
% 8.64/4.84 => ( ( ord_less_nat @ N @ P )
% 8.64/4.84 => ( ( ord_less_nat @ M2 @ P )
% 8.64/4.84 => ( ! [N3: nat] :
% 8.64/4.84 ( ( ord_less_nat @ N3 @ P )
% 8.64/4.84 => ( ( P2 @ N3 )
% 8.64/4.84 => ( P2 @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P ) ) ) )
% 8.64/4.84 => ( P2 @ M2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4827_mod__less__divisor,axiom,
% 8.64/4.84 ! [N: nat,M2: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ord_less_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4828_gcd__nat__induct,axiom,
% 8.64/4.84 ! [P2: nat > nat > $o,M2: nat,N: nat] :
% 8.64/4.84 ( ! [M: nat] : ( P2 @ M @ zero_zero_nat )
% 8.64/4.84 => ( ! [M: nat,N3: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.64/4.84 => ( ( P2 @ N3 @ ( modulo_modulo_nat @ M @ N3 ) )
% 8.64/4.84 => ( P2 @ M @ N3 ) ) )
% 8.64/4.84 => ( P2 @ M2 @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4829_mod__Suc__le__divisor,axiom,
% 8.64/4.84 ! [M2: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ ( suc @ N ) ) @ N ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4830_mod__eq__0D,axiom,
% 8.64/4.84 ! [M2: nat,D: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ M2 @ D )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 => ? [Q3: nat] :
% 8.64/4.84 ( M2
% 8.64/4.84 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4831_mod__geq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat] :
% 8.64/4.84 ( ~ ( ord_less_nat @ M2 @ N )
% 8.64/4.84 => ( ( modulo_modulo_nat @ M2 @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4832_le__mod__geq,axiom,
% 8.64/4.84 ! [N: nat,M2: nat] :
% 8.64/4.84 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.84 => ( ( modulo_modulo_nat @ M2 @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ ( minus_minus_nat @ M2 @ N ) @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4833_nat__mod__eq__iff,axiom,
% 8.64/4.84 ! [X: nat,N: nat,Y: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ X @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ Y @ N ) )
% 8.64/4.84 = ( ? [Q1: nat,Q22: nat] :
% 8.64/4.84 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 8.64/4.84 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4834_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.64/4.84 => ( ( ord_less_nat @ A @ B )
% 8.64/4.84 => ( ( modulo_modulo_nat @ A @ B )
% 8.64/4.84 = A ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4835_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.84 => ( ( ord_less_int @ A @ B )
% 8.64/4.84 => ( ( modulo_modulo_int @ A @ B )
% 8.64/4.84 = A ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4836_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.64/4.84 ! [B: nat,A: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.64/4.84 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4837_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 8.64/4.84 ! [B: int,A: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.84 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4838_cong__exp__iff__simps_I2_J,axiom,
% 8.64/4.84 ! [N: num,Q2: num] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4839_cong__exp__iff__simps_I2_J,axiom,
% 8.64/4.84 ! [N: num,Q2: num] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 = zero_zero_int )
% 8.64/4.84 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 8.64/4.84 = zero_zero_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4840_cong__exp__iff__simps_I1_J,axiom,
% 8.64/4.84 ! [N: num] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 8.64/4.84 = zero_zero_nat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4841_cong__exp__iff__simps_I1_J,axiom,
% 8.64/4.84 ! [N: num] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 8.64/4.84 = zero_zero_int ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4842_cong__exp__iff__simps_I6_J,axiom,
% 8.64/4.84 ! [Q2: num,N: num] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4843_cong__exp__iff__simps_I6_J,axiom,
% 8.64/4.84 ! [Q2: num,N: num] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4844_cong__exp__iff__simps_I8_J,axiom,
% 8.64/4.84 ! [M2: num,Q2: num] :
% 8.64/4.84 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4845_cong__exp__iff__simps_I8_J,axiom,
% 8.64/4.84 ! [M2: num,Q2: num] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.84 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4846_div__mult1__eq,axiom,
% 8.64/4.84 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.84 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.64/4.84 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C2 ) ) @ C2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4847_div__mult1__eq,axiom,
% 8.64/4.84 ! [A: int,B: int,C2: int] :
% 8.64/4.84 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C2 ) ) @ C2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4848_div__mult1__eq,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 8.64/4.84 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C2 )
% 8.64/4.84 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C2 ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C2 ) ) @ C2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4849_cancel__div__mod__rules_I2_J,axiom,
% 8.64/4.84 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.84 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 8.64/4.84 = ( plus_plus_nat @ A @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4850_cancel__div__mod__rules_I2_J,axiom,
% 8.64/4.84 ! [B: int,A: int,C2: int] :
% 8.64/4.84 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 8.64/4.84 = ( plus_plus_int @ A @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4851_cancel__div__mod__rules_I2_J,axiom,
% 8.64/4.84 ! [B: code_natural,A: code_natural,C2: code_natural] :
% 8.64/4.84 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 8.64/4.84 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4852_cancel__div__mod__rules_I1_J,axiom,
% 8.64/4.84 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.84 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C2 )
% 8.64/4.84 = ( plus_plus_nat @ A @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4853_cancel__div__mod__rules_I1_J,axiom,
% 8.64/4.84 ! [A: int,B: int,C2: int] :
% 8.64/4.84 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C2 )
% 8.64/4.84 = ( plus_plus_int @ A @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4854_cancel__div__mod__rules_I1_J,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural,C2: code_natural] :
% 8.64/4.84 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C2 )
% 8.64/4.84 = ( plus_p4538020629002901425atural @ A @ C2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4855_mod__div__decomp,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( A
% 8.64/4.84 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4856_mod__div__decomp,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( A
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4857_mod__div__decomp,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( A
% 8.64/4.84 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4858_div__mult__mod__eq,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4859_div__mult__mod__eq,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4860_div__mult__mod__eq,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4861_mod__div__mult__eq,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4862_mod__div__mult__eq,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4863_mod__div__mult__eq,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4864_mod__mult__div__eq,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4865_mod__mult__div__eq,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4866_mod__mult__div__eq,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4867_mult__div__mod__eq,axiom,
% 8.64/4.84 ! [B: nat,A: nat] :
% 8.64/4.84 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4868_mult__div__mod__eq,axiom,
% 8.64/4.84 ! [B: int,A: int] :
% 8.64/4.84 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4869_mult__div__mod__eq,axiom,
% 8.64/4.84 ! [B: code_natural,A: code_natural] :
% 8.64/4.84 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.64/4.84 = A ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4870_minus__div__mult__eq__mod,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 8.64/4.84 = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4871_minus__div__mult__eq__mod,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 8.64/4.84 = ( modulo_modulo_int @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4872_minus__div__mult__eq__mod,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 8.64/4.84 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4873_minus__mod__eq__div__mult,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.84 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4874_minus__mod__eq__div__mult,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.84 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4875_minus__mod__eq__div__mult,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.64/4.84 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4876_minus__mod__eq__mult__div,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.84 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4877_minus__mod__eq__mult__div,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.84 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4878_minus__mod__eq__mult__div,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.64/4.84 = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4879_minus__mult__div__eq__mod,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 8.64/4.84 = ( modulo_modulo_nat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4880_minus__mult__div__eq__mod,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 8.64/4.84 = ( modulo_modulo_int @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4881_minus__mult__div__eq__mod,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 8.64/4.84 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4882_mod__le__divisor,axiom,
% 8.64/4.84 ! [N: nat,M2: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M2 @ N ) @ N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4883_div__less__mono,axiom,
% 8.64/4.84 ! [A4: nat,B5: nat,N: nat] :
% 8.64/4.84 ( ( ord_less_nat @ A4 @ B5 )
% 8.64/4.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ( ( modulo_modulo_nat @ A4 @ N )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 => ( ( ( modulo_modulo_nat @ B5 @ N )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 => ( ord_less_nat @ ( divide_divide_nat @ A4 @ N ) @ ( divide_divide_nat @ B5 @ N ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4884_nat__mod__eq__lemma,axiom,
% 8.64/4.84 ! [X: nat,N: nat,Y: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ X @ N )
% 8.64/4.84 = ( modulo_modulo_nat @ Y @ N ) )
% 8.64/4.84 => ( ( ord_less_eq_nat @ Y @ X )
% 8.64/4.84 => ? [Q3: nat] :
% 8.64/4.84 ( X
% 8.64/4.84 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4885_mod__eq__nat2E,axiom,
% 8.64/4.84 ! [M2: nat,Q2: nat,N: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 8.64/4.84 = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.64/4.84 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.84 => ~ ! [S: nat] :
% 8.64/4.84 ( N
% 8.64/4.84 != ( plus_plus_nat @ M2 @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4886_mod__eq__nat1E,axiom,
% 8.64/4.84 ! [M2: nat,Q2: nat,N: nat] :
% 8.64/4.84 ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 8.64/4.84 = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.64/4.84 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.84 => ~ ! [S: nat] :
% 8.64/4.84 ( M2
% 8.64/4.84 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4887_mod__mult2__eq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ M2 @ ( times_times_nat @ N @ Q2 ) )
% 8.64/4.84 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M2 @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M2 @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4888_div__mod__decomp,axiom,
% 8.64/4.84 ! [A4: nat,N: nat] :
% 8.64/4.84 ( A4
% 8.64/4.84 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A4 @ N ) @ N ) @ ( modulo_modulo_nat @ A4 @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4889_modulo__nat__def,axiom,
% 8.64/4.84 ( modulo_modulo_nat
% 8.64/4.84 = ( ^ [M6: nat,N4: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N4 ) @ N4 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4890_mod__mult2__eq_H,axiom,
% 8.64/4.84 ! [A: code_natural,M2: nat,N: nat] :
% 8.64/4.84 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( semiri3763490453095760265atural @ N ) ) )
% 8.64/4.84 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M2 ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) @ ( semiri3763490453095760265atural @ N ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4891_mod__mult2__eq_H,axiom,
% 8.64/4.84 ! [A: int,M2: nat,N: nat] :
% 8.64/4.84 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M2 ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4892_mod__mult2__eq_H,axiom,
% 8.64/4.84 ! [A: nat,M2: nat,N: nat] :
% 8.64/4.84 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 8.64/4.84 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M2 ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4893_split__mod,axiom,
% 8.64/4.84 ! [P2: nat > $o,M2: nat,N: nat] :
% 8.64/4.84 ( ( P2 @ ( modulo_modulo_nat @ M2 @ N ) )
% 8.64/4.84 = ( ( ( N = zero_zero_nat )
% 8.64/4.84 => ( P2 @ M2 ) )
% 8.64/4.84 & ( ( N != zero_zero_nat )
% 8.64/4.84 => ! [I: nat,J: nat] :
% 8.64/4.84 ( ( ord_less_nat @ J @ N )
% 8.64/4.84 => ( ( M2
% 8.64/4.84 = ( plus_plus_nat @ ( times_times_nat @ N @ I ) @ J ) )
% 8.64/4.84 => ( P2 @ J ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4894_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.64/4.84 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.84 ( ( ord_less_eq_nat @ zero_zero_nat @ C2 )
% 8.64/4.84 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.84 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4895_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 8.64/4.84 ! [C2: int,A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.64/4.84 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4896_Suc__times__mod__eq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat] :
% 8.64/4.84 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M2 )
% 8.64/4.84 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M2 @ N ) ) @ M2 )
% 8.64/4.84 = one_one_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4897_nth__rotate1,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_VEBT_VEBT] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.84 => ( ( nth_VEBT_VEBT @ ( rotate1_VEBT_VEBT @ Xs2 ) @ N )
% 8.64/4.84 = ( nth_VEBT_VEBT @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4898_nth__rotate1,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_o] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.84 => ( ( nth_o @ ( rotate1_o @ Xs2 ) @ N )
% 8.64/4.84 = ( nth_o @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_o @ Xs2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4899_nth__rotate1,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_nat] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.84 => ( ( nth_nat @ ( rotate1_nat @ Xs2 ) @ N )
% 8.64/4.84 = ( nth_nat @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_nat @ Xs2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4900_nth__rotate1,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_int] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.84 => ( ( nth_int @ ( rotate1_int @ Xs2 ) @ N )
% 8.64/4.84 = ( nth_int @ Xs2 @ ( modulo_modulo_nat @ ( suc @ N ) @ ( size_size_list_int @ Xs2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4901_divmod__digit__0_I2_J,axiom,
% 8.64/4.84 ! [B: nat,A: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.64/4.84 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.64/4.84 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 8.64/4.84 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4902_divmod__digit__0_I2_J,axiom,
% 8.64/4.84 ! [B: int,A: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.84 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.64/4.84 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 8.64/4.84 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4903_bits__stable__imp__add__self,axiom,
% 8.64/4.84 ! [A: nat] :
% 8.64/4.84 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.84 = A )
% 8.64/4.84 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4904_bits__stable__imp__add__self,axiom,
% 8.64/4.84 ! [A: int] :
% 8.64/4.84 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.84 = A )
% 8.64/4.84 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 8.64/4.84 = zero_zero_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4905_bits__stable__imp__add__self,axiom,
% 8.64/4.84 ! [A: code_natural] :
% 8.64/4.84 ( ( ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.84 = A )
% 8.64/4.84 => ( ( plus_p4538020629002901425atural @ A @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 8.64/4.84 = zero_z2226904508553997617atural ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4906_verit__le__mono__div,axiom,
% 8.64/4.84 ! [A4: nat,B5: nat,N: nat] :
% 8.64/4.84 ( ( ord_less_nat @ A4 @ B5 )
% 8.64/4.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ord_less_eq_nat
% 8.64/4.84 @ ( plus_plus_nat @ ( divide_divide_nat @ A4 @ N )
% 8.64/4.84 @ ( if_nat
% 8.64/4.84 @ ( ( modulo_modulo_nat @ B5 @ N )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 @ one_one_nat
% 8.64/4.84 @ zero_zero_nat ) )
% 8.64/4.84 @ ( divide_divide_nat @ B5 @ N ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4907_divmod__digit__0_I1_J,axiom,
% 8.64/4.84 ! [B: nat,A: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.64/4.84 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.64/4.84 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 8.64/4.84 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4908_divmod__digit__0_I1_J,axiom,
% 8.64/4.84 ! [B: int,A: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.84 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.64/4.84 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 8.64/4.84 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4909_mult__exp__mod__exp__eq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat,A: nat] :
% 8.64/4.84 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.84 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.84 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4910_mult__exp__mod__exp__eq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat,A: int] :
% 8.64/4.84 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.84 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.84 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4911_mult__exp__mod__exp__eq,axiom,
% 8.64/4.84 ! [M2: nat,N: nat,A: code_natural] :
% 8.64/4.84 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.84 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.84 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4912_mod__double__modulus,axiom,
% 8.64/4.84 ! [M2: nat,X: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.84 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 8.64/4.84 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.84 = ( modulo_modulo_nat @ X @ M2 ) )
% 8.64/4.84 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.84 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4913_mod__double__modulus,axiom,
% 8.64/4.84 ! [M2: int,X: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ M2 )
% 8.64/4.84 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.64/4.84 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.84 = ( modulo_modulo_int @ X @ M2 ) )
% 8.64/4.84 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) )
% 8.64/4.84 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M2 ) @ M2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4914_divmod__digit__1_I2_J,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.64/4.84 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.64/4.84 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 8.64/4.84 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.64/4.84 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4915_divmod__digit__1_I2_J,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.84 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.84 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 8.64/4.84 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 8.64/4.84 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4916_unset__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: nat] :
% 8.64/4.84 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4917_unset__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: code_natural] :
% 8.64/4.84 ( ( bit_se7083795435491715335atural @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4918_unset__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: int] :
% 8.64/4.84 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4919_set__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: nat] :
% 8.64/4.84 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4920_set__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: code_natural] :
% 8.64/4.84 ( ( bit_se1617098188084679374atural @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4921_set__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: int] :
% 8.64/4.84 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4922_card__roots__unity__eq,axiom,
% 8.64/4.84 ! [N: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ( finite_card_complex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [Z4: complex] :
% 8.64/4.84 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.84 = one_one_complex ) ) )
% 8.64/4.84 = N ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4923_card__nth__roots,axiom,
% 8.64/4.84 ! [C2: complex,N: nat] :
% 8.64/4.84 ( ( C2 != zero_zero_complex )
% 8.64/4.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ( finite_card_complex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [Z4: complex] :
% 8.64/4.84 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.84 = C2 ) ) )
% 8.64/4.84 = N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4924_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_Code_integer,Ys: list_Code_integer] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs2 ) @ ( size_s3445333598471063425nteger @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr2304437835452373666nteger @ ( produc8792966785426426881nteger @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( produc1086072967326762835nteger @ ( nth_Code_integer @ Xs2 @ ( divide_divide_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) @ ( nth_Code_integer @ Ys @ ( modulo_modulo_nat @ N @ ( size_s3445333598471063425nteger @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4925_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4926_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_o] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4927_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_nat] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4928_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_VEBT_VEBT,Ys: list_int] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4929_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_o,Ys: list_VEBT_VEBT] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4930_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_o,Ys: list_o] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_o @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( product_Pair_o_o @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4931_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_o,Ys: list_nat] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_nat @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( product_Pair_o_nat @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4932_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_o,Ys: list_int] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs2 ) @ ( size_size_list_int @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( product_Pair_o_int @ ( nth_o @ Xs2 @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4933_product__nth,axiom,
% 8.64/4.84 ! [N: nat,Xs2: list_nat,Ys: list_VEBT_VEBT] :
% 8.64/4.84 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs2 ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 8.64/4.84 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs2 @ Ys ) @ N )
% 8.64/4.84 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs2 @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4934_divmod__digit__1_I1_J,axiom,
% 8.64/4.84 ! [A: code_integer,B: code_integer] :
% 8.64/4.84 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.64/4.84 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 8.64/4.84 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 8.64/4.84 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 8.64/4.84 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4935_divmod__digit__1_I1_J,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 8.64/4.84 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 8.64/4.84 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 8.64/4.84 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 8.64/4.84 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4936_divmod__digit__1_I1_J,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.84 => ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.84 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 8.64/4.84 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 8.64/4.84 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4937_VEBT__internal_Oinsert_H_Opelims,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 8.64/4.84 ( ( ( vEBT_VEBT_insert @ X @ Xa2 )
% 8.64/4.84 = Y )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [A3: $o,B3: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( vEBT_vebt_insert @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.84 => ( ( ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 8.64/4.84 => ( Y
% 8.64/4.84 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) ) )
% 8.64/4.84 & ( ~ ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) @ Xa2 )
% 8.64/4.84 => ( Y
% 8.64/4.84 = ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4938_vebt__member_Opelims_I1_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.84 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.64/4.84 = Y )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [A3: $o,B3: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.84 => A3 )
% 8.64/4.84 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.84 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.84 => B3 )
% 8.64/4.84 & ( Xa2 = one_one_nat ) ) ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.64/4.84 => ( ~ Y
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ Xa2 ) ) ) )
% 8.64/4.84 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 8.64/4.84 => ( ~ Y
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.64/4.84 => ( ~ Y
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( ( Xa2 != Mi2 )
% 8.64/4.84 => ( ( Xa2 != Ma2 )
% 8.64/4.84 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.84 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.84 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.84 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.84 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4939_vebt__member_Opelims_I3_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.84 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [A3: $o,B3: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 8.64/4.84 => ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.84 => A3 )
% 8.64/4.84 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.84 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.84 => B3 )
% 8.64/4.84 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.64/4.84 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw ) @ Xa2 ) ) )
% 8.64/4.84 => ( ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz2 ) @ Xa2 ) ) )
% 8.64/4.84 => ( ! [V: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 8.64/4.84 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 8.64/4.84 => ( ( Xa2 != Mi2 )
% 8.64/4.84 => ( ( Xa2 != Ma2 )
% 8.64/4.84 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.84 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.84 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.84 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.84 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4940_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.84 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.64/4.84 = Y )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [A3: $o,B3: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.84 => A3 )
% 8.64/4.84 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.84 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.84 => B3 )
% 8.64/4.84 & ( Xa2 = one_one_nat ) ) ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 8.64/4.84 => ( ~ Y
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Xa2 ) ) ) )
% 8.64/4.84 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4941_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.84 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [A3: $o,B3: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 8.64/4.84 => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.84 => A3 )
% 8.64/4.84 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.84 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.84 => B3 )
% 8.64/4.84 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.64/4.84 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) )
% 8.64/4.84 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4942_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.84 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [A3: $o,B3: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 8.64/4.84 => ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.84 => A3 )
% 8.64/4.84 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.84 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.84 => B3 )
% 8.64/4.84 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.64/4.84 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw ) @ Xa2 ) ) )
% 8.64/4.84 => ~ ! [Uy: option4927543243414619207at_nat,V: nat,TreeList: list_VEBT_VEBT,S: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList @ S ) @ Xa2 ) )
% 8.64/4.84 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4943_vebt__member_Opelims_I2_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.84 ( ( vEBT_vebt_member @ X @ Xa2 )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [A3: $o,B3: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) )
% 8.64/4.84 => ~ ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.84 => A3 )
% 8.64/4.84 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.84 => ( ( ( Xa2 = one_one_nat )
% 8.64/4.84 => B3 )
% 8.64/4.84 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 8.64/4.84 => ~ ! [Mi2: nat,Ma2: nat,Va: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList @ Summary2 ) @ Xa2 ) )
% 8.64/4.84 => ~ ( ( Xa2 != Mi2 )
% 8.64/4.84 => ( ( Xa2 != Ma2 )
% 8.64/4.84 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.84 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 8.64/4.84 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.84 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 8.64/4.84 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4944_zmod__numeral__Bit0,axiom,
% 8.64/4.84 ! [V2: num,W2: num] :
% 8.64/4.84 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 8.64/4.84 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4945_zmod__le__nonneg__dividend,axiom,
% 8.64/4.84 ! [M2: int,K2: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ M2 )
% 8.64/4.84 => ( ord_less_eq_int @ ( modulo_modulo_int @ M2 @ K2 ) @ M2 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4946_zmod__eq__0__iff,axiom,
% 8.64/4.84 ! [M2: int,D: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ M2 @ D )
% 8.64/4.84 = zero_zero_int )
% 8.64/4.84 = ( ? [Q5: int] :
% 8.64/4.84 ( M2
% 8.64/4.84 = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4947_zmod__eq__0D,axiom,
% 8.64/4.84 ! [M2: int,D: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ M2 @ D )
% 8.64/4.84 = zero_zero_int )
% 8.64/4.84 => ? [Q3: int] :
% 8.64/4.84 ( M2
% 8.64/4.84 = ( times_times_int @ D @ Q3 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4948_zmod__int,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.84 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4949_mod__int__unique,axiom,
% 8.64/4.84 ! [K2: int,L: int,Q2: int,R3: int] :
% 8.64/4.84 ( ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.84 => ( ( modulo_modulo_int @ K2 @ L )
% 8.64/4.84 = R3 ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4950_neg__mod__conj,axiom,
% 8.64/4.84 ! [B: int,A: int] :
% 8.64/4.84 ( ( ord_less_int @ B @ zero_zero_int )
% 8.64/4.84 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 8.64/4.84 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4951_pos__mod__conj,axiom,
% 8.64/4.84 ! [B: int,A: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.84 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.84 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4952_zmod__trivial__iff,axiom,
% 8.64/4.84 ! [I2: int,K2: int] :
% 8.64/4.84 ( ( ( modulo_modulo_int @ I2 @ K2 )
% 8.64/4.84 = I2 )
% 8.64/4.84 = ( ( K2 = zero_zero_int )
% 8.64/4.84 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 8.64/4.84 & ( ord_less_int @ I2 @ K2 ) )
% 8.64/4.84 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 8.64/4.84 & ( ord_less_int @ K2 @ I2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4953_div__mod__decomp__int,axiom,
% 8.64/4.84 ! [A4: int,N: int] :
% 8.64/4.84 ( A4
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A4 @ N ) @ N ) @ ( modulo_modulo_int @ A4 @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4954_eucl__rel__int,axiom,
% 8.64/4.84 ! [K2: int,L: int] : ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K2 @ L ) @ ( modulo_modulo_int @ K2 @ L ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4955_mod__pos__geq,axiom,
% 8.64/4.84 ! [L: int,K2: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ L )
% 8.64/4.84 => ( ( ord_less_eq_int @ L @ K2 )
% 8.64/4.84 => ( ( modulo_modulo_int @ K2 @ L )
% 8.64/4.84 = ( modulo_modulo_int @ ( minus_minus_int @ K2 @ L ) @ L ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4956_int__mod__pos__eq,axiom,
% 8.64/4.84 ! [A: int,B: int,Q2: int,R3: int] :
% 8.64/4.84 ( ( A
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 8.64/4.84 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 8.64/4.84 => ( ( ord_less_int @ R3 @ B )
% 8.64/4.84 => ( ( modulo_modulo_int @ A @ B )
% 8.64/4.84 = R3 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4957_int__mod__neg__eq,axiom,
% 8.64/4.84 ! [A: int,B: int,Q2: int,R3: int] :
% 8.64/4.84 ( ( A
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R3 ) )
% 8.64/4.84 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 8.64/4.84 => ( ( ord_less_int @ B @ R3 )
% 8.64/4.84 => ( ( modulo_modulo_int @ A @ B )
% 8.64/4.84 = R3 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4958_split__zmod,axiom,
% 8.64/4.84 ! [P2: int > $o,N: int,K2: int] :
% 8.64/4.84 ( ( P2 @ ( modulo_modulo_int @ N @ K2 ) )
% 8.64/4.84 = ( ( ( K2 = zero_zero_int )
% 8.64/4.84 => ( P2 @ N ) )
% 8.64/4.84 & ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.84 => ! [I: int,J: int] :
% 8.64/4.84 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 8.64/4.84 & ( ord_less_int @ J @ K2 )
% 8.64/4.84 & ( N
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 8.64/4.84 => ( P2 @ J ) ) )
% 8.64/4.84 & ( ( ord_less_int @ K2 @ zero_zero_int )
% 8.64/4.84 => ! [I: int,J: int] :
% 8.64/4.84 ( ( ( ord_less_int @ K2 @ J )
% 8.64/4.84 & ( ord_less_eq_int @ J @ zero_zero_int )
% 8.64/4.84 & ( N
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 8.64/4.84 => ( P2 @ J ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4959_zmod__zmult2__eq,axiom,
% 8.64/4.84 ! [C2: int,A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ C2 )
% 8.64/4.84 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4960_split__pos__lemma,axiom,
% 8.64/4.84 ! [K2: int,P2: int > int > $o,N: int] :
% 8.64/4.84 ( ( ord_less_int @ zero_zero_int @ K2 )
% 8.64/4.84 => ( ( P2 @ ( divide_divide_int @ N @ K2 ) @ ( modulo_modulo_int @ N @ K2 ) )
% 8.64/4.84 = ( ! [I: int,J: int] :
% 8.64/4.84 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 8.64/4.84 & ( ord_less_int @ J @ K2 )
% 8.64/4.84 & ( N
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 8.64/4.84 => ( P2 @ I @ J ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4961_split__neg__lemma,axiom,
% 8.64/4.84 ! [K2: int,P2: int > int > $o,N: int] :
% 8.64/4.84 ( ( ord_less_int @ K2 @ zero_zero_int )
% 8.64/4.84 => ( ( P2 @ ( divide_divide_int @ N @ K2 ) @ ( modulo_modulo_int @ N @ K2 ) )
% 8.64/4.84 = ( ! [I: int,J: int] :
% 8.64/4.84 ( ( ( ord_less_int @ K2 @ J )
% 8.64/4.84 & ( ord_less_eq_int @ J @ zero_zero_int )
% 8.64/4.84 & ( N
% 8.64/4.84 = ( plus_plus_int @ ( times_times_int @ K2 @ I ) @ J ) ) )
% 8.64/4.84 => ( P2 @ I @ J ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4962_pos__zmod__mult__2,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.84 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.64/4.84 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4963_neg__zmod__mult__2,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.64/4.84 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 8.64/4.84 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4964_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.84 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.64/4.84 = Y )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [Uu2: $o,Uv2: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.84 => ( ~ Y
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 8.64/4.84 => ( ~ Y
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) ) )
% 8.64/4.84 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( ( Xa2 = Mi2 )
% 8.64/4.84 | ( Xa2 = Ma2 ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( ( Xa2 = Mi2 )
% 8.64/4.84 | ( Xa2 = Ma2 )
% 8.64/4.84 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) ) ) )
% 8.64/4.84 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 8.64/4.84 => ( ( Y
% 8.64/4.84 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4965_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.84 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [Uu2: $o,Uv2: $o] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 8.64/4.84 => ( ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) )
% 8.64/4.84 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Xa2 ) ) )
% 8.64/4.84 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 8.64/4.84 => ( ( Xa2 = Mi2 )
% 8.64/4.84 | ( Xa2 = Ma2 ) ) ) )
% 8.64/4.84 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 8.64/4.84 => ( ( Xa2 = Mi2 )
% 8.64/4.84 | ( Xa2 = Ma2 )
% 8.64/4.84 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 8.64/4.84 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) )
% 8.64/4.84 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4966_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 8.64/4.84 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.84 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.84 => ( ! [Mi2: nat,Ma2: nat,Va2: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va2 @ Vb2 ) @ Xa2 ) )
% 8.64/4.84 => ~ ( ( Xa2 = Mi2 )
% 8.64/4.84 | ( Xa2 = Ma2 ) ) ) )
% 8.64/4.84 => ( ! [Mi2: nat,Ma2: nat,V: nat,TreeList: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V ) @ TreeList @ Vc2 ) @ Xa2 ) )
% 8.64/4.84 => ~ ( ( Xa2 = Mi2 )
% 8.64/4.84 | ( Xa2 = Ma2 )
% 8.64/4.84 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) )
% 8.64/4.84 => ~ ! [V: nat,TreeList: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) )
% 8.64/4.84 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList @ Vd ) @ Xa2 ) )
% 8.64/4.84 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) )
% 8.64/4.84 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.84 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4967_arcosh__1,axiom,
% 8.64/4.84 ( ( arcosh_real @ one_one_real )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4968_lemma__termdiff3,axiom,
% 8.64/4.84 ! [H: real,Z3: real,K5: real,N: nat] :
% 8.64/4.84 ( ( H != zero_zero_real )
% 8.64/4.84 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z3 ) @ K5 )
% 8.64/4.84 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z3 @ H ) ) @ K5 )
% 8.64/4.84 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ N ) @ ( power_power_real @ Z3 @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4969_lemma__termdiff3,axiom,
% 8.64/4.84 ! [H: complex,Z3: complex,K5: real,N: nat] :
% 8.64/4.84 ( ( H != zero_zero_complex )
% 8.64/4.84 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z3 ) @ K5 )
% 8.64/4.84 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z3 @ H ) ) @ K5 )
% 8.64/4.84 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ N ) @ ( power_power_complex @ Z3 @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4970_flip__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: nat] :
% 8.64/4.84 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4971_flip__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: int] :
% 8.64/4.84 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4972_flip__bit__Suc,axiom,
% 8.64/4.84 ! [N: nat,A: code_natural] :
% 8.64/4.84 ( ( bit_se168947363167071951atural @ ( suc @ N ) @ A )
% 8.64/4.84 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4973_artanh__0,axiom,
% 8.64/4.84 ( ( artanh_real @ zero_zero_real )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4974_norm__mult__numeral1,axiom,
% 8.64/4.84 ! [W2: num,A: real] :
% 8.64/4.84 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ A ) )
% 8.64/4.84 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4975_norm__mult__numeral1,axiom,
% 8.64/4.84 ! [W2: num,A: complex] :
% 8.64/4.84 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ A ) )
% 8.64/4.84 = ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4976_norm__mult__numeral2,axiom,
% 8.64/4.84 ! [A: real,W2: num] :
% 8.64/4.84 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.84 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4977_norm__mult__numeral2,axiom,
% 8.64/4.84 ! [A: complex,W2: num] :
% 8.64/4.84 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W2 ) ) )
% 8.64/4.84 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4978_norm__le__zero__iff,axiom,
% 8.64/4.84 ! [X: real] :
% 8.64/4.84 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 8.64/4.84 = ( X = zero_zero_real ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4979_norm__le__zero__iff,axiom,
% 8.64/4.84 ! [X: complex] :
% 8.64/4.84 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 8.64/4.84 = ( X = zero_zero_complex ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4980_zero__less__norm__iff,axiom,
% 8.64/4.84 ! [X: real] :
% 8.64/4.84 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 8.64/4.84 = ( X != zero_zero_real ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4981_zero__less__norm__iff,axiom,
% 8.64/4.84 ! [X: complex] :
% 8.64/4.84 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 8.64/4.84 = ( X != zero_zero_complex ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4982_norm__zero,axiom,
% 8.64/4.84 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4983_norm__zero,axiom,
% 8.64/4.84 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4984_norm__eq__zero,axiom,
% 8.64/4.84 ! [X: real] :
% 8.64/4.84 ( ( ( real_V7735802525324610683m_real @ X )
% 8.64/4.84 = zero_zero_real )
% 8.64/4.84 = ( X = zero_zero_real ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4985_norm__eq__zero,axiom,
% 8.64/4.84 ! [X: complex] :
% 8.64/4.84 ( ( ( real_V1022390504157884413omplex @ X )
% 8.64/4.84 = zero_zero_real )
% 8.64/4.84 = ( X = zero_zero_complex ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4986_norm__power__diff,axiom,
% 8.64/4.84 ! [Z3: real,W2: real,M2: nat] :
% 8.64/4.84 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z3 ) @ one_one_real )
% 8.64/4.84 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W2 ) @ one_one_real )
% 8.64/4.84 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( power_power_real @ Z3 @ M2 ) @ ( power_power_real @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Z3 @ W2 ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4987_norm__power__diff,axiom,
% 8.64/4.84 ! [Z3: complex,W2: complex,M2: nat] :
% 8.64/4.84 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z3 ) @ one_one_real )
% 8.64/4.84 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W2 ) @ one_one_real )
% 8.64/4.84 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z3 @ M2 ) @ ( power_power_complex @ W2 @ M2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z3 @ W2 ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4988_norm__mult,axiom,
% 8.64/4.84 ! [X: real,Y: real] :
% 8.64/4.84 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 8.64/4.84 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4989_norm__mult,axiom,
% 8.64/4.84 ! [X: complex,Y: complex] :
% 8.64/4.84 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 8.64/4.84 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4990_nonzero__norm__divide,axiom,
% 8.64/4.84 ! [B: real,A: real] :
% 8.64/4.84 ( ( B != zero_zero_real )
% 8.64/4.84 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 8.64/4.84 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4991_nonzero__norm__divide,axiom,
% 8.64/4.84 ! [B: complex,A: complex] :
% 8.64/4.84 ( ( B != zero_zero_complex )
% 8.64/4.84 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.64/4.84 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4992_power__eq__imp__eq__norm,axiom,
% 8.64/4.84 ! [W2: real,N: nat,Z3: real] :
% 8.64/4.84 ( ( ( power_power_real @ W2 @ N )
% 8.64/4.84 = ( power_power_real @ Z3 @ N ) )
% 8.64/4.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ( real_V7735802525324610683m_real @ W2 )
% 8.64/4.84 = ( real_V7735802525324610683m_real @ Z3 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4993_power__eq__imp__eq__norm,axiom,
% 8.64/4.84 ! [W2: complex,N: nat,Z3: complex] :
% 8.64/4.84 ( ( ( power_power_complex @ W2 @ N )
% 8.64/4.84 = ( power_power_complex @ Z3 @ N ) )
% 8.64/4.84 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ( real_V1022390504157884413omplex @ W2 )
% 8.64/4.84 = ( real_V1022390504157884413omplex @ Z3 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4994_norm__mult__less,axiom,
% 8.64/4.84 ! [X: real,R3: real,Y: real,S2: real] :
% 8.64/4.84 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R3 )
% 8.64/4.84 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S2 )
% 8.64/4.84 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R3 @ S2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4995_norm__mult__less,axiom,
% 8.64/4.84 ! [X: complex,R3: real,Y: complex,S2: real] :
% 8.64/4.84 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R3 )
% 8.64/4.84 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S2 )
% 8.64/4.84 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R3 @ S2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4996_norm__mult__ineq,axiom,
% 8.64/4.84 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4997_norm__mult__ineq,axiom,
% 8.64/4.84 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4998_power__eq__1__iff,axiom,
% 8.64/4.84 ! [W2: real,N: nat] :
% 8.64/4.84 ( ( ( power_power_real @ W2 @ N )
% 8.64/4.84 = one_one_real )
% 8.64/4.84 => ( ( ( real_V7735802525324610683m_real @ W2 )
% 8.64/4.84 = one_one_real )
% 8.64/4.84 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_4999_power__eq__1__iff,axiom,
% 8.64/4.84 ! [W2: complex,N: nat] :
% 8.64/4.84 ( ( ( power_power_complex @ W2 @ N )
% 8.64/4.84 = one_one_complex )
% 8.64/4.84 => ( ( ( real_V1022390504157884413omplex @ W2 )
% 8.64/4.84 = one_one_real )
% 8.64/4.84 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5000_arsinh__0,axiom,
% 8.64/4.84 ( ( arsinh_real @ zero_zero_real )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5001_vebt__buildup_Oelims,axiom,
% 8.64/4.84 ! [X: nat,Y: vEBT_VEBT] :
% 8.64/4.84 ( ( ( vEBT_vebt_buildup @ X )
% 8.64/4.84 = Y )
% 8.64/4.84 => ( ( ( X = zero_zero_nat )
% 8.64/4.84 => ( Y
% 8.64/4.84 != ( vEBT_Leaf @ $false @ $false ) ) )
% 8.64/4.84 => ( ( ( X
% 8.64/4.84 = ( suc @ zero_zero_nat ) )
% 8.64/4.84 => ( Y
% 8.64/4.84 != ( vEBT_Leaf @ $false @ $false ) ) )
% 8.64/4.84 => ~ ! [Va: nat] :
% 8.64/4.84 ( ( X
% 8.64/4.84 = ( suc @ ( suc @ Va ) ) )
% 8.64/4.84 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 8.64/4.84 => ( Y
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 8.64/4.84 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 8.64/4.84 => ( Y
% 8.64/4.84 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5002_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_real,X: real > code_integer,Y: real > code_integer] :
% 8.64/4.84 ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_Code_integer ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5003_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 8.64/4.84 ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_Code_integer ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5004_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_int,X: int > code_integer,Y: int > code_integer] :
% 8.64/4.84 ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_Code_integer ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5005_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_complex,X: complex > code_integer,Y: complex > code_integer] :
% 8.64/4.84 ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_Code_integer ) ) ) )
% 8.64/4.84 => ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( times_3573771949741848930nteger @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_Code_integer ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5006_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 8.64/4.84 ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5007_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 8.64/4.84 ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5008_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 8.64/4.84 ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5009_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 8.64/4.84 ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_complex ) ) ) )
% 8.64/4.84 => ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( times_times_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5010_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_real,X: real > real,Y: real > real] :
% 8.64/4.84 ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_real ) ) ) )
% 8.64/4.84 => ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_real ) ) ) )
% 8.64/4.84 => ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( times_times_real @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_real ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5011_prod_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 8.64/4.84 ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != one_one_real ) ) ) )
% 8.64/4.84 => ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != one_one_real ) ) ) )
% 8.64/4.84 => ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( times_times_real @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != one_one_real ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5012_sum__gp,axiom,
% 8.64/4.84 ! [N: nat,M2: nat,X: complex] :
% 8.64/4.84 ( ( ( ord_less_nat @ N @ M2 )
% 8.64/4.84 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = zero_zero_complex ) )
% 8.64/4.84 & ( ~ ( ord_less_nat @ N @ M2 )
% 8.64/4.84 => ( ( ( X = one_one_complex )
% 8.64/4.84 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 8.64/4.84 & ( ( X != one_one_complex )
% 8.64/4.84 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5013_sum__gp,axiom,
% 8.64/4.84 ! [N: nat,M2: nat,X: rat] :
% 8.64/4.84 ( ( ( ord_less_nat @ N @ M2 )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = zero_zero_rat ) )
% 8.64/4.84 & ( ~ ( ord_less_nat @ N @ M2 )
% 8.64/4.84 => ( ( ( X = one_one_rat )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 8.64/4.84 & ( ( X != one_one_rat )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5014_sum__gp,axiom,
% 8.64/4.84 ! [N: nat,M2: nat,X: real] :
% 8.64/4.84 ( ( ( ord_less_nat @ N @ M2 )
% 8.64/4.84 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = zero_zero_real ) )
% 8.64/4.84 & ( ~ ( ord_less_nat @ N @ M2 )
% 8.64/4.84 => ( ( ( X = one_one_real )
% 8.64/4.84 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) )
% 8.64/4.84 & ( ( X != one_one_real )
% 8.64/4.84 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.84 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5015_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_real,X: real > complex,Y: real > complex] :
% 8.64/4.84 ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5016_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_nat,X: nat > complex,Y: nat > complex] :
% 8.64/4.84 ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5017_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_int,X: int > complex,Y: int > complex] :
% 8.64/4.84 ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5018_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_complex,X: complex > complex,Y: complex > complex] :
% 8.64/4.84 ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_complex ) ) ) )
% 8.64/4.84 => ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_complex @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_complex ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5019_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_real,X: real > real,Y: real > real] :
% 8.64/4.84 ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5020_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_nat,X: nat > real,Y: nat > real] :
% 8.64/4.84 ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5021_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_int,X: int > real,Y: int > real] :
% 8.64/4.84 ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( finite_finite_int
% 8.64/4.84 @ ( collect_int
% 8.64/4.84 @ ^ [I: int] :
% 8.64/4.84 ( ( member_int @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5022_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_complex,X: complex > real,Y: complex > real] :
% 8.64/4.84 ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_real ) ) ) )
% 8.64/4.84 => ( finite3207457112153483333omplex
% 8.64/4.84 @ ( collect_complex
% 8.64/4.84 @ ^ [I: complex] :
% 8.64/4.84 ( ( member_complex @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_real @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5023_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_real,X: real > rat,Y: real > rat] :
% 8.64/4.84 ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_rat ) ) ) )
% 8.64/4.84 => ( ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_rat ) ) ) )
% 8.64/4.84 => ( finite_finite_real
% 8.64/4.84 @ ( collect_real
% 8.64/4.84 @ ^ [I: real] :
% 8.64/4.84 ( ( member_real @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5024_sum_Ofinite__Collect__op,axiom,
% 8.64/4.84 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 8.64/4.84 ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( X @ I )
% 8.64/4.84 != zero_zero_rat ) ) ) )
% 8.64/4.84 => ( ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( Y @ I )
% 8.64/4.84 != zero_zero_rat ) ) ) )
% 8.64/4.84 => ( finite_finite_nat
% 8.64/4.84 @ ( collect_nat
% 8.64/4.84 @ ^ [I: nat] :
% 8.64/4.84 ( ( member_nat @ I @ I5 )
% 8.64/4.84 & ( ( plus_plus_rat @ ( X @ I ) @ ( Y @ I ) )
% 8.64/4.84 != zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5025_geometric__deriv__sums,axiom,
% 8.64/4.84 ! [Z3: real] :
% 8.64/4.84 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z3 ) @ one_one_real )
% 8.64/4.84 => ( sums_real
% 8.64/4.84 @ ^ [N4: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) @ ( power_power_real @ Z3 @ N4 ) )
% 8.64/4.84 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5026_geometric__deriv__sums,axiom,
% 8.64/4.84 ! [Z3: complex] :
% 8.64/4.84 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z3 ) @ one_one_real )
% 8.64/4.84 => ( sums_complex
% 8.64/4.84 @ ^ [N4: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N4 ) ) @ ( power_power_complex @ Z3 @ N4 ) )
% 8.64/4.84 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5027_pochhammer__double,axiom,
% 8.64/4.84 ! [Z3: complex,N: nat] :
% 8.64/4.84 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.84 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s2602460028002588243omplex @ Z3 @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5028_pochhammer__double,axiom,
% 8.64/4.84 ! [Z3: rat,N: nat] :
% 8.64/4.84 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.84 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5029_pochhammer__double,axiom,
% 8.64/4.84 ! [Z3: real,N: nat] :
% 8.64/4.84 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.84 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( comm_s7457072308508201937r_real @ Z3 @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5030_dvd__0__right,axiom,
% 8.64/4.84 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5031_dvd__0__right,axiom,
% 8.64/4.84 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5032_dvd__0__right,axiom,
% 8.64/4.84 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5033_dvd__0__right,axiom,
% 8.64/4.84 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5034_dvd__0__right,axiom,
% 8.64/4.84 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5035_dvd__0__left__iff,axiom,
% 8.64/4.84 ! [A: complex] :
% 8.64/4.84 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 8.64/4.84 = ( A = zero_zero_complex ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5036_dvd__0__left__iff,axiom,
% 8.64/4.84 ! [A: real] :
% 8.64/4.84 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 8.64/4.84 = ( A = zero_zero_real ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5037_dvd__0__left__iff,axiom,
% 8.64/4.84 ! [A: rat] :
% 8.64/4.84 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 8.64/4.84 = ( A = zero_zero_rat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5038_dvd__0__left__iff,axiom,
% 8.64/4.84 ! [A: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.64/4.84 = ( A = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5039_dvd__0__left__iff,axiom,
% 8.64/4.84 ! [A: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 8.64/4.84 = ( A = zero_zero_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5040_dvd__add__triv__right__iff,axiom,
% 8.64/4.84 ! [A: real,B: real] :
% 8.64/4.84 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 8.64/4.84 = ( dvd_dvd_real @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5041_dvd__add__triv__right__iff,axiom,
% 8.64/4.84 ! [A: rat,B: rat] :
% 8.64/4.84 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 8.64/4.84 = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5042_dvd__add__triv__right__iff,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 8.64/4.84 = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5043_dvd__add__triv__right__iff,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 8.64/4.84 = ( dvd_dvd_int @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5044_dvd__add__triv__left__iff,axiom,
% 8.64/4.84 ! [A: real,B: real] :
% 8.64/4.84 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 8.64/4.84 = ( dvd_dvd_real @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5045_dvd__add__triv__left__iff,axiom,
% 8.64/4.84 ! [A: rat,B: rat] :
% 8.64/4.84 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 8.64/4.84 = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5046_dvd__add__triv__left__iff,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 8.64/4.84 = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5047_dvd__add__triv__left__iff,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 8.64/4.84 = ( dvd_dvd_int @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5048_div__dvd__div,axiom,
% 8.64/4.84 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.84 => ( ( dvd_dvd_nat @ A @ C2 )
% 8.64/4.84 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C2 @ A ) )
% 8.64/4.84 = ( dvd_dvd_nat @ B @ C2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5049_div__dvd__div,axiom,
% 8.64/4.84 ! [A: int,B: int,C2: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.84 => ( ( dvd_dvd_int @ A @ C2 )
% 8.64/4.84 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C2 @ A ) )
% 8.64/4.84 = ( dvd_dvd_int @ B @ C2 ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5050_nat__dvd__1__iff__1,axiom,
% 8.64/4.84 ! [M2: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ M2 @ one_one_nat )
% 8.64/4.84 = ( M2 = one_one_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5051_sum_Oneutral__const,axiom,
% 8.64/4.84 ! [A4: set_nat] :
% 8.64/4.84 ( ( groups3542108847815614940at_nat
% 8.64/4.84 @ ^ [Uu3: nat] : zero_zero_nat
% 8.64/4.84 @ A4 )
% 8.64/4.84 = zero_zero_nat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5052_sum_Oneutral__const,axiom,
% 8.64/4.84 ! [A4: set_int] :
% 8.64/4.84 ( ( groups4538972089207619220nt_int
% 8.64/4.84 @ ^ [Uu3: int] : zero_zero_int
% 8.64/4.84 @ A4 )
% 8.64/4.84 = zero_zero_int ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5053_sum_Oneutral__const,axiom,
% 8.64/4.84 ! [A4: set_nat] :
% 8.64/4.84 ( ( groups6591440286371151544t_real
% 8.64/4.84 @ ^ [Uu3: nat] : zero_zero_real
% 8.64/4.84 @ A4 )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5054_dvd__times__right__cancel__iff,axiom,
% 8.64/4.84 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.84 ( ( A != zero_zero_nat )
% 8.64/4.84 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C2 @ A ) )
% 8.64/4.84 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5055_dvd__times__right__cancel__iff,axiom,
% 8.64/4.84 ! [A: int,B: int,C2: int] :
% 8.64/4.84 ( ( A != zero_zero_int )
% 8.64/4.84 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C2 @ A ) )
% 8.64/4.84 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5056_dvd__times__left__cancel__iff,axiom,
% 8.64/4.84 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.84 ( ( A != zero_zero_nat )
% 8.64/4.84 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C2 ) )
% 8.64/4.84 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5057_dvd__times__left__cancel__iff,axiom,
% 8.64/4.84 ! [A: int,B: int,C2: int] :
% 8.64/4.84 ( ( A != zero_zero_int )
% 8.64/4.84 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C2 ) )
% 8.64/4.84 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5058_dvd__mult__cancel__right,axiom,
% 8.64/4.84 ! [A: complex,C2: complex,B: complex] :
% 8.64/4.84 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C2 ) @ ( times_times_complex @ B @ C2 ) )
% 8.64/4.84 = ( ( C2 = zero_zero_complex )
% 8.64/4.84 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5059_dvd__mult__cancel__right,axiom,
% 8.64/4.84 ! [A: real,C2: real,B: real] :
% 8.64/4.84 ( ( dvd_dvd_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ C2 ) )
% 8.64/4.84 = ( ( C2 = zero_zero_real )
% 8.64/4.84 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5060_dvd__mult__cancel__right,axiom,
% 8.64/4.84 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.84 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ C2 ) )
% 8.64/4.84 = ( ( C2 = zero_zero_rat )
% 8.64/4.84 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5061_dvd__mult__cancel__right,axiom,
% 8.64/4.84 ! [A: int,C2: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ C2 ) )
% 8.64/4.84 = ( ( C2 = zero_zero_int )
% 8.64/4.84 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5062_dvd__mult__cancel__left,axiom,
% 8.64/4.84 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.84 ( ( dvd_dvd_complex @ ( times_times_complex @ C2 @ A ) @ ( times_times_complex @ C2 @ B ) )
% 8.64/4.84 = ( ( C2 = zero_zero_complex )
% 8.64/4.84 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5063_dvd__mult__cancel__left,axiom,
% 8.64/4.84 ! [C2: real,A: real,B: real] :
% 8.64/4.84 ( ( dvd_dvd_real @ ( times_times_real @ C2 @ A ) @ ( times_times_real @ C2 @ B ) )
% 8.64/4.84 = ( ( C2 = zero_zero_real )
% 8.64/4.84 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5064_dvd__mult__cancel__left,axiom,
% 8.64/4.84 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.84 ( ( dvd_dvd_rat @ ( times_times_rat @ C2 @ A ) @ ( times_times_rat @ C2 @ B ) )
% 8.64/4.84 = ( ( C2 = zero_zero_rat )
% 8.64/4.84 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5065_dvd__mult__cancel__left,axiom,
% 8.64/4.84 ! [C2: int,A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.64/4.84 = ( ( C2 = zero_zero_int )
% 8.64/4.84 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5066_dvd__add__times__triv__right__iff,axiom,
% 8.64/4.84 ! [A: real,B: real,C2: real] :
% 8.64/4.84 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C2 @ A ) ) )
% 8.64/4.84 = ( dvd_dvd_real @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5067_dvd__add__times__triv__right__iff,axiom,
% 8.64/4.84 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.84 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C2 @ A ) ) )
% 8.64/4.84 = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5068_dvd__add__times__triv__right__iff,axiom,
% 8.64/4.84 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C2 @ A ) ) )
% 8.64/4.84 = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5069_dvd__add__times__triv__right__iff,axiom,
% 8.64/4.84 ! [A: int,B: int,C2: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C2 @ A ) ) )
% 8.64/4.84 = ( dvd_dvd_int @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5070_dvd__add__times__triv__left__iff,axiom,
% 8.64/4.84 ! [A: real,C2: real,B: real] :
% 8.64/4.84 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C2 @ A ) @ B ) )
% 8.64/4.84 = ( dvd_dvd_real @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5071_dvd__add__times__triv__left__iff,axiom,
% 8.64/4.84 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.84 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C2 @ A ) @ B ) )
% 8.64/4.84 = ( dvd_dvd_rat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5072_dvd__add__times__triv__left__iff,axiom,
% 8.64/4.84 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C2 @ A ) @ B ) )
% 8.64/4.84 = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5073_dvd__add__times__triv__left__iff,axiom,
% 8.64/4.84 ! [A: int,C2: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C2 @ A ) @ B ) )
% 8.64/4.84 = ( dvd_dvd_int @ A @ B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5074_unit__prod,axiom,
% 8.64/4.84 ! [A: code_integer,B: code_integer] :
% 8.64/4.84 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.84 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.84 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5075_unit__prod,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.84 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.84 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5076_unit__prod,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.84 => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.84 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5077_dvd__div__mult__self,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.84 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 8.64/4.84 = B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5078_dvd__div__mult__self,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.84 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 8.64/4.84 = B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5079_dvd__mult__div__cancel,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.84 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 8.64/4.84 = B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5080_dvd__mult__div__cancel,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.84 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 8.64/4.84 = B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5081_div__add,axiom,
% 8.64/4.84 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ C2 @ A )
% 8.64/4.84 => ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.84 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C2 )
% 8.64/4.84 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C2 ) @ ( divide_divide_nat @ B @ C2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5082_div__add,axiom,
% 8.64/4.84 ! [C2: int,A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ C2 @ A )
% 8.64/4.84 => ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.84 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C2 )
% 8.64/4.84 = ( plus_plus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5083_unit__div,axiom,
% 8.64/4.84 ! [A: code_integer,B: code_integer] :
% 8.64/4.84 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.84 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.84 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5084_unit__div,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.84 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.84 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5085_unit__div,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.84 => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.84 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5086_unit__div__1__unit,axiom,
% 8.64/4.84 ! [A: code_integer] :
% 8.64/4.84 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.84 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5087_unit__div__1__unit,axiom,
% 8.64/4.84 ! [A: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.84 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5088_unit__div__1__unit,axiom,
% 8.64/4.84 ! [A: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.84 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5089_unit__div__1__div__1,axiom,
% 8.64/4.84 ! [A: code_integer] :
% 8.64/4.84 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.84 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 8.64/4.84 = A ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5090_unit__div__1__div__1,axiom,
% 8.64/4.84 ! [A: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.84 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 8.64/4.84 = A ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5091_unit__div__1__div__1,axiom,
% 8.64/4.84 ! [A: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.84 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 8.64/4.84 = A ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5092_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: nat > complex] :
% 8.64/4.84 ( ( groups2073611262835488442omplex @ G2 @ bot_bot_set_nat )
% 8.64/4.84 = zero_zero_complex ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5093_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: nat > rat] :
% 8.64/4.84 ( ( groups2906978787729119204at_rat @ G2 @ bot_bot_set_nat )
% 8.64/4.84 = zero_zero_rat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5094_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: nat > int] :
% 8.64/4.84 ( ( groups3539618377306564664at_int @ G2 @ bot_bot_set_nat )
% 8.64/4.84 = zero_zero_int ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5095_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: int > complex] :
% 8.64/4.84 ( ( groups3049146728041665814omplex @ G2 @ bot_bot_set_int )
% 8.64/4.84 = zero_zero_complex ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5096_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: int > real] :
% 8.64/4.84 ( ( groups8778361861064173332t_real @ G2 @ bot_bot_set_int )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5097_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: int > rat] :
% 8.64/4.84 ( ( groups3906332499630173760nt_rat @ G2 @ bot_bot_set_int )
% 8.64/4.84 = zero_zero_rat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5098_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: int > nat] :
% 8.64/4.84 ( ( groups4541462559716669496nt_nat @ G2 @ bot_bot_set_int )
% 8.64/4.84 = zero_zero_nat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5099_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: real > complex] :
% 8.64/4.84 ( ( groups5754745047067104278omplex @ G2 @ bot_bot_set_real )
% 8.64/4.84 = zero_zero_complex ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5100_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: real > real] :
% 8.64/4.84 ( ( groups8097168146408367636l_real @ G2 @ bot_bot_set_real )
% 8.64/4.84 = zero_zero_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5101_sum_Oempty,axiom,
% 8.64/4.84 ! [G2: real > rat] :
% 8.64/4.84 ( ( groups1300246762558778688al_rat @ G2 @ bot_bot_set_real )
% 8.64/4.84 = zero_zero_rat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5102_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_nat,G2: nat > complex] :
% 8.64/4.84 ( ~ ( finite_finite_nat @ A4 )
% 8.64/4.84 => ( ( groups2073611262835488442omplex @ G2 @ A4 )
% 8.64/4.84 = zero_zero_complex ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5103_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_int,G2: int > complex] :
% 8.64/4.84 ( ~ ( finite_finite_int @ A4 )
% 8.64/4.84 => ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 8.64/4.84 = zero_zero_complex ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5104_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_complex,G2: complex > complex] :
% 8.64/4.84 ( ~ ( finite3207457112153483333omplex @ A4 )
% 8.64/4.84 => ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 8.64/4.84 = zero_zero_complex ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5105_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_int,G2: int > real] :
% 8.64/4.84 ( ~ ( finite_finite_int @ A4 )
% 8.64/4.84 => ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 8.64/4.84 = zero_zero_real ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5106_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_complex,G2: complex > real] :
% 8.64/4.84 ( ~ ( finite3207457112153483333omplex @ A4 )
% 8.64/4.84 => ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 8.64/4.84 = zero_zero_real ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5107_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_nat,G2: nat > rat] :
% 8.64/4.84 ( ~ ( finite_finite_nat @ A4 )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat @ G2 @ A4 )
% 8.64/4.84 = zero_zero_rat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5108_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_int,G2: int > rat] :
% 8.64/4.84 ( ~ ( finite_finite_int @ A4 )
% 8.64/4.84 => ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 8.64/4.84 = zero_zero_rat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5109_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_complex,G2: complex > rat] :
% 8.64/4.84 ( ~ ( finite3207457112153483333omplex @ A4 )
% 8.64/4.84 => ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 8.64/4.84 = zero_zero_rat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5110_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_int,G2: int > nat] :
% 8.64/4.84 ( ~ ( finite_finite_int @ A4 )
% 8.64/4.84 => ( ( groups4541462559716669496nt_nat @ G2 @ A4 )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5111_sum_Oinfinite,axiom,
% 8.64/4.84 ! [A4: set_complex,G2: complex > nat] :
% 8.64/4.84 ( ~ ( finite3207457112153483333omplex @ A4 )
% 8.64/4.84 => ( ( groups5693394587270226106ex_nat @ G2 @ A4 )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5112_sum__eq__0__iff,axiom,
% 8.64/4.84 ! [F3: set_int,F2: int > nat] :
% 8.64/4.84 ( ( finite_finite_int @ F3 )
% 8.64/4.84 => ( ( ( groups4541462559716669496nt_nat @ F2 @ F3 )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 = ( ! [X4: int] :
% 8.64/4.84 ( ( member_int @ X4 @ F3 )
% 8.64/4.84 => ( ( F2 @ X4 )
% 8.64/4.84 = zero_zero_nat ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5113_sum__eq__0__iff,axiom,
% 8.64/4.84 ! [F3: set_complex,F2: complex > nat] :
% 8.64/4.84 ( ( finite3207457112153483333omplex @ F3 )
% 8.64/4.84 => ( ( ( groups5693394587270226106ex_nat @ F2 @ F3 )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 = ( ! [X4: complex] :
% 8.64/4.84 ( ( member_complex @ X4 @ F3 )
% 8.64/4.84 => ( ( F2 @ X4 )
% 8.64/4.84 = zero_zero_nat ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5114_sum__eq__0__iff,axiom,
% 8.64/4.84 ! [F3: set_nat,F2: nat > nat] :
% 8.64/4.84 ( ( finite_finite_nat @ F3 )
% 8.64/4.84 => ( ( ( groups3542108847815614940at_nat @ F2 @ F3 )
% 8.64/4.84 = zero_zero_nat )
% 8.64/4.84 = ( ! [X4: nat] :
% 8.64/4.84 ( ( member_nat @ X4 @ F3 )
% 8.64/4.84 => ( ( F2 @ X4 )
% 8.64/4.84 = zero_zero_nat ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5115_div__diff,axiom,
% 8.64/4.84 ! [C2: int,A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ C2 @ A )
% 8.64/4.84 => ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.84 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C2 )
% 8.64/4.84 = ( minus_minus_int @ ( divide_divide_int @ A @ C2 ) @ ( divide_divide_int @ B @ C2 ) ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5116_dvd__imp__mod__0,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.84 => ( ( modulo_modulo_nat @ B @ A )
% 8.64/4.84 = zero_zero_nat ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5117_dvd__imp__mod__0,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.84 => ( ( modulo_modulo_int @ B @ A )
% 8.64/4.84 = zero_zero_int ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5118_dvd__imp__mod__0,axiom,
% 8.64/4.84 ! [A: code_natural,B: code_natural] :
% 8.64/4.84 ( ( dvd_dvd_Code_natural @ A @ B )
% 8.64/4.84 => ( ( modulo8411746178871703098atural @ B @ A )
% 8.64/4.84 = zero_z2226904508553997617atural ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5119_dvd__1__left,axiom,
% 8.64/4.84 ! [K2: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K2 ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5120_dvd__1__iff__1,axiom,
% 8.64/4.84 ! [M2: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 8.64/4.84 = ( M2
% 8.64/4.84 = ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5121_nat__mult__dvd__cancel__disj,axiom,
% 8.64/4.84 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.64/4.84 = ( ( K2 = zero_zero_nat )
% 8.64/4.84 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5122_pochhammer__0,axiom,
% 8.64/4.84 ! [A: code_integer] :
% 8.64/4.84 ( ( comm_s8582702949713902594nteger @ A @ zero_zero_nat )
% 8.64/4.84 = one_one_Code_integer ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5123_pochhammer__0,axiom,
% 8.64/4.84 ! [A: complex] :
% 8.64/4.84 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 8.64/4.84 = one_one_complex ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5124_pochhammer__0,axiom,
% 8.64/4.84 ! [A: real] :
% 8.64/4.84 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 8.64/4.84 = one_one_real ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5125_pochhammer__0,axiom,
% 8.64/4.84 ! [A: nat] :
% 8.64/4.84 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 8.64/4.84 = one_one_nat ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5126_pochhammer__0,axiom,
% 8.64/4.84 ! [A: int] :
% 8.64/4.84 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 8.64/4.84 = one_one_int ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5127_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_real,A: real,B: real > complex] :
% 8.64/4.84 ( ( finite_finite_real @ S3 )
% 8.64/4.84 => ( ( ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups5754745047067104278omplex
% 8.64/4.84 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups5754745047067104278omplex
% 8.64/4.84 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5128_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_nat,A: nat,B: nat > complex] :
% 8.64/4.84 ( ( finite_finite_nat @ S3 )
% 8.64/4.84 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2073611262835488442omplex
% 8.64/4.84 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2073611262835488442omplex
% 8.64/4.84 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5129_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_int,A: int,B: int > complex] :
% 8.64/4.84 ( ( finite_finite_int @ S3 )
% 8.64/4.84 => ( ( ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3049146728041665814omplex
% 8.64/4.84 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3049146728041665814omplex
% 8.64/4.84 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5130_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_complex,A: complex,B: complex > complex] :
% 8.64/4.84 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.84 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups7754918857620584856omplex
% 8.64/4.84 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups7754918857620584856omplex
% 8.64/4.84 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5131_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_real,A: real,B: real > real] :
% 8.64/4.84 ( ( finite_finite_real @ S3 )
% 8.64/4.84 => ( ( ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups8097168146408367636l_real
% 8.64/4.84 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups8097168146408367636l_real
% 8.64/4.84 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_real ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5132_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_int,A: int,B: int > real] :
% 8.64/4.84 ( ( finite_finite_int @ S3 )
% 8.64/4.84 => ( ( ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups8778361861064173332t_real
% 8.64/4.84 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups8778361861064173332t_real
% 8.64/4.84 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_real ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5133_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_complex,A: complex,B: complex > real] :
% 8.64/4.84 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.84 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups5808333547571424918x_real
% 8.64/4.84 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups5808333547571424918x_real
% 8.64/4.84 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_real ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5134_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_real,A: real,B: real > rat] :
% 8.64/4.84 ( ( finite_finite_real @ S3 )
% 8.64/4.84 => ( ( ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups1300246762558778688al_rat
% 8.64/4.84 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups1300246762558778688al_rat
% 8.64/4.84 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_rat ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5135_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_nat,A: nat,B: nat > rat] :
% 8.64/4.84 ( ( finite_finite_nat @ S3 )
% 8.64/4.84 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat
% 8.64/4.84 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat
% 8.64/4.84 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_rat ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5136_sum_Odelta,axiom,
% 8.64/4.84 ! [S3: set_int,A: int,B: int > rat] :
% 8.64/4.84 ( ( finite_finite_int @ S3 )
% 8.64/4.84 => ( ( ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3906332499630173760nt_rat
% 8.64/4.84 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3906332499630173760nt_rat
% 8.64/4.84 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_rat ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5137_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_real,A: real,B: real > complex] :
% 8.64/4.84 ( ( finite_finite_real @ S3 )
% 8.64/4.84 => ( ( ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups5754745047067104278omplex
% 8.64/4.84 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups5754745047067104278omplex
% 8.64/4.84 @ ^ [K3: real] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5138_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_nat,A: nat,B: nat > complex] :
% 8.64/4.84 ( ( finite_finite_nat @ S3 )
% 8.64/4.84 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2073611262835488442omplex
% 8.64/4.84 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2073611262835488442omplex
% 8.64/4.84 @ ^ [K3: nat] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5139_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_int,A: int,B: int > complex] :
% 8.64/4.84 ( ( finite_finite_int @ S3 )
% 8.64/4.84 => ( ( ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3049146728041665814omplex
% 8.64/4.84 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3049146728041665814omplex
% 8.64/4.84 @ ^ [K3: int] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5140_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_complex,A: complex,B: complex > complex] :
% 8.64/4.84 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.84 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups7754918857620584856omplex
% 8.64/4.84 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups7754918857620584856omplex
% 8.64/4.84 @ ^ [K3: complex] : ( if_complex @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_complex )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_complex ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5141_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_real,A: real,B: real > real] :
% 8.64/4.84 ( ( finite_finite_real @ S3 )
% 8.64/4.84 => ( ( ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups8097168146408367636l_real
% 8.64/4.84 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups8097168146408367636l_real
% 8.64/4.84 @ ^ [K3: real] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_real ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5142_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_int,A: int,B: int > real] :
% 8.64/4.84 ( ( finite_finite_int @ S3 )
% 8.64/4.84 => ( ( ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups8778361861064173332t_real
% 8.64/4.84 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups8778361861064173332t_real
% 8.64/4.84 @ ^ [K3: int] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_real ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5143_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_complex,A: complex,B: complex > real] :
% 8.64/4.84 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.84 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups5808333547571424918x_real
% 8.64/4.84 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.84 => ( ( groups5808333547571424918x_real
% 8.64/4.84 @ ^ [K3: complex] : ( if_real @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_real )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_real ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5144_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_real,A: real,B: real > rat] :
% 8.64/4.84 ( ( finite_finite_real @ S3 )
% 8.64/4.84 => ( ( ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups1300246762558778688al_rat
% 8.64/4.84 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.84 => ( ( groups1300246762558778688al_rat
% 8.64/4.84 @ ^ [K3: real] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_rat ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5145_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_nat,A: nat,B: nat > rat] :
% 8.64/4.84 ( ( finite_finite_nat @ S3 )
% 8.64/4.84 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat
% 8.64/4.84 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.84 => ( ( groups2906978787729119204at_rat
% 8.64/4.84 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_rat ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5146_sum_Odelta_H,axiom,
% 8.64/4.84 ! [S3: set_int,A: int,B: int > rat] :
% 8.64/4.84 ( ( finite_finite_int @ S3 )
% 8.64/4.84 => ( ( ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3906332499630173760nt_rat
% 8.64/4.84 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = ( B @ A ) ) )
% 8.64/4.84 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.84 => ( ( groups3906332499630173760nt_rat
% 8.64/4.84 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 8.64/4.84 @ S3 )
% 8.64/4.84 = zero_zero_rat ) ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5147_unit__mult__div__div,axiom,
% 8.64/4.84 ! [A: code_integer,B: code_integer] :
% 8.64/4.84 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.84 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 8.64/4.84 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5148_unit__mult__div__div,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.84 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 8.64/4.84 = ( divide_divide_nat @ B @ A ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5149_unit__mult__div__div,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.84 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 8.64/4.84 = ( divide_divide_int @ B @ A ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5150_unit__div__mult__self,axiom,
% 8.64/4.84 ! [A: code_integer,B: code_integer] :
% 8.64/4.84 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.84 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 8.64/4.84 = B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5151_unit__div__mult__self,axiom,
% 8.64/4.84 ! [A: nat,B: nat] :
% 8.64/4.84 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.84 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 8.64/4.84 = B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5152_unit__div__mult__self,axiom,
% 8.64/4.84 ! [A: int,B: int] :
% 8.64/4.84 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.84 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 8.64/4.84 = B ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5153_pow__divides__pow__iff,axiom,
% 8.64/4.84 ! [N: nat,A: nat,B: nat] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 8.64/4.84 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5154_pow__divides__pow__iff,axiom,
% 8.64/4.84 ! [N: nat,A: int,B: int] :
% 8.64/4.84 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.84 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 8.64/4.84 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5155_sum__constant,axiom,
% 8.64/4.84 ! [Y: rat,A4: set_nat] :
% 8.64/4.84 ( ( groups2906978787729119204at_rat
% 8.64/4.84 @ ^ [X4: nat] : Y
% 8.64/4.84 @ A4 )
% 8.64/4.84 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5156_sum__constant,axiom,
% 8.64/4.84 ! [Y: rat,A4: set_complex] :
% 8.64/4.84 ( ( groups5058264527183730370ex_rat
% 8.64/4.84 @ ^ [X4: complex] : Y
% 8.64/4.84 @ A4 )
% 8.64/4.84 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 8.64/4.84
% 8.64/4.84 thf(fact_5157_sum__constant,axiom,
% 8.64/4.84 ! [Y: rat,A4: set_int] :
% 8.64/4.84 ( ( groups3906332499630173760nt_rat
% 8.64/4.84 @ ^ [X4: int] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5158_sum__constant,axiom,
% 8.64/4.85 ! [Y: real,A4: set_complex] :
% 8.64/4.85 ( ( groups5808333547571424918x_real
% 8.64/4.85 @ ^ [X4: complex] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5159_sum__constant,axiom,
% 8.64/4.85 ! [Y: real,A4: set_int] :
% 8.64/4.85 ( ( groups8778361861064173332t_real
% 8.64/4.85 @ ^ [X4: int] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5160_sum__constant,axiom,
% 8.64/4.85 ! [Y: int,A4: set_nat] :
% 8.64/4.85 ( ( groups3539618377306564664at_int
% 8.64/4.85 @ ^ [X4: nat] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5161_sum__constant,axiom,
% 8.64/4.85 ! [Y: int,A4: set_complex] :
% 8.64/4.85 ( ( groups5690904116761175830ex_int
% 8.64/4.85 @ ^ [X4: complex] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5162_sum__constant,axiom,
% 8.64/4.85 ! [Y: nat,A4: set_complex] :
% 8.64/4.85 ( ( groups5693394587270226106ex_nat
% 8.64/4.85 @ ^ [X4: complex] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5163_sum__constant,axiom,
% 8.64/4.85 ! [Y: nat,A4: set_int] :
% 8.64/4.85 ( ( groups4541462559716669496nt_nat
% 8.64/4.85 @ ^ [X4: int] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5164_sum__constant,axiom,
% 8.64/4.85 ! [Y: nat,A4: set_nat] :
% 8.64/4.85 ( ( groups3542108847815614940at_nat
% 8.64/4.85 @ ^ [X4: nat] : Y
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_nat @ A4 ) ) @ Y ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5165_even__mult__iff,axiom,
% 8.64/4.85 ! [A: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 8.64/4.85 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5166_even__mult__iff,axiom,
% 8.64/4.85 ! [A: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 8.64/4.85 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5167_even__Suc__Suc__iff,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 8.64/4.85 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5168_even__Suc,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 8.64/4.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5169_powser__sums__zero__iff,axiom,
% 8.64/4.85 ! [A: nat > complex,X: complex] :
% 8.64/4.85 ( ( sums_complex
% 8.64/4.85 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 8.64/4.85 @ X )
% 8.64/4.85 = ( ( A @ zero_zero_nat )
% 8.64/4.85 = X ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5170_powser__sums__zero__iff,axiom,
% 8.64/4.85 ! [A: nat > real,X: real] :
% 8.64/4.85 ( ( sums_real
% 8.64/4.85 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 8.64/4.85 @ X )
% 8.64/4.85 = ( ( A @ zero_zero_nat )
% 8.64/4.85 = X ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5171_even__Suc__div__two,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.85 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.85 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5172_odd__Suc__div__two,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.85 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.85 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5173_sum_Ocl__ivl__Suc,axiom,
% 8.64/4.85 ! [N: nat,M2: nat,G2: nat > complex] :
% 8.64/4.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5174_sum_Ocl__ivl__Suc,axiom,
% 8.64/4.85 ! [N: nat,M2: nat,G2: nat > rat] :
% 8.64/4.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = zero_zero_rat ) )
% 8.64/4.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5175_sum_Ocl__ivl__Suc,axiom,
% 8.64/4.85 ! [N: nat,M2: nat,G2: nat > int] :
% 8.64/4.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = zero_zero_int ) )
% 8.64/4.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5176_sum_Ocl__ivl__Suc,axiom,
% 8.64/4.85 ! [N: nat,M2: nat,G2: nat > nat] :
% 8.64/4.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = zero_zero_nat ) )
% 8.64/4.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5177_sum_Ocl__ivl__Suc,axiom,
% 8.64/4.85 ! [N: nat,M2: nat,G2: nat > real] :
% 8.64/4.85 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = zero_zero_real ) )
% 8.64/4.85 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.85 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.85 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5178_sum__zero__power,axiom,
% 8.64/4.85 ! [A4: set_nat,C2: nat > complex] :
% 8.64/4.85 ( ( ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2073611262835488442omplex
% 8.64/4.85 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( C2 @ zero_zero_nat ) ) )
% 8.64/4.85 & ( ~ ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2073611262835488442omplex
% 8.64/4.85 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = zero_zero_complex ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5179_sum__zero__power,axiom,
% 8.64/4.85 ! [A4: set_nat,C2: nat > rat] :
% 8.64/4.85 ( ( ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2906978787729119204at_rat
% 8.64/4.85 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( C2 @ zero_zero_nat ) ) )
% 8.64/4.85 & ( ~ ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2906978787729119204at_rat
% 8.64/4.85 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5180_sum__zero__power,axiom,
% 8.64/4.85 ! [A4: set_nat,C2: nat > real] :
% 8.64/4.85 ( ( ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( C2 @ zero_zero_nat ) ) )
% 8.64/4.85 & ( ~ ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5181_zero__le__power__eq__numeral,axiom,
% 8.64/4.85 ! [A: real,W2: num] :
% 8.64/4.85 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 8.64/4.85 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5182_zero__le__power__eq__numeral,axiom,
% 8.64/4.85 ! [A: rat,W2: num] :
% 8.64/4.85 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 8.64/4.85 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5183_zero__le__power__eq__numeral,axiom,
% 8.64/4.85 ! [A: int,W2: num] :
% 8.64/4.85 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 8.64/4.85 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5184_even__power,axiom,
% 8.64/4.85 ! [A: nat,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 8.64/4.85 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5185_even__power,axiom,
% 8.64/4.85 ! [A: int,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 8.64/4.85 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5186_power__less__zero__eq,axiom,
% 8.64/4.85 ! [A: real,N: nat] :
% 8.64/4.85 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 8.64/4.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.85 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5187_power__less__zero__eq,axiom,
% 8.64/4.85 ! [A: rat,N: nat] :
% 8.64/4.85 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 8.64/4.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.85 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5188_power__less__zero__eq,axiom,
% 8.64/4.85 ! [A: int,N: nat] :
% 8.64/4.85 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 8.64/4.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.85 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5189_power__less__zero__eq__numeral,axiom,
% 8.64/4.85 ! [A: real,W2: num] :
% 8.64/4.85 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 8.64/4.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5190_power__less__zero__eq__numeral,axiom,
% 8.64/4.85 ! [A: rat,W2: num] :
% 8.64/4.85 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 8.64/4.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5191_power__less__zero__eq__numeral,axiom,
% 8.64/4.85 ! [A: int,W2: num] :
% 8.64/4.85 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 8.64/4.85 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5192_odd__Suc__minus__one,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.85 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 8.64/4.85 = N ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5193_sum__zero__power_H,axiom,
% 8.64/4.85 ! [A4: set_nat,C2: nat > complex,D: nat > complex] :
% 8.64/4.85 ( ( ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2073611262835488442omplex
% 8.64/4.85 @ ^ [I: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) ) @ ( D @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( divide1717551699836669952omplex @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 8.64/4.85 & ( ~ ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2073611262835488442omplex
% 8.64/4.85 @ ^ [I: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ zero_zero_complex @ I ) ) @ ( D @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = zero_zero_complex ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5194_sum__zero__power_H,axiom,
% 8.64/4.85 ! [A4: set_nat,C2: nat > rat,D: nat > rat] :
% 8.64/4.85 ( ( ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2906978787729119204at_rat
% 8.64/4.85 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( divide_divide_rat @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 8.64/4.85 & ( ~ ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups2906978787729119204at_rat
% 8.64/4.85 @ ^ [I: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ zero_zero_rat @ I ) ) @ ( D @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5195_sum__zero__power_H,axiom,
% 8.64/4.85 ! [A4: set_nat,C2: nat > real,D: nat > real] :
% 8.64/4.85 ( ( ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [I: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) ) @ ( D @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = ( divide_divide_real @ ( C2 @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 8.64/4.85 & ( ~ ( ( finite_finite_nat @ A4 )
% 8.64/4.85 & ( member_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.85 => ( ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [I: nat] : ( divide_divide_real @ ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ zero_zero_real @ I ) ) @ ( D @ I ) )
% 8.64/4.85 @ A4 )
% 8.64/4.85 = zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5196_odd__two__times__div__two__succ,axiom,
% 8.64/4.85 ! [A: code_integer] :
% 8.64/4.85 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 8.64/4.85 = A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5197_odd__two__times__div__two__succ,axiom,
% 8.64/4.85 ! [A: nat] :
% 8.64/4.85 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 8.64/4.85 = A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5198_odd__two__times__div__two__succ,axiom,
% 8.64/4.85 ! [A: int] :
% 8.64/4.85 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 8.64/4.85 = A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5199_semiring__parity__class_Oeven__mask__iff,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 8.64/4.85 = ( N = zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5200_semiring__parity__class_Oeven__mask__iff,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 8.64/4.85 = ( N = zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5201_semiring__parity__class_Oeven__mask__iff,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 8.64/4.85 = ( N = zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5202_zero__less__power__eq__numeral,axiom,
% 8.64/4.85 ! [A: real,W2: num] :
% 8.64/4.85 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 8.64/4.85 = ( ( ( numeral_numeral_nat @ W2 )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( A != zero_zero_real ) )
% 8.64/4.85 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5203_zero__less__power__eq__numeral,axiom,
% 8.64/4.85 ! [A: rat,W2: num] :
% 8.64/4.85 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 8.64/4.85 = ( ( ( numeral_numeral_nat @ W2 )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( A != zero_zero_rat ) )
% 8.64/4.85 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5204_zero__less__power__eq__numeral,axiom,
% 8.64/4.85 ! [A: int,W2: num] :
% 8.64/4.85 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 8.64/4.85 = ( ( ( numeral_numeral_nat @ W2 )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( A != zero_zero_int ) )
% 8.64/4.85 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5205_odd__two__times__div__two__nat,axiom,
% 8.64/4.85 ! [N: nat] :
% 8.64/4.85 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.85 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.85 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5206_power__le__zero__eq__numeral,axiom,
% 8.64/4.85 ! [A: real,W2: num] :
% 8.64/4.85 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_real )
% 8.64/4.85 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 8.64/4.85 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( A = zero_zero_real ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5207_power__le__zero__eq__numeral,axiom,
% 8.64/4.85 ! [A: rat,W2: num] :
% 8.64/4.85 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 8.64/4.85 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 8.64/4.85 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( A = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5208_power__le__zero__eq__numeral,axiom,
% 8.64/4.85 ! [A: int,W2: num] :
% 8.64/4.85 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 8.64/4.85 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 8.64/4.85 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 8.64/4.85 & ( A = zero_zero_int ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5209_even__succ__div__exp,axiom,
% 8.64/4.85 ! [A: code_integer,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.85 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.85 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5210_even__succ__div__exp,axiom,
% 8.64/4.85 ! [A: nat,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.85 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.85 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5211_even__succ__div__exp,axiom,
% 8.64/4.85 ! [A: int,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.85 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.85 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5212_even__succ__mod__exp,axiom,
% 8.64/4.85 ! [A: code_integer,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.85 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.85 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5213_even__succ__mod__exp,axiom,
% 8.64/4.85 ! [A: nat,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.85 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.85 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5214_even__succ__mod__exp,axiom,
% 8.64/4.85 ! [A: int,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.85 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.85 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5215_even__succ__mod__exp,axiom,
% 8.64/4.85 ! [A: code_natural,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 8.64/4.85 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.85 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.85 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5216_sum_Oneutral,axiom,
% 8.64/4.85 ! [A4: set_nat,G2: nat > nat] :
% 8.64/4.85 ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ( G2 @ X3 )
% 8.64/4.85 = zero_zero_nat ) )
% 8.64/4.85 => ( ( groups3542108847815614940at_nat @ G2 @ A4 )
% 8.64/4.85 = zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5217_sum_Oneutral,axiom,
% 8.64/4.85 ! [A4: set_int,G2: int > int] :
% 8.64/4.85 ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ( G2 @ X3 )
% 8.64/4.85 = zero_zero_int ) )
% 8.64/4.85 => ( ( groups4538972089207619220nt_int @ G2 @ A4 )
% 8.64/4.85 = zero_zero_int ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5218_sum_Oneutral,axiom,
% 8.64/4.85 ! [A4: set_nat,G2: nat > real] :
% 8.64/4.85 ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ( G2 @ X3 )
% 8.64/4.85 = zero_zero_real ) )
% 8.64/4.85 => ( ( groups6591440286371151544t_real @ G2 @ A4 )
% 8.64/4.85 = zero_zero_real ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5219_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: complex > complex,A4: set_complex] :
% 8.64/4.85 ( ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 8.64/4.85 != zero_zero_complex )
% 8.64/4.85 => ~ ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5220_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: real > complex,A4: set_real] :
% 8.64/4.85 ( ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 8.64/4.85 != zero_zero_complex )
% 8.64/4.85 => ~ ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5221_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: nat > complex,A4: set_nat] :
% 8.64/4.85 ( ( ( groups2073611262835488442omplex @ G2 @ A4 )
% 8.64/4.85 != zero_zero_complex )
% 8.64/4.85 => ~ ! [A3: nat] :
% 8.64/4.85 ( ( member_nat @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5222_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: int > complex,A4: set_int] :
% 8.64/4.85 ( ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 8.64/4.85 != zero_zero_complex )
% 8.64/4.85 => ~ ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5223_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: complex > real,A4: set_complex] :
% 8.64/4.85 ( ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 8.64/4.85 != zero_zero_real )
% 8.64/4.85 => ~ ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5224_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: real > real,A4: set_real] :
% 8.64/4.85 ( ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 8.64/4.85 != zero_zero_real )
% 8.64/4.85 => ~ ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5225_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: int > real,A4: set_int] :
% 8.64/4.85 ( ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 8.64/4.85 != zero_zero_real )
% 8.64/4.85 => ~ ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5226_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: complex > rat,A4: set_complex] :
% 8.64/4.85 ( ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 8.64/4.85 != zero_zero_rat )
% 8.64/4.85 => ~ ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5227_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: real > rat,A4: set_real] :
% 8.64/4.85 ( ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 8.64/4.85 != zero_zero_rat )
% 8.64/4.85 => ~ ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5228_sum_Onot__neutral__contains__not__neutral,axiom,
% 8.64/4.85 ! [G2: nat > rat,A4: set_nat] :
% 8.64/4.85 ( ( ( groups2906978787729119204at_rat @ G2 @ A4 )
% 8.64/4.85 != zero_zero_rat )
% 8.64/4.85 => ~ ! [A3: nat] :
% 8.64/4.85 ( ( member_nat @ A3 @ A4 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5229_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_complex,F2: complex > rat,G2: complex > rat] :
% 8.64/4.85 ( ! [I3: complex] :
% 8.64/4.85 ( ( member_complex @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ K5 ) @ ( groups5058264527183730370ex_rat @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5230_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_real,F2: real > rat,G2: real > rat] :
% 8.64/4.85 ( ! [I3: real] :
% 8.64/4.85 ( ( member_real @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ K5 ) @ ( groups1300246762558778688al_rat @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5231_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_nat,F2: nat > rat,G2: nat > rat] :
% 8.64/4.85 ( ! [I3: nat] :
% 8.64/4.85 ( ( member_nat @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ K5 ) @ ( groups2906978787729119204at_rat @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5232_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_int,F2: int > rat,G2: int > rat] :
% 8.64/4.85 ( ! [I3: int] :
% 8.64/4.85 ( ( member_int @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ K5 ) @ ( groups3906332499630173760nt_rat @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5233_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_complex,F2: complex > nat,G2: complex > nat] :
% 8.64/4.85 ( ! [I3: complex] :
% 8.64/4.85 ( ( member_complex @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ K5 ) @ ( groups5693394587270226106ex_nat @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5234_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_real,F2: real > nat,G2: real > nat] :
% 8.64/4.85 ( ! [I3: real] :
% 8.64/4.85 ( ( member_real @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ K5 ) @ ( groups1935376822645274424al_nat @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5235_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_int,F2: int > nat,G2: int > nat] :
% 8.64/4.85 ( ! [I3: int] :
% 8.64/4.85 ( ( member_int @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ K5 ) @ ( groups4541462559716669496nt_nat @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5236_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_complex,F2: complex > int,G2: complex > int] :
% 8.64/4.85 ( ! [I3: complex] :
% 8.64/4.85 ( ( member_complex @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F2 @ K5 ) @ ( groups5690904116761175830ex_int @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5237_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_real,F2: real > int,G2: real > int] :
% 8.64/4.85 ( ! [I3: real] :
% 8.64/4.85 ( ( member_real @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F2 @ K5 ) @ ( groups1932886352136224148al_int @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5238_sum__mono,axiom,
% 8.64/4.85 ! [K5: set_nat,F2: nat > int,G2: nat > int] :
% 8.64/4.85 ( ! [I3: nat] :
% 8.64/4.85 ( ( member_nat @ I3 @ K5 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ K5 ) @ ( groups3539618377306564664at_int @ G2 @ K5 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5239_sum__distrib__left,axiom,
% 8.64/4.85 ! [R3: nat,F2: nat > nat,A4: set_nat] :
% 8.64/4.85 ( ( times_times_nat @ R3 @ ( groups3542108847815614940at_nat @ F2 @ A4 ) )
% 8.64/4.85 = ( groups3542108847815614940at_nat
% 8.64/4.85 @ ^ [N4: nat] : ( times_times_nat @ R3 @ ( F2 @ N4 ) )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5240_sum__distrib__left,axiom,
% 8.64/4.85 ! [R3: int,F2: int > int,A4: set_int] :
% 8.64/4.85 ( ( times_times_int @ R3 @ ( groups4538972089207619220nt_int @ F2 @ A4 ) )
% 8.64/4.85 = ( groups4538972089207619220nt_int
% 8.64/4.85 @ ^ [N4: int] : ( times_times_int @ R3 @ ( F2 @ N4 ) )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5241_sum__distrib__left,axiom,
% 8.64/4.85 ! [R3: real,F2: nat > real,A4: set_nat] :
% 8.64/4.85 ( ( times_times_real @ R3 @ ( groups6591440286371151544t_real @ F2 @ A4 ) )
% 8.64/4.85 = ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [N4: nat] : ( times_times_real @ R3 @ ( F2 @ N4 ) )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5242_sum__distrib__right,axiom,
% 8.64/4.85 ! [F2: nat > nat,A4: set_nat,R3: nat] :
% 8.64/4.85 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ R3 )
% 8.64/4.85 = ( groups3542108847815614940at_nat
% 8.64/4.85 @ ^ [N4: nat] : ( times_times_nat @ ( F2 @ N4 ) @ R3 )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5243_sum__distrib__right,axiom,
% 8.64/4.85 ! [F2: int > int,A4: set_int,R3: int] :
% 8.64/4.85 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) @ R3 )
% 8.64/4.85 = ( groups4538972089207619220nt_int
% 8.64/4.85 @ ^ [N4: int] : ( times_times_int @ ( F2 @ N4 ) @ R3 )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5244_sum__distrib__right,axiom,
% 8.64/4.85 ! [F2: nat > real,A4: set_nat,R3: real] :
% 8.64/4.85 ( ( times_times_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ R3 )
% 8.64/4.85 = ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ R3 )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5245_sum__product,axiom,
% 8.64/4.85 ! [F2: nat > nat,A4: set_nat,G2: nat > nat,B5: set_nat] :
% 8.64/4.85 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ B5 ) )
% 8.64/4.85 = ( groups3542108847815614940at_nat
% 8.64/4.85 @ ^ [I: nat] :
% 8.64/4.85 ( groups3542108847815614940at_nat
% 8.64/4.85 @ ^ [J: nat] : ( times_times_nat @ ( F2 @ I ) @ ( G2 @ J ) )
% 8.64/4.85 @ B5 )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5246_sum__product,axiom,
% 8.64/4.85 ! [F2: int > int,A4: set_int,G2: int > int,B5: set_int] :
% 8.64/4.85 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) @ ( groups4538972089207619220nt_int @ G2 @ B5 ) )
% 8.64/4.85 = ( groups4538972089207619220nt_int
% 8.64/4.85 @ ^ [I: int] :
% 8.64/4.85 ( groups4538972089207619220nt_int
% 8.64/4.85 @ ^ [J: int] : ( times_times_int @ ( F2 @ I ) @ ( G2 @ J ) )
% 8.64/4.85 @ B5 )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5247_sum__product,axiom,
% 8.64/4.85 ! [F2: nat > real,A4: set_nat,G2: nat > real,B5: set_nat] :
% 8.64/4.85 ( ( times_times_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ ( groups6591440286371151544t_real @ G2 @ B5 ) )
% 8.64/4.85 = ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [I: nat] :
% 8.64/4.85 ( groups6591440286371151544t_real
% 8.64/4.85 @ ^ [J: nat] : ( times_times_real @ ( F2 @ I ) @ ( G2 @ J ) )
% 8.64/4.85 @ B5 )
% 8.64/4.85 @ A4 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5248_dvd__antisym,axiom,
% 8.64/4.85 ! [M2: nat,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ M2 @ N )
% 8.64/4.85 => ( ( dvd_dvd_nat @ N @ M2 )
% 8.64/4.85 => ( M2 = N ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5249_dvd__trans,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ B @ C2 )
% 8.64/4.85 => ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5250_dvd__trans,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ B @ C2 )
% 8.64/4.85 => ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5251_dvd__refl,axiom,
% 8.64/4.85 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5252_dvd__refl,axiom,
% 8.64/4.85 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5253_dvd__field__iff,axiom,
% 8.64/4.85 ( dvd_dvd_complex
% 8.64/4.85 = ( ^ [A5: complex,B4: complex] :
% 8.64/4.85 ( ( A5 = zero_zero_complex )
% 8.64/4.85 => ( B4 = zero_zero_complex ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5254_dvd__field__iff,axiom,
% 8.64/4.85 ( dvd_dvd_real
% 8.64/4.85 = ( ^ [A5: real,B4: real] :
% 8.64/4.85 ( ( A5 = zero_zero_real )
% 8.64/4.85 => ( B4 = zero_zero_real ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5255_dvd__field__iff,axiom,
% 8.64/4.85 ( dvd_dvd_rat
% 8.64/4.85 = ( ^ [A5: rat,B4: rat] :
% 8.64/4.85 ( ( A5 = zero_zero_rat )
% 8.64/4.85 => ( B4 = zero_zero_rat ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5256_dvd__0__left,axiom,
% 8.64/4.85 ! [A: complex] :
% 8.64/4.85 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 8.64/4.85 => ( A = zero_zero_complex ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5257_dvd__0__left,axiom,
% 8.64/4.85 ! [A: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 8.64/4.85 => ( A = zero_zero_real ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5258_dvd__0__left,axiom,
% 8.64/4.85 ! [A: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 8.64/4.85 => ( A = zero_zero_rat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5259_dvd__0__left,axiom,
% 8.64/4.85 ! [A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.64/4.85 => ( A = zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5260_dvd__0__left,axiom,
% 8.64/4.85 ! [A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 8.64/4.85 => ( A = zero_zero_int ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5261_dvd__productE,axiom,
% 8.64/4.85 ! [P: nat,A: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ P @ ( times_times_nat @ A @ B ) )
% 8.64/4.85 => ~ ! [X3: nat,Y3: nat] :
% 8.64/4.85 ( ( P
% 8.64/4.85 = ( times_times_nat @ X3 @ Y3 ) )
% 8.64/4.85 => ( ( dvd_dvd_nat @ X3 @ A )
% 8.64/4.85 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5262_dvd__productE,axiom,
% 8.64/4.85 ! [P: int,A: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ P @ ( times_times_int @ A @ B ) )
% 8.64/4.85 => ~ ! [X3: int,Y3: int] :
% 8.64/4.85 ( ( P
% 8.64/4.85 = ( times_times_int @ X3 @ Y3 ) )
% 8.64/4.85 => ( ( dvd_dvd_int @ X3 @ A )
% 8.64/4.85 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5263_division__decomp,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.85 => ? [B9: nat,C5: nat] :
% 8.64/4.85 ( ( A
% 8.64/4.85 = ( times_times_nat @ B9 @ C5 ) )
% 8.64/4.85 & ( dvd_dvd_nat @ B9 @ B )
% 8.64/4.85 & ( dvd_dvd_nat @ C5 @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5264_division__decomp,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.85 => ? [B9: int,C5: int] :
% 8.64/4.85 ( ( A
% 8.64/4.85 = ( times_times_int @ B9 @ C5 ) )
% 8.64/4.85 & ( dvd_dvd_int @ B9 @ B )
% 8.64/4.85 & ( dvd_dvd_int @ C5 @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5265_dvdE,axiom,
% 8.64/4.85 ! [B: real,A: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ B @ A )
% 8.64/4.85 => ~ ! [K: real] :
% 8.64/4.85 ( A
% 8.64/4.85 != ( times_times_real @ B @ K ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5266_dvdE,axiom,
% 8.64/4.85 ! [B: rat,A: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ B @ A )
% 8.64/4.85 => ~ ! [K: rat] :
% 8.64/4.85 ( A
% 8.64/4.85 != ( times_times_rat @ B @ K ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5267_dvdE,axiom,
% 8.64/4.85 ! [B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ A )
% 8.64/4.85 => ~ ! [K: nat] :
% 8.64/4.85 ( A
% 8.64/4.85 != ( times_times_nat @ B @ K ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5268_dvdE,axiom,
% 8.64/4.85 ! [B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ A )
% 8.64/4.85 => ~ ! [K: int] :
% 8.64/4.85 ( A
% 8.64/4.85 != ( times_times_int @ B @ K ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5269_dvdI,axiom,
% 8.64/4.85 ! [A: real,B: real,K2: real] :
% 8.64/4.85 ( ( A
% 8.64/4.85 = ( times_times_real @ B @ K2 ) )
% 8.64/4.85 => ( dvd_dvd_real @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5270_dvdI,axiom,
% 8.64/4.85 ! [A: rat,B: rat,K2: rat] :
% 8.64/4.85 ( ( A
% 8.64/4.85 = ( times_times_rat @ B @ K2 ) )
% 8.64/4.85 => ( dvd_dvd_rat @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5271_dvdI,axiom,
% 8.64/4.85 ! [A: nat,B: nat,K2: nat] :
% 8.64/4.85 ( ( A
% 8.64/4.85 = ( times_times_nat @ B @ K2 ) )
% 8.64/4.85 => ( dvd_dvd_nat @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5272_dvdI,axiom,
% 8.64/4.85 ! [A: int,B: int,K2: int] :
% 8.64/4.85 ( ( A
% 8.64/4.85 = ( times_times_int @ B @ K2 ) )
% 8.64/4.85 => ( dvd_dvd_int @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5273_dvd__def,axiom,
% 8.64/4.85 ( dvd_dvd_real
% 8.64/4.85 = ( ^ [B4: real,A5: real] :
% 8.64/4.85 ? [K3: real] :
% 8.64/4.85 ( A5
% 8.64/4.85 = ( times_times_real @ B4 @ K3 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5274_dvd__def,axiom,
% 8.64/4.85 ( dvd_dvd_rat
% 8.64/4.85 = ( ^ [B4: rat,A5: rat] :
% 8.64/4.85 ? [K3: rat] :
% 8.64/4.85 ( A5
% 8.64/4.85 = ( times_times_rat @ B4 @ K3 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5275_dvd__def,axiom,
% 8.64/4.85 ( dvd_dvd_nat
% 8.64/4.85 = ( ^ [B4: nat,A5: nat] :
% 8.64/4.85 ? [K3: nat] :
% 8.64/4.85 ( A5
% 8.64/4.85 = ( times_times_nat @ B4 @ K3 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5276_dvd__def,axiom,
% 8.64/4.85 ( dvd_dvd_int
% 8.64/4.85 = ( ^ [B4: int,A5: int] :
% 8.64/4.85 ? [K3: int] :
% 8.64/4.85 ( A5
% 8.64/4.85 = ( times_times_int @ B4 @ K3 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5277_dvd__mult,axiom,
% 8.64/4.85 ! [A: real,C2: real,B: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5278_dvd__mult,axiom,
% 8.64/4.85 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5279_dvd__mult,axiom,
% 8.64/4.85 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5280_dvd__mult,axiom,
% 8.64/4.85 ! [A: int,C2: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5281_dvd__mult2,axiom,
% 8.64/4.85 ! [A: real,B: real,C2: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ A @ B )
% 8.64/4.85 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5282_dvd__mult2,axiom,
% 8.64/4.85 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ A @ B )
% 8.64/4.85 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5283_dvd__mult2,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.85 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5284_dvd__mult2,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.85 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5285_dvd__mult__left,axiom,
% 8.64/4.85 ! [A: real,B: real,C2: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_real @ A @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5286_dvd__mult__left,axiom,
% 8.64/4.85 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_rat @ A @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5287_dvd__mult__left,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_nat @ A @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5288_dvd__mult__left,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_int @ A @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5289_dvd__triv__left,axiom,
% 8.64/4.85 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5290_dvd__triv__left,axiom,
% 8.64/4.85 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5291_dvd__triv__left,axiom,
% 8.64/4.85 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5292_dvd__triv__left,axiom,
% 8.64/4.85 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5293_mult__dvd__mono,axiom,
% 8.64/4.85 ! [A: real,B: real,C2: real,D: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_real @ C2 @ D )
% 8.64/4.85 => ( dvd_dvd_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5294_mult__dvd__mono,axiom,
% 8.64/4.85 ! [A: rat,B: rat,C2: rat,D: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_rat @ C2 @ D )
% 8.64/4.85 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C2 ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5295_mult__dvd__mono,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat,D: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ C2 @ D )
% 8.64/4.85 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5296_mult__dvd__mono,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int,D: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ C2 @ D )
% 8.64/4.85 => ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5297_dvd__mult__right,axiom,
% 8.64/4.85 ! [A: real,B: real,C2: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_real @ B @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5298_dvd__mult__right,axiom,
% 8.64/4.85 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_rat @ B @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5299_dvd__mult__right,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_nat @ B @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5300_dvd__mult__right,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.64/4.85 => ( dvd_dvd_int @ B @ C2 ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5301_dvd__triv__right,axiom,
% 8.64/4.85 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5302_dvd__triv__right,axiom,
% 8.64/4.85 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5303_dvd__triv__right,axiom,
% 8.64/4.85 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5304_dvd__triv__right,axiom,
% 8.64/4.85 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5305_dvd__add__right__iff,axiom,
% 8.64/4.85 ! [A: real,B: real,C2: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_real @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5306_dvd__add__right__iff,axiom,
% 8.64/4.85 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_rat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5307_dvd__add__right__iff,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5308_dvd__add__right__iff,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5309_dvd__add__left__iff,axiom,
% 8.64/4.85 ! [A: real,C2: real,B: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ A @ C2 )
% 8.64/4.85 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5310_dvd__add__left__iff,axiom,
% 8.64/4.85 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ A @ C2 )
% 8.64/4.85 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5311_dvd__add__left__iff,axiom,
% 8.64/4.85 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ C2 )
% 8.64/4.85 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5312_dvd__add__left__iff,axiom,
% 8.64/4.85 ! [A: int,C2: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ C2 )
% 8.64/4.85 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5313_dvd__add,axiom,
% 8.64/4.85 ! [A: real,B: real,C2: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_real @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5314_dvd__add,axiom,
% 8.64/4.85 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_rat @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5315_dvd__add,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5316_dvd__add,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ A @ C2 )
% 8.64/4.85 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5317_dvd__unit__imp__unit,axiom,
% 8.64/4.85 ! [A: code_integer,B: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.85 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5318_dvd__unit__imp__unit,axiom,
% 8.64/4.85 ! [A: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.85 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5319_dvd__unit__imp__unit,axiom,
% 8.64/4.85 ! [A: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.85 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5320_unit__imp__dvd,axiom,
% 8.64/4.85 ! [B: code_integer,A: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.85 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5321_unit__imp__dvd,axiom,
% 8.64/4.85 ! [B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.85 => ( dvd_dvd_nat @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5322_unit__imp__dvd,axiom,
% 8.64/4.85 ! [B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.85 => ( dvd_dvd_int @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5323_one__dvd,axiom,
% 8.64/4.85 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5324_one__dvd,axiom,
% 8.64/4.85 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5325_one__dvd,axiom,
% 8.64/4.85 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5326_one__dvd,axiom,
% 8.64/4.85 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5327_one__dvd,axiom,
% 8.64/4.85 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5328_dvd__diff,axiom,
% 8.64/4.85 ! [X: rat,Y: rat,Z3: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ X @ Y )
% 8.64/4.85 => ( ( dvd_dvd_rat @ X @ Z3 )
% 8.64/4.85 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z3 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5329_dvd__diff,axiom,
% 8.64/4.85 ! [X: int,Y: int,Z3: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ X @ Y )
% 8.64/4.85 => ( ( dvd_dvd_int @ X @ Z3 )
% 8.64/4.85 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z3 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5330_div__div__div__same,axiom,
% 8.64/4.85 ! [D: nat,B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ D @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ B @ A )
% 8.64/4.85 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 8.64/4.85 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5331_div__div__div__same,axiom,
% 8.64/4.85 ! [D: int,B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ D @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ B @ A )
% 8.64/4.85 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 8.64/4.85 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5332_dvd__div__eq__cancel,axiom,
% 8.64/4.85 ! [A: complex,C2: complex,B: complex] :
% 8.64/4.85 ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 8.64/4.85 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.85 => ( ( dvd_dvd_complex @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_complex @ C2 @ B )
% 8.64/4.85 => ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5333_dvd__div__eq__cancel,axiom,
% 8.64/4.85 ! [A: real,C2: real,B: real] :
% 8.64/4.85 ( ( ( divide_divide_real @ A @ C2 )
% 8.64/4.85 = ( divide_divide_real @ B @ C2 ) )
% 8.64/4.85 => ( ( dvd_dvd_real @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_real @ C2 @ B )
% 8.64/4.85 => ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5334_dvd__div__eq__cancel,axiom,
% 8.64/4.85 ! [A: rat,C2: rat,B: rat] :
% 8.64/4.85 ( ( ( divide_divide_rat @ A @ C2 )
% 8.64/4.85 = ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.85 => ( ( dvd_dvd_rat @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_rat @ C2 @ B )
% 8.64/4.85 => ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5335_dvd__div__eq__cancel,axiom,
% 8.64/4.85 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.85 ( ( ( divide_divide_nat @ A @ C2 )
% 8.64/4.85 = ( divide_divide_nat @ B @ C2 ) )
% 8.64/4.85 => ( ( dvd_dvd_nat @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.85 => ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5336_dvd__div__eq__cancel,axiom,
% 8.64/4.85 ! [A: int,C2: int,B: int] :
% 8.64/4.85 ( ( ( divide_divide_int @ A @ C2 )
% 8.64/4.85 = ( divide_divide_int @ B @ C2 ) )
% 8.64/4.85 => ( ( dvd_dvd_int @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.85 => ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5337_dvd__div__eq__iff,axiom,
% 8.64/4.85 ! [C2: complex,A: complex,B: complex] :
% 8.64/4.85 ( ( dvd_dvd_complex @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_complex @ C2 @ B )
% 8.64/4.85 => ( ( ( divide1717551699836669952omplex @ A @ C2 )
% 8.64/4.85 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.85 = ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5338_dvd__div__eq__iff,axiom,
% 8.64/4.85 ! [C2: real,A: real,B: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_real @ C2 @ B )
% 8.64/4.85 => ( ( ( divide_divide_real @ A @ C2 )
% 8.64/4.85 = ( divide_divide_real @ B @ C2 ) )
% 8.64/4.85 = ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5339_dvd__div__eq__iff,axiom,
% 8.64/4.85 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_rat @ C2 @ B )
% 8.64/4.85 => ( ( ( divide_divide_rat @ A @ C2 )
% 8.64/4.85 = ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.85 = ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5340_dvd__div__eq__iff,axiom,
% 8.64/4.85 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.85 => ( ( ( divide_divide_nat @ A @ C2 )
% 8.64/4.85 = ( divide_divide_nat @ B @ C2 ) )
% 8.64/4.85 = ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5341_dvd__div__eq__iff,axiom,
% 8.64/4.85 ! [C2: int,A: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ C2 @ A )
% 8.64/4.85 => ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.85 => ( ( ( divide_divide_int @ A @ C2 )
% 8.64/4.85 = ( divide_divide_int @ B @ C2 ) )
% 8.64/4.85 = ( A = B ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5342_gcd__nat_Oextremum,axiom,
% 8.64/4.85 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5343_gcd__nat_Oextremum__strict,axiom,
% 8.64/4.85 ! [A: nat] :
% 8.64/4.85 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.64/4.85 & ( zero_zero_nat != A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5344_gcd__nat_Oextremum__unique,axiom,
% 8.64/4.85 ! [A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.64/4.85 = ( A = zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5345_gcd__nat_Onot__eq__extremum,axiom,
% 8.64/4.85 ! [A: nat] :
% 8.64/4.85 ( ( A != zero_zero_nat )
% 8.64/4.85 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 8.64/4.85 & ( A != zero_zero_nat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5346_gcd__nat_Oextremum__uniqueI,axiom,
% 8.64/4.85 ! [A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 8.64/4.85 => ( A = zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5347_dvd__mod__imp__dvd,axiom,
% 8.64/4.85 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.85 => ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.85 => ( dvd_dvd_nat @ C2 @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5348_dvd__mod__imp__dvd,axiom,
% 8.64/4.85 ! [C2: int,A: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.85 => ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.85 => ( dvd_dvd_int @ C2 @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5349_dvd__mod__imp__dvd,axiom,
% 8.64/4.85 ! [C2: code_natural,A: code_natural,B: code_natural] :
% 8.64/4.85 ( ( dvd_dvd_Code_natural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.64/4.85 => ( ( dvd_dvd_Code_natural @ C2 @ B )
% 8.64/4.85 => ( dvd_dvd_Code_natural @ C2 @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5350_dvd__mod__iff,axiom,
% 8.64/4.85 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ C2 @ ( modulo_modulo_nat @ A @ B ) )
% 8.64/4.85 = ( dvd_dvd_nat @ C2 @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5351_dvd__mod__iff,axiom,
% 8.64/4.85 ! [C2: int,B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ C2 @ ( modulo_modulo_int @ A @ B ) )
% 8.64/4.85 = ( dvd_dvd_int @ C2 @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5352_dvd__mod__iff,axiom,
% 8.64/4.85 ! [C2: code_natural,B: code_natural,A: code_natural] :
% 8.64/4.85 ( ( dvd_dvd_Code_natural @ C2 @ B )
% 8.64/4.85 => ( ( dvd_dvd_Code_natural @ C2 @ ( modulo8411746178871703098atural @ A @ B ) )
% 8.64/4.85 = ( dvd_dvd_Code_natural @ C2 @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5353_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > real] :
% 8.64/4.85 ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5354_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > real] :
% 8.64/4.85 ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5355_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > real] :
% 8.64/4.85 ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5356_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > rat] :
% 8.64/4.85 ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5357_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > rat] :
% 8.64/4.85 ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5358_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > rat] :
% 8.64/4.85 ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5359_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > rat] :
% 8.64/4.85 ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5360_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > nat] :
% 8.64/4.85 ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5361_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > nat] :
% 8.64/4.85 ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5362_sum__nonneg,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > nat] :
% 8.64/4.85 ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5363_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > real] :
% 8.64/4.85 ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 8.64/4.85 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5364_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > real] :
% 8.64/4.85 ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 8.64/4.85 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5365_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > real] :
% 8.64/4.85 ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ ( F2 @ X3 ) @ zero_zero_real ) )
% 8.64/4.85 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ zero_zero_real ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5366_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > rat] :
% 8.64/4.85 ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5367_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > rat] :
% 8.64/4.85 ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5368_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > rat] :
% 8.64/4.85 ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5369_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > rat] :
% 8.64/4.85 ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ zero_zero_rat ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ zero_zero_rat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5370_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > nat] :
% 8.64/4.85 ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 8.64/4.85 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5371_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > nat] :
% 8.64/4.85 ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 8.64/4.85 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5372_sum__nonpos,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > nat] :
% 8.64/4.85 ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ zero_zero_nat ) )
% 8.64/4.85 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ zero_zero_nat ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5373_dvd__diff__nat,axiom,
% 8.64/4.85 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ K2 @ M2 )
% 8.64/4.85 => ( ( dvd_dvd_nat @ K2 @ N )
% 8.64/4.85 => ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5374_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: real > rat,I5: set_real,G2: real > rat,I2: real] :
% 8.64/4.85 ( ( ( groups1300246762558778688al_rat @ F2 @ I5 )
% 8.64/4.85 = ( groups1300246762558778688al_rat @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: real] :
% 8.64/4.85 ( ( member_real @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_real @ I2 @ I5 )
% 8.64/4.85 => ( ( finite_finite_real @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5375_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: nat > rat,I5: set_nat,G2: nat > rat,I2: nat] :
% 8.64/4.85 ( ( ( groups2906978787729119204at_rat @ F2 @ I5 )
% 8.64/4.85 = ( groups2906978787729119204at_rat @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: nat] :
% 8.64/4.85 ( ( member_nat @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_nat @ I2 @ I5 )
% 8.64/4.85 => ( ( finite_finite_nat @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5376_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: int > rat,I5: set_int,G2: int > rat,I2: int] :
% 8.64/4.85 ( ( ( groups3906332499630173760nt_rat @ F2 @ I5 )
% 8.64/4.85 = ( groups3906332499630173760nt_rat @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: int] :
% 8.64/4.85 ( ( member_int @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_int @ I2 @ I5 )
% 8.64/4.85 => ( ( finite_finite_int @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5377_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: complex > rat,I5: set_complex,G2: complex > rat,I2: complex] :
% 8.64/4.85 ( ( ( groups5058264527183730370ex_rat @ F2 @ I5 )
% 8.64/4.85 = ( groups5058264527183730370ex_rat @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: complex] :
% 8.64/4.85 ( ( member_complex @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5378_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: real > nat,I5: set_real,G2: real > nat,I2: real] :
% 8.64/4.85 ( ( ( groups1935376822645274424al_nat @ F2 @ I5 )
% 8.64/4.85 = ( groups1935376822645274424al_nat @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: real] :
% 8.64/4.85 ( ( member_real @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_real @ I2 @ I5 )
% 8.64/4.85 => ( ( finite_finite_real @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5379_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: int > nat,I5: set_int,G2: int > nat,I2: int] :
% 8.64/4.85 ( ( ( groups4541462559716669496nt_nat @ F2 @ I5 )
% 8.64/4.85 = ( groups4541462559716669496nt_nat @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: int] :
% 8.64/4.85 ( ( member_int @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_int @ I2 @ I5 )
% 8.64/4.85 => ( ( finite_finite_int @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5380_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: complex > nat,I5: set_complex,G2: complex > nat,I2: complex] :
% 8.64/4.85 ( ( ( groups5693394587270226106ex_nat @ F2 @ I5 )
% 8.64/4.85 = ( groups5693394587270226106ex_nat @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: complex] :
% 8.64/4.85 ( ( member_complex @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5381_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: real > int,I5: set_real,G2: real > int,I2: real] :
% 8.64/4.85 ( ( ( groups1932886352136224148al_int @ F2 @ I5 )
% 8.64/4.85 = ( groups1932886352136224148al_int @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: real] :
% 8.64/4.85 ( ( member_real @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_real @ I2 @ I5 )
% 8.64/4.85 => ( ( finite_finite_real @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5382_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: nat > int,I5: set_nat,G2: nat > int,I2: nat] :
% 8.64/4.85 ( ( ( groups3539618377306564664at_int @ F2 @ I5 )
% 8.64/4.85 = ( groups3539618377306564664at_int @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: nat] :
% 8.64/4.85 ( ( member_nat @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_nat @ I2 @ I5 )
% 8.64/4.85 => ( ( finite_finite_nat @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5383_sum__mono__inv,axiom,
% 8.64/4.85 ! [F2: complex > int,I5: set_complex,G2: complex > int,I2: complex] :
% 8.64/4.85 ( ( ( groups5690904116761175830ex_int @ F2 @ I5 )
% 8.64/4.85 = ( groups5690904116761175830ex_int @ G2 @ I5 ) )
% 8.64/4.85 => ( ! [I3: complex] :
% 8.64/4.85 ( ( member_complex @ I3 @ I5 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) )
% 8.64/4.85 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.85 => ( ( F2 @ I2 )
% 8.64/4.85 = ( G2 @ I2 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5384_sum__cong__Suc,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > nat,G2: nat > nat] :
% 8.64/4.85 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 8.64/4.85 => ( ( F2 @ ( suc @ X3 ) )
% 8.64/4.85 = ( G2 @ ( suc @ X3 ) ) ) )
% 8.64/4.85 => ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 8.64/4.85 = ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5385_sum__cong__Suc,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 8.64/4.85 ( ~ ( member_nat @ zero_zero_nat @ A4 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ ( suc @ X3 ) @ A4 )
% 8.64/4.85 => ( ( F2 @ ( suc @ X3 ) )
% 8.64/4.85 = ( G2 @ ( suc @ X3 ) ) ) )
% 8.64/4.85 => ( ( groups6591440286371151544t_real @ F2 @ A4 )
% 8.64/4.85 = ( groups6591440286371151544t_real @ G2 @ A4 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5386_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_real,G2: real > complex,P2: real > $o] :
% 8.64/4.85 ( ( finite_finite_real @ A4 )
% 8.64/4.85 => ( ( groups5754745047067104278omplex @ G2
% 8.64/4.85 @ ( collect_real
% 8.64/4.85 @ ^ [X4: real] :
% 8.64/4.85 ( ( member_real @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups5754745047067104278omplex
% 8.64/4.85 @ ^ [X4: real] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5387_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_nat,G2: nat > complex,P2: nat > $o] :
% 8.64/4.85 ( ( finite_finite_nat @ A4 )
% 8.64/4.85 => ( ( groups2073611262835488442omplex @ G2
% 8.64/4.85 @ ( collect_nat
% 8.64/4.85 @ ^ [X4: nat] :
% 8.64/4.85 ( ( member_nat @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups2073611262835488442omplex
% 8.64/4.85 @ ^ [X4: nat] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5388_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_int,G2: int > complex,P2: int > $o] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ( groups3049146728041665814omplex @ G2
% 8.64/4.85 @ ( collect_int
% 8.64/4.85 @ ^ [X4: int] :
% 8.64/4.85 ( ( member_int @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups3049146728041665814omplex
% 8.64/4.85 @ ^ [X4: int] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5389_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_complex,G2: complex > complex,P2: complex > $o] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ( groups7754918857620584856omplex @ G2
% 8.64/4.85 @ ( collect_complex
% 8.64/4.85 @ ^ [X4: complex] :
% 8.64/4.85 ( ( member_complex @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups7754918857620584856omplex
% 8.64/4.85 @ ^ [X4: complex] : ( if_complex @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5390_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_real,G2: real > real,P2: real > $o] :
% 8.64/4.85 ( ( finite_finite_real @ A4 )
% 8.64/4.85 => ( ( groups8097168146408367636l_real @ G2
% 8.64/4.85 @ ( collect_real
% 8.64/4.85 @ ^ [X4: real] :
% 8.64/4.85 ( ( member_real @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups8097168146408367636l_real
% 8.64/4.85 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5391_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_int,G2: int > real,P2: int > $o] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ( groups8778361861064173332t_real @ G2
% 8.64/4.85 @ ( collect_int
% 8.64/4.85 @ ^ [X4: int] :
% 8.64/4.85 ( ( member_int @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups8778361861064173332t_real
% 8.64/4.85 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5392_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_complex,G2: complex > real,P2: complex > $o] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ( groups5808333547571424918x_real @ G2
% 8.64/4.85 @ ( collect_complex
% 8.64/4.85 @ ^ [X4: complex] :
% 8.64/4.85 ( ( member_complex @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups5808333547571424918x_real
% 8.64/4.85 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5393_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_real,G2: real > rat,P2: real > $o] :
% 8.64/4.85 ( ( finite_finite_real @ A4 )
% 8.64/4.85 => ( ( groups1300246762558778688al_rat @ G2
% 8.64/4.85 @ ( collect_real
% 8.64/4.85 @ ^ [X4: real] :
% 8.64/4.85 ( ( member_real @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups1300246762558778688al_rat
% 8.64/4.85 @ ^ [X4: real] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5394_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_nat,G2: nat > rat,P2: nat > $o] :
% 8.64/4.85 ( ( finite_finite_nat @ A4 )
% 8.64/4.85 => ( ( groups2906978787729119204at_rat @ G2
% 8.64/4.85 @ ( collect_nat
% 8.64/4.85 @ ^ [X4: nat] :
% 8.64/4.85 ( ( member_nat @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups2906978787729119204at_rat
% 8.64/4.85 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5395_sum_Ointer__filter,axiom,
% 8.64/4.85 ! [A4: set_int,G2: int > rat,P2: int > $o] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ( groups3906332499630173760nt_rat @ G2
% 8.64/4.85 @ ( collect_int
% 8.64/4.85 @ ^ [X4: int] :
% 8.64/4.85 ( ( member_int @ X4 @ A4 )
% 8.64/4.85 & ( P2 @ X4 ) ) ) )
% 8.64/4.85 = ( groups3906332499630173760nt_rat
% 8.64/4.85 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 8.64/4.85 @ A4 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5396_subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: complex,B: complex] :
% 8.64/4.85 ( ( ord_le211207098394363844omplex
% 8.64/4.85 @ ( collect_complex
% 8.64/4.85 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 8.64/4.85 @ ( collect_complex
% 8.64/4.85 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 8.64/4.85 = ( dvd_dvd_complex @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5397_subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: real,B: real] :
% 8.64/4.85 ( ( ord_less_eq_set_real
% 8.64/4.85 @ ( collect_real
% 8.64/4.85 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 8.64/4.85 @ ( collect_real
% 8.64/4.85 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 8.64/4.85 = ( dvd_dvd_real @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5398_subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: int,B: int] :
% 8.64/4.85 ( ( ord_less_eq_set_int
% 8.64/4.85 @ ( collect_int
% 8.64/4.85 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 8.64/4.85 @ ( collect_int
% 8.64/4.85 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 8.64/4.85 = ( dvd_dvd_int @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5399_subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: nat,B: nat] :
% 8.64/4.85 ( ( ord_less_eq_set_nat
% 8.64/4.85 @ ( collect_nat
% 8.64/4.85 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 8.64/4.85 @ ( collect_nat
% 8.64/4.85 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ B ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5400_strict__subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: complex,B: complex] :
% 8.64/4.85 ( ( ord_less_set_complex
% 8.64/4.85 @ ( collect_complex
% 8.64/4.85 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 8.64/4.85 @ ( collect_complex
% 8.64/4.85 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 8.64/4.85 = ( ( dvd_dvd_complex @ A @ B )
% 8.64/4.85 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5401_strict__subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: real,B: real] :
% 8.64/4.85 ( ( ord_less_set_real
% 8.64/4.85 @ ( collect_real
% 8.64/4.85 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ A ) )
% 8.64/4.85 @ ( collect_real
% 8.64/4.85 @ ^ [C3: real] : ( dvd_dvd_real @ C3 @ B ) ) )
% 8.64/4.85 = ( ( dvd_dvd_real @ A @ B )
% 8.64/4.85 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5402_strict__subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: nat,B: nat] :
% 8.64/4.85 ( ( ord_less_set_nat
% 8.64/4.85 @ ( collect_nat
% 8.64/4.85 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 8.64/4.85 @ ( collect_nat
% 8.64/4.85 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 8.64/4.85 = ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.85 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5403_strict__subset__divisors__dvd,axiom,
% 8.64/4.85 ! [A: int,B: int] :
% 8.64/4.85 ( ( ord_less_set_int
% 8.64/4.85 @ ( collect_int
% 8.64/4.85 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 8.64/4.85 @ ( collect_int
% 8.64/4.85 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 8.64/4.85 = ( ( dvd_dvd_int @ A @ B )
% 8.64/4.85 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5404_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_int,T: set_int,G2: int > real,I2: int > int,F2: int > real] :
% 8.64/4.85 ( ( finite_finite_int @ S2 )
% 8.64/4.85 => ( ( finite_finite_int @ T )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: int] :
% 8.64/4.85 ( ( member_int @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ S2 ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5405_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_int,T: set_complex,G2: complex > real,I2: complex > int,F2: int > real] :
% 8.64/4.85 ( ( finite_finite_int @ S2 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ T )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: complex] :
% 8.64/4.85 ( ( member_complex @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ S2 ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5406_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_complex,T: set_int,G2: int > real,I2: int > complex,F2: complex > real] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.85 => ( ( finite_finite_int @ T )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: int] :
% 8.64/4.85 ( ( member_int @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ S2 ) @ ( groups8778361861064173332t_real @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5407_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_complex,T: set_complex,G2: complex > real,I2: complex > complex,F2: complex > real] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ T )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: complex] :
% 8.64/4.85 ( ( member_complex @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ S2 ) @ ( groups5808333547571424918x_real @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5408_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_nat,T: set_nat,G2: nat > rat,I2: nat > nat,F2: nat > rat] :
% 8.64/4.85 ( ( finite_finite_nat @ S2 )
% 8.64/4.85 => ( ( finite_finite_nat @ T )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: nat] :
% 8.64/4.85 ( ( member_nat @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups2906978787729119204at_rat @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5409_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_nat,T: set_int,G2: int > rat,I2: int > nat,F2: nat > rat] :
% 8.64/4.85 ( ( finite_finite_nat @ S2 )
% 8.64/4.85 => ( ( finite_finite_int @ T )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: int] :
% 8.64/4.85 ( ( member_int @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5410_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_nat,T: set_complex,G2: complex > rat,I2: complex > nat,F2: nat > rat] :
% 8.64/4.85 ( ( finite_finite_nat @ S2 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ T )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: complex] :
% 8.64/4.85 ( ( member_complex @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5411_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_int,T: set_nat,G2: nat > rat,I2: nat > int,F2: int > rat] :
% 8.64/4.85 ( ( finite_finite_int @ S2 )
% 8.64/4.85 => ( ( finite_finite_nat @ T )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: nat] :
% 8.64/4.85 ( ( member_nat @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups2906978787729119204at_rat @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5412_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_int,T: set_int,G2: int > rat,I2: int > int,F2: int > rat] :
% 8.64/4.85 ( ( finite_finite_int @ S2 )
% 8.64/4.85 => ( ( finite_finite_int @ T )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: int] :
% 8.64/4.85 ( ( member_int @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5413_sum__le__included,axiom,
% 8.64/4.85 ! [S2: set_int,T: set_complex,G2: complex > rat,I2: complex > int,F2: int > rat] :
% 8.64/4.85 ( ( finite_finite_int @ S2 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ T )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ T )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S2 )
% 8.64/4.85 => ? [Xa: complex] :
% 8.64/4.85 ( ( member_complex @ Xa @ T )
% 8.64/4.85 & ( ( I2 @ Xa )
% 8.64/4.85 = X3 )
% 8.64/4.85 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ Xa ) ) ) )
% 8.64/4.85 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G2 @ T ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5414_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > real] :
% 8.64/4.85 ( ( finite_finite_real @ A4 )
% 8.64/4.85 => ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups8097168146408367636l_real @ F2 @ A4 )
% 8.64/4.85 = zero_zero_real )
% 8.64/4.85 = ( ! [X4: real] :
% 8.64/4.85 ( ( member_real @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5415_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > real] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups8778361861064173332t_real @ F2 @ A4 )
% 8.64/4.85 = zero_zero_real )
% 8.64/4.85 = ( ! [X4: int] :
% 8.64/4.85 ( ( member_int @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5416_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > real] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups5808333547571424918x_real @ F2 @ A4 )
% 8.64/4.85 = zero_zero_real )
% 8.64/4.85 = ( ! [X4: complex] :
% 8.64/4.85 ( ( member_complex @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5417_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > rat] :
% 8.64/4.85 ( ( finite_finite_real @ A4 )
% 8.64/4.85 => ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups1300246762558778688al_rat @ F2 @ A4 )
% 8.64/4.85 = zero_zero_rat )
% 8.64/4.85 = ( ! [X4: real] :
% 8.64/4.85 ( ( member_real @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5418_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > rat] :
% 8.64/4.85 ( ( finite_finite_nat @ A4 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups2906978787729119204at_rat @ F2 @ A4 )
% 8.64/4.85 = zero_zero_rat )
% 8.64/4.85 = ( ! [X4: nat] :
% 8.64/4.85 ( ( member_nat @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5419_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > rat] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups3906332499630173760nt_rat @ F2 @ A4 )
% 8.64/4.85 = zero_zero_rat )
% 8.64/4.85 = ( ! [X4: int] :
% 8.64/4.85 ( ( member_int @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5420_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > rat] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups5058264527183730370ex_rat @ F2 @ A4 )
% 8.64/4.85 = zero_zero_rat )
% 8.64/4.85 = ( ! [X4: complex] :
% 8.64/4.85 ( ( member_complex @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5421_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_real,F2: real > nat] :
% 8.64/4.85 ( ( finite_finite_real @ A4 )
% 8.64/4.85 => ( ! [X3: real] :
% 8.64/4.85 ( ( member_real @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups1935376822645274424al_nat @ F2 @ A4 )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 = ( ! [X4: real] :
% 8.64/4.85 ( ( member_real @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_nat ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5422_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > nat] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 = ( ! [X4: int] :
% 8.64/4.85 ( ( member_int @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_nat ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5423_sum__nonneg__eq__0__iff,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > nat] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.85 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 = ( ! [X4: complex] :
% 8.64/4.85 ( ( member_complex @ X4 @ A4 )
% 8.64/4.85 => ( ( F2 @ X4 )
% 8.64/4.85 = zero_zero_nat ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5424_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > real,G2: int > real] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: int] :
% 8.64/4.85 ( ( member_int @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_real @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5425_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_real @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: complex] :
% 8.64/4.85 ( ( member_complex @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_real @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5426_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 8.64/4.85 ( ( finite_finite_nat @ A4 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: nat] :
% 8.64/4.85 ( ( member_nat @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( groups2906978787729119204at_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5427_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: int] :
% 8.64/4.85 ( ( member_int @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5428_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_rat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: complex] :
% 8.64/4.85 ( ( member_complex @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_rat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5429_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_int,F2: int > nat,G2: int > nat] :
% 8.64/4.85 ( ( finite_finite_int @ A4 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: int] :
% 8.64/4.85 ( ( member_int @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5430_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: complex] :
% 8.64/4.85 ( ( member_complex @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5431_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > int,G2: nat > int] :
% 8.64/4.85 ( ( finite_finite_nat @ A4 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: nat] :
% 8.64/4.85 ( ( member_nat @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_int @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A4 ) @ ( groups3539618377306564664at_int @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5432_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_complex,F2: complex > int,G2: complex > int] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_int @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: complex] :
% 8.64/4.85 ( ( member_complex @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_int @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F2 @ A4 ) @ ( groups5690904116761175830ex_int @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5433_sum__strict__mono__ex1,axiom,
% 8.64/4.85 ! [A4: set_nat,F2: nat > nat,G2: nat > nat] :
% 8.64/4.85 ( ( finite_finite_nat @ A4 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ A4 )
% 8.64/4.85 => ( ord_less_eq_nat @ ( F2 @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( ? [X5: nat] :
% 8.64/4.85 ( ( member_nat @ X5 @ A4 )
% 8.64/4.85 & ( ord_less_nat @ ( F2 @ X5 ) @ ( G2 @ X5 ) ) )
% 8.64/4.85 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5434_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: complex > complex > $o,S3: set_nat,H: nat > complex,G2: nat > complex] :
% 8.64/4.85 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 8.64/4.85 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite_finite_nat @ S3 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups2073611262835488442omplex @ H @ S3 ) @ ( groups2073611262835488442omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5435_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: complex > complex > $o,S3: set_int,H: int > complex,G2: int > complex] :
% 8.64/4.85 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 8.64/4.85 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite_finite_int @ S3 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups3049146728041665814omplex @ H @ S3 ) @ ( groups3049146728041665814omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5436_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: complex > complex > $o,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 8.64/4.85 ( ( R2 @ zero_zero_complex @ zero_zero_complex )
% 8.64/4.85 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups7754918857620584856omplex @ H @ S3 ) @ ( groups7754918857620584856omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5437_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: real > real > $o,S3: set_int,H: int > real,G2: int > real] :
% 8.64/4.85 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 8.64/4.85 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite_finite_int @ S3 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups8778361861064173332t_real @ H @ S3 ) @ ( groups8778361861064173332t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5438_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: real > real > $o,S3: set_complex,H: complex > real,G2: complex > real] :
% 8.64/4.85 ( ( R2 @ zero_zero_real @ zero_zero_real )
% 8.64/4.85 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups5808333547571424918x_real @ H @ S3 ) @ ( groups5808333547571424918x_real @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5439_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: rat > rat > $o,S3: set_nat,H: nat > rat,G2: nat > rat] :
% 8.64/4.85 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 8.64/4.85 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite_finite_nat @ S3 )
% 8.64/4.85 => ( ! [X3: nat] :
% 8.64/4.85 ( ( member_nat @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups2906978787729119204at_rat @ H @ S3 ) @ ( groups2906978787729119204at_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5440_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: rat > rat > $o,S3: set_int,H: int > rat,G2: int > rat] :
% 8.64/4.85 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 8.64/4.85 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite_finite_int @ S3 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups3906332499630173760nt_rat @ H @ S3 ) @ ( groups3906332499630173760nt_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5441_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: rat > rat > $o,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 8.64/4.85 ( ( R2 @ zero_zero_rat @ zero_zero_rat )
% 8.64/4.85 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups5058264527183730370ex_rat @ H @ S3 ) @ ( groups5058264527183730370ex_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5442_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: nat > nat > $o,S3: set_int,H: int > nat,G2: int > nat] :
% 8.64/4.85 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 8.64/4.85 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite_finite_int @ S3 )
% 8.64/4.85 => ( ! [X3: int] :
% 8.64/4.85 ( ( member_int @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups4541462559716669496nt_nat @ H @ S3 ) @ ( groups4541462559716669496nt_nat @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5443_sum_Orelated,axiom,
% 8.64/4.85 ! [R2: nat > nat > $o,S3: set_complex,H: complex > nat,G2: complex > nat] :
% 8.64/4.85 ( ( R2 @ zero_zero_nat @ zero_zero_nat )
% 8.64/4.85 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 8.64/4.85 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.85 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.85 => ( R2 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.85 => ( ! [X3: complex] :
% 8.64/4.85 ( ( member_complex @ X3 @ S3 )
% 8.64/4.85 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.85 => ( R2 @ ( groups5693394587270226106ex_nat @ H @ S3 ) @ ( groups5693394587270226106ex_nat @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5444_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_real,T4: set_real,S3: set_real,I2: real > real,J2: real > real,T5: set_real,G2: real > complex,H: real > complex] :
% 8.64/4.85 ( ( finite_finite_real @ S5 )
% 8.64/4.85 => ( ( finite_finite_real @ T4 )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5445_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_real,T4: set_int,S3: set_real,I2: int > real,J2: real > int,T5: set_int,G2: real > complex,H: int > complex] :
% 8.64/4.85 ( ( finite_finite_real @ S5 )
% 8.64/4.85 => ( ( finite_finite_int @ T4 )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 8.64/4.85 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5446_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_real,T4: set_complex,S3: set_real,I2: complex > real,J2: real > complex,T5: set_complex,G2: real > complex,H: complex > complex] :
% 8.64/4.85 ( ( finite_finite_real @ S5 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ T4 )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 8.64/4.85 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5447_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_int,T4: set_real,S3: set_int,I2: real > int,J2: int > real,T5: set_real,G2: int > complex,H: real > complex] :
% 8.64/4.85 ( ( finite_finite_int @ S5 )
% 8.64/4.85 => ( ( finite_finite_real @ T4 )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 8.64/4.85 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5448_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_int,T4: set_int,S3: set_int,I2: int > int,J2: int > int,T5: set_int,G2: int > complex,H: int > complex] :
% 8.64/4.85 ( ( finite_finite_int @ S5 )
% 8.64/4.85 => ( ( finite_finite_int @ T4 )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 8.64/4.85 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 8.64/4.85 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5449_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_int,T4: set_complex,S3: set_int,I2: complex > int,J2: int > complex,T5: set_complex,G2: int > complex,H: complex > complex] :
% 8.64/4.85 ( ( finite_finite_int @ S5 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ T4 )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ ( minus_minus_set_int @ S3 @ S5 ) )
% 8.64/4.85 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 8.64/4.85 => ( member_int @ ( I2 @ B3 ) @ ( minus_minus_set_int @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: int] :
% 8.64/4.85 ( ( member_int @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5450_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_complex,T4: set_real,S3: set_complex,I2: real > complex,J2: complex > real,T5: set_real,G2: complex > complex,H: real > complex] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ S5 )
% 8.64/4.85 => ( ( finite_finite_real @ T4 )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 8.64/4.85 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5451_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_complex,T4: set_int,S3: set_complex,I2: int > complex,J2: complex > int,T5: set_int,G2: complex > complex,H: int > complex] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ S5 )
% 8.64/4.85 => ( ( finite_finite_int @ T4 )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 8.64/4.85 => ( member_int @ ( J2 @ A3 ) @ ( minus_minus_set_int @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ ( minus_minus_set_int @ T5 @ T4 ) )
% 8.64/4.85 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: int] :
% 8.64/4.85 ( ( member_int @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5452_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_complex,T4: set_complex,S3: set_complex,I2: complex > complex,J2: complex > complex,T5: set_complex,G2: complex > complex,H: complex > complex] :
% 8.64/4.85 ( ( finite3207457112153483333omplex @ S5 )
% 8.64/4.85 => ( ( finite3207457112153483333omplex @ T4 )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ S3 @ S5 ) )
% 8.64/4.85 => ( member_complex @ ( J2 @ A3 ) @ ( minus_811609699411566653omplex @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ T5 @ T4 ) )
% 8.64/4.85 => ( member_complex @ ( I2 @ B3 ) @ ( minus_811609699411566653omplex @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [B3: complex] :
% 8.64/4.85 ( ( member_complex @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_complex ) )
% 8.64/4.85 => ( ! [A3: complex] :
% 8.64/4.85 ( ( member_complex @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 8.64/4.85 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5453_sum_Oreindex__bij__witness__not__neutral,axiom,
% 8.64/4.85 ! [S5: set_real,T4: set_real,S3: set_real,I2: real > real,J2: real > real,T5: set_real,G2: real > real,H: real > real] :
% 8.64/4.85 ( ( finite_finite_real @ S5 )
% 8.64/4.85 => ( ( finite_finite_real @ T4 )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( ( I2 @ ( J2 @ A3 ) )
% 8.64/4.85 = A3 ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ ( minus_minus_set_real @ S3 @ S5 ) )
% 8.64/4.85 => ( member_real @ ( J2 @ A3 ) @ ( minus_minus_set_real @ T5 @ T4 ) ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( ( J2 @ ( I2 @ B3 ) )
% 8.64/4.85 = B3 ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ ( minus_minus_set_real @ T5 @ T4 ) )
% 8.64/4.85 => ( member_real @ ( I2 @ B3 ) @ ( minus_minus_set_real @ S3 @ S5 ) ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S5 )
% 8.64/4.85 => ( ( G2 @ A3 )
% 8.64/4.85 = zero_zero_real ) )
% 8.64/4.85 => ( ! [B3: real] :
% 8.64/4.85 ( ( member_real @ B3 @ T4 )
% 8.64/4.85 => ( ( H @ B3 )
% 8.64/4.85 = zero_zero_real ) )
% 8.64/4.85 => ( ! [A3: real] :
% 8.64/4.85 ( ( member_real @ A3 @ S3 )
% 8.64/4.85 => ( ( H @ ( J2 @ A3 ) )
% 8.64/4.85 = ( G2 @ A3 ) ) )
% 8.64/4.85 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 8.64/4.85 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5454_not__is__unit__0,axiom,
% 8.64/4.85 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5455_not__is__unit__0,axiom,
% 8.64/4.85 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5456_not__is__unit__0,axiom,
% 8.64/4.85 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5457_dvd__div__eq__0__iff,axiom,
% 8.64/4.85 ! [B: complex,A: complex] :
% 8.64/4.85 ( ( dvd_dvd_complex @ B @ A )
% 8.64/4.85 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.64/4.85 = zero_zero_complex )
% 8.64/4.85 = ( A = zero_zero_complex ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5458_dvd__div__eq__0__iff,axiom,
% 8.64/4.85 ! [B: real,A: real] :
% 8.64/4.85 ( ( dvd_dvd_real @ B @ A )
% 8.64/4.85 => ( ( ( divide_divide_real @ A @ B )
% 8.64/4.85 = zero_zero_real )
% 8.64/4.85 = ( A = zero_zero_real ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5459_dvd__div__eq__0__iff,axiom,
% 8.64/4.85 ! [B: rat,A: rat] :
% 8.64/4.85 ( ( dvd_dvd_rat @ B @ A )
% 8.64/4.85 => ( ( ( divide_divide_rat @ A @ B )
% 8.64/4.85 = zero_zero_rat )
% 8.64/4.85 = ( A = zero_zero_rat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5460_dvd__div__eq__0__iff,axiom,
% 8.64/4.85 ! [B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ A )
% 8.64/4.85 => ( ( ( divide_divide_nat @ A @ B )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 = ( A = zero_zero_nat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5461_dvd__div__eq__0__iff,axiom,
% 8.64/4.85 ! [B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ A )
% 8.64/4.85 => ( ( ( divide_divide_int @ A @ B )
% 8.64/4.85 = zero_zero_int )
% 8.64/4.85 = ( A = zero_zero_int ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5462_unit__mult__right__cancel,axiom,
% 8.64/4.85 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.85 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 8.64/4.85 = ( times_3573771949741848930nteger @ C2 @ A ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5463_unit__mult__right__cancel,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.85 => ( ( ( times_times_nat @ B @ A )
% 8.64/4.85 = ( times_times_nat @ C2 @ A ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5464_unit__mult__right__cancel,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.85 => ( ( ( times_times_int @ B @ A )
% 8.64/4.85 = ( times_times_int @ C2 @ A ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5465_unit__mult__left__cancel,axiom,
% 8.64/4.85 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.85 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 8.64/4.85 = ( times_3573771949741848930nteger @ A @ C2 ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5466_unit__mult__left__cancel,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.85 => ( ( ( times_times_nat @ A @ B )
% 8.64/4.85 = ( times_times_nat @ A @ C2 ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5467_unit__mult__left__cancel,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.85 => ( ( ( times_times_int @ A @ B )
% 8.64/4.85 = ( times_times_int @ A @ C2 ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5468_mult__unit__dvd__iff_H,axiom,
% 8.64/4.85 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.85 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_Code_integer @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5469_mult__unit__dvd__iff_H,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.85 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_nat @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5470_mult__unit__dvd__iff_H,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.85 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_int @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5471_dvd__mult__unit__iff_H,axiom,
% 8.64/4.85 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.85 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5472_dvd__mult__unit__iff_H,axiom,
% 8.64/4.85 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.85 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5473_dvd__mult__unit__iff_H,axiom,
% 8.64/4.85 ! [B: int,A: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.85 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.85 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5474_mult__unit__dvd__iff,axiom,
% 8.64/4.85 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.85 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5475_mult__unit__dvd__iff,axiom,
% 8.64/4.85 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.85 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5476_mult__unit__dvd__iff,axiom,
% 8.64/4.85 ! [B: int,A: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.85 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5477_dvd__mult__unit__iff,axiom,
% 8.64/4.85 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.85 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C2 @ B ) )
% 8.64/4.85 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5478_dvd__mult__unit__iff,axiom,
% 8.64/4.85 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.85 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C2 @ B ) )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5479_dvd__mult__unit__iff,axiom,
% 8.64/4.85 ! [B: int,A: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.85 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C2 @ B ) )
% 8.64/4.85 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5480_is__unit__mult__iff,axiom,
% 8.64/4.85 ! [A: code_integer,B: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 8.64/4.85 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.85 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5481_is__unit__mult__iff,axiom,
% 8.64/4.85 ! [A: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 8.64/4.85 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.85 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5482_is__unit__mult__iff,axiom,
% 8.64/4.85 ! [A: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 8.64/4.85 = ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.85 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5483_dvd__div__mult,axiom,
% 8.64/4.85 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.85 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C2 ) @ A )
% 8.64/4.85 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5484_dvd__div__mult,axiom,
% 8.64/4.85 ! [C2: int,B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.85 => ( ( times_times_int @ ( divide_divide_int @ B @ C2 ) @ A )
% 8.64/4.85 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5485_div__mult__swap,axiom,
% 8.64/4.85 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.85 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 8.64/4.85 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5486_div__mult__swap,axiom,
% 8.64/4.85 ! [C2: int,B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.85 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 8.64/4.85 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5487_div__div__eq__right,axiom,
% 8.64/4.85 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.85 => ( ( dvd_dvd_nat @ B @ A )
% 8.64/4.85 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 8.64/4.85 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5488_div__div__eq__right,axiom,
% 8.64/4.85 ! [C2: int,B: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.85 => ( ( dvd_dvd_int @ B @ A )
% 8.64/4.85 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 8.64/4.85 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5489_dvd__div__mult2__eq,axiom,
% 8.64/4.85 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C2 ) @ A )
% 8.64/4.85 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.85 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5490_dvd__div__mult2__eq,axiom,
% 8.64/4.85 ! [B: int,C2: int,A: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( times_times_int @ B @ C2 ) @ A )
% 8.64/4.85 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.85 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5491_dvd__mult__imp__div,axiom,
% 8.64/4.85 ! [A: nat,C2: nat,B: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ B )
% 8.64/4.85 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5492_dvd__mult__imp__div,axiom,
% 8.64/4.85 ! [A: int,C2: int,B: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ B )
% 8.64/4.85 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5493_div__mult__div__if__dvd,axiom,
% 8.64/4.85 ! [B: nat,A: nat,D: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ A )
% 8.64/4.85 => ( ( dvd_dvd_nat @ D @ C2 )
% 8.64/4.85 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C2 @ D ) )
% 8.64/4.85 = ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5494_div__mult__div__if__dvd,axiom,
% 8.64/4.85 ! [B: int,A: int,D: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ A )
% 8.64/4.85 => ( ( dvd_dvd_int @ D @ C2 )
% 8.64/4.85 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C2 @ D ) )
% 8.64/4.85 = ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5495_unit__div__cancel,axiom,
% 8.64/4.85 ! [A: code_integer,B: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.85 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 8.64/4.85 = ( divide6298287555418463151nteger @ C2 @ A ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5496_unit__div__cancel,axiom,
% 8.64/4.85 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.85 => ( ( ( divide_divide_nat @ B @ A )
% 8.64/4.85 = ( divide_divide_nat @ C2 @ A ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5497_unit__div__cancel,axiom,
% 8.64/4.85 ! [A: int,B: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.85 => ( ( ( divide_divide_int @ B @ A )
% 8.64/4.85 = ( divide_divide_int @ C2 @ A ) )
% 8.64/4.85 = ( B = C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5498_div__unit__dvd__iff,axiom,
% 8.64/4.85 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.85 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5499_div__unit__dvd__iff,axiom,
% 8.64/4.85 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.85 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5500_div__unit__dvd__iff,axiom,
% 8.64/4.85 ! [B: int,A: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.85 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 8.64/4.85 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5501_dvd__div__unit__iff,axiom,
% 8.64/4.85 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.85 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.85 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C2 @ B ) )
% 8.64/4.85 = ( dvd_dvd_Code_integer @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5502_dvd__div__unit__iff,axiom,
% 8.64/4.85 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.85 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C2 @ B ) )
% 8.64/4.85 = ( dvd_dvd_nat @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5503_dvd__div__unit__iff,axiom,
% 8.64/4.85 ! [B: int,A: int,C2: int] :
% 8.64/4.85 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.85 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C2 @ B ) )
% 8.64/4.85 = ( dvd_dvd_int @ A @ C2 ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5504_mod__eq__0__iff__dvd,axiom,
% 8.64/4.85 ! [A: nat,B: nat] :
% 8.64/4.85 ( ( ( modulo_modulo_nat @ A @ B )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 = ( dvd_dvd_nat @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5505_mod__eq__0__iff__dvd,axiom,
% 8.64/4.85 ! [A: int,B: int] :
% 8.64/4.85 ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.85 = zero_zero_int )
% 8.64/4.85 = ( dvd_dvd_int @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5506_mod__eq__0__iff__dvd,axiom,
% 8.64/4.85 ! [A: code_natural,B: code_natural] :
% 8.64/4.85 ( ( ( modulo8411746178871703098atural @ A @ B )
% 8.64/4.85 = zero_z2226904508553997617atural )
% 8.64/4.85 = ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5507_dvd__eq__mod__eq__0,axiom,
% 8.64/4.85 ( dvd_dvd_nat
% 8.64/4.85 = ( ^ [A5: nat,B4: nat] :
% 8.64/4.85 ( ( modulo_modulo_nat @ B4 @ A5 )
% 8.64/4.85 = zero_zero_nat ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5508_dvd__eq__mod__eq__0,axiom,
% 8.64/4.85 ( dvd_dvd_int
% 8.64/4.85 = ( ^ [A5: int,B4: int] :
% 8.64/4.85 ( ( modulo_modulo_int @ B4 @ A5 )
% 8.64/4.85 = zero_zero_int ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5509_dvd__eq__mod__eq__0,axiom,
% 8.64/4.85 ( dvd_dvd_Code_natural
% 8.64/4.85 = ( ^ [A5: code_natural,B4: code_natural] :
% 8.64/4.85 ( ( modulo8411746178871703098atural @ B4 @ A5 )
% 8.64/4.85 = zero_z2226904508553997617atural ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5510_mod__0__imp__dvd,axiom,
% 8.64/4.85 ! [A: nat,B: nat] :
% 8.64/4.85 ( ( ( modulo_modulo_nat @ A @ B )
% 8.64/4.85 = zero_zero_nat )
% 8.64/4.85 => ( dvd_dvd_nat @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5511_mod__0__imp__dvd,axiom,
% 8.64/4.85 ! [A: int,B: int] :
% 8.64/4.85 ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.85 = zero_zero_int )
% 8.64/4.85 => ( dvd_dvd_int @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5512_mod__0__imp__dvd,axiom,
% 8.64/4.85 ! [A: code_natural,B: code_natural] :
% 8.64/4.85 ( ( ( modulo8411746178871703098atural @ A @ B )
% 8.64/4.85 = zero_z2226904508553997617atural )
% 8.64/4.85 => ( dvd_dvd_Code_natural @ B @ A ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5513_dvd__power__le,axiom,
% 8.64/4.85 ! [X: nat,Y: nat,N: nat,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ X @ Y )
% 8.64/4.85 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.85 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ M2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5514_dvd__power__le,axiom,
% 8.64/4.85 ! [X: real,Y: real,N: nat,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_real @ X @ Y )
% 8.64/4.85 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.85 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ M2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5515_dvd__power__le,axiom,
% 8.64/4.85 ! [X: int,Y: int,N: nat,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_int @ X @ Y )
% 8.64/4.85 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.85 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ M2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5516_dvd__power__le,axiom,
% 8.64/4.85 ! [X: complex,Y: complex,N: nat,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_complex @ X @ Y )
% 8.64/4.85 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.85 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ M2 ) ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5517_power__le__dvd,axiom,
% 8.64/4.85 ! [A: nat,N: nat,B: nat,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 8.64/4.85 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.85 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5518_power__le__dvd,axiom,
% 8.64/4.85 ! [A: real,N: nat,B: real,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 8.64/4.85 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.85 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5519_power__le__dvd,axiom,
% 8.64/4.85 ! [A: int,N: nat,B: int,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 8.64/4.85 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.85 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5520_power__le__dvd,axiom,
% 8.64/4.85 ! [A: complex,N: nat,B: complex,M2: nat] :
% 8.64/4.85 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 8.64/4.85 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.85 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ B ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5521_le__imp__power__dvd,axiom,
% 8.64/4.85 ! [M2: nat,N: nat,A: nat] :
% 8.64/4.85 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.85 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M2 ) @ ( power_power_nat @ A @ N ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5522_le__imp__power__dvd,axiom,
% 8.64/4.85 ! [M2: nat,N: nat,A: real] :
% 8.64/4.85 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.85 => ( dvd_dvd_real @ ( power_power_real @ A @ M2 ) @ ( power_power_real @ A @ N ) ) ) ).
% 8.64/4.85
% 8.64/4.85 thf(fact_5523_le__imp__power__dvd,axiom,
% 8.64/4.85 ! [M2: nat,N: nat,A: int] :
% 8.64/4.85 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.86 => ( dvd_dvd_int @ ( power_power_int @ A @ M2 ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5524_le__imp__power__dvd,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,A: complex] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.86 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M2 ) @ ( power_power_complex @ A @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5525_dvd__minus__mod,axiom,
% 8.64/4.86 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5526_dvd__minus__mod,axiom,
% 8.64/4.86 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5527_dvd__minus__mod,axiom,
% 8.64/4.86 ! [B: code_natural,A: code_natural] : ( dvd_dvd_Code_natural @ B @ ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5528_dvd__pos__nat,axiom,
% 8.64/4.86 ! [N: nat,M2: nat] :
% 8.64/4.86 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.86 => ( ( dvd_dvd_nat @ M2 @ N )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ M2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5529_nat__dvd__not__less,axiom,
% 8.64/4.86 ! [M2: nat,N: nat] :
% 8.64/4.86 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.86 => ( ( ord_less_nat @ M2 @ N )
% 8.64/4.86 => ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5530_pochhammer__pos,axiom,
% 8.64/4.86 ! [X: real,N: nat] :
% 8.64/4.86 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5531_pochhammer__pos,axiom,
% 8.64/4.86 ! [X: rat,N: nat] :
% 8.64/4.86 ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5532_pochhammer__pos,axiom,
% 8.64/4.86 ! [X: nat,N: nat] :
% 8.64/4.86 ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5533_pochhammer__pos,axiom,
% 8.64/4.86 ! [X: int,N: nat] :
% 8.64/4.86 ( ( ord_less_int @ zero_zero_int @ X )
% 8.64/4.86 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5534_dvd__minus__self,axiom,
% 8.64/4.86 ! [M2: nat,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) )
% 8.64/4.86 = ( ( ord_less_nat @ N @ M2 )
% 8.64/4.86 | ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5535_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_real,F2: real > real,I2: real] :
% 8.64/4.86 ( ( finite_finite_real @ S2 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups8097168146408367636l_real @ F2 @ S2 )
% 8.64/4.86 = zero_zero_real )
% 8.64/4.86 => ( ( member_real @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5536_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_int,F2: int > real,I2: int] :
% 8.64/4.86 ( ( finite_finite_int @ S2 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups8778361861064173332t_real @ F2 @ S2 )
% 8.64/4.86 = zero_zero_real )
% 8.64/4.86 => ( ( member_int @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5537_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_complex,F2: complex > real,I2: complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups5808333547571424918x_real @ F2 @ S2 )
% 8.64/4.86 = zero_zero_real )
% 8.64/4.86 => ( ( member_complex @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5538_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_real,F2: real > rat,I2: real] :
% 8.64/4.86 ( ( finite_finite_real @ S2 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups1300246762558778688al_rat @ F2 @ S2 )
% 8.64/4.86 = zero_zero_rat )
% 8.64/4.86 => ( ( member_real @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5539_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_nat,F2: nat > rat,I2: nat] :
% 8.64/4.86 ( ( finite_finite_nat @ S2 )
% 8.64/4.86 => ( ! [I3: nat] :
% 8.64/4.86 ( ( member_nat @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups2906978787729119204at_rat @ F2 @ S2 )
% 8.64/4.86 = zero_zero_rat )
% 8.64/4.86 => ( ( member_nat @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5540_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_int,F2: int > rat,I2: int] :
% 8.64/4.86 ( ( finite_finite_int @ S2 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups3906332499630173760nt_rat @ F2 @ S2 )
% 8.64/4.86 = zero_zero_rat )
% 8.64/4.86 => ( ( member_int @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5541_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_complex,F2: complex > rat,I2: complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups5058264527183730370ex_rat @ F2 @ S2 )
% 8.64/4.86 = zero_zero_rat )
% 8.64/4.86 => ( ( member_complex @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5542_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_real,F2: real > nat,I2: real] :
% 8.64/4.86 ( ( finite_finite_real @ S2 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups1935376822645274424al_nat @ F2 @ S2 )
% 8.64/4.86 = zero_zero_nat )
% 8.64/4.86 => ( ( member_real @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_nat ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5543_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_int,F2: int > nat,I2: int] :
% 8.64/4.86 ( ( finite_finite_int @ S2 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups4541462559716669496nt_nat @ F2 @ S2 )
% 8.64/4.86 = zero_zero_nat )
% 8.64/4.86 => ( ( member_int @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_nat ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5544_sum__nonneg__0,axiom,
% 8.64/4.86 ! [S2: set_complex,F2: complex > nat,I2: complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups5693394587270226106ex_nat @ F2 @ S2 )
% 8.64/4.86 = zero_zero_nat )
% 8.64/4.86 => ( ( member_complex @ I2 @ S2 )
% 8.64/4.86 => ( ( F2 @ I2 )
% 8.64/4.86 = zero_zero_nat ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5545_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_real,F2: real > real,B5: real,I2: real] :
% 8.64/4.86 ( ( finite_finite_real @ S2 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups8097168146408367636l_real @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_real @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5546_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_int,F2: int > real,B5: real,I2: int] :
% 8.64/4.86 ( ( finite_finite_int @ S2 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups8778361861064173332t_real @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_int @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5547_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_complex,F2: complex > real,B5: real,I2: complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups5808333547571424918x_real @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_complex @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_real @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5548_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_real,F2: real > rat,B5: rat,I2: real] :
% 8.64/4.86 ( ( finite_finite_real @ S2 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups1300246762558778688al_rat @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_real @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5549_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_nat,F2: nat > rat,B5: rat,I2: nat] :
% 8.64/4.86 ( ( finite_finite_nat @ S2 )
% 8.64/4.86 => ( ! [I3: nat] :
% 8.64/4.86 ( ( member_nat @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups2906978787729119204at_rat @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_nat @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5550_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_int,F2: int > rat,B5: rat,I2: int] :
% 8.64/4.86 ( ( finite_finite_int @ S2 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups3906332499630173760nt_rat @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_int @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5551_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_complex,F2: complex > rat,B5: rat,I2: complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups5058264527183730370ex_rat @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_complex @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5552_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_real,F2: real > nat,B5: nat,I2: real] :
% 8.64/4.86 ( ( finite_finite_real @ S2 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups1935376822645274424al_nat @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_real @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5553_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_int,F2: int > nat,B5: nat,I2: int] :
% 8.64/4.86 ( ( finite_finite_int @ S2 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups4541462559716669496nt_nat @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_int @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5554_sum__nonneg__leq__bound,axiom,
% 8.64/4.86 ! [S2: set_complex,F2: complex > nat,B5: nat,I2: complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ S2 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ( ( groups5693394587270226106ex_nat @ F2 @ S2 )
% 8.64/4.86 = B5 )
% 8.64/4.86 => ( ( member_complex @ I2 @ S2 )
% 8.64/4.86 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5555_less__eq__dvd__minus,axiom,
% 8.64/4.86 ! [M2: nat,N: nat] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.86 => ( ( dvd_dvd_nat @ M2 @ N )
% 8.64/4.86 = ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5556_dvd__diffD1,axiom,
% 8.64/4.86 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.86 => ( ( dvd_dvd_nat @ K2 @ M2 )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( dvd_dvd_nat @ K2 @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5557_dvd__diffD,axiom,
% 8.64/4.86 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ K2 @ ( minus_minus_nat @ M2 @ N ) )
% 8.64/4.86 => ( ( dvd_dvd_nat @ K2 @ N )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( dvd_dvd_nat @ K2 @ M2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5558_pochhammer__eq__0__mono,axiom,
% 8.64/4.86 ! [A: complex,N: nat,M2: nat] :
% 8.64/4.86 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 8.64/4.86 = zero_zero_complex )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 8.64/4.86 = zero_zero_complex ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5559_pochhammer__eq__0__mono,axiom,
% 8.64/4.86 ! [A: real,N: nat,M2: nat] :
% 8.64/4.86 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 8.64/4.86 = zero_zero_real )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 8.64/4.86 = zero_zero_real ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5560_pochhammer__eq__0__mono,axiom,
% 8.64/4.86 ! [A: rat,N: nat,M2: nat] :
% 8.64/4.86 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 8.64/4.86 = zero_zero_rat )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 8.64/4.86 = zero_zero_rat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5561_pochhammer__neq__0__mono,axiom,
% 8.64/4.86 ! [A: complex,M2: nat,N: nat] :
% 8.64/4.86 ( ( ( comm_s2602460028002588243omplex @ A @ M2 )
% 8.64/4.86 != zero_zero_complex )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( ( comm_s2602460028002588243omplex @ A @ N )
% 8.64/4.86 != zero_zero_complex ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5562_pochhammer__neq__0__mono,axiom,
% 8.64/4.86 ! [A: real,M2: nat,N: nat] :
% 8.64/4.86 ( ( ( comm_s7457072308508201937r_real @ A @ M2 )
% 8.64/4.86 != zero_zero_real )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( ( comm_s7457072308508201937r_real @ A @ N )
% 8.64/4.86 != zero_zero_real ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5563_pochhammer__neq__0__mono,axiom,
% 8.64/4.86 ! [A: rat,M2: nat,N: nat] :
% 8.64/4.86 ( ( ( comm_s4028243227959126397er_rat @ A @ M2 )
% 8.64/4.86 != zero_zero_rat )
% 8.64/4.86 => ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( ( comm_s4028243227959126397er_rat @ A @ N )
% 8.64/4.86 != zero_zero_rat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5564_bezout__add__nat,axiom,
% 8.64/4.86 ! [A: nat,B: nat] :
% 8.64/4.86 ? [D5: nat,X3: nat,Y3: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ D5 @ A )
% 8.64/4.86 & ( dvd_dvd_nat @ D5 @ B )
% 8.64/4.86 & ( ( ( times_times_nat @ A @ X3 )
% 8.64/4.86 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D5 ) )
% 8.64/4.86 | ( ( times_times_nat @ B @ X3 )
% 8.64/4.86 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D5 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5565_bezout__lemma__nat,axiom,
% 8.64/4.86 ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ D @ A )
% 8.64/4.86 => ( ( dvd_dvd_nat @ D @ B )
% 8.64/4.86 => ( ( ( ( times_times_nat @ A @ X )
% 8.64/4.86 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 8.64/4.86 | ( ( times_times_nat @ B @ X )
% 8.64/4.86 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 8.64/4.86 => ? [X3: nat,Y3: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ D @ A )
% 8.64/4.86 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 8.64/4.86 & ( ( ( times_times_nat @ A @ X3 )
% 8.64/4.86 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 8.64/4.86 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X3 )
% 8.64/4.86 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5566_bezout1__nat,axiom,
% 8.64/4.86 ! [A: nat,B: nat] :
% 8.64/4.86 ? [D5: nat,X3: nat,Y3: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ D5 @ A )
% 8.64/4.86 & ( dvd_dvd_nat @ D5 @ B )
% 8.64/4.86 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 8.64/4.86 = D5 )
% 8.64/4.86 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 8.64/4.86 = D5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5567_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > complex,B5: set_real] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups5754745047067104278omplex @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 8.64/4.86 = ( groups5754745047067104278omplex
% 8.64/4.86 @ ^ [X4: real] : ( if_complex @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5568_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_int,G2: int > complex,B5: set_int] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.86 = ( groups3049146728041665814omplex
% 8.64/4.86 @ ^ [X4: int] : ( if_complex @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5569_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_complex,G2: complex > complex,B5: set_complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( groups7754918857620584856omplex
% 8.64/4.86 @ ^ [X4: complex] : ( if_complex @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_complex )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5570_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > real,B5: set_real] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups8097168146408367636l_real @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 8.64/4.86 = ( groups8097168146408367636l_real
% 8.64/4.86 @ ^ [X4: real] : ( if_real @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5571_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_int,G2: int > real,B5: set_int] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.86 = ( groups8778361861064173332t_real
% 8.64/4.86 @ ^ [X4: int] : ( if_real @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5572_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_complex,G2: complex > real,B5: set_complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( groups5808333547571424918x_real
% 8.64/4.86 @ ^ [X4: complex] : ( if_real @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_real )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5573_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > rat,B5: set_real] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups1300246762558778688al_rat @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 8.64/4.86 = ( groups1300246762558778688al_rat
% 8.64/4.86 @ ^ [X4: real] : ( if_rat @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5574_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_int,G2: int > rat,B5: set_int] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.86 = ( groups3906332499630173760nt_rat
% 8.64/4.86 @ ^ [X4: int] : ( if_rat @ ( member_int @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5575_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_complex,G2: complex > rat,B5: set_complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( groups5058264527183730370ex_rat
% 8.64/4.86 @ ^ [X4: complex] : ( if_rat @ ( member_complex @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_rat )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5576_sum_Ointer__restrict,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > nat,B5: set_real] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups1935376822645274424al_nat @ G2 @ ( inf_inf_set_real @ A4 @ B5 ) )
% 8.64/4.86 = ( groups1935376822645274424al_nat
% 8.64/4.86 @ ^ [X4: real] : ( if_nat @ ( member_real @ X4 @ B5 ) @ ( G2 @ X4 ) @ zero_zero_nat )
% 8.64/4.86 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5577_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > complex] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups5754745047067104278omplex @ G2
% 8.64/4.86 @ ( minus_minus_set_real @ A4
% 8.64/4.86 @ ( collect_real
% 8.64/4.86 @ ^ [X4: real] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_complex ) ) ) )
% 8.64/4.86 = ( groups5754745047067104278omplex @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5578_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_int,G2: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2
% 8.64/4.86 @ ( minus_minus_set_int @ A4
% 8.64/4.86 @ ( collect_int
% 8.64/4.86 @ ^ [X4: int] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_complex ) ) ) )
% 8.64/4.86 = ( groups3049146728041665814omplex @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5579_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_complex,G2: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2
% 8.64/4.86 @ ( minus_811609699411566653omplex @ A4
% 8.64/4.86 @ ( collect_complex
% 8.64/4.86 @ ^ [X4: complex] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_complex ) ) ) )
% 8.64/4.86 = ( groups7754918857620584856omplex @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5580_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups8097168146408367636l_real @ G2
% 8.64/4.86 @ ( minus_minus_set_real @ A4
% 8.64/4.86 @ ( collect_real
% 8.64/4.86 @ ^ [X4: real] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_real ) ) ) )
% 8.64/4.86 = ( groups8097168146408367636l_real @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5581_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_int,G2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2
% 8.64/4.86 @ ( minus_minus_set_int @ A4
% 8.64/4.86 @ ( collect_int
% 8.64/4.86 @ ^ [X4: int] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_real ) ) ) )
% 8.64/4.86 = ( groups8778361861064173332t_real @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5582_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_complex,G2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2
% 8.64/4.86 @ ( minus_811609699411566653omplex @ A4
% 8.64/4.86 @ ( collect_complex
% 8.64/4.86 @ ^ [X4: complex] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_real ) ) ) )
% 8.64/4.86 = ( groups5808333547571424918x_real @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5583_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups1300246762558778688al_rat @ G2
% 8.64/4.86 @ ( minus_minus_set_real @ A4
% 8.64/4.86 @ ( collect_real
% 8.64/4.86 @ ^ [X4: real] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_rat ) ) ) )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5584_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_int,G2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2
% 8.64/4.86 @ ( minus_minus_set_int @ A4
% 8.64/4.86 @ ( collect_int
% 8.64/4.86 @ ^ [X4: int] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_rat ) ) ) )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5585_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_complex,G2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2
% 8.64/4.86 @ ( minus_811609699411566653omplex @ A4
% 8.64/4.86 @ ( collect_complex
% 8.64/4.86 @ ^ [X4: complex] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_rat ) ) ) )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5586_sum_Osetdiff__irrelevant,axiom,
% 8.64/4.86 ! [A4: set_real,G2: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ A4 )
% 8.64/4.86 => ( ( groups1935376822645274424al_nat @ G2
% 8.64/4.86 @ ( minus_minus_set_real @ A4
% 8.64/4.86 @ ( collect_real
% 8.64/4.86 @ ^ [X4: real] :
% 8.64/4.86 ( ( G2 @ X4 )
% 8.64/4.86 = zero_zero_nat ) ) ) )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ G2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5587_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 8.64/4.86 ! [G2: nat > nat,M2: nat,N: nat] :
% 8.64/4.86 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 8.64/4.86 = ( groups3542108847815614940at_nat
% 8.64/4.86 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.86 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5588_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 8.64/4.86 ! [G2: nat > real,M2: nat,N: nat] :
% 8.64/4.86 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 8.64/4.86 = ( groups6591440286371151544t_real
% 8.64/4.86 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.86 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5589_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 8.64/4.86 ! [G2: nat > nat,M2: nat,K2: nat,N: nat] :
% 8.64/4.86 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 8.64/4.86 = ( groups3542108847815614940at_nat
% 8.64/4.86 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 8.64/4.86 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5590_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 8.64/4.86 ! [G2: nat > real,M2: nat,K2: nat,N: nat] :
% 8.64/4.86 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 8.64/4.86 = ( groups6591440286371151544t_real
% 8.64/4.86 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 8.64/4.86 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5591_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_real,I2: real,F2: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ I5 )
% 8.64/4.86 => ( ( member_real @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5592_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_int,I2: int,F2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ I5 )
% 8.64/4.86 => ( ( member_int @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5593_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_complex,I2: complex,F2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.86 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5594_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_real,I2: real,F2: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ I5 )
% 8.64/4.86 => ( ( member_real @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5595_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_nat,I2: nat,F2: nat > rat] :
% 8.64/4.86 ( ( finite_finite_nat @ I5 )
% 8.64/4.86 => ( ( member_nat @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: nat] :
% 8.64/4.86 ( ( member_nat @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5596_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_int,I2: int,F2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ I5 )
% 8.64/4.86 => ( ( member_int @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5597_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_complex,I2: complex,F2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.86 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5598_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_real,I2: real,F2: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ I5 )
% 8.64/4.86 => ( ( member_real @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5599_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_int,I2: int,F2: int > nat] :
% 8.64/4.86 ( ( finite_finite_int @ I5 )
% 8.64/4.86 => ( ( member_int @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5600_sum__pos2,axiom,
% 8.64/4.86 ! [I5: set_complex,I2: complex,F2: complex > nat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.86 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.86 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ I2 ) )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5601_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_complex,F2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_complex )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5602_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_int,F2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_int )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5603_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_real,F2: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_real )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5604_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_complex,F2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_complex )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5605_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_nat,F2: nat > rat] :
% 8.64/4.86 ( ( finite_finite_nat @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_nat )
% 8.64/4.86 => ( ! [I3: nat] :
% 8.64/4.86 ( ( member_nat @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5606_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_int,F2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_int )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5607_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_real,F2: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_real )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5608_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_complex,F2: complex > nat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_complex )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5609_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_int,F2: int > nat] :
% 8.64/4.86 ( ( finite_finite_int @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_int )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5610_sum__pos,axiom,
% 8.64/4.86 ! [I5: set_real,F2: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ I5 )
% 8.64/4.86 => ( ( I5 != bot_bot_set_real )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ I5 )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F2 @ I5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5611_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_real,K5: real,F2: real > real] :
% 8.64/4.86 ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5612_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_complex,K5: real,F2: complex > real] :
% 8.64/4.86 ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5613_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_int,K5: real,F2: int > real] :
% 8.64/4.86 ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_real @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5614_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_real,K5: rat,F2: real > rat] :
% 8.64/4.86 ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5615_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_nat,K5: rat,F2: nat > rat] :
% 8.64/4.86 ( ! [I3: nat] :
% 8.64/4.86 ( ( member_nat @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5616_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_complex,K5: rat,F2: complex > rat] :
% 8.64/4.86 ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5617_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_int,K5: rat,F2: int > rat] :
% 8.64/4.86 ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5618_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_real,K5: nat,F2: real > nat] :
% 8.64/4.86 ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A4 ) ) @ K5 ) @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5619_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_complex,K5: nat,F2: complex > nat] :
% 8.64/4.86 ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ K5 ) @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5620_sum__bounded__below,axiom,
% 8.64/4.86 ! [A4: set_int,K5: nat,F2: int > nat] :
% 8.64/4.86 ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_nat @ K5 @ ( F2 @ I3 ) ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ K5 ) @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5621_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_real,F2: real > real,K5: real] :
% 8.64/4.86 ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5622_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_complex,F2: complex > real,K5: real] :
% 8.64/4.86 ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5623_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_int,F2: int > real,K5: real] :
% 8.64/4.86 ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_real @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5624_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_real,F2: real > rat,K5: rat] :
% 8.64/4.86 ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5625_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 8.64/4.86 ( ! [I3: nat] :
% 8.64/4.86 ( ( member_nat @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5626_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 8.64/4.86 ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5627_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_int,F2: int > rat,K5: rat] :
% 8.64/4.86 ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5628_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_real,F2: real > nat,K5: nat] :
% 8.64/4.86 ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5629_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_complex,F2: complex > nat,K5: nat] :
% 8.64/4.86 ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5630_sum__bounded__above,axiom,
% 8.64/4.86 ! [A4: set_int,F2: int > nat,K5: nat] :
% 8.64/4.86 ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ A4 )
% 8.64/4.86 => ( ord_less_eq_nat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5631_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,G2: real > complex,H: real > complex] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5754745047067104278omplex @ G2 @ T5 )
% 8.64/4.86 = ( groups5754745047067104278omplex @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5632_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > complex,H: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ T5 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5633_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > complex,H: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ T5 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5634_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,G2: real > real,H: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups8097168146408367636l_real @ G2 @ T5 )
% 8.64/4.86 = ( groups8097168146408367636l_real @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5635_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > real,H: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ T5 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5636_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > real,H: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ T5 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5637_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,G2: real > rat,H: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups1300246762558778688al_rat @ G2 @ T5 )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5638_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > rat,H: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ T5 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5639_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > rat,H: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ T5 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5640_sum_Omono__neutral__cong__right,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,G2: real > nat,H: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups1935376822645274424al_nat @ G2 @ T5 )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ H @ S3 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5641_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > complex,G2: real > complex] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5642_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,H: int > complex,G2: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5643_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5644_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > real,G2: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 8.64/4.86 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5645_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,H: int > real,G2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5646_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,H: complex > real,G2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5647_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > rat,G2: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups1300246762558778688al_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5648_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,H: int > rat,G2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5649_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5650_sum_Omono__neutral__cong__left,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > nat,G2: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ S3 )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups1935376822645274424al_nat @ G2 @ S3 )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ H @ T5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5651_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ T5 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5652_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ T5 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5653_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ T5 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5654_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ T5 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5655_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ T5 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5656_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ T5 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5657_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > nat] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( groups4541462559716669496nt_nat @ G2 @ T5 )
% 8.64/4.86 = ( groups4541462559716669496nt_nat @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5658_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > nat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( groups5693394587270226106ex_nat @ G2 @ T5 )
% 8.64/4.86 = ( groups5693394587270226106ex_nat @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5659_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > int] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_int ) )
% 8.64/4.86 => ( ( groups5690904116761175830ex_int @ G2 @ T5 )
% 8.64/4.86 = ( groups5690904116761175830ex_int @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5660_sum_Omono__neutral__right,axiom,
% 8.64/4.86 ! [T5: set_nat,S3: set_nat,G2: nat > complex] :
% 8.64/4.86 ( ( finite_finite_nat @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: nat] :
% 8.64/4.86 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups2073611262835488442omplex @ G2 @ T5 )
% 8.64/4.86 = ( groups2073611262835488442omplex @ G2 @ S3 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5661_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5662_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5663_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5664_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5665_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5666_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5667_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,G2: int > nat] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( groups4541462559716669496nt_nat @ G2 @ S3 )
% 8.64/4.86 = ( groups4541462559716669496nt_nat @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5668_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > nat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( groups5693394587270226106ex_nat @ G2 @ S3 )
% 8.64/4.86 = ( groups5693394587270226106ex_nat @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5669_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,G2: complex > int] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_int ) )
% 8.64/4.86 => ( ( groups5690904116761175830ex_int @ G2 @ S3 )
% 8.64/4.86 = ( groups5690904116761175830ex_int @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5670_sum_Omono__neutral__left,axiom,
% 8.64/4.86 ! [T5: set_nat,S3: set_nat,G2: nat > complex] :
% 8.64/4.86 ( ( finite_finite_nat @ T5 )
% 8.64/4.86 => ( ( ord_less_eq_set_nat @ S3 @ T5 )
% 8.64/4.86 => ( ! [X3: nat] :
% 8.64/4.86 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T5 @ S3 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups2073611262835488442omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups2073611262835488442omplex @ G2 @ T5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5671_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > complex,H: real > complex] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( ( groups5754745047067104278omplex @ G2 @ C4 )
% 8.64/4.86 = ( groups5754745047067104278omplex @ H @ C4 ) )
% 8.64/4.86 => ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 8.64/4.86 = ( groups5754745047067104278omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5672_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > complex,H: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: int] :
% 8.64/4.86 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( ( groups3049146728041665814omplex @ G2 @ C4 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ H @ C4 ) )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5673_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > complex,H: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: complex] :
% 8.64/4.86 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( ( groups7754918857620584856omplex @ G2 @ C4 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ H @ C4 ) )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5674_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > real,H: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( ( groups8097168146408367636l_real @ G2 @ C4 )
% 8.64/4.86 = ( groups8097168146408367636l_real @ H @ C4 ) )
% 8.64/4.86 => ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 8.64/4.86 = ( groups8097168146408367636l_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5675_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > real,H: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: int] :
% 8.64/4.86 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( ( groups8778361861064173332t_real @ G2 @ C4 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ H @ C4 ) )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5676_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > real,H: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: complex] :
% 8.64/4.86 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( ( groups5808333547571424918x_real @ G2 @ C4 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ H @ C4 ) )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5677_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > rat,H: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( ( groups1300246762558778688al_rat @ G2 @ C4 )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ H @ C4 ) )
% 8.64/4.86 => ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5678_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > rat,H: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: int] :
% 8.64/4.86 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( ( groups3906332499630173760nt_rat @ G2 @ C4 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ H @ C4 ) )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5679_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > rat,H: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: complex] :
% 8.64/4.86 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( ( groups5058264527183730370ex_rat @ G2 @ C4 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ H @ C4 ) )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5680_sum_Osame__carrierI,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > nat,H: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( ( groups1935376822645274424al_nat @ G2 @ C4 )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ H @ C4 ) )
% 8.64/4.86 => ( ( groups1935376822645274424al_nat @ G2 @ A4 )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ H @ B5 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5681_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > complex,H: real > complex] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( ( groups5754745047067104278omplex @ G2 @ A4 )
% 8.64/4.86 = ( groups5754745047067104278omplex @ H @ B5 ) )
% 8.64/4.86 = ( ( groups5754745047067104278omplex @ G2 @ C4 )
% 8.64/4.86 = ( groups5754745047067104278omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5682_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > complex,H: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: int] :
% 8.64/4.86 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( ( groups3049146728041665814omplex @ G2 @ A4 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ H @ B5 ) )
% 8.64/4.86 = ( ( groups3049146728041665814omplex @ G2 @ C4 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5683_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > complex,H: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: complex] :
% 8.64/4.86 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( ( groups7754918857620584856omplex @ G2 @ A4 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ H @ B5 ) )
% 8.64/4.86 = ( ( groups7754918857620584856omplex @ G2 @ C4 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5684_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > real,H: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( ( groups8097168146408367636l_real @ G2 @ A4 )
% 8.64/4.86 = ( groups8097168146408367636l_real @ H @ B5 ) )
% 8.64/4.86 = ( ( groups8097168146408367636l_real @ G2 @ C4 )
% 8.64/4.86 = ( groups8097168146408367636l_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5685_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > real,H: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: int] :
% 8.64/4.86 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( ( groups8778361861064173332t_real @ G2 @ A4 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ H @ B5 ) )
% 8.64/4.86 = ( ( groups8778361861064173332t_real @ G2 @ C4 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5686_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > real,H: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: complex] :
% 8.64/4.86 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( ( groups5808333547571424918x_real @ G2 @ A4 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ H @ B5 ) )
% 8.64/4.86 = ( ( groups5808333547571424918x_real @ G2 @ C4 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5687_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > rat,H: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( ( groups1300246762558778688al_rat @ G2 @ A4 )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ H @ B5 ) )
% 8.64/4.86 = ( ( groups1300246762558778688al_rat @ G2 @ C4 )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5688_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_int,A4: set_int,B5: set_int,G2: int > rat,H: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: int] :
% 8.64/4.86 ( ( member_int @ A3 @ ( minus_minus_set_int @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( ( groups3906332499630173760nt_rat @ G2 @ A4 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ H @ B5 ) )
% 8.64/4.86 = ( ( groups3906332499630173760nt_rat @ G2 @ C4 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5689_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_complex,A4: set_complex,B5: set_complex,G2: complex > rat,H: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: complex] :
% 8.64/4.86 ( ( member_complex @ A3 @ ( minus_811609699411566653omplex @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( ( groups5058264527183730370ex_rat @ G2 @ A4 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ H @ B5 ) )
% 8.64/4.86 = ( ( groups5058264527183730370ex_rat @ G2 @ C4 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5690_sum_Osame__carrier,axiom,
% 8.64/4.86 ! [C4: set_real,A4: set_real,B5: set_real,G2: real > nat,H: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ C4 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ B5 @ C4 )
% 8.64/4.86 => ( ! [A3: real] :
% 8.64/4.86 ( ( member_real @ A3 @ ( minus_minus_set_real @ C4 @ A4 ) )
% 8.64/4.86 => ( ( G2 @ A3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ C4 @ B5 ) )
% 8.64/4.86 => ( ( H @ B3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( ( groups1935376822645274424al_nat @ G2 @ A4 )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ H @ B5 ) )
% 8.64/4.86 = ( ( groups1935376822645274424al_nat @ G2 @ C4 )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ H @ C4 ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5691_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > complex,G2: real > complex] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( finite_finite_real @ S3 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5754745047067104278omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups5754745047067104278omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5692_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,H: int > complex,G2: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( finite_finite_int @ S3 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups3049146728041665814omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5693_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ S3 )
% 8.64/4.86 = ( groups7754918857620584856omplex @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5694_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > real,G2: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( finite_finite_real @ S3 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups8097168146408367636l_real @ G2 @ S3 )
% 8.64/4.86 = ( groups8097168146408367636l_real @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5695_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,H: int > real,G2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( finite_finite_int @ S3 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ S3 )
% 8.64/4.86 = ( groups8778361861064173332t_real @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5696_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,H: complex > real,G2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ S3 )
% 8.64/4.86 = ( groups5808333547571424918x_real @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5697_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > rat,G2: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( finite_finite_real @ S3 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups1300246762558778688al_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups1300246762558778688al_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5698_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_int,S3: set_int,H: int > rat,G2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ T5 )
% 8.64/4.86 => ( ( finite_finite_int @ S3 )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ ( minus_minus_set_int @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [I3: int] :
% 8.64/4.86 ( ( member_int @ I3 @ ( minus_minus_set_int @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( inf_inf_set_int @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups3906332499630173760nt_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5699_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_complex,S3: set_complex,H: complex > rat,G2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [I3: complex] :
% 8.64/4.86 ( ( member_complex @ I3 @ ( minus_811609699411566653omplex @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ S3 )
% 8.64/4.86 = ( groups5058264527183730370ex_rat @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5700_sum_Omono__neutral__cong,axiom,
% 8.64/4.86 ! [T5: set_real,S3: set_real,H: real > nat,G2: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ T5 )
% 8.64/4.86 => ( ( finite_finite_real @ S3 )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ T5 @ S3 ) )
% 8.64/4.86 => ( ( H @ I3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ! [I3: real] :
% 8.64/4.86 ( ( member_real @ I3 @ ( minus_minus_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ I3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ ( inf_inf_set_real @ S3 @ T5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = ( H @ X3 ) ) )
% 8.64/4.86 => ( ( groups1935376822645274424al_nat @ G2 @ S3 )
% 8.64/4.86 = ( groups1935376822645274424al_nat @ H @ T5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5701_unity__coeff__ex,axiom,
% 8.64/4.86 ! [P2: complex > $o,L: complex] :
% 8.64/4.86 ( ( ? [X4: complex] : ( P2 @ ( times_times_complex @ L @ X4 ) ) )
% 8.64/4.86 = ( ? [X4: complex] :
% 8.64/4.86 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X4 @ zero_zero_complex ) )
% 8.64/4.86 & ( P2 @ X4 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5702_unity__coeff__ex,axiom,
% 8.64/4.86 ! [P2: real > $o,L: real] :
% 8.64/4.86 ( ( ? [X4: real] : ( P2 @ ( times_times_real @ L @ X4 ) ) )
% 8.64/4.86 = ( ? [X4: real] :
% 8.64/4.86 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X4 @ zero_zero_real ) )
% 8.64/4.86 & ( P2 @ X4 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5703_unity__coeff__ex,axiom,
% 8.64/4.86 ! [P2: rat > $o,L: rat] :
% 8.64/4.86 ( ( ? [X4: rat] : ( P2 @ ( times_times_rat @ L @ X4 ) ) )
% 8.64/4.86 = ( ? [X4: rat] :
% 8.64/4.86 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X4 @ zero_zero_rat ) )
% 8.64/4.86 & ( P2 @ X4 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5704_unity__coeff__ex,axiom,
% 8.64/4.86 ! [P2: nat > $o,L: nat] :
% 8.64/4.86 ( ( ? [X4: nat] : ( P2 @ ( times_times_nat @ L @ X4 ) ) )
% 8.64/4.86 = ( ? [X4: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X4 @ zero_zero_nat ) )
% 8.64/4.86 & ( P2 @ X4 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5705_unity__coeff__ex,axiom,
% 8.64/4.86 ! [P2: int > $o,L: int] :
% 8.64/4.86 ( ( ? [X4: int] : ( P2 @ ( times_times_int @ L @ X4 ) ) )
% 8.64/4.86 = ( ? [X4: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X4 @ zero_zero_int ) )
% 8.64/4.86 & ( P2 @ X4 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5706_unit__dvdE,axiom,
% 8.64/4.86 ! [A: code_integer,B: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.86 => ~ ( ( A != zero_z3403309356797280102nteger )
% 8.64/4.86 => ! [C: code_integer] :
% 8.64/4.86 ( B
% 8.64/4.86 != ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5707_unit__dvdE,axiom,
% 8.64/4.86 ! [A: nat,B: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.86 => ~ ( ( A != zero_zero_nat )
% 8.64/4.86 => ! [C: nat] :
% 8.64/4.86 ( B
% 8.64/4.86 != ( times_times_nat @ A @ C ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5708_unit__dvdE,axiom,
% 8.64/4.86 ! [A: int,B: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.86 => ~ ( ( A != zero_zero_int )
% 8.64/4.86 => ! [C: int] :
% 8.64/4.86 ( B
% 8.64/4.86 != ( times_times_int @ A @ C ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5709_dvd__div__div__eq__mult,axiom,
% 8.64/4.86 ! [A: nat,C2: nat,B: nat,D: nat] :
% 8.64/4.86 ( ( A != zero_zero_nat )
% 8.64/4.86 => ( ( C2 != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.86 => ( ( dvd_dvd_nat @ C2 @ D )
% 8.64/4.86 => ( ( ( divide_divide_nat @ B @ A )
% 8.64/4.86 = ( divide_divide_nat @ D @ C2 ) )
% 8.64/4.86 = ( ( times_times_nat @ B @ C2 )
% 8.64/4.86 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5710_dvd__div__div__eq__mult,axiom,
% 8.64/4.86 ! [A: int,C2: int,B: int,D: int] :
% 8.64/4.86 ( ( A != zero_zero_int )
% 8.64/4.86 => ( ( C2 != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ A @ B )
% 8.64/4.86 => ( ( dvd_dvd_int @ C2 @ D )
% 8.64/4.86 => ( ( ( divide_divide_int @ B @ A )
% 8.64/4.86 = ( divide_divide_int @ D @ C2 ) )
% 8.64/4.86 = ( ( times_times_int @ B @ C2 )
% 8.64/4.86 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5711_dvd__div__iff__mult,axiom,
% 8.64/4.86 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.86 ( ( C2 != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ C2 @ B )
% 8.64/4.86 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 8.64/4.86 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C2 ) @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5712_dvd__div__iff__mult,axiom,
% 8.64/4.86 ! [C2: int,B: int,A: int] :
% 8.64/4.86 ( ( C2 != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ C2 @ B )
% 8.64/4.86 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 8.64/4.86 = ( dvd_dvd_int @ ( times_times_int @ A @ C2 ) @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5713_div__dvd__iff__mult,axiom,
% 8.64/4.86 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.86 ( ( B != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ B @ A )
% 8.64/4.86 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 8.64/4.86 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C2 @ B ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5714_div__dvd__iff__mult,axiom,
% 8.64/4.86 ! [B: int,A: int,C2: int] :
% 8.64/4.86 ( ( B != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ B @ A )
% 8.64/4.86 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 8.64/4.86 = ( dvd_dvd_int @ A @ ( times_times_int @ C2 @ B ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5715_dvd__div__eq__mult,axiom,
% 8.64/4.86 ! [A: nat,B: nat,C2: nat] :
% 8.64/4.86 ( ( A != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ A @ B )
% 8.64/4.86 => ( ( ( divide_divide_nat @ B @ A )
% 8.64/4.86 = C2 )
% 8.64/4.86 = ( B
% 8.64/4.86 = ( times_times_nat @ C2 @ A ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5716_dvd__div__eq__mult,axiom,
% 8.64/4.86 ! [A: int,B: int,C2: int] :
% 8.64/4.86 ( ( A != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ A @ B )
% 8.64/4.86 => ( ( ( divide_divide_int @ B @ A )
% 8.64/4.86 = C2 )
% 8.64/4.86 = ( B
% 8.64/4.86 = ( times_times_int @ C2 @ A ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5717_unit__div__eq__0__iff,axiom,
% 8.64/4.86 ! [B: code_integer,A: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 8.64/4.86 = zero_z3403309356797280102nteger )
% 8.64/4.86 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5718_unit__div__eq__0__iff,axiom,
% 8.64/4.86 ! [B: nat,A: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( ( divide_divide_nat @ A @ B )
% 8.64/4.86 = zero_zero_nat )
% 8.64/4.86 = ( A = zero_zero_nat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5719_unit__div__eq__0__iff,axiom,
% 8.64/4.86 ! [B: int,A: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( ( divide_divide_int @ A @ B )
% 8.64/4.86 = zero_zero_int )
% 8.64/4.86 = ( A = zero_zero_int ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5720_inf__period_I4_J,axiom,
% 8.64/4.86 ! [D: real,D3: real,T: real] :
% 8.64/4.86 ( ( dvd_dvd_real @ D @ D3 )
% 8.64/4.86 => ! [X5: real,K4: real] :
% 8.64/4.86 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) ) )
% 8.64/4.86 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5721_inf__period_I4_J,axiom,
% 8.64/4.86 ! [D: rat,D3: rat,T: rat] :
% 8.64/4.86 ( ( dvd_dvd_rat @ D @ D3 )
% 8.64/4.86 => ! [X5: rat,K4: rat] :
% 8.64/4.86 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) ) )
% 8.64/4.86 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5722_inf__period_I4_J,axiom,
% 8.64/4.86 ! [D: int,D3: int,T: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ D @ D3 )
% 8.64/4.86 => ! [X5: int,K4: int] :
% 8.64/4.86 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) ) )
% 8.64/4.86 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5723_inf__period_I3_J,axiom,
% 8.64/4.86 ! [D: real,D3: real,T: real] :
% 8.64/4.86 ( ( dvd_dvd_real @ D @ D3 )
% 8.64/4.86 => ! [X5: real,K4: real] :
% 8.64/4.86 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X5 @ T ) )
% 8.64/4.86 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X5 @ ( times_times_real @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5724_inf__period_I3_J,axiom,
% 8.64/4.86 ! [D: rat,D3: rat,T: rat] :
% 8.64/4.86 ( ( dvd_dvd_rat @ D @ D3 )
% 8.64/4.86 => ! [X5: rat,K4: rat] :
% 8.64/4.86 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X5 @ T ) )
% 8.64/4.86 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X5 @ ( times_times_rat @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5725_inf__period_I3_J,axiom,
% 8.64/4.86 ! [D: int,D3: int,T: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ D @ D3 )
% 8.64/4.86 => ! [X5: int,K4: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X5 @ T ) )
% 8.64/4.86 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X5 @ ( times_times_int @ K4 @ D3 ) ) @ T ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5726_unit__eq__div1,axiom,
% 8.64/4.86 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 8.64/4.86 = C2 )
% 8.64/4.86 = ( A
% 8.64/4.86 = ( times_3573771949741848930nteger @ C2 @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5727_unit__eq__div1,axiom,
% 8.64/4.86 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( ( divide_divide_nat @ A @ B )
% 8.64/4.86 = C2 )
% 8.64/4.86 = ( A
% 8.64/4.86 = ( times_times_nat @ C2 @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5728_unit__eq__div1,axiom,
% 8.64/4.86 ! [B: int,A: int,C2: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( ( divide_divide_int @ A @ B )
% 8.64/4.86 = C2 )
% 8.64/4.86 = ( A
% 8.64/4.86 = ( times_times_int @ C2 @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5729_unit__eq__div2,axiom,
% 8.64/4.86 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( A
% 8.64/4.86 = ( divide6298287555418463151nteger @ C2 @ B ) )
% 8.64/4.86 = ( ( times_3573771949741848930nteger @ A @ B )
% 8.64/4.86 = C2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5730_unit__eq__div2,axiom,
% 8.64/4.86 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( A
% 8.64/4.86 = ( divide_divide_nat @ C2 @ B ) )
% 8.64/4.86 = ( ( times_times_nat @ A @ B )
% 8.64/4.86 = C2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5731_unit__eq__div2,axiom,
% 8.64/4.86 ! [B: int,A: int,C2: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( A
% 8.64/4.86 = ( divide_divide_int @ C2 @ B ) )
% 8.64/4.86 = ( ( times_times_int @ A @ B )
% 8.64/4.86 = C2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5732_div__mult__unit2,axiom,
% 8.64/4.86 ! [C2: code_integer,B: code_integer,A: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 8.64/4.86 => ( ( dvd_dvd_Code_integer @ B @ A )
% 8.64/4.86 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 8.64/4.86 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5733_div__mult__unit2,axiom,
% 8.64/4.86 ! [C2: nat,B: nat,A: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ B @ A )
% 8.64/4.86 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.86 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5734_div__mult__unit2,axiom,
% 8.64/4.86 ! [C2: int,B: int,A: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ B @ A )
% 8.64/4.86 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.86 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5735_unit__div__commute,axiom,
% 8.64/4.86 ! [B: code_integer,A: code_integer,C2: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 )
% 8.64/4.86 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5736_unit__div__commute,axiom,
% 8.64/4.86 ! [B: nat,A: nat,C2: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C2 )
% 8.64/4.86 = ( divide_divide_nat @ ( times_times_nat @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5737_unit__div__commute,axiom,
% 8.64/4.86 ! [B: int,A: int,C2: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C2 )
% 8.64/4.86 = ( divide_divide_int @ ( times_times_int @ A @ C2 ) @ B ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5738_unit__div__mult__swap,axiom,
% 8.64/4.86 ! [C2: code_integer,A: code_integer,B: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 8.64/4.86 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C2 ) )
% 8.64/4.86 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5739_unit__div__mult__swap,axiom,
% 8.64/4.86 ! [C2: nat,A: nat,B: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 8.64/4.86 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C2 ) )
% 8.64/4.86 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5740_unit__div__mult__swap,axiom,
% 8.64/4.86 ! [C2: int,A: int,B: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ C2 @ one_one_int )
% 8.64/4.86 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C2 ) )
% 8.64/4.86 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5741_is__unit__div__mult2__eq,axiom,
% 8.64/4.86 ! [B: code_integer,C2: code_integer,A: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( dvd_dvd_Code_integer @ C2 @ one_one_Code_integer )
% 8.64/4.86 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C2 ) )
% 8.64/4.86 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5742_is__unit__div__mult2__eq,axiom,
% 8.64/4.86 ! [B: nat,C2: nat,A: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ C2 @ one_one_nat )
% 8.64/4.86 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C2 ) )
% 8.64/4.86 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5743_is__unit__div__mult2__eq,axiom,
% 8.64/4.86 ! [B: int,C2: int,A: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ C2 @ one_one_int )
% 8.64/4.86 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C2 ) )
% 8.64/4.86 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5744_is__unit__power__iff,axiom,
% 8.64/4.86 ! [A: code_integer,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 8.64/4.86 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.86 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5745_is__unit__power__iff,axiom,
% 8.64/4.86 ! [A: nat,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 8.64/4.86 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.86 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5746_is__unit__power__iff,axiom,
% 8.64/4.86 ! [A: int,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 8.64/4.86 = ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.86 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5747_unit__imp__mod__eq__0,axiom,
% 8.64/4.86 ! [B: code_integer,A: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( modulo364778990260209775nteger @ A @ B )
% 8.64/4.86 = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5748_unit__imp__mod__eq__0,axiom,
% 8.64/4.86 ! [B: nat,A: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( modulo_modulo_nat @ A @ B )
% 8.64/4.86 = zero_zero_nat ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5749_unit__imp__mod__eq__0,axiom,
% 8.64/4.86 ! [B: int,A: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( modulo_modulo_int @ A @ B )
% 8.64/4.86 = zero_zero_int ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5750_unit__imp__mod__eq__0,axiom,
% 8.64/4.86 ! [B: code_natural,A: code_natural] :
% 8.64/4.86 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 8.64/4.86 => ( ( modulo8411746178871703098atural @ A @ B )
% 8.64/4.86 = zero_z2226904508553997617atural ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5751_pochhammer__nonneg,axiom,
% 8.64/4.86 ! [X: real,N: nat] :
% 8.64/4.86 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5752_pochhammer__nonneg,axiom,
% 8.64/4.86 ! [X: rat,N: nat] :
% 8.64/4.86 ( ( ord_less_rat @ zero_zero_rat @ X )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5753_pochhammer__nonneg,axiom,
% 8.64/4.86 ! [X: nat,N: nat] :
% 8.64/4.86 ( ( ord_less_nat @ zero_zero_nat @ X )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5754_pochhammer__nonneg,axiom,
% 8.64/4.86 ! [X: int,N: nat] :
% 8.64/4.86 ( ( ord_less_int @ zero_zero_int @ X )
% 8.64/4.86 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5755_dvd__imp__le,axiom,
% 8.64/4.86 ! [K2: nat,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ K2 @ N )
% 8.64/4.86 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.86 => ( ord_less_eq_nat @ K2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5756_dvd__mult__cancel,axiom,
% 8.64/4.86 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.64/4.86 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.86 => ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5757_nat__mult__dvd__cancel1,axiom,
% 8.64/4.86 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.86 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.86 => ( ( dvd_dvd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) )
% 8.64/4.86 = ( dvd_dvd_nat @ M2 @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5758_pochhammer__0__left,axiom,
% 8.64/4.86 ! [N: nat] :
% 8.64/4.86 ( ( ( N = zero_zero_nat )
% 8.64/4.86 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 8.64/4.86 = one_one_Code_integer ) )
% 8.64/4.86 & ( ( N != zero_zero_nat )
% 8.64/4.86 => ( ( comm_s8582702949713902594nteger @ zero_z3403309356797280102nteger @ N )
% 8.64/4.86 = zero_z3403309356797280102nteger ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5759_pochhammer__0__left,axiom,
% 8.64/4.86 ! [N: nat] :
% 8.64/4.86 ( ( ( N = zero_zero_nat )
% 8.64/4.86 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 8.64/4.86 = one_one_complex ) )
% 8.64/4.86 & ( ( N != zero_zero_nat )
% 8.64/4.86 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N )
% 8.64/4.86 = zero_zero_complex ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5760_pochhammer__0__left,axiom,
% 8.64/4.86 ! [N: nat] :
% 8.64/4.86 ( ( ( N = zero_zero_nat )
% 8.64/4.86 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 8.64/4.86 = one_one_real ) )
% 8.64/4.86 & ( ( N != zero_zero_nat )
% 8.64/4.86 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N )
% 8.64/4.86 = zero_zero_real ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5761_pochhammer__0__left,axiom,
% 8.64/4.86 ! [N: nat] :
% 8.64/4.86 ( ( ( N = zero_zero_nat )
% 8.64/4.86 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 8.64/4.86 = one_one_rat ) )
% 8.64/4.86 & ( ( N != zero_zero_nat )
% 8.64/4.86 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N )
% 8.64/4.86 = zero_zero_rat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5762_pochhammer__0__left,axiom,
% 8.64/4.86 ! [N: nat] :
% 8.64/4.86 ( ( ( N = zero_zero_nat )
% 8.64/4.86 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 8.64/4.86 = one_one_nat ) )
% 8.64/4.86 & ( ( N != zero_zero_nat )
% 8.64/4.86 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N )
% 8.64/4.86 = zero_zero_nat ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5763_pochhammer__0__left,axiom,
% 8.64/4.86 ! [N: nat] :
% 8.64/4.86 ( ( ( N = zero_zero_nat )
% 8.64/4.86 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 8.64/4.86 = one_one_int ) )
% 8.64/4.86 & ( ( N != zero_zero_nat )
% 8.64/4.86 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N )
% 8.64/4.86 = zero_zero_int ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5764_bezout__add__strong__nat,axiom,
% 8.64/4.86 ! [A: nat,B: nat] :
% 8.64/4.86 ( ( A != zero_zero_nat )
% 8.64/4.86 => ? [D5: nat,X3: nat,Y3: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ D5 @ A )
% 8.64/4.86 & ( dvd_dvd_nat @ D5 @ B )
% 8.64/4.86 & ( ( times_times_nat @ A @ X3 )
% 8.64/4.86 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D5 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5765_mod__greater__zero__iff__not__dvd,axiom,
% 8.64/4.86 ! [M2: nat,N: nat] :
% 8.64/4.86 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M2 @ N ) )
% 8.64/4.86 = ( ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5766_mod__eq__dvd__iff__nat,axiom,
% 8.64/4.86 ! [N: nat,M2: nat,Q2: nat] :
% 8.64/4.86 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.86 => ( ( ( modulo_modulo_nat @ M2 @ Q2 )
% 8.64/4.86 = ( modulo_modulo_nat @ N @ Q2 ) )
% 8.64/4.86 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5767_sum__power__add,axiom,
% 8.64/4.86 ! [X: complex,M2: nat,I5: set_nat] :
% 8.64/4.86 ( ( groups2073611262835488442omplex
% 8.64/4.86 @ ^ [I: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M2 @ I ) )
% 8.64/4.86 @ I5 )
% 8.64/4.86 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5768_sum__power__add,axiom,
% 8.64/4.86 ! [X: rat,M2: nat,I5: set_nat] :
% 8.64/4.86 ( ( groups2906978787729119204at_rat
% 8.64/4.86 @ ^ [I: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M2 @ I ) )
% 8.64/4.86 @ I5 )
% 8.64/4.86 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5769_sum__power__add,axiom,
% 8.64/4.86 ! [X: int,M2: nat,I5: set_nat] :
% 8.64/4.86 ( ( groups3539618377306564664at_int
% 8.64/4.86 @ ^ [I: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M2 @ I ) )
% 8.64/4.86 @ I5 )
% 8.64/4.86 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5770_sum__power__add,axiom,
% 8.64/4.86 ! [X: real,M2: nat,I5: set_nat] :
% 8.64/4.86 ( ( groups6591440286371151544t_real
% 8.64/4.86 @ ^ [I: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M2 @ I ) )
% 8.64/4.86 @ I5 )
% 8.64/4.86 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I5 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5771_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_real,A4: set_real,F2: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( groups8097168146408367636l_real @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5772_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_int,A4: set_int,F2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5773_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_complex,A4: set_complex,F2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5774_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_real,A4: set_real,F2: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( groups1300246762558778688al_rat @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5775_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_int,A4: set_int,F2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5776_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_complex,A4: set_complex,F2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5777_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_real,A4: set_real,F2: real > nat] :
% 8.64/4.86 ( ( finite_finite_real @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5778_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_int,A4: set_int,F2: int > nat] :
% 8.64/4.86 ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: int] :
% 8.64/4.86 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5779_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_complex,A4: set_complex,F2: complex > nat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: complex] :
% 8.64/4.86 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5780_sum__mono2,axiom,
% 8.64/4.86 ! [B5: set_real,A4: set_real,F2: real > int] :
% 8.64/4.86 ( ( finite_finite_real @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.86 => ( ! [B3: real] :
% 8.64/4.86 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.86 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ B3 ) ) )
% 8.64/4.86 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( groups1932886352136224148al_int @ F2 @ B5 ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5781_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_int,B5: set_int,G2: int > complex] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups3049146728041665814omplex @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_complex @ ( groups3049146728041665814omplex @ G2 @ A4 ) @ ( groups3049146728041665814omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5782_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_complex,B5: set_complex,G2: complex > complex] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups7754918857620584856omplex @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G2 @ A4 ) @ ( groups7754918857620584856omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5783_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_int,B5: set_int,G2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( groups8778361861064173332t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G2 @ A4 ) @ ( groups8778361861064173332t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5784_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_real ) )
% 8.64/4.86 => ( ( groups5808333547571424918x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G2 @ A4 ) @ ( groups5808333547571424918x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5785_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( groups3906332499630173760nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G2 @ A4 ) @ ( groups3906332499630173760nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5786_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_rat ) )
% 8.64/4.86 => ( ( groups5058264527183730370ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G2 @ A4 ) @ ( groups5058264527183730370ex_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5787_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 8.64/4.86 ( ( finite_finite_int @ A4 )
% 8.64/4.86 => ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( groups4541462559716669496nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5788_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_nat ) )
% 8.64/4.86 => ( ( groups5693394587270226106ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5789_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.86 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_int ) )
% 8.64/4.86 => ( ( groups5690904116761175830ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G2 @ A4 ) @ ( groups5690904116761175830ex_int @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5790_sum_Ounion__inter__neutral,axiom,
% 8.64/4.86 ! [A4: set_nat,B5: set_nat,G2: nat > complex] :
% 8.64/4.86 ( ( finite_finite_nat @ A4 )
% 8.64/4.86 => ( ( finite_finite_nat @ B5 )
% 8.64/4.86 => ( ! [X3: nat] :
% 8.64/4.86 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 8.64/4.86 => ( ( G2 @ X3 )
% 8.64/4.86 = zero_zero_complex ) )
% 8.64/4.86 => ( ( groups2073611262835488442omplex @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.86 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G2 @ A4 ) @ ( groups2073611262835488442omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5791_sum_OatLeastAtMost__rev,axiom,
% 8.64/4.86 ! [G2: nat > nat,N: nat,M2: nat] :
% 8.64/4.86 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 8.64/4.86 = ( groups3542108847815614940at_nat
% 8.64/4.86 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 8.64/4.86 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5792_sum_OatLeastAtMost__rev,axiom,
% 8.64/4.86 ! [G2: nat > real,N: nat,M2: nat] :
% 8.64/4.86 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 8.64/4.86 = ( groups6591440286371151544t_real
% 8.64/4.86 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 8.64/4.86 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5793_finite__divisors__nat,axiom,
% 8.64/4.86 ! [M2: nat] :
% 8.64/4.86 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.86 => ( finite_finite_nat
% 8.64/4.86 @ ( collect_nat
% 8.64/4.86 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5794_powser__sums__zero,axiom,
% 8.64/4.86 ! [A: nat > complex] :
% 8.64/4.86 ( sums_complex
% 8.64/4.86 @ ^ [N4: nat] : ( times_times_complex @ ( A @ N4 ) @ ( power_power_complex @ zero_zero_complex @ N4 ) )
% 8.64/4.86 @ ( A @ zero_zero_nat ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5795_powser__sums__zero,axiom,
% 8.64/4.86 ! [A: nat > real] :
% 8.64/4.86 ( sums_real
% 8.64/4.86 @ ^ [N4: nat] : ( times_times_real @ ( A @ N4 ) @ ( power_power_real @ zero_zero_real @ N4 ) )
% 8.64/4.86 @ ( A @ zero_zero_nat ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5796_sum__shift__lb__Suc0__0,axiom,
% 8.64/4.86 ! [F2: nat > complex,K2: nat] :
% 8.64/4.86 ( ( ( F2 @ zero_zero_nat )
% 8.64/4.86 = zero_zero_complex )
% 8.64/4.86 => ( ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 8.64/4.86 = ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5797_sum__shift__lb__Suc0__0,axiom,
% 8.64/4.86 ! [F2: nat > rat,K2: nat] :
% 8.64/4.86 ( ( ( F2 @ zero_zero_nat )
% 8.64/4.86 = zero_zero_rat )
% 8.64/4.86 => ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 8.64/4.86 = ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5798_sum__shift__lb__Suc0__0,axiom,
% 8.64/4.86 ! [F2: nat > int,K2: nat] :
% 8.64/4.86 ( ( ( F2 @ zero_zero_nat )
% 8.64/4.86 = zero_zero_int )
% 8.64/4.86 => ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 8.64/4.86 = ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5799_sum__shift__lb__Suc0__0,axiom,
% 8.64/4.86 ! [F2: nat > nat,K2: nat] :
% 8.64/4.86 ( ( ( F2 @ zero_zero_nat )
% 8.64/4.86 = zero_zero_nat )
% 8.64/4.86 => ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 8.64/4.86 = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5800_sum__shift__lb__Suc0__0,axiom,
% 8.64/4.86 ! [F2: nat > real,K2: nat] :
% 8.64/4.86 ( ( ( F2 @ zero_zero_nat )
% 8.64/4.86 = zero_zero_real )
% 8.64/4.86 => ( ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K2 ) )
% 8.64/4.86 = ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5801_sum_OatLeast0__atMost__Suc,axiom,
% 8.64/4.86 ! [G2: nat > rat,N: nat] :
% 8.64/4.86 ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5802_sum_OatLeast0__atMost__Suc,axiom,
% 8.64/4.86 ! [G2: nat > int,N: nat] :
% 8.64/4.86 ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5803_sum_OatLeast0__atMost__Suc,axiom,
% 8.64/4.86 ! [G2: nat > nat,N: nat] :
% 8.64/4.86 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5804_sum_OatLeast0__atMost__Suc,axiom,
% 8.64/4.86 ! [G2: nat > real,N: nat] :
% 8.64/4.86 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5805_sum_OatLeast__Suc__atMost,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > rat] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.86 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.86 = ( plus_plus_rat @ ( G2 @ M2 ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5806_sum_OatLeast__Suc__atMost,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > int] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.86 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.86 = ( plus_plus_int @ ( G2 @ M2 ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5807_sum_OatLeast__Suc__atMost,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > nat] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.86 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.86 = ( plus_plus_nat @ ( G2 @ M2 ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5808_sum_OatLeast__Suc__atMost,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > real] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.86 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.86 = ( plus_plus_real @ ( G2 @ M2 ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5809_sum_Onat__ivl__Suc_H,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > rat] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.86 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_rat @ ( G2 @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5810_sum_Onat__ivl__Suc_H,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > int] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.86 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_int @ ( G2 @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5811_sum_Onat__ivl__Suc_H,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > nat] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.86 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_nat @ ( G2 @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5812_sum_Onat__ivl__Suc_H,axiom,
% 8.64/4.86 ! [M2: nat,N: nat,G2: nat > real] :
% 8.64/4.86 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.86 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.86 = ( plus_plus_real @ ( G2 @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5813_even__zero,axiom,
% 8.64/4.86 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5814_even__zero,axiom,
% 8.64/4.86 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5815_is__unitE,axiom,
% 8.64/4.86 ! [A: code_integer,C2: code_integer] :
% 8.64/4.86 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 8.64/4.86 => ~ ( ( A != zero_z3403309356797280102nteger )
% 8.64/4.86 => ! [B3: code_integer] :
% 8.64/4.86 ( ( B3 != zero_z3403309356797280102nteger )
% 8.64/4.86 => ( ( dvd_dvd_Code_integer @ B3 @ one_one_Code_integer )
% 8.64/4.86 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 8.64/4.86 = B3 )
% 8.64/4.86 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B3 )
% 8.64/4.86 = A )
% 8.64/4.86 => ( ( ( times_3573771949741848930nteger @ A @ B3 )
% 8.64/4.86 = one_one_Code_integer )
% 8.64/4.86 => ( ( divide6298287555418463151nteger @ C2 @ A )
% 8.64/4.86 != ( times_3573771949741848930nteger @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5816_is__unitE,axiom,
% 8.64/4.86 ! [A: nat,C2: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 8.64/4.86 => ~ ( ( A != zero_zero_nat )
% 8.64/4.86 => ! [B3: nat] :
% 8.64/4.86 ( ( B3 != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ B3 @ one_one_nat )
% 8.64/4.86 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 8.64/4.86 = B3 )
% 8.64/4.86 => ( ( ( divide_divide_nat @ one_one_nat @ B3 )
% 8.64/4.86 = A )
% 8.64/4.86 => ( ( ( times_times_nat @ A @ B3 )
% 8.64/4.86 = one_one_nat )
% 8.64/4.86 => ( ( divide_divide_nat @ C2 @ A )
% 8.64/4.86 != ( times_times_nat @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5817_is__unitE,axiom,
% 8.64/4.86 ! [A: int,C2: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ A @ one_one_int )
% 8.64/4.86 => ~ ( ( A != zero_zero_int )
% 8.64/4.86 => ! [B3: int] :
% 8.64/4.86 ( ( B3 != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ B3 @ one_one_int )
% 8.64/4.86 => ( ( ( divide_divide_int @ one_one_int @ A )
% 8.64/4.86 = B3 )
% 8.64/4.86 => ( ( ( divide_divide_int @ one_one_int @ B3 )
% 8.64/4.86 = A )
% 8.64/4.86 => ( ( ( times_times_int @ A @ B3 )
% 8.64/4.86 = one_one_int )
% 8.64/4.86 => ( ( divide_divide_int @ C2 @ A )
% 8.64/4.86 != ( times_times_int @ C2 @ B3 ) ) ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5818_is__unit__div__mult__cancel__left,axiom,
% 8.64/4.86 ! [A: code_integer,B: code_integer] :
% 8.64/4.86 ( ( A != zero_z3403309356797280102nteger )
% 8.64/4.86 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.64/4.86 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5819_is__unit__div__mult__cancel__left,axiom,
% 8.64/4.86 ! [A: nat,B: nat] :
% 8.64/4.86 ( ( A != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 8.64/4.86 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5820_is__unit__div__mult__cancel__left,axiom,
% 8.64/4.86 ! [A: int,B: int] :
% 8.64/4.86 ( ( A != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 8.64/4.86 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5821_is__unit__div__mult__cancel__right,axiom,
% 8.64/4.86 ! [A: code_integer,B: code_integer] :
% 8.64/4.86 ( ( A != zero_z3403309356797280102nteger )
% 8.64/4.86 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 8.64/4.86 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 8.64/4.86 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5822_is__unit__div__mult__cancel__right,axiom,
% 8.64/4.86 ! [A: nat,B: nat] :
% 8.64/4.86 ( ( A != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 8.64/4.86 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 8.64/4.86 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5823_is__unit__div__mult__cancel__right,axiom,
% 8.64/4.86 ! [A: int,B: int] :
% 8.64/4.86 ( ( A != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ B @ one_one_int )
% 8.64/4.86 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 8.64/4.86 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5824_evenE,axiom,
% 8.64/4.86 ! [A: nat] :
% 8.64/4.86 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.86 => ~ ! [B3: nat] :
% 8.64/4.86 ( A
% 8.64/4.86 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5825_evenE,axiom,
% 8.64/4.86 ! [A: int] :
% 8.64/4.86 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.86 => ~ ! [B3: int] :
% 8.64/4.86 ( A
% 8.64/4.86 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5826_dvd__power__iff,axiom,
% 8.64/4.86 ! [X: code_integer,M2: nat,N: nat] :
% 8.64/4.86 ( ( X != zero_z3403309356797280102nteger )
% 8.64/4.86 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 8.64/4.86 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 8.64/4.86 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5827_dvd__power__iff,axiom,
% 8.64/4.86 ! [X: nat,M2: nat,N: nat] :
% 8.64/4.86 ( ( X != zero_zero_nat )
% 8.64/4.86 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M2 ) @ ( power_power_nat @ X @ N ) )
% 8.64/4.86 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 8.64/4.86 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5828_dvd__power__iff,axiom,
% 8.64/4.86 ! [X: int,M2: nat,N: nat] :
% 8.64/4.86 ( ( X != zero_zero_int )
% 8.64/4.86 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ N ) )
% 8.64/4.86 = ( ( dvd_dvd_int @ X @ one_one_int )
% 8.64/4.86 | ( ord_less_eq_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5829_dvd__power,axiom,
% 8.64/4.86 ! [N: nat,X: code_integer] :
% 8.64/4.86 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.86 | ( X = one_one_Code_integer ) )
% 8.64/4.86 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5830_dvd__power,axiom,
% 8.64/4.86 ! [N: nat,X: nat] :
% 8.64/4.86 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.86 | ( X = one_one_nat ) )
% 8.64/4.86 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5831_dvd__power,axiom,
% 8.64/4.86 ! [N: nat,X: real] :
% 8.64/4.86 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.86 | ( X = one_one_real ) )
% 8.64/4.86 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5832_dvd__power,axiom,
% 8.64/4.86 ! [N: nat,X: int] :
% 8.64/4.86 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.86 | ( X = one_one_int ) )
% 8.64/4.86 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5833_dvd__power,axiom,
% 8.64/4.86 ! [N: nat,X: complex] :
% 8.64/4.86 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.86 | ( X = one_one_complex ) )
% 8.64/4.86 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5834_sum__strict__mono2,axiom,
% 8.64/4.86 ! [B5: set_real,A4: set_real,B: real,F2: real > real] :
% 8.64/4.86 ( ( finite_finite_real @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.86 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.86 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ B5 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.86 => ( ord_less_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( groups8097168146408367636l_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5835_sum__strict__mono2,axiom,
% 8.64/4.86 ! [B5: set_int,A4: set_int,B: int,F2: int > real] :
% 8.64/4.86 ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.86 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.86 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ B5 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.86 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( groups8778361861064173332t_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5836_sum__strict__mono2,axiom,
% 8.64/4.86 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > real] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.86 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.86 => ( ( ord_less_real @ zero_zero_real @ ( F2 @ B ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ B5 )
% 8.64/4.86 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.86 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( groups5808333547571424918x_real @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5837_sum__strict__mono2,axiom,
% 8.64/4.86 ! [B5: set_real,A4: set_real,B: real,F2: real > rat] :
% 8.64/4.86 ( ( finite_finite_real @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.86 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.86 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 8.64/4.86 => ( ! [X3: real] :
% 8.64/4.86 ( ( member_real @ X3 @ B5 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( groups1300246762558778688al_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5838_sum__strict__mono2,axiom,
% 8.64/4.86 ! [B5: set_int,A4: set_int,B: int,F2: int > rat] :
% 8.64/4.86 ( ( finite_finite_int @ B5 )
% 8.64/4.86 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.86 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.86 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 8.64/4.86 => ( ! [X3: int] :
% 8.64/4.86 ( ( member_int @ X3 @ B5 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( groups3906332499630173760nt_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.86
% 8.64/4.86 thf(fact_5839_sum__strict__mono2,axiom,
% 8.64/4.86 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > rat] :
% 8.64/4.86 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.86 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.86 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.86 => ( ( ord_less_rat @ zero_zero_rat @ ( F2 @ B ) )
% 8.64/4.86 => ( ! [X3: complex] :
% 8.64/4.86 ( ( member_complex @ X3 @ B5 )
% 8.64/4.86 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.86 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( groups5058264527183730370ex_rat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5840_sum__strict__mono2,axiom,
% 8.64/4.87 ! [B5: set_real,A4: set_real,B: real,F2: real > nat] :
% 8.64/4.87 ( ( finite_finite_real @ B5 )
% 8.64/4.87 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.87 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ B5 )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5841_sum__strict__mono2,axiom,
% 8.64/4.87 ! [B5: set_int,A4: set_int,B: int,F2: int > nat] :
% 8.64/4.87 ( ( finite_finite_int @ B5 )
% 8.64/4.87 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.87 => ( ( member_int @ B @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ B5 )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5842_sum__strict__mono2,axiom,
% 8.64/4.87 ! [B5: set_complex,A4: set_complex,B: complex,F2: complex > nat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.87 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.87 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( F2 @ B ) )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ B5 )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5843_sum__strict__mono2,axiom,
% 8.64/4.87 ! [B5: set_real,A4: set_real,B: real,F2: real > int] :
% 8.64/4.87 ( ( finite_finite_real @ B5 )
% 8.64/4.87 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.87 => ( ( member_real @ B @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.87 => ( ( ord_less_int @ zero_zero_int @ ( F2 @ B ) )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ B5 )
% 8.64/4.87 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( groups1932886352136224148al_int @ F2 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5844_member__le__sum,axiom,
% 8.64/4.87 ! [I2: complex,A4: set_complex,F2: complex > real] :
% 8.64/4.87 ( ( member_complex @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups5808333547571424918x_real @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5845_member__le__sum,axiom,
% 8.64/4.87 ! [I2: int,A4: set_int,F2: int > real] :
% 8.64/4.87 ( ( member_int @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups8778361861064173332t_real @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5846_member__le__sum,axiom,
% 8.64/4.87 ! [I2: real,A4: set_real,F2: real > real] :
% 8.64/4.87 ( ( member_real @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I2 ) @ ( groups8097168146408367636l_real @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5847_member__le__sum,axiom,
% 8.64/4.87 ! [I2: complex,A4: set_complex,F2: complex > rat] :
% 8.64/4.87 ( ( member_complex @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5848_member__le__sum,axiom,
% 8.64/4.87 ! [I2: int,A4: set_int,F2: int > rat] :
% 8.64/4.87 ( ( member_int @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5849_member__le__sum,axiom,
% 8.64/4.87 ! [I2: real,A4: set_real,F2: real > rat] :
% 8.64/4.87 ( ( member_real @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups1300246762558778688al_rat @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5850_member__le__sum,axiom,
% 8.64/4.87 ! [I2: nat,A4: set_nat,F2: nat > rat] :
% 8.64/4.87 ( ( member_nat @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ I2 @ bot_bot_set_nat ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I2 ) @ ( groups2906978787729119204at_rat @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5851_member__le__sum,axiom,
% 8.64/4.87 ! [I2: complex,A4: set_complex,F2: complex > nat] :
% 8.64/4.87 ( ( member_complex @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ I2 @ bot_bot_set_complex ) ) )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5852_member__le__sum,axiom,
% 8.64/4.87 ! [I2: int,A4: set_int,F2: int > nat] :
% 8.64/4.87 ( ( member_int @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ ( minus_minus_set_int @ A4 @ ( insert_int @ I2 @ bot_bot_set_int ) ) )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5853_member__le__sum,axiom,
% 8.64/4.87 ! [I2: real,A4: set_real,F2: real > nat] :
% 8.64/4.87 ( ( member_real @ I2 @ A4 )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ ( minus_minus_set_real @ A4 @ ( insert_real @ I2 @ bot_bot_set_real ) ) )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( F2 @ I2 ) @ ( groups1935376822645274424al_nat @ F2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5854_div2__even__ext__nat,axiom,
% 8.64/4.87 ! [X: nat,Y: nat] :
% 8.64/4.87 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.87 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.87 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 8.64/4.87 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 8.64/4.87 => ( X = Y ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5855_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 8.64/4.87 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5856_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 8.64/4.87 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5857_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 8.64/4.87 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5858_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_rat @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 8.64/4.87 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5859_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > real,K5: real] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 8.64/4.87 => ( ord_less_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5860_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > real,K5: real] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 8.64/4.87 => ( ord_less_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5861_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > real,K5: real] :
% 8.64/4.87 ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_real @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A4 ) )
% 8.64/4.87 => ( ord_less_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5862_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > int,K5: int] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_real @ A4 ) )
% 8.64/4.87 => ( ord_less_int @ ( groups1932886352136224148al_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_real @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5863_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > int,K5: int] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A4 ) )
% 8.64/4.87 => ( ord_less_int @ ( groups3539618377306564664at_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5864_sum__bounded__above__strict,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > int,K5: int] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_int @ ( F2 @ I3 ) @ K5 ) )
% 8.64/4.87 => ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_complex @ A4 ) )
% 8.64/4.87 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F2 @ A4 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_complex @ A4 ) ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5865_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > real,K5: real] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_complex )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5866_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > real,K5: real] :
% 8.64/4.87 ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_int @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_int )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5867_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > real,K5: real] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_real @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_real )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5868_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_complex @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_complex )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5869_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_nat )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5870_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_int )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5871_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > rat,K5: rat] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( divide_divide_rat @ K5 @ ( semiri681578069525770553at_rat @ ( finite_card_real @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_real )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5872_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > real,K5: real] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_nat )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5873_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_list_nat,F2: list_nat > real,K5: real] :
% 8.64/4.87 ( ! [I3: list_nat] :
% 8.64/4.87 ( ( member_list_nat @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_list_nat @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite8100373058378681591st_nat @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_list_nat )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups8399112307953289288t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5874_sum__bounded__above__divide,axiom,
% 8.64/4.87 ! [A4: set_set_nat,F2: set_nat > real,K5: real] :
% 8.64/4.87 ( ! [I3: set_nat] :
% 8.64/4.87 ( ( member_set_nat @ I3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ ( F2 @ I3 ) @ ( divide_divide_real @ K5 @ ( semiri5074537144036343181t_real @ ( finite_card_set_nat @ A4 ) ) ) ) )
% 8.64/4.87 => ( ( finite1152437895449049373et_nat @ A4 )
% 8.64/4.87 => ( ( A4 != bot_bot_set_set_nat )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups5107569545109728110t_real @ F2 @ A4 ) @ K5 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5875_pochhammer__rec,axiom,
% 8.64/4.87 ! [A: code_integer,N: nat] :
% 8.64/4.87 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5876_pochhammer__rec,axiom,
% 8.64/4.87 ! [A: complex,N: nat] :
% 8.64/4.87 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5877_pochhammer__rec,axiom,
% 8.64/4.87 ! [A: real,N: nat] :
% 8.64/4.87 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5878_pochhammer__rec,axiom,
% 8.64/4.87 ! [A: rat,N: nat] :
% 8.64/4.87 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5879_pochhammer__rec,axiom,
% 8.64/4.87 ! [A: nat,N: nat] :
% 8.64/4.87 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5880_pochhammer__rec,axiom,
% 8.64/4.87 ! [A: int,N: nat] :
% 8.64/4.87 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5881_dvd__mult__cancel1,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.87 => ( ( dvd_dvd_nat @ ( times_times_nat @ M2 @ N ) @ M2 )
% 8.64/4.87 = ( N = one_one_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5882_dvd__mult__cancel2,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.87 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M2 ) @ M2 )
% 8.64/4.87 = ( N = one_one_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5883_pochhammer__rec_H,axiom,
% 8.64/4.87 ! [Z3: rat,N: nat] :
% 8.64/4.87 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N ) ) @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5884_pochhammer__rec_H,axiom,
% 8.64/4.87 ! [Z3: real,N: nat] :
% 8.64/4.87 ( ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N ) ) @ ( comm_s7457072308508201937r_real @ Z3 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5885_pochhammer__rec_H,axiom,
% 8.64/4.87 ! [Z3: int,N: nat] :
% 8.64/4.87 ( ( comm_s4660882817536571857er_int @ Z3 @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N ) ) @ ( comm_s4660882817536571857er_int @ Z3 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5886_pochhammer__rec_H,axiom,
% 8.64/4.87 ! [Z3: nat,N: nat] :
% 8.64/4.87 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N ) ) @ ( comm_s4663373288045622133er_nat @ Z3 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5887_pochhammer__Suc,axiom,
% 8.64/4.87 ! [A: rat,N: nat] :
% 8.64/4.87 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5888_pochhammer__Suc,axiom,
% 8.64/4.87 ! [A: real,N: nat] :
% 8.64/4.87 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5889_pochhammer__Suc,axiom,
% 8.64/4.87 ! [A: int,N: nat] :
% 8.64/4.87 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5890_pochhammer__Suc,axiom,
% 8.64/4.87 ! [A: nat,N: nat] :
% 8.64/4.87 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 8.64/4.87 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5891_dvd__minus__add,axiom,
% 8.64/4.87 ! [Q2: nat,N: nat,R3: nat,M2: nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ Q2 @ N )
% 8.64/4.87 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R3 @ M2 ) )
% 8.64/4.87 => ( ( dvd_dvd_nat @ M2 @ ( minus_minus_nat @ N @ Q2 ) )
% 8.64/4.87 = ( dvd_dvd_nat @ M2 @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R3 @ M2 ) @ Q2 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5892_power__dvd__imp__le,axiom,
% 8.64/4.87 ! [I2: nat,M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M2 ) @ ( power_power_nat @ I2 @ N ) )
% 8.64/4.87 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 8.64/4.87 => ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5893_pochhammer__product_H,axiom,
% 8.64/4.87 ! [Z3: rat,N: nat,M2: nat] :
% 8.64/4.87 ( ( comm_s4028243227959126397er_rat @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.87 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ N ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ N ) ) @ M2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5894_pochhammer__product_H,axiom,
% 8.64/4.87 ! [Z3: real,N: nat,M2: nat] :
% 8.64/4.87 ( ( comm_s7457072308508201937r_real @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.87 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ N ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ N ) ) @ M2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5895_pochhammer__product_H,axiom,
% 8.64/4.87 ! [Z3: int,N: nat,M2: nat] :
% 8.64/4.87 ( ( comm_s4660882817536571857er_int @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.87 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ N ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ N ) ) @ M2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5896_pochhammer__product_H,axiom,
% 8.64/4.87 ! [Z3: nat,N: nat,M2: nat] :
% 8.64/4.87 ( ( comm_s4663373288045622133er_nat @ Z3 @ ( plus_plus_nat @ N @ M2 ) )
% 8.64/4.87 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ N ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ N ) ) @ M2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5897_mod__nat__eqI,axiom,
% 8.64/4.87 ! [R3: nat,N: nat,M2: nat] :
% 8.64/4.87 ( ( ord_less_nat @ R3 @ N )
% 8.64/4.87 => ( ( ord_less_eq_nat @ R3 @ M2 )
% 8.64/4.87 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M2 @ R3 ) )
% 8.64/4.87 => ( ( modulo_modulo_nat @ M2 @ N )
% 8.64/4.87 = R3 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5898_sum_OSuc__reindex__ivl,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > rat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_rat @ ( G2 @ M2 )
% 8.64/4.87 @ ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5899_sum_OSuc__reindex__ivl,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > int] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_int @ ( G2 @ M2 )
% 8.64/4.87 @ ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5900_sum_OSuc__reindex__ivl,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_nat @ ( G2 @ M2 )
% 8.64/4.87 @ ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5901_sum_OSuc__reindex__ivl,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > real] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_real @ ( G2 @ M2 )
% 8.64/4.87 @ ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5902_sum__Suc__diff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > rat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.87 => ( ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( minus_minus_rat @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5903_sum__Suc__diff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > int] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.87 => ( ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( minus_minus_int @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5904_sum__Suc__diff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > real] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.87 => ( ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ ( suc @ I ) ) @ ( F2 @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( minus_minus_real @ ( F2 @ ( suc @ N ) ) @ ( F2 @ M2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5905_sum__norm__bound,axiom,
% 8.64/4.87 ! [S3: set_real,F2: real > complex,K5: real] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ S3 )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_real @ S3 ) ) @ K5 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5906_sum__norm__bound,axiom,
% 8.64/4.87 ! [S3: set_nat,F2: nat > complex,K5: real] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ S3 )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S3 ) ) @ K5 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5907_sum__norm__bound,axiom,
% 8.64/4.87 ! [S3: set_complex,F2: complex > complex,K5: real] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ S3 )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_complex @ S3 ) ) @ K5 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5908_sum__norm__bound,axiom,
% 8.64/4.87 ! [S3: set_int,F2: int > complex,K5: real] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ S3 )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_int @ S3 ) ) @ K5 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5909_sum__norm__bound,axiom,
% 8.64/4.87 ! [S3: set_list_nat,F2: list_nat > complex,K5: real] :
% 8.64/4.87 ( ! [X3: list_nat] :
% 8.64/4.87 ( ( member_list_nat @ X3 @ S3 )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6529277132148336714omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_list_nat @ S3 ) ) @ K5 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5910_sum__norm__bound,axiom,
% 8.64/4.87 ! [S3: set_set_nat,F2: set_nat > complex,K5: real] :
% 8.64/4.87 ( ! [X3: set_nat] :
% 8.64/4.87 ( ( member_set_nat @ X3 @ S3 )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F2 @ X3 ) ) @ K5 ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_set_nat @ S3 ) ) @ K5 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5911_sum__norm__bound,axiom,
% 8.64/4.87 ! [S3: set_nat,F2: nat > real,K5: real] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ S3 )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F2 @ X3 ) ) @ K5 ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F2 @ S3 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( finite_card_nat @ S3 ) ) @ K5 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5912_sum_Oub__add__nat,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > rat,P: nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.87 => ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.87 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5913_sum_Oub__add__nat,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > int,P: nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.87 => ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.87 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5914_sum_Oub__add__nat,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > nat,P: nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.87 => ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.87 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5915_sum_Oub__add__nat,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,G2: nat > real,P: nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.87 => ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.87 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5916_even__two__times__div__two,axiom,
% 8.64/4.87 ! [A: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.87 = A ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5917_even__two__times__div__two,axiom,
% 8.64/4.87 ! [A: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 8.64/4.87 = A ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5918_even__iff__mod__2__eq__zero,axiom,
% 8.64/4.87 ! [A: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.87 = zero_zero_nat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5919_even__iff__mod__2__eq__zero,axiom,
% 8.64/4.87 ! [A: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.87 = zero_zero_int ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5920_even__iff__mod__2__eq__zero,axiom,
% 8.64/4.87 ! [A: code_natural] :
% 8.64/4.87 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 = ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.87 = zero_z2226904508553997617atural ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5921_power__mono__odd,axiom,
% 8.64/4.87 ! [N: nat,A: real,B: real] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ( ord_less_eq_real @ A @ B )
% 8.64/4.87 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5922_power__mono__odd,axiom,
% 8.64/4.87 ! [N: nat,A: rat,B: rat] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.87 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5923_power__mono__odd,axiom,
% 8.64/4.87 ! [N: nat,A: int,B: int] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ( ord_less_eq_int @ A @ B )
% 8.64/4.87 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5924_odd__pos,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5925_dvd__power__iff__le,axiom,
% 8.64/4.87 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 8.64/4.87 => ( ( dvd_dvd_nat @ ( power_power_nat @ K2 @ M2 ) @ ( power_power_nat @ K2 @ N ) )
% 8.64/4.87 = ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5926_even__unset__bit__iff,axiom,
% 8.64/4.87 ! [M2: nat,A: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M2 @ A ) )
% 8.64/4.87 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 | ( M2 = zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5927_even__unset__bit__iff,axiom,
% 8.64/4.87 ! [M2: nat,A: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M2 @ A ) )
% 8.64/4.87 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 | ( M2 = zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5928_set__encode__def,axiom,
% 8.64/4.87 ( nat_set_encode
% 8.64/4.87 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5929_even__set__bit__iff,axiom,
% 8.64/4.87 ! [M2: nat,A: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M2 @ A ) )
% 8.64/4.87 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 & ( M2 != zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5930_even__set__bit__iff,axiom,
% 8.64/4.87 ! [M2: nat,A: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M2 @ A ) )
% 8.64/4.87 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 & ( M2 != zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5931_even__flip__bit__iff,axiom,
% 8.64/4.87 ! [M2: nat,A: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M2 @ A ) )
% 8.64/4.87 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 != ( M2 = zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5932_even__flip__bit__iff,axiom,
% 8.64/4.87 ! [M2: nat,A: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M2 @ A ) )
% 8.64/4.87 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 != ( M2 = zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5933_pochhammer__product,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,Z3: rat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( comm_s4028243227959126397er_rat @ Z3 @ N )
% 8.64/4.87 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ M2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( semiri681578069525770553at_rat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5934_pochhammer__product,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,Z3: real] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( comm_s7457072308508201937r_real @ Z3 @ N )
% 8.64/4.87 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ M2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5935_pochhammer__product,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,Z3: int] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( comm_s4660882817536571857er_int @ Z3 @ N )
% 8.64/4.87 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z3 @ M2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5936_pochhammer__product,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,Z3: nat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( comm_s4663373288045622133er_nat @ Z3 @ N )
% 8.64/4.87 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z3 @ M2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z3 @ ( semiri1316708129612266289at_nat @ M2 ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5937_oddE,axiom,
% 8.64/4.87 ! [A: code_integer] :
% 8.64/4.87 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ~ ! [B3: code_integer] :
% 8.64/4.87 ( A
% 8.64/4.87 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B3 ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5938_oddE,axiom,
% 8.64/4.87 ! [A: nat] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ~ ! [B3: nat] :
% 8.64/4.87 ( A
% 8.64/4.87 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B3 ) @ one_one_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5939_oddE,axiom,
% 8.64/4.87 ! [A: int] :
% 8.64/4.87 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ~ ! [B3: int] :
% 8.64/4.87 ( A
% 8.64/4.87 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B3 ) @ one_one_int ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5940_mod2__eq__if,axiom,
% 8.64/4.87 ! [A: code_integer] :
% 8.64/4.87 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.87 = zero_z3403309356797280102nteger ) )
% 8.64/4.87 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.87 = one_one_Code_integer ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5941_mod2__eq__if,axiom,
% 8.64/4.87 ! [A: nat] :
% 8.64/4.87 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.87 = zero_zero_nat ) )
% 8.64/4.87 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.87 = one_one_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5942_mod2__eq__if,axiom,
% 8.64/4.87 ! [A: int] :
% 8.64/4.87 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.87 = zero_zero_int ) )
% 8.64/4.87 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.87 = one_one_int ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5943_mod2__eq__if,axiom,
% 8.64/4.87 ! [A: code_natural] :
% 8.64/4.87 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.87 = zero_z2226904508553997617atural ) )
% 8.64/4.87 & ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.87 = one_one_Code_natural ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5944_parity__cases,axiom,
% 8.64/4.87 ! [A: code_integer] :
% 8.64/4.87 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.87 != zero_z3403309356797280102nteger ) )
% 8.64/4.87 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.87 != one_one_Code_integer ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5945_parity__cases,axiom,
% 8.64/4.87 ! [A: nat] :
% 8.64/4.87 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.87 != zero_zero_nat ) )
% 8.64/4.87 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.87 != one_one_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5946_parity__cases,axiom,
% 8.64/4.87 ! [A: int] :
% 8.64/4.87 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.87 != zero_zero_int ) )
% 8.64/4.87 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.87 != one_one_int ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5947_parity__cases,axiom,
% 8.64/4.87 ! [A: code_natural] :
% 8.64/4.87 ( ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.87 != zero_z2226904508553997617atural ) )
% 8.64/4.87 => ~ ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 8.64/4.87 => ( ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 8.64/4.87 != one_one_Code_natural ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5948_zero__le__even__power,axiom,
% 8.64/4.87 ! [N: nat,A: real] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5949_zero__le__even__power,axiom,
% 8.64/4.87 ! [N: nat,A: rat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5950_zero__le__even__power,axiom,
% 8.64/4.87 ! [N: nat,A: int] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5951_zero__le__odd__power,axiom,
% 8.64/4.87 ! [N: nat,A: real] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 8.64/4.87 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5952_zero__le__odd__power,axiom,
% 8.64/4.87 ! [N: nat,A: rat] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 8.64/4.87 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5953_zero__le__odd__power,axiom,
% 8.64/4.87 ! [N: nat,A: int] :
% 8.64/4.87 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 8.64/4.87 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5954_zero__le__power__eq,axiom,
% 8.64/4.87 ! [A: real,N: nat] :
% 8.64/4.87 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 8.64/4.87 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5955_zero__le__power__eq,axiom,
% 8.64/4.87 ! [A: rat,N: nat] :
% 8.64/4.87 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 8.64/4.87 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5956_zero__le__power__eq,axiom,
% 8.64/4.87 ! [A: int,N: nat] :
% 8.64/4.87 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 8.64/4.87 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5957_sum__natinterval__diff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > complex] :
% 8.64/4.87 ( ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups2073611262835488442omplex
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_complex @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( minus_minus_complex @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.64/4.87 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups2073611262835488442omplex
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_complex @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = zero_zero_complex ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5958_sum__natinterval__diff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > rat] :
% 8.64/4.87 ( ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( minus_minus_rat @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.64/4.87 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = zero_zero_rat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5959_sum__natinterval__diff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > int] :
% 8.64/4.87 ( ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( minus_minus_int @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.64/4.87 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = zero_zero_int ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5960_sum__natinterval__diff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > real] :
% 8.64/4.87 ( ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( minus_minus_real @ ( F2 @ M2 ) @ ( F2 @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 8.64/4.87 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = zero_zero_real ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5961_sum__telescope_H_H,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > rat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_rat @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 8.64/4.87 = ( minus_minus_rat @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5962_sum__telescope_H_H,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > int] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_int @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 8.64/4.87 = ( minus_minus_int @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5963_sum__telescope_H_H,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,F2: nat > real] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [K3: nat] : ( minus_minus_real @ ( F2 @ K3 ) @ ( F2 @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) )
% 8.64/4.87 = ( minus_minus_real @ ( F2 @ N ) @ ( F2 @ M2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5964_even__set__encode__iff,axiom,
% 8.64/4.87 ! [A4: set_nat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A4 ) )
% 8.64/4.87 = ( ~ ( member_nat @ zero_zero_nat @ A4 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5965_zero__less__power__eq,axiom,
% 8.64/4.87 ! [A: real,N: nat] :
% 8.64/4.87 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 8.64/4.87 = ( ( N = zero_zero_nat )
% 8.64/4.87 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( A != zero_zero_real ) )
% 8.64/4.87 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5966_zero__less__power__eq,axiom,
% 8.64/4.87 ! [A: rat,N: nat] :
% 8.64/4.87 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 8.64/4.87 = ( ( N = zero_zero_nat )
% 8.64/4.87 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( A != zero_zero_rat ) )
% 8.64/4.87 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5967_zero__less__power__eq,axiom,
% 8.64/4.87 ! [A: int,N: nat] :
% 8.64/4.87 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 8.64/4.87 = ( ( N = zero_zero_nat )
% 8.64/4.87 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( A != zero_zero_int ) )
% 8.64/4.87 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5968_sum__gp__multiplied,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,X: code_integer] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M2 ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5969_sum__gp__multiplied,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,X: complex] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( minus_minus_complex @ ( power_power_complex @ X @ M2 ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5970_sum__gp__multiplied,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,X: rat] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( minus_minus_rat @ ( power_power_rat @ X @ M2 ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5971_sum__gp__multiplied,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,X: int] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( minus_minus_int @ ( power_power_int @ X @ M2 ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5972_sum__gp__multiplied,axiom,
% 8.64/4.87 ! [M2: nat,N: nat,X: real] :
% 8.64/4.87 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( minus_minus_real @ ( power_power_real @ X @ M2 ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5973_sum_Oin__pairs,axiom,
% 8.64/4.87 ! [G2: nat > rat,M2: nat,N: nat] :
% 8.64/4.87 ( ( groups2906978787729119204at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.87 = ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5974_sum_Oin__pairs,axiom,
% 8.64/4.87 ! [G2: nat > int,M2: nat,N: nat] :
% 8.64/4.87 ( ( groups3539618377306564664at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.87 = ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5975_sum_Oin__pairs,axiom,
% 8.64/4.87 ! [G2: nat > nat,M2: nat,N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.87 = ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5976_sum_Oin__pairs,axiom,
% 8.64/4.87 ! [G2: nat > real,M2: nat,N: nat] :
% 8.64/4.87 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.87 = ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5977_even__mask__div__iff_H,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5978_even__mask__div__iff_H,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5979_even__mask__div__iff_H,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5980_power__le__zero__eq,axiom,
% 8.64/4.87 ! [A: real,N: nat] :
% 8.64/4.87 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 8.64/4.87 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.87 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 8.64/4.87 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( A = zero_zero_real ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5981_power__le__zero__eq,axiom,
% 8.64/4.87 ! [A: rat,N: nat] :
% 8.64/4.87 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 8.64/4.87 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.87 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 8.64/4.87 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( A = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5982_power__le__zero__eq,axiom,
% 8.64/4.87 ! [A: int,N: nat] :
% 8.64/4.87 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 8.64/4.87 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.87 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 8.64/4.87 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 & ( A = zero_zero_int ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5983_mask__eq__sum__exp__nat,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 8.64/4.87 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.87 @ ( collect_nat
% 8.64/4.87 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5984_gauss__sum__nat,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [X4: nat] : X4
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5985_even__mod__4__div__2,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.87 = ( suc @ zero_zero_nat ) )
% 8.64/4.87 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5986_even__mask__div__iff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 = zero_z3403309356797280102nteger )
% 8.64/4.87 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5987_even__mask__div__iff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 = zero_zero_nat )
% 8.64/4.87 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5988_even__mask__div__iff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 = zero_zero_int )
% 8.64/4.87 | ( ord_less_eq_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5989_double__gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5990_double__gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5991_double__gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5992_double__gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5993_double__gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5994_double__gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5995_double__gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5996_double__arith__series,axiom,
% 8.64/4.87 ! [A: code_integer,D: code_integer,N: nat] :
% 8.64/4.87 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 8.64/4.87 @ ( groups7501900531339628137nteger
% 8.64/4.87 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5997_double__arith__series,axiom,
% 8.64/4.87 ! [A: rat,D: rat,N: nat] :
% 8.64/4.87 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 8.64/4.87 @ ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5998_double__arith__series,axiom,
% 8.64/4.87 ! [A: extended_enat,D: extended_enat,N: nat] :
% 8.64/4.87 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 8.64/4.87 @ ( groups7108830773950497114d_enat
% 8.64/4.87 @ ^ [I: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ D ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_5999_double__arith__series,axiom,
% 8.64/4.87 ! [A: complex,D: complex,N: nat] :
% 8.64/4.87 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 8.64/4.87 @ ( groups2073611262835488442omplex
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6000_double__arith__series,axiom,
% 8.64/4.87 ! [A: int,D: int,N: nat] :
% 8.64/4.87 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 8.64/4.87 @ ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6001_double__arith__series,axiom,
% 8.64/4.87 ! [A: nat,D: nat,N: nat] :
% 8.64/4.87 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 8.64/4.87 @ ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6002_double__arith__series,axiom,
% 8.64/4.87 ! [A: real,D: real,N: nat] :
% 8.64/4.87 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 8.64/4.87 @ ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.87 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6003_arith__series__nat,axiom,
% 8.64/4.87 ! [A: nat,D: nat,N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6004_Sum__Icc__nat,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [X4: nat] : X4
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.87 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6005_Bernoulli__inequality__even,axiom,
% 8.64/4.87 ! [N: nat,X: real] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6006_gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6007_gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6008_gauss__sum,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6009_arith__series,axiom,
% 8.64/4.87 ! [A: code_integer,D: code_integer,N: nat] :
% 8.64/4.87 ( ( groups7501900531339628137nteger
% 8.64/4.87 @ ^ [I: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6010_arith__series,axiom,
% 8.64/4.87 ! [A: int,D: int,N: nat] :
% 8.64/4.87 ( ( groups3539618377306564664at_int
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6011_arith__series,axiom,
% 8.64/4.87 ! [A: nat,D: nat,N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I ) @ D ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.87 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6012_double__gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.64/4.87 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6013_double__gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.64/4.87 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6014_double__gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.64/4.87 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N ) @ one_on7984719198319812577d_enat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6015_double__gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.64/4.87 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6016_double__gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.64/4.87 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6017_double__gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.64/4.87 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6018_double__gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 8.64/4.87 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6019_even__mult__exp__div__exp__iff,axiom,
% 8.64/4.87 ! [A: nat,M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ( ord_less_nat @ N @ M2 )
% 8.64/4.87 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 = zero_zero_nat )
% 8.64/4.87 | ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6020_even__mult__exp__div__exp__iff,axiom,
% 8.64/4.87 ! [A: int,M2: nat,N: nat] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.87 = ( ( ord_less_nat @ N @ M2 )
% 8.64/4.87 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.64/4.87 = zero_zero_int )
% 8.64/4.87 | ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.87 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6021_sum__gp__offset,axiom,
% 8.64/4.87 ! [X: complex,M2: nat,N: nat] :
% 8.64/4.87 ( ( ( X = one_one_complex )
% 8.64/4.87 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 8.64/4.87 & ( ( X != one_one_complex )
% 8.64/4.87 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6022_sum__gp__offset,axiom,
% 8.64/4.87 ! [X: rat,M2: nat,N: nat] :
% 8.64/4.87 ( ( ( X = one_one_rat )
% 8.64/4.87 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 8.64/4.87 & ( ( X != one_one_rat )
% 8.64/4.87 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6023_sum__gp__offset,axiom,
% 8.64/4.87 ! [X: real,M2: nat,N: nat] :
% 8.64/4.87 ( ( ( X = one_one_real )
% 8.64/4.87 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 8.64/4.87 & ( ( X != one_one_real )
% 8.64/4.87 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.87 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6024_vebt__buildup_Osimps_I3_J,axiom,
% 8.64/4.87 ! [Va3: nat] :
% 8.64/4.87 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 8.64/4.87 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 8.64/4.87 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 8.64/4.87 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va3 ) ) )
% 8.64/4.87 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va3 ) ) )
% 8.64/4.87 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va3 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6025_gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.87 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6026_gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.87 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6027_gauss__sum__from__Suc__0,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.87 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6028_power__half__series,axiom,
% 8.64/4.87 ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N4 ) )
% 8.64/4.87 @ one_one_real ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6029_sums__zero,axiom,
% 8.64/4.87 ( sums_complex
% 8.64/4.87 @ ^ [N4: nat] : zero_zero_complex
% 8.64/4.87 @ zero_zero_complex ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6030_sums__zero,axiom,
% 8.64/4.87 ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : zero_zero_real
% 8.64/4.87 @ zero_zero_real ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6031_sums__zero,axiom,
% 8.64/4.87 ( sums_nat
% 8.64/4.87 @ ^ [N4: nat] : zero_zero_nat
% 8.64/4.87 @ zero_zero_nat ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6032_sums__zero,axiom,
% 8.64/4.87 ( sums_int
% 8.64/4.87 @ ^ [N4: nat] : zero_zero_int
% 8.64/4.87 @ zero_zero_int ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6033_powser__sums__if,axiom,
% 8.64/4.87 ! [M2: nat,Z3: complex] :
% 8.64/4.87 ( sums_complex
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_complex @ ( if_complex @ ( N4 = M2 ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z3 @ N4 ) )
% 8.64/4.87 @ ( power_power_complex @ Z3 @ M2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6034_powser__sums__if,axiom,
% 8.64/4.87 ! [M2: nat,Z3: real] :
% 8.64/4.87 ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_real @ ( if_real @ ( N4 = M2 ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z3 @ N4 ) )
% 8.64/4.87 @ ( power_power_real @ Z3 @ M2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6035_powser__sums__if,axiom,
% 8.64/4.87 ! [M2: nat,Z3: int] :
% 8.64/4.87 ( sums_int
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_int @ ( if_int @ ( N4 = M2 ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z3 @ N4 ) )
% 8.64/4.87 @ ( power_power_int @ Z3 @ M2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6036_sums__If__finite__set,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > complex] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( sums_complex
% 8.64/4.87 @ ^ [R: nat] : ( if_complex @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_complex )
% 8.64/4.87 @ ( groups2073611262835488442omplex @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6037_sums__If__finite__set,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > int] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( sums_int
% 8.64/4.87 @ ^ [R: nat] : ( if_int @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_int )
% 8.64/4.87 @ ( groups3539618377306564664at_int @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6038_sums__If__finite__set,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > nat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( sums_nat
% 8.64/4.87 @ ^ [R: nat] : ( if_nat @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_nat )
% 8.64/4.87 @ ( groups3542108847815614940at_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6039_sums__If__finite__set,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( sums_real
% 8.64/4.87 @ ^ [R: nat] : ( if_real @ ( member_nat @ R @ A4 ) @ ( F2 @ R ) @ zero_zero_real )
% 8.64/4.87 @ ( groups6591440286371151544t_real @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6040_sums__If__finite,axiom,
% 8.64/4.87 ! [P2: nat > $o,F2: nat > complex] :
% 8.64/4.87 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 8.64/4.87 => ( sums_complex
% 8.64/4.87 @ ^ [R: nat] : ( if_complex @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_complex )
% 8.64/4.87 @ ( groups2073611262835488442omplex @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6041_sums__If__finite,axiom,
% 8.64/4.87 ! [P2: nat > $o,F2: nat > int] :
% 8.64/4.87 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 8.64/4.87 => ( sums_int
% 8.64/4.87 @ ^ [R: nat] : ( if_int @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_int )
% 8.64/4.87 @ ( groups3539618377306564664at_int @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6042_sums__If__finite,axiom,
% 8.64/4.87 ! [P2: nat > $o,F2: nat > nat] :
% 8.64/4.87 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 8.64/4.87 => ( sums_nat
% 8.64/4.87 @ ^ [R: nat] : ( if_nat @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_nat )
% 8.64/4.87 @ ( groups3542108847815614940at_nat @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6043_sums__If__finite,axiom,
% 8.64/4.87 ! [P2: nat > $o,F2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ ( collect_nat @ P2 ) )
% 8.64/4.87 => ( sums_real
% 8.64/4.87 @ ^ [R: nat] : ( if_real @ ( P2 @ R ) @ ( F2 @ R ) @ zero_zero_real )
% 8.64/4.87 @ ( groups6591440286371151544t_real @ F2 @ ( collect_nat @ P2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6044_sums__finite,axiom,
% 8.64/4.87 ! [N6: set_nat,F2: nat > complex] :
% 8.64/4.87 ( ( finite_finite_nat @ N6 )
% 8.64/4.87 => ( ! [N3: nat] :
% 8.64/4.87 ( ~ ( member_nat @ N3 @ N6 )
% 8.64/4.87 => ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_complex ) )
% 8.64/4.87 => ( sums_complex @ F2 @ ( groups2073611262835488442omplex @ F2 @ N6 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6045_sums__finite,axiom,
% 8.64/4.87 ! [N6: set_nat,F2: nat > int] :
% 8.64/4.87 ( ( finite_finite_nat @ N6 )
% 8.64/4.87 => ( ! [N3: nat] :
% 8.64/4.87 ( ~ ( member_nat @ N3 @ N6 )
% 8.64/4.87 => ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_int ) )
% 8.64/4.87 => ( sums_int @ F2 @ ( groups3539618377306564664at_int @ F2 @ N6 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6046_sums__finite,axiom,
% 8.64/4.87 ! [N6: set_nat,F2: nat > nat] :
% 8.64/4.87 ( ( finite_finite_nat @ N6 )
% 8.64/4.87 => ( ! [N3: nat] :
% 8.64/4.87 ( ~ ( member_nat @ N3 @ N6 )
% 8.64/4.87 => ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_nat ) )
% 8.64/4.87 => ( sums_nat @ F2 @ ( groups3542108847815614940at_nat @ F2 @ N6 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6047_sums__finite,axiom,
% 8.64/4.87 ! [N6: set_nat,F2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ N6 )
% 8.64/4.87 => ( ! [N3: nat] :
% 8.64/4.87 ( ~ ( member_nat @ N3 @ N6 )
% 8.64/4.87 => ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_real ) )
% 8.64/4.87 => ( sums_real @ F2 @ ( groups6591440286371151544t_real @ F2 @ N6 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6048_sums__zero__iff__shift,axiom,
% 8.64/4.87 ! [N: nat,F2: nat > complex,S2: complex] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( ord_less_nat @ I3 @ N )
% 8.64/4.87 => ( ( F2 @ I3 )
% 8.64/4.87 = zero_zero_complex ) )
% 8.64/4.87 => ( ( sums_complex
% 8.64/4.87 @ ^ [I: nat] : ( F2 @ ( plus_plus_nat @ I @ N ) )
% 8.64/4.87 @ S2 )
% 8.64/4.87 = ( sums_complex @ F2 @ S2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6049_sums__zero__iff__shift,axiom,
% 8.64/4.87 ! [N: nat,F2: nat > real,S2: real] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( ord_less_nat @ I3 @ N )
% 8.64/4.87 => ( ( F2 @ I3 )
% 8.64/4.87 = zero_zero_real ) )
% 8.64/4.87 => ( ( sums_real
% 8.64/4.87 @ ^ [I: nat] : ( F2 @ ( plus_plus_nat @ I @ N ) )
% 8.64/4.87 @ S2 )
% 8.64/4.87 = ( sums_real @ F2 @ S2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6050_zdvd__mono,axiom,
% 8.64/4.87 ! [K2: int,M2: int,T: int] :
% 8.64/4.87 ( ( K2 != zero_zero_int )
% 8.64/4.87 => ( ( dvd_dvd_int @ M2 @ T )
% 8.64/4.87 = ( dvd_dvd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ T ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6051_zdvd__mult__cancel,axiom,
% 8.64/4.87 ! [K2: int,M2: int,N: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ N ) )
% 8.64/4.87 => ( ( K2 != zero_zero_int )
% 8.64/4.87 => ( dvd_dvd_int @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6052_zdvd__period,axiom,
% 8.64/4.87 ! [A: int,D: int,X: int,T: int,C2: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ A @ D )
% 8.64/4.87 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 8.64/4.87 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C2 @ D ) ) @ T ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6053_zdvd__reduce,axiom,
% 8.64/4.87 ! [K2: int,N: int,M2: int] :
% 8.64/4.87 ( ( dvd_dvd_int @ K2 @ ( plus_plus_int @ N @ ( times_times_int @ K2 @ M2 ) ) )
% 8.64/4.87 = ( dvd_dvd_int @ K2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6054_sum__subtractf__nat,axiom,
% 8.64/4.87 ! [A4: set_complex,G2: complex > nat,F2: complex > nat] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( groups5693394587270226106ex_nat
% 8.64/4.87 @ ^ [X4: complex] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( groups5693394587270226106ex_nat @ G2 @ A4 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6055_sum__subtractf__nat,axiom,
% 8.64/4.87 ! [A4: set_real,G2: real > nat,F2: real > nat] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( groups1935376822645274424al_nat
% 8.64/4.87 @ ^ [X4: real] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F2 @ A4 ) @ ( groups1935376822645274424al_nat @ G2 @ A4 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6056_sum__subtractf__nat,axiom,
% 8.64/4.87 ! [A4: set_set_nat,G2: set_nat > nat,F2: set_nat > nat] :
% 8.64/4.87 ( ! [X3: set_nat] :
% 8.64/4.87 ( ( member_set_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( groups8294997508430121362at_nat
% 8.64/4.87 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F2 @ A4 ) @ ( groups8294997508430121362at_nat @ G2 @ A4 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6057_sum__subtractf__nat,axiom,
% 8.64/4.87 ! [A4: set_int,G2: int > nat,F2: int > nat] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( groups4541462559716669496nt_nat
% 8.64/4.87 @ ^ [X4: int] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( groups4541462559716669496nt_nat @ G2 @ A4 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6058_sum__subtractf__nat,axiom,
% 8.64/4.87 ! [A4: set_nat,G2: nat > nat,F2: nat > nat] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ ( G2 @ X3 ) @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [X4: nat] : ( minus_minus_nat @ ( F2 @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( groups3542108847815614940at_nat @ G2 @ A4 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6059_sum__eq__Suc0__iff,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > nat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 8.64/4.87 = ( suc @ zero_zero_nat ) )
% 8.64/4.87 = ( ? [X4: int] :
% 8.64/4.87 ( ( member_int @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = ( suc @ zero_zero_nat ) )
% 8.64/4.87 & ! [Y4: int] :
% 8.64/4.87 ( ( member_int @ Y4 @ A4 )
% 8.64/4.87 => ( ( X4 != Y4 )
% 8.64/4.87 => ( ( F2 @ Y4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6060_sum__eq__Suc0__iff,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > nat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 8.64/4.87 = ( suc @ zero_zero_nat ) )
% 8.64/4.87 = ( ? [X4: complex] :
% 8.64/4.87 ( ( member_complex @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = ( suc @ zero_zero_nat ) )
% 8.64/4.87 & ! [Y4: complex] :
% 8.64/4.87 ( ( member_complex @ Y4 @ A4 )
% 8.64/4.87 => ( ( X4 != Y4 )
% 8.64/4.87 => ( ( F2 @ Y4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6061_sum__eq__Suc0__iff,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > nat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 8.64/4.87 = ( suc @ zero_zero_nat ) )
% 8.64/4.87 = ( ? [X4: nat] :
% 8.64/4.87 ( ( member_nat @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = ( suc @ zero_zero_nat ) )
% 8.64/4.87 & ! [Y4: nat] :
% 8.64/4.87 ( ( member_nat @ Y4 @ A4 )
% 8.64/4.87 => ( ( X4 != Y4 )
% 8.64/4.87 => ( ( F2 @ Y4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6062_sum__SucD,axiom,
% 8.64/4.87 ! [F2: nat > nat,A4: set_nat,N: nat] :
% 8.64/4.87 ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 8.64/4.87 = ( suc @ N ) )
% 8.64/4.87 => ? [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 & ( ord_less_nat @ zero_zero_nat @ ( F2 @ X3 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6063_sum__eq__1__iff,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > nat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( groups4541462559716669496nt_nat @ F2 @ A4 )
% 8.64/4.87 = one_one_nat )
% 8.64/4.87 = ( ? [X4: int] :
% 8.64/4.87 ( ( member_int @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = one_one_nat )
% 8.64/4.87 & ! [Y4: int] :
% 8.64/4.87 ( ( member_int @ Y4 @ A4 )
% 8.64/4.87 => ( ( X4 != Y4 )
% 8.64/4.87 => ( ( F2 @ Y4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6064_sum__eq__1__iff,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > nat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( ( groups5693394587270226106ex_nat @ F2 @ A4 )
% 8.64/4.87 = one_one_nat )
% 8.64/4.87 = ( ? [X4: complex] :
% 8.64/4.87 ( ( member_complex @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = one_one_nat )
% 8.64/4.87 & ! [Y4: complex] :
% 8.64/4.87 ( ( member_complex @ Y4 @ A4 )
% 8.64/4.87 => ( ( X4 != Y4 )
% 8.64/4.87 => ( ( F2 @ Y4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6065_sum__eq__1__iff,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > nat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( ( groups3542108847815614940at_nat @ F2 @ A4 )
% 8.64/4.87 = one_one_nat )
% 8.64/4.87 = ( ? [X4: nat] :
% 8.64/4.87 ( ( member_nat @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = one_one_nat )
% 8.64/4.87 & ! [Y4: nat] :
% 8.64/4.87 ( ( member_nat @ Y4 @ A4 )
% 8.64/4.87 => ( ( X4 != Y4 )
% 8.64/4.87 => ( ( F2 @ Y4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6066_sum__Suc,axiom,
% 8.64/4.87 ! [F2: complex > nat,A4: set_complex] :
% 8.64/4.87 ( ( groups5693394587270226106ex_nat
% 8.64/4.87 @ ^ [X4: complex] : ( suc @ ( F2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ F2 @ A4 ) @ ( finite_card_complex @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6067_sum__Suc,axiom,
% 8.64/4.87 ! [F2: int > nat,A4: set_int] :
% 8.64/4.87 ( ( groups4541462559716669496nt_nat
% 8.64/4.87 @ ^ [X4: int] : ( suc @ ( F2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F2 @ A4 ) @ ( finite_card_int @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6068_sum__Suc,axiom,
% 8.64/4.87 ! [F2: list_nat > nat,A4: set_list_nat] :
% 8.64/4.87 ( ( groups4396056296759096172at_nat
% 8.64/4.87 @ ^ [X4: list_nat] : ( suc @ ( F2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F2 @ A4 ) @ ( finite_card_list_nat @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6069_sum__Suc,axiom,
% 8.64/4.87 ! [F2: set_nat > nat,A4: set_set_nat] :
% 8.64/4.87 ( ( groups8294997508430121362at_nat
% 8.64/4.87 @ ^ [X4: set_nat] : ( suc @ ( F2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ F2 @ A4 ) @ ( finite_card_set_nat @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6070_sum__Suc,axiom,
% 8.64/4.87 ! [F2: nat > nat,A4: set_nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [X4: nat] : ( suc @ ( F2 @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ A4 ) @ ( finite_card_nat @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6071_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_real,T5: set_real,R2: real > real > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_real @ S3 )
% 8.64/4.87 => ( ( finite_finite_real @ T5 )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_real
% 8.64/4.87 @ ( collect_real
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( ( member_real @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups1935376822645274424al_nat
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( finite_card_real
% 8.64/4.87 @ ( collect_real
% 8.64/4.87 @ ^ [J: real] :
% 8.64/4.87 ( ( member_real @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6072_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_real,T5: set_nat,R2: real > nat > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_real @ S3 )
% 8.64/4.87 => ( ( finite_finite_nat @ T5 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_real
% 8.64/4.87 @ ( collect_real
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( ( member_real @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups1935376822645274424al_nat
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( finite_card_nat
% 8.64/4.87 @ ( collect_nat
% 8.64/4.87 @ ^ [J: nat] :
% 8.64/4.87 ( ( member_nat @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6073_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_real,T5: set_int,R2: real > int > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_real @ S3 )
% 8.64/4.87 => ( ( finite_finite_int @ T5 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_real
% 8.64/4.87 @ ( collect_real
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( ( member_real @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups1935376822645274424al_nat
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( finite_card_int
% 8.64/4.87 @ ( collect_int
% 8.64/4.87 @ ^ [J: int] :
% 8.64/4.87 ( ( member_int @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_int @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6074_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_real,T5: set_complex,R2: real > complex > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_real @ S3 )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_real
% 8.64/4.87 @ ( collect_real
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( ( member_real @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups1935376822645274424al_nat
% 8.64/4.87 @ ^ [I: real] :
% 8.64/4.87 ( finite_card_complex
% 8.64/4.87 @ ( collect_complex
% 8.64/4.87 @ ^ [J: complex] :
% 8.64/4.87 ( ( member_complex @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_complex @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6075_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_int,T5: set_real,R2: int > real > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_int @ S3 )
% 8.64/4.87 => ( ( finite_finite_real @ T5 )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_int
% 8.64/4.87 @ ( collect_int
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( ( member_int @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups4541462559716669496nt_nat
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( finite_card_real
% 8.64/4.87 @ ( collect_real
% 8.64/4.87 @ ^ [J: real] :
% 8.64/4.87 ( ( member_real @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6076_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_int,T5: set_nat,R2: int > nat > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_int @ S3 )
% 8.64/4.87 => ( ( finite_finite_nat @ T5 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_int
% 8.64/4.87 @ ( collect_int
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( ( member_int @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups4541462559716669496nt_nat
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( finite_card_nat
% 8.64/4.87 @ ( collect_nat
% 8.64/4.87 @ ^ [J: nat] :
% 8.64/4.87 ( ( member_nat @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6077_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_int,T5: set_int,R2: int > int > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_int @ S3 )
% 8.64/4.87 => ( ( finite_finite_int @ T5 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_int
% 8.64/4.87 @ ( collect_int
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( ( member_int @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups4541462559716669496nt_nat
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( finite_card_int
% 8.64/4.87 @ ( collect_int
% 8.64/4.87 @ ^ [J: int] :
% 8.64/4.87 ( ( member_int @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_int @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6078_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_int,T5: set_complex,R2: int > complex > $o,K2: nat] :
% 8.64/4.87 ( ( finite_finite_int @ S3 )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ T5 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_int
% 8.64/4.87 @ ( collect_int
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( ( member_int @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups4541462559716669496nt_nat
% 8.64/4.87 @ ^ [I: int] :
% 8.64/4.87 ( finite_card_complex
% 8.64/4.87 @ ( collect_complex
% 8.64/4.87 @ ^ [J: complex] :
% 8.64/4.87 ( ( member_complex @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_complex @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6079_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_complex,T5: set_real,R2: complex > real > $o,K2: nat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.87 => ( ( finite_finite_real @ T5 )
% 8.64/4.87 => ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_complex
% 8.64/4.87 @ ( collect_complex
% 8.64/4.87 @ ^ [I: complex] :
% 8.64/4.87 ( ( member_complex @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups5693394587270226106ex_nat
% 8.64/4.87 @ ^ [I: complex] :
% 8.64/4.87 ( finite_card_real
% 8.64/4.87 @ ( collect_real
% 8.64/4.87 @ ^ [J: real] :
% 8.64/4.87 ( ( member_real @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_real @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6080_sum__multicount,axiom,
% 8.64/4.87 ! [S3: set_complex,T5: set_nat,R2: complex > nat > $o,K2: nat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.87 => ( ( finite_finite_nat @ T5 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ T5 )
% 8.64/4.87 => ( ( finite_card_complex
% 8.64/4.87 @ ( collect_complex
% 8.64/4.87 @ ^ [I: complex] :
% 8.64/4.87 ( ( member_complex @ I @ S3 )
% 8.64/4.87 & ( R2 @ I @ X3 ) ) ) )
% 8.64/4.87 = K2 ) )
% 8.64/4.87 => ( ( groups5693394587270226106ex_nat
% 8.64/4.87 @ ^ [I: complex] :
% 8.64/4.87 ( finite_card_nat
% 8.64/4.87 @ ( collect_nat
% 8.64/4.87 @ ^ [J: nat] :
% 8.64/4.87 ( ( member_nat @ J @ T5 )
% 8.64/4.87 & ( R2 @ I @ J ) ) ) )
% 8.64/4.87 @ S3 )
% 8.64/4.87 = ( times_times_nat @ K2 @ ( finite_card_nat @ T5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6081_mod__int__pos__iff,axiom,
% 8.64/4.87 ! [K2: int,L: int] :
% 8.64/4.87 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K2 @ L ) )
% 8.64/4.87 = ( ( dvd_dvd_int @ L @ K2 )
% 8.64/4.87 | ( ( L = zero_zero_int )
% 8.64/4.87 & ( ord_less_eq_int @ zero_zero_int @ K2 ) )
% 8.64/4.87 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6082_sum__count__set,axiom,
% 8.64/4.87 ! [Xs2: list_complex,X8: set_complex] :
% 8.64/4.87 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ X8 )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ X8 )
% 8.64/4.87 => ( ( groups5693394587270226106ex_nat @ ( count_list_complex @ Xs2 ) @ X8 )
% 8.64/4.87 = ( size_s3451745648224563538omplex @ Xs2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6083_sum__count__set,axiom,
% 8.64/4.87 ! [Xs2: list_VEBT_VEBT,X8: set_VEBT_VEBT] :
% 8.64/4.87 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ X8 )
% 8.64/4.87 => ( ( finite5795047828879050333T_VEBT @ X8 )
% 8.64/4.87 => ( ( groups771621172384141258BT_nat @ ( count_list_VEBT_VEBT @ Xs2 ) @ X8 )
% 8.64/4.87 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6084_sum__count__set,axiom,
% 8.64/4.87 ! [Xs2: list_o,X8: set_o] :
% 8.64/4.87 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ X8 )
% 8.64/4.87 => ( ( finite_finite_o @ X8 )
% 8.64/4.87 => ( ( groups8507830703676809646_o_nat @ ( count_list_o @ Xs2 ) @ X8 )
% 8.64/4.87 = ( size_size_list_o @ Xs2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6085_sum__count__set,axiom,
% 8.64/4.87 ! [Xs2: list_int,X8: set_int] :
% 8.64/4.87 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ X8 )
% 8.64/4.87 => ( ( finite_finite_int @ X8 )
% 8.64/4.87 => ( ( groups4541462559716669496nt_nat @ ( count_list_int @ Xs2 ) @ X8 )
% 8.64/4.87 = ( size_size_list_int @ Xs2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6086_sum__count__set,axiom,
% 8.64/4.87 ! [Xs2: list_nat,X8: set_nat] :
% 8.64/4.87 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ X8 )
% 8.64/4.87 => ( ( finite_finite_nat @ X8 )
% 8.64/4.87 => ( ( groups3542108847815614940at_nat @ ( count_list_nat @ Xs2 ) @ X8 )
% 8.64/4.87 = ( size_size_list_nat @ Xs2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6087_sums__le,axiom,
% 8.64/4.87 ! [F2: nat > real,G2: nat > real,S2: real,T: real] :
% 8.64/4.87 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 8.64/4.87 => ( ( sums_real @ F2 @ S2 )
% 8.64/4.87 => ( ( sums_real @ G2 @ T )
% 8.64/4.87 => ( ord_less_eq_real @ S2 @ T ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6088_sums__le,axiom,
% 8.64/4.87 ! [F2: nat > nat,G2: nat > nat,S2: nat,T: nat] :
% 8.64/4.87 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 8.64/4.87 => ( ( sums_nat @ F2 @ S2 )
% 8.64/4.87 => ( ( sums_nat @ G2 @ T )
% 8.64/4.87 => ( ord_less_eq_nat @ S2 @ T ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6089_sums__le,axiom,
% 8.64/4.87 ! [F2: nat > int,G2: nat > int,S2: int,T: int] :
% 8.64/4.87 ( ! [N3: nat] : ( ord_less_eq_int @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 8.64/4.87 => ( ( sums_int @ F2 @ S2 )
% 8.64/4.87 => ( ( sums_int @ G2 @ T )
% 8.64/4.87 => ( ord_less_eq_int @ S2 @ T ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6090_sums__0,axiom,
% 8.64/4.87 ! [F2: nat > complex] :
% 8.64/4.87 ( ! [N3: nat] :
% 8.64/4.87 ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_complex )
% 8.64/4.87 => ( sums_complex @ F2 @ zero_zero_complex ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6091_sums__0,axiom,
% 8.64/4.87 ! [F2: nat > real] :
% 8.64/4.87 ( ! [N3: nat] :
% 8.64/4.87 ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_real )
% 8.64/4.87 => ( sums_real @ F2 @ zero_zero_real ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6092_sums__0,axiom,
% 8.64/4.87 ! [F2: nat > nat] :
% 8.64/4.87 ( ! [N3: nat] :
% 8.64/4.87 ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_nat )
% 8.64/4.87 => ( sums_nat @ F2 @ zero_zero_nat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6093_sums__0,axiom,
% 8.64/4.87 ! [F2: nat > int] :
% 8.64/4.87 ( ! [N3: nat] :
% 8.64/4.87 ( ( F2 @ N3 )
% 8.64/4.87 = zero_zero_int )
% 8.64/4.87 => ( sums_int @ F2 @ zero_zero_int ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6094_sums__single,axiom,
% 8.64/4.87 ! [I2: nat,F2: nat > complex] :
% 8.64/4.87 ( sums_complex
% 8.64/4.87 @ ^ [R: nat] : ( if_complex @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_complex )
% 8.64/4.87 @ ( F2 @ I2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6095_sums__single,axiom,
% 8.64/4.87 ! [I2: nat,F2: nat > real] :
% 8.64/4.87 ( sums_real
% 8.64/4.87 @ ^ [R: nat] : ( if_real @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_real )
% 8.64/4.87 @ ( F2 @ I2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6096_sums__single,axiom,
% 8.64/4.87 ! [I2: nat,F2: nat > nat] :
% 8.64/4.87 ( sums_nat
% 8.64/4.87 @ ^ [R: nat] : ( if_nat @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_nat )
% 8.64/4.87 @ ( F2 @ I2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6097_sums__single,axiom,
% 8.64/4.87 ! [I2: nat,F2: nat > int] :
% 8.64/4.87 ( sums_int
% 8.64/4.87 @ ^ [R: nat] : ( if_int @ ( R = I2 ) @ ( F2 @ R ) @ zero_zero_int )
% 8.64/4.87 @ ( F2 @ I2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6098_sums__mult2,axiom,
% 8.64/4.87 ! [F2: nat > real,A: real,C2: real] :
% 8.64/4.87 ( ( sums_real @ F2 @ A )
% 8.64/4.87 => ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ C2 )
% 8.64/4.87 @ ( times_times_real @ A @ C2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6099_sums__mult,axiom,
% 8.64/4.87 ! [F2: nat > real,A: real,C2: real] :
% 8.64/4.87 ( ( sums_real @ F2 @ A )
% 8.64/4.87 => ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 8.64/4.87 @ ( times_times_real @ C2 @ A ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6100_Sum__Icc__int,axiom,
% 8.64/4.87 ! [M2: int,N: int] :
% 8.64/4.87 ( ( ord_less_eq_int @ M2 @ N )
% 8.64/4.87 => ( ( groups4538972089207619220nt_int
% 8.64/4.87 @ ^ [X4: int] : X4
% 8.64/4.87 @ ( set_or1266510415728281911st_int @ M2 @ N ) )
% 8.64/4.87 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M2 @ ( minus_minus_int @ M2 @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6101_sums__mult__iff,axiom,
% 8.64/4.87 ! [C2: complex,F2: nat > complex,D: complex] :
% 8.64/4.87 ( ( C2 != zero_zero_complex )
% 8.64/4.87 => ( ( sums_complex
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F2 @ N4 ) )
% 8.64/4.87 @ ( times_times_complex @ C2 @ D ) )
% 8.64/4.87 = ( sums_complex @ F2 @ D ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6102_sums__mult__iff,axiom,
% 8.64/4.87 ! [C2: real,F2: nat > real,D: real] :
% 8.64/4.87 ( ( C2 != zero_zero_real )
% 8.64/4.87 => ( ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 8.64/4.87 @ ( times_times_real @ C2 @ D ) )
% 8.64/4.87 = ( sums_real @ F2 @ D ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6103_sums__mult2__iff,axiom,
% 8.64/4.87 ! [C2: complex,F2: nat > complex,D: complex] :
% 8.64/4.87 ( ( C2 != zero_zero_complex )
% 8.64/4.87 => ( ( sums_complex
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_complex @ ( F2 @ N4 ) @ C2 )
% 8.64/4.87 @ ( times_times_complex @ D @ C2 ) )
% 8.64/4.87 = ( sums_complex @ F2 @ D ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6104_sums__mult2__iff,axiom,
% 8.64/4.87 ! [C2: real,F2: nat > real,D: real] :
% 8.64/4.87 ( ( C2 != zero_zero_real )
% 8.64/4.87 => ( ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ C2 )
% 8.64/4.87 @ ( times_times_real @ D @ C2 ) )
% 8.64/4.87 = ( sums_real @ F2 @ D ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6105_sums__mult__D,axiom,
% 8.64/4.87 ! [C2: complex,F2: nat > complex,A: complex] :
% 8.64/4.87 ( ( sums_complex
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_complex @ C2 @ ( F2 @ N4 ) )
% 8.64/4.87 @ A )
% 8.64/4.87 => ( ( C2 != zero_zero_complex )
% 8.64/4.87 => ( sums_complex @ F2 @ ( divide1717551699836669952omplex @ A @ C2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6106_sums__mult__D,axiom,
% 8.64/4.87 ! [C2: real,F2: nat > real,A: real] :
% 8.64/4.87 ( ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( times_times_real @ C2 @ ( F2 @ N4 ) )
% 8.64/4.87 @ A )
% 8.64/4.87 => ( ( C2 != zero_zero_real )
% 8.64/4.87 => ( sums_real @ F2 @ ( divide_divide_real @ A @ C2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6107_sums__Suc__imp,axiom,
% 8.64/4.87 ! [F2: nat > complex,S2: complex] :
% 8.64/4.87 ( ( ( F2 @ zero_zero_nat )
% 8.64/4.87 = zero_zero_complex )
% 8.64/4.87 => ( ( sums_complex
% 8.64/4.87 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 8.64/4.87 @ S2 )
% 8.64/4.87 => ( sums_complex @ F2 @ S2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6108_sums__Suc__imp,axiom,
% 8.64/4.87 ! [F2: nat > real,S2: real] :
% 8.64/4.87 ( ( ( F2 @ zero_zero_nat )
% 8.64/4.87 = zero_zero_real )
% 8.64/4.87 => ( ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 8.64/4.87 @ S2 )
% 8.64/4.87 => ( sums_real @ F2 @ S2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6109_sums__Suc__iff,axiom,
% 8.64/4.87 ! [F2: nat > real,S2: real] :
% 8.64/4.87 ( ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 8.64/4.87 @ S2 )
% 8.64/4.87 = ( sums_real @ F2 @ ( plus_plus_real @ S2 @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6110_sums__Suc,axiom,
% 8.64/4.87 ! [F2: nat > real,L: real] :
% 8.64/4.87 ( ( sums_real
% 8.64/4.87 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 8.64/4.87 @ L )
% 8.64/4.87 => ( sums_real @ F2 @ ( plus_plus_real @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6111_sums__Suc,axiom,
% 8.64/4.87 ! [F2: nat > nat,L: nat] :
% 8.64/4.87 ( ( sums_nat
% 8.64/4.87 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 8.64/4.87 @ L )
% 8.64/4.87 => ( sums_nat @ F2 @ ( plus_plus_nat @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6112_sums__Suc,axiom,
% 8.64/4.87 ! [F2: nat > int,L: int] :
% 8.64/4.87 ( ( sums_int
% 8.64/4.87 @ ^ [N4: nat] : ( F2 @ ( suc @ N4 ) )
% 8.64/4.87 @ L )
% 8.64/4.87 => ( sums_int @ F2 @ ( plus_plus_int @ L @ ( F2 @ zero_zero_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6113_pochhammer__times__pochhammer__half,axiom,
% 8.64/4.87 ! [Z3: complex,N: nat] :
% 8.64/4.87 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z3 @ ( suc @ N ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 8.64/4.87 = ( groups6464643781859351333omplex
% 8.64/4.87 @ ^ [K3: nat] : ( plus_plus_complex @ Z3 @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6114_pochhammer__times__pochhammer__half,axiom,
% 8.64/4.87 ! [Z3: rat,N: nat] :
% 8.64/4.87 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z3 @ ( suc @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 8.64/4.87 = ( groups73079841787564623at_rat
% 8.64/4.87 @ ^ [K3: nat] : ( plus_plus_rat @ Z3 @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6115_pochhammer__times__pochhammer__half,axiom,
% 8.64/4.87 ! [Z3: real,N: nat] :
% 8.64/4.87 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z3 @ ( suc @ N ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z3 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N ) ) )
% 8.64/4.87 = ( groups129246275422532515t_real
% 8.64/4.87 @ ^ [K3: nat] : ( plus_plus_real @ Z3 @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6116_lemma__termdiff2,axiom,
% 8.64/4.87 ! [H: complex,Z3: complex,N: nat] :
% 8.64/4.87 ( ( H != zero_zero_complex )
% 8.64/4.87 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ N ) @ ( power_power_complex @ Z3 @ N ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.87 = ( times_times_complex @ H
% 8.64/4.87 @ ( groups2073611262835488442omplex
% 8.64/4.87 @ ^ [P5: nat] :
% 8.64/4.87 ( groups2073611262835488442omplex
% 8.64/4.87 @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ Q5 ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6117_lemma__termdiff2,axiom,
% 8.64/4.87 ! [H: rat,Z3: rat,N: nat] :
% 8.64/4.87 ( ( H != zero_zero_rat )
% 8.64/4.87 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ N ) @ ( power_power_rat @ Z3 @ N ) ) @ H ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.87 = ( times_times_rat @ H
% 8.64/4.87 @ ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [P5: nat] :
% 8.64/4.87 ( groups2906978787729119204at_rat
% 8.64/4.87 @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ Q5 ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6118_lemma__termdiff2,axiom,
% 8.64/4.87 ! [H: real,Z3: real,N: nat] :
% 8.64/4.87 ( ( H != zero_zero_real )
% 8.64/4.87 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ N ) @ ( power_power_real @ Z3 @ N ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.87 = ( times_times_real @ H
% 8.64/4.87 @ ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [P5: nat] :
% 8.64/4.87 ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ Q5 ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6119_pochhammer__code,axiom,
% 8.64/4.87 ( comm_s8582702949713902594nteger
% 8.64/4.87 = ( ^ [A5: code_integer,N4: nat] :
% 8.64/4.87 ( if_Code_integer @ ( N4 = zero_zero_nat ) @ one_one_Code_integer
% 8.64/4.87 @ ( set_fo1084959871951514735nteger
% 8.64/4.87 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ O ) ) )
% 8.64/4.87 @ zero_zero_nat
% 8.64/4.87 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 8.64/4.87 @ one_one_Code_integer ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6120_pochhammer__code,axiom,
% 8.64/4.87 ( comm_s2602460028002588243omplex
% 8.64/4.87 = ( ^ [A5: complex,N4: nat] :
% 8.64/4.87 ( if_complex @ ( N4 = zero_zero_nat ) @ one_one_complex
% 8.64/4.87 @ ( set_fo1517530859248394432omplex
% 8.64/4.87 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A5 @ ( semiri8010041392384452111omplex @ O ) ) )
% 8.64/4.87 @ zero_zero_nat
% 8.64/4.87 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 8.64/4.87 @ one_one_complex ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6121_pochhammer__code,axiom,
% 8.64/4.87 ( comm_s4028243227959126397er_rat
% 8.64/4.87 = ( ^ [A5: rat,N4: nat] :
% 8.64/4.87 ( if_rat @ ( N4 = zero_zero_nat ) @ one_one_rat
% 8.64/4.87 @ ( set_fo1949268297981939178at_rat
% 8.64/4.87 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 8.64/4.87 @ zero_zero_nat
% 8.64/4.87 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 8.64/4.87 @ one_one_rat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6122_pochhammer__code,axiom,
% 8.64/4.87 ( comm_s7457072308508201937r_real
% 8.64/4.87 = ( ^ [A5: real,N4: nat] :
% 8.64/4.87 ( if_real @ ( N4 = zero_zero_nat ) @ one_one_real
% 8.64/4.87 @ ( set_fo3111899725591712190t_real
% 8.64/4.87 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A5 @ ( semiri5074537144036343181t_real @ O ) ) )
% 8.64/4.87 @ zero_zero_nat
% 8.64/4.87 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 8.64/4.87 @ one_one_real ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6123_pochhammer__code,axiom,
% 8.64/4.87 ( comm_s4660882817536571857er_int
% 8.64/4.87 = ( ^ [A5: int,N4: nat] :
% 8.64/4.87 ( if_int @ ( N4 = zero_zero_nat ) @ one_one_int
% 8.64/4.87 @ ( set_fo2581907887559384638at_int
% 8.64/4.87 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 8.64/4.87 @ zero_zero_nat
% 8.64/4.87 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 8.64/4.87 @ one_one_int ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6124_pochhammer__code,axiom,
% 8.64/4.87 ( comm_s4663373288045622133er_nat
% 8.64/4.87 = ( ^ [A5: nat,N4: nat] :
% 8.64/4.87 ( if_nat @ ( N4 = zero_zero_nat ) @ one_one_nat
% 8.64/4.87 @ ( set_fo2584398358068434914at_nat
% 8.64/4.87 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 8.64/4.87 @ zero_zero_nat
% 8.64/4.87 @ ( minus_minus_nat @ N4 @ one_one_nat )
% 8.64/4.87 @ one_one_nat ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6125_of__nat__code,axiom,
% 8.64/4.87 ( semiri4939895301339042750nteger
% 8.64/4.87 = ( ^ [N4: nat] :
% 8.64/4.87 ( semiri4055485073559036834nteger
% 8.64/4.87 @ ^ [I: code_integer] : ( plus_p5714425477246183910nteger @ I @ one_one_Code_integer )
% 8.64/4.87 @ N4
% 8.64/4.87 @ zero_z3403309356797280102nteger ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6126_of__nat__code,axiom,
% 8.64/4.87 ( semiri8010041392384452111omplex
% 8.64/4.87 = ( ^ [N4: nat] :
% 8.64/4.87 ( semiri2816024913162550771omplex
% 8.64/4.87 @ ^ [I: complex] : ( plus_plus_complex @ I @ one_one_complex )
% 8.64/4.87 @ N4
% 8.64/4.87 @ zero_zero_complex ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6127_of__nat__code,axiom,
% 8.64/4.87 ( semiri681578069525770553at_rat
% 8.64/4.87 = ( ^ [N4: nat] :
% 8.64/4.87 ( semiri7787848453975740701ux_rat
% 8.64/4.87 @ ^ [I: rat] : ( plus_plus_rat @ I @ one_one_rat )
% 8.64/4.87 @ N4
% 8.64/4.87 @ zero_zero_rat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6128_of__nat__code,axiom,
% 8.64/4.87 ( semiri5074537144036343181t_real
% 8.64/4.87 = ( ^ [N4: nat] :
% 8.64/4.87 ( semiri7260567687927622513x_real
% 8.64/4.87 @ ^ [I: real] : ( plus_plus_real @ I @ one_one_real )
% 8.64/4.87 @ N4
% 8.64/4.87 @ zero_zero_real ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6129_of__nat__code,axiom,
% 8.64/4.87 ( semiri1314217659103216013at_int
% 8.64/4.87 = ( ^ [N4: nat] :
% 8.64/4.87 ( semiri8420488043553186161ux_int
% 8.64/4.87 @ ^ [I: int] : ( plus_plus_int @ I @ one_one_int )
% 8.64/4.87 @ N4
% 8.64/4.87 @ zero_zero_int ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6130_of__nat__code,axiom,
% 8.64/4.87 ( semiri1316708129612266289at_nat
% 8.64/4.87 = ( ^ [N4: nat] :
% 8.64/4.87 ( semiri8422978514062236437ux_nat
% 8.64/4.87 @ ^ [I: nat] : ( plus_plus_nat @ I @ one_one_nat )
% 8.64/4.87 @ N4
% 8.64/4.87 @ zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6131_central__binomial__lower__bound,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.87 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6132_concat__bit__Suc,axiom,
% 8.64/4.87 ! [N: nat,K2: int,L: int] :
% 8.64/4.87 ( ( bit_concat_bit @ ( suc @ N ) @ K2 @ L )
% 8.64/4.87 = ( plus_plus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6133_dbl__simps_I3_J,axiom,
% 8.64/4.87 ( ( neg_nu8804712462038260780nteger @ one_one_Code_integer )
% 8.64/4.87 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6134_dbl__simps_I3_J,axiom,
% 8.64/4.87 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 8.64/4.87 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6135_dbl__simps_I3_J,axiom,
% 8.64/4.87 ( ( neg_numeral_dbl_real @ one_one_real )
% 8.64/4.87 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6136_dbl__simps_I3_J,axiom,
% 8.64/4.87 ( ( neg_numeral_dbl_int @ one_one_int )
% 8.64/4.87 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6137_lessThan__eq__iff,axiom,
% 8.64/4.87 ! [X: nat,Y: nat] :
% 8.64/4.87 ( ( ( set_ord_lessThan_nat @ X )
% 8.64/4.87 = ( set_ord_lessThan_nat @ Y ) )
% 8.64/4.87 = ( X = Y ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6138_lessThan__iff,axiom,
% 8.64/4.87 ! [I2: set_nat,K2: set_nat] :
% 8.64/4.87 ( ( member_set_nat @ I2 @ ( set_or890127255671739683et_nat @ K2 ) )
% 8.64/4.87 = ( ord_less_set_nat @ I2 @ K2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6139_lessThan__iff,axiom,
% 8.64/4.87 ! [I2: real,K2: real] :
% 8.64/4.87 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K2 ) )
% 8.64/4.87 = ( ord_less_real @ I2 @ K2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6140_lessThan__iff,axiom,
% 8.64/4.87 ! [I2: rat,K2: rat] :
% 8.64/4.87 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K2 ) )
% 8.64/4.87 = ( ord_less_rat @ I2 @ K2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6141_lessThan__iff,axiom,
% 8.64/4.87 ! [I2: num,K2: num] :
% 8.64/4.87 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K2 ) )
% 8.64/4.87 = ( ord_less_num @ I2 @ K2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6142_lessThan__iff,axiom,
% 8.64/4.87 ! [I2: int,K2: int] :
% 8.64/4.87 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K2 ) )
% 8.64/4.87 = ( ord_less_int @ I2 @ K2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6143_lessThan__iff,axiom,
% 8.64/4.87 ! [I2: nat,K2: nat] :
% 8.64/4.87 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K2 ) )
% 8.64/4.87 = ( ord_less_nat @ I2 @ K2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6144_finite__lessThan,axiom,
% 8.64/4.87 ! [K2: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K2 ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6145_concat__bit__0,axiom,
% 8.64/4.87 ! [K2: int,L: int] :
% 8.64/4.87 ( ( bit_concat_bit @ zero_zero_nat @ K2 @ L )
% 8.64/4.87 = L ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6146_card__lessThan,axiom,
% 8.64/4.87 ! [U: nat] :
% 8.64/4.87 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 8.64/4.87 = U ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6147_dbl__simps_I2_J,axiom,
% 8.64/4.87 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 8.64/4.87 = zero_zero_complex ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6148_dbl__simps_I2_J,axiom,
% 8.64/4.87 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 8.64/4.87 = zero_zero_real ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6149_dbl__simps_I2_J,axiom,
% 8.64/4.87 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 8.64/4.87 = zero_zero_rat ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6150_dbl__simps_I2_J,axiom,
% 8.64/4.87 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 8.64/4.87 = zero_zero_int ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6151_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > complex] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( ( groups6464643781859351333omplex @ F2 @ A4 )
% 8.64/4.87 = zero_zero_complex )
% 8.64/4.87 = ( ? [X4: nat] :
% 8.64/4.87 ( ( member_nat @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_complex ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6152_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > complex] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( groups7440179247065528705omplex @ F2 @ A4 )
% 8.64/4.87 = zero_zero_complex )
% 8.64/4.87 = ( ? [X4: int] :
% 8.64/4.87 ( ( member_int @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_complex ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6153_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > complex] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( ( groups3708469109370488835omplex @ F2 @ A4 )
% 8.64/4.87 = zero_zero_complex )
% 8.64/4.87 = ( ? [X4: complex] :
% 8.64/4.87 ( ( member_complex @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_complex ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6154_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( ( groups129246275422532515t_real @ F2 @ A4 )
% 8.64/4.87 = zero_zero_real )
% 8.64/4.87 = ( ? [X4: nat] :
% 8.64/4.87 ( ( member_nat @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6155_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > real] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( groups2316167850115554303t_real @ F2 @ A4 )
% 8.64/4.87 = zero_zero_real )
% 8.64/4.87 = ( ? [X4: int] :
% 8.64/4.87 ( ( member_int @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6156_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > real] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( ( groups766887009212190081x_real @ F2 @ A4 )
% 8.64/4.87 = zero_zero_real )
% 8.64/4.87 = ( ? [X4: complex] :
% 8.64/4.87 ( ( member_complex @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6157_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > rat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( ( groups73079841787564623at_rat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_rat )
% 8.64/4.87 = ( ? [X4: nat] :
% 8.64/4.87 ( ( member_nat @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6158_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > rat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( groups1072433553688619179nt_rat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_rat )
% 8.64/4.87 = ( ? [X4: int] :
% 8.64/4.87 ( ( member_int @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6159_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > rat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( ( groups225925009352817453ex_rat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_rat )
% 8.64/4.87 = ( ? [X4: complex] :
% 8.64/4.87 ( ( member_complex @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_rat ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6160_prod__zero__iff,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > nat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( groups1707563613775114915nt_nat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_nat )
% 8.64/4.87 = ( ? [X4: int] :
% 8.64/4.87 ( ( member_int @ X4 @ A4 )
% 8.64/4.87 & ( ( F2 @ X4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6161_lessThan__subset__iff,axiom,
% 8.64/4.87 ! [X: rat,Y: rat] :
% 8.64/4.87 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 8.64/4.87 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6162_lessThan__subset__iff,axiom,
% 8.64/4.87 ! [X: num,Y: num] :
% 8.64/4.87 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 8.64/4.87 = ( ord_less_eq_num @ X @ Y ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6163_lessThan__subset__iff,axiom,
% 8.64/4.87 ! [X: int,Y: int] :
% 8.64/4.87 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 8.64/4.87 = ( ord_less_eq_int @ X @ Y ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6164_lessThan__subset__iff,axiom,
% 8.64/4.87 ! [X: nat,Y: nat] :
% 8.64/4.87 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 8.64/4.87 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6165_lessThan__0,axiom,
% 8.64/4.87 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 8.64/4.87 = bot_bot_set_nat ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6166_dbl__simps_I5_J,axiom,
% 8.64/4.87 ! [K2: num] :
% 8.64/4.87 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K2 ) )
% 8.64/4.87 = ( numera6690914467698888265omplex @ ( bit0 @ K2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6167_dbl__simps_I5_J,axiom,
% 8.64/4.87 ! [K2: num] :
% 8.64/4.87 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K2 ) )
% 8.64/4.87 = ( numeral_numeral_real @ ( bit0 @ K2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6168_dbl__simps_I5_J,axiom,
% 8.64/4.87 ! [K2: num] :
% 8.64/4.87 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K2 ) )
% 8.64/4.87 = ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6169_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_real,X: real,G2: real > real] :
% 8.64/4.87 ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ~ ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6170_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_nat,X: nat,G2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ~ ( member_nat @ X @ A4 )
% 8.64/4.87 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6171_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_int,X: int,G2: int > real] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ~ ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6172_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_complex,X: complex,G2: complex > real] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ~ ( member_complex @ X @ A4 )
% 8.64/4.87 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6173_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_real,X: real,G2: real > rat] :
% 8.64/4.87 ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ~ ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6174_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ~ ( member_nat @ X @ A4 )
% 8.64/4.87 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6175_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_int,X: int,G2: int > rat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ~ ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6176_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ~ ( member_complex @ X @ A4 )
% 8.64/4.87 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6177_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_real,X: real,G2: real > nat] :
% 8.64/4.87 ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ~ ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( times_times_nat @ ( G2 @ X ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6178_prod_Oinsert,axiom,
% 8.64/4.87 ! [A4: set_int,X: int,G2: int > nat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ~ ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6179_sum_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > rat,N: nat] :
% 8.64/4.87 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6180_sum_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > int,N: nat] :
% 8.64/4.87 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6181_sum_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > nat,N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6182_sum_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > real,N: nat] :
% 8.64/4.87 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6183_single__Diff__lessThan,axiom,
% 8.64/4.87 ! [K2: int] :
% 8.64/4.87 ( ( minus_minus_set_int @ ( insert_int @ K2 @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K2 ) )
% 8.64/4.87 = ( insert_int @ K2 @ bot_bot_set_int ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6184_single__Diff__lessThan,axiom,
% 8.64/4.87 ! [K2: real] :
% 8.64/4.87 ( ( minus_minus_set_real @ ( insert_real @ K2 @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K2 ) )
% 8.64/4.87 = ( insert_real @ K2 @ bot_bot_set_real ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6185_single__Diff__lessThan,axiom,
% 8.64/4.87 ! [K2: nat] :
% 8.64/4.87 ( ( minus_minus_set_nat @ ( insert_nat @ K2 @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K2 ) )
% 8.64/4.87 = ( insert_nat @ K2 @ bot_bot_set_nat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6186_prod_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > real,N: nat] :
% 8.64/4.87 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6187_prod_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > rat,N: nat] :
% 8.64/4.87 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6188_prod_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > int,N: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6189_prod_OlessThan__Suc,axiom,
% 8.64/4.87 ! [G2: nat > nat,N: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) @ ( G2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6190_prod_Ocl__ivl__Suc,axiom,
% 8.64/4.87 ! [N: nat,M2: nat,G2: nat > code_integer] :
% 8.64/4.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = one_one_Code_integer ) )
% 8.64/4.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6191_prod_Ocl__ivl__Suc,axiom,
% 8.64/4.87 ! [N: nat,M2: nat,G2: nat > complex] :
% 8.64/4.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = one_one_complex ) )
% 8.64/4.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_complex @ ( groups6464643781859351333omplex @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6192_prod_Ocl__ivl__Suc,axiom,
% 8.64/4.87 ! [N: nat,M2: nat,G2: nat > real] :
% 8.64/4.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = one_one_real ) )
% 8.64/4.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6193_prod_Ocl__ivl__Suc,axiom,
% 8.64/4.87 ! [N: nat,M2: nat,G2: nat > rat] :
% 8.64/4.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = one_one_rat ) )
% 8.64/4.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6194_prod_Ocl__ivl__Suc,axiom,
% 8.64/4.87 ! [N: nat,M2: nat,G2: nat > int] :
% 8.64/4.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = one_one_int ) )
% 8.64/4.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6195_prod_Ocl__ivl__Suc,axiom,
% 8.64/4.87 ! [N: nat,M2: nat,G2: nat > nat] :
% 8.64/4.87 ( ( ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = one_one_nat ) )
% 8.64/4.87 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M2 )
% 8.64/4.87 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6196_prod_Onat__diff__reindex,axiom,
% 8.64/4.87 ! [G2: nat > int,N: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.87 = ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6197_prod_Onat__diff__reindex,axiom,
% 8.64/4.87 ! [G2: nat > nat,N: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.87 = ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6198_lessThan__non__empty,axiom,
% 8.64/4.87 ! [X: int] :
% 8.64/4.87 ( ( set_ord_lessThan_int @ X )
% 8.64/4.87 != bot_bot_set_int ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6199_lessThan__non__empty,axiom,
% 8.64/4.87 ! [X: real] :
% 8.64/4.87 ( ( set_or5984915006950818249n_real @ X )
% 8.64/4.87 != bot_bot_set_real ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6200_infinite__Iio,axiom,
% 8.64/4.87 ! [A: int] :
% 8.64/4.87 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6201_prod_Odistrib,axiom,
% 8.64/4.87 ! [G2: nat > int,H: nat > int,A4: set_nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int
% 8.64/4.87 @ ^ [X4: nat] : ( times_times_int @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A4 ) @ ( groups705719431365010083at_int @ H @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6202_prod_Odistrib,axiom,
% 8.64/4.87 ! [G2: int > int,H: int > int,A4: set_int] :
% 8.64/4.87 ( ( groups1705073143266064639nt_int
% 8.64/4.87 @ ^ [X4: int] : ( times_times_int @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( times_times_int @ ( groups1705073143266064639nt_int @ G2 @ A4 ) @ ( groups1705073143266064639nt_int @ H @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6203_prod_Odistrib,axiom,
% 8.64/4.87 ! [G2: nat > nat,H: nat > nat,A4: set_nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat
% 8.64/4.87 @ ^ [X4: nat] : ( times_times_nat @ ( G2 @ X4 ) @ ( H @ X4 ) )
% 8.64/4.87 @ A4 )
% 8.64/4.87 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ A4 ) @ ( groups708209901874060359at_nat @ H @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6204_lessThan__def,axiom,
% 8.64/4.87 ( set_or890127255671739683et_nat
% 8.64/4.87 = ( ^ [U2: set_nat] :
% 8.64/4.87 ( collect_set_nat
% 8.64/4.87 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6205_lessThan__def,axiom,
% 8.64/4.87 ( set_or5984915006950818249n_real
% 8.64/4.87 = ( ^ [U2: real] :
% 8.64/4.87 ( collect_real
% 8.64/4.87 @ ^ [X4: real] : ( ord_less_real @ X4 @ U2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6206_lessThan__def,axiom,
% 8.64/4.87 ( set_ord_lessThan_rat
% 8.64/4.87 = ( ^ [U2: rat] :
% 8.64/4.87 ( collect_rat
% 8.64/4.87 @ ^ [X4: rat] : ( ord_less_rat @ X4 @ U2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6207_lessThan__def,axiom,
% 8.64/4.87 ( set_ord_lessThan_num
% 8.64/4.87 = ( ^ [U2: num] :
% 8.64/4.87 ( collect_num
% 8.64/4.87 @ ^ [X4: num] : ( ord_less_num @ X4 @ U2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6208_lessThan__def,axiom,
% 8.64/4.87 ( set_ord_lessThan_int
% 8.64/4.87 = ( ^ [U2: int] :
% 8.64/4.87 ( collect_int
% 8.64/4.87 @ ^ [X4: int] : ( ord_less_int @ X4 @ U2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6209_lessThan__def,axiom,
% 8.64/4.87 ( set_ord_lessThan_nat
% 8.64/4.87 = ( ^ [U2: nat] :
% 8.64/4.87 ( collect_nat
% 8.64/4.87 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U2 ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6210_prod_OlessThan__Suc__shift,axiom,
% 8.64/4.87 ! [G2: nat > real,N: nat] :
% 8.64/4.87 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 8.64/4.87 @ ( groups129246275422532515t_real
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6211_prod_OlessThan__Suc__shift,axiom,
% 8.64/4.87 ! [G2: nat > rat,N: nat] :
% 8.64/4.87 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 8.64/4.87 @ ( groups73079841787564623at_rat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6212_prod_OlessThan__Suc__shift,axiom,
% 8.64/4.87 ! [G2: nat > int,N: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 8.64/4.87 @ ( groups705719431365010083at_int
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6213_prod_OlessThan__Suc__shift,axiom,
% 8.64/4.87 ! [G2: nat > nat,N: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.87 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 8.64/4.87 @ ( groups708209901874060359at_nat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6214_prod_OatLeast1__atMost__eq,axiom,
% 8.64/4.87 ! [G2: nat > int,N: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.87 = ( groups705719431365010083at_int
% 8.64/4.87 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6215_prod_OatLeast1__atMost__eq,axiom,
% 8.64/4.87 ! [G2: nat > nat,N: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.87 = ( groups708209901874060359at_nat
% 8.64/4.87 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6216_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6217_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > real,G2: real > real] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6218_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6219_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > real,G2: int > real] :
% 8.64/4.87 ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6220_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6221_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > rat,G2: real > rat] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6222_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 8.64/4.87 ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6223_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 8.64/4.87 ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6224_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 8.64/4.87 ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6225_prod__mono,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > nat,G2: real > nat] :
% 8.64/4.87 ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 8.64/4.87 & ( ord_less_eq_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.87 => ( ord_less_eq_nat @ ( groups4696554848551431203al_nat @ F2 @ A4 ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6226_prod__nonneg,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > int] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6227_prod__nonneg,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > int] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6228_prod__nonneg,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > nat] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6229_prod__pos,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > int] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6230_prod__pos,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > int] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_int @ zero_zero_int @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6231_prod__pos,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > nat] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6232_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > code_integer] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ A4 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups8682486955453173170nteger @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6233_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > code_integer] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ A4 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups6225526099057966256nteger @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6234_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > code_integer] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6235_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > code_integer] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ A4 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6236_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > real] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( groups766887009212190081x_real @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6237_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > real] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6238_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > real] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( groups129246275422532515t_real @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6239_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > real] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6240_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > rat] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ one_one_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6241_prod__ge__1,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > rat] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ A4 )
% 8.64/4.87 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ X3 ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6242_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > complex] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ? [X5: nat] :
% 8.64/4.87 ( ( member_nat @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_complex ) )
% 8.64/4.87 => ( ( groups6464643781859351333omplex @ F2 @ A4 )
% 8.64/4.87 = zero_zero_complex ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6243_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > complex] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ? [X5: int] :
% 8.64/4.87 ( ( member_int @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_complex ) )
% 8.64/4.87 => ( ( groups7440179247065528705omplex @ F2 @ A4 )
% 8.64/4.87 = zero_zero_complex ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6244_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > complex] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ? [X5: complex] :
% 8.64/4.87 ( ( member_complex @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_complex ) )
% 8.64/4.87 => ( ( groups3708469109370488835omplex @ F2 @ A4 )
% 8.64/4.87 = zero_zero_complex ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6245_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ? [X5: nat] :
% 8.64/4.87 ( ( member_nat @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_real ) )
% 8.64/4.87 => ( ( groups129246275422532515t_real @ F2 @ A4 )
% 8.64/4.87 = zero_zero_real ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6246_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > real] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ? [X5: int] :
% 8.64/4.87 ( ( member_int @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_real ) )
% 8.64/4.87 => ( ( groups2316167850115554303t_real @ F2 @ A4 )
% 8.64/4.87 = zero_zero_real ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6247_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > real] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ? [X5: complex] :
% 8.64/4.87 ( ( member_complex @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_real ) )
% 8.64/4.87 => ( ( groups766887009212190081x_real @ F2 @ A4 )
% 8.64/4.87 = zero_zero_real ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6248_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > rat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ? [X5: nat] :
% 8.64/4.87 ( ( member_nat @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_rat ) )
% 8.64/4.87 => ( ( groups73079841787564623at_rat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_rat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6249_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > rat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ? [X5: int] :
% 8.64/4.87 ( ( member_int @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_rat ) )
% 8.64/4.87 => ( ( groups1072433553688619179nt_rat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_rat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6250_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > rat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ? [X5: complex] :
% 8.64/4.87 ( ( member_complex @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_rat ) )
% 8.64/4.87 => ( ( groups225925009352817453ex_rat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_rat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6251_prod__zero,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > nat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ? [X5: int] :
% 8.64/4.87 ( ( member_int @ X5 @ A4 )
% 8.64/4.87 & ( ( F2 @ X5 )
% 8.64/4.87 = zero_zero_nat ) )
% 8.64/4.87 => ( ( groups1707563613775114915nt_nat @ F2 @ A4 )
% 8.64/4.87 = zero_zero_nat ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6252_prod__atLeastAtMost__code,axiom,
% 8.64/4.87 ! [F2: nat > code_integer,A: nat,B: nat] :
% 8.64/4.87 ( ( groups3455450783089532116nteger @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.87 = ( set_fo1084959871951514735nteger
% 8.64/4.87 @ ^ [A5: nat] : ( times_3573771949741848930nteger @ ( F2 @ A5 ) )
% 8.64/4.87 @ A
% 8.64/4.87 @ B
% 8.64/4.87 @ one_one_Code_integer ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6253_prod__atLeastAtMost__code,axiom,
% 8.64/4.87 ! [F2: nat > complex,A: nat,B: nat] :
% 8.64/4.87 ( ( groups6464643781859351333omplex @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.87 = ( set_fo1517530859248394432omplex
% 8.64/4.87 @ ^ [A5: nat] : ( times_times_complex @ ( F2 @ A5 ) )
% 8.64/4.87 @ A
% 8.64/4.87 @ B
% 8.64/4.87 @ one_one_complex ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6254_prod__atLeastAtMost__code,axiom,
% 8.64/4.87 ! [F2: nat > real,A: nat,B: nat] :
% 8.64/4.87 ( ( groups129246275422532515t_real @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.87 = ( set_fo3111899725591712190t_real
% 8.64/4.87 @ ^ [A5: nat] : ( times_times_real @ ( F2 @ A5 ) )
% 8.64/4.87 @ A
% 8.64/4.87 @ B
% 8.64/4.87 @ one_one_real ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6255_prod__atLeastAtMost__code,axiom,
% 8.64/4.87 ! [F2: nat > rat,A: nat,B: nat] :
% 8.64/4.87 ( ( groups73079841787564623at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.87 = ( set_fo1949268297981939178at_rat
% 8.64/4.87 @ ^ [A5: nat] : ( times_times_rat @ ( F2 @ A5 ) )
% 8.64/4.87 @ A
% 8.64/4.87 @ B
% 8.64/4.87 @ one_one_rat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6256_prod__atLeastAtMost__code,axiom,
% 8.64/4.87 ! [F2: nat > int,A: nat,B: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.87 = ( set_fo2581907887559384638at_int
% 8.64/4.87 @ ^ [A5: nat] : ( times_times_int @ ( F2 @ A5 ) )
% 8.64/4.87 @ A
% 8.64/4.87 @ B
% 8.64/4.87 @ one_one_int ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6257_prod__atLeastAtMost__code,axiom,
% 8.64/4.87 ! [F2: nat > nat,A: nat,B: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.87 = ( set_fo2584398358068434914at_nat
% 8.64/4.87 @ ^ [A5: nat] : ( times_times_nat @ ( F2 @ A5 ) )
% 8.64/4.87 @ A
% 8.64/4.87 @ B
% 8.64/4.87 @ one_one_nat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6258_Iio__eq__empty__iff,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( ( set_ord_lessThan_nat @ N )
% 8.64/4.87 = bot_bot_set_nat )
% 8.64/4.87 = ( N = bot_bot_nat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6259_lessThan__strict__subset__iff,axiom,
% 8.64/4.87 ! [M2: real,N: real] :
% 8.64/4.87 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M2 ) @ ( set_or5984915006950818249n_real @ N ) )
% 8.64/4.87 = ( ord_less_real @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6260_lessThan__strict__subset__iff,axiom,
% 8.64/4.87 ! [M2: rat,N: rat] :
% 8.64/4.87 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M2 ) @ ( set_ord_lessThan_rat @ N ) )
% 8.64/4.87 = ( ord_less_rat @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6261_lessThan__strict__subset__iff,axiom,
% 8.64/4.87 ! [M2: num,N: num] :
% 8.64/4.87 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M2 ) @ ( set_ord_lessThan_num @ N ) )
% 8.64/4.87 = ( ord_less_num @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6262_lessThan__strict__subset__iff,axiom,
% 8.64/4.87 ! [M2: int,N: int] :
% 8.64/4.87 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M2 ) @ ( set_ord_lessThan_int @ N ) )
% 8.64/4.87 = ( ord_less_int @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6263_lessThan__strict__subset__iff,axiom,
% 8.64/4.87 ! [M2: nat,N: nat] :
% 8.64/4.87 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M2 ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.87 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6264_lessThan__Suc,axiom,
% 8.64/4.87 ! [K2: nat] :
% 8.64/4.87 ( ( set_ord_lessThan_nat @ ( suc @ K2 ) )
% 8.64/4.87 = ( insert_nat @ K2 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6265_lessThan__empty__iff,axiom,
% 8.64/4.87 ! [N: nat] :
% 8.64/4.87 ( ( ( set_ord_lessThan_nat @ N )
% 8.64/4.87 = bot_bot_set_nat )
% 8.64/4.87 = ( N = zero_zero_nat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6266_dbl__def,axiom,
% 8.64/4.87 ( neg_numeral_dbl_real
% 8.64/4.87 = ( ^ [X4: real] : ( plus_plus_real @ X4 @ X4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6267_dbl__def,axiom,
% 8.64/4.87 ( neg_numeral_dbl_rat
% 8.64/4.87 = ( ^ [X4: rat] : ( plus_plus_rat @ X4 @ X4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6268_dbl__def,axiom,
% 8.64/4.87 ( neg_numeral_dbl_int
% 8.64/4.87 = ( ^ [X4: int] : ( plus_plus_int @ X4 @ X4 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6269_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 8.64/4.87 ! [G2: nat > int,M2: nat,N: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 8.64/4.87 = ( groups705719431365010083at_int
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6270_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 8.64/4.87 ! [G2: nat > nat,M2: nat,N: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 8.64/4.87 = ( groups708209901874060359at_nat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6271_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 8.64/4.87 ! [G2: nat > int,M2: nat,K2: nat,N: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 8.64/4.87 = ( groups705719431365010083at_int
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6272_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 8.64/4.87 ! [G2: nat > nat,M2: nat,K2: nat,N: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M2 @ K2 ) @ ( plus_plus_nat @ N @ K2 ) ) )
% 8.64/4.87 = ( groups708209901874060359at_nat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ I @ K2 ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6273_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > code_integer] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6274_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > code_integer] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6275_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > code_integer] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6276_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > code_integer] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_le3102999989581377725nteger @ ( F2 @ X3 ) @ one_one_Code_integer ) ) )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ one_one_Code_integer ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6277_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > real] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6278_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > real] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6279_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_nat,F2: nat > real] :
% 8.64/4.87 ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6280_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_int,F2: int > real] :
% 8.64/4.87 ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_less_eq_real @ ( F2 @ X3 ) @ one_one_real ) ) )
% 8.64/4.87 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ one_one_real ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6281_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_complex,F2: complex > rat] :
% 8.64/4.87 ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ one_one_rat ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ one_one_rat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6282_prod__le__1,axiom,
% 8.64/4.87 ! [A4: set_real,F2: real > rat] :
% 8.64/4.87 ( ! [X3: real] :
% 8.64/4.87 ( ( member_real @ X3 @ A4 )
% 8.64/4.87 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ X3 ) )
% 8.64/4.87 & ( ord_less_eq_rat @ ( F2 @ X3 ) @ one_one_rat ) ) )
% 8.64/4.87 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ one_one_rat ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6283_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: code_integer > code_integer > $o,S3: set_nat,H: nat > code_integer,G2: nat > code_integer] :
% 8.64/4.87 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 8.64/4.87 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite_finite_nat @ S3 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups3455450783089532116nteger @ H @ S3 ) @ ( groups3455450783089532116nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6284_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: code_integer > code_integer > $o,S3: set_int,H: int > code_integer,G2: int > code_integer] :
% 8.64/4.87 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 8.64/4.87 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ S3 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups3827104343326376752nteger @ H @ S3 ) @ ( groups3827104343326376752nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6285_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: code_integer > code_integer > $o,S3: set_complex,H: complex > code_integer,G2: complex > code_integer] :
% 8.64/4.87 ( ( R2 @ one_one_Code_integer @ one_one_Code_integer )
% 8.64/4.87 => ( ! [X15: code_integer,Y15: code_integer,X23: code_integer,Y23: code_integer] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_3573771949741848930nteger @ X15 @ Y15 ) @ ( times_3573771949741848930nteger @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups8682486955453173170nteger @ H @ S3 ) @ ( groups8682486955453173170nteger @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6286_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: complex > complex > $o,S3: set_nat,H: nat > complex,G2: nat > complex] :
% 8.64/4.87 ( ( R2 @ one_one_complex @ one_one_complex )
% 8.64/4.87 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite_finite_nat @ S3 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups6464643781859351333omplex @ H @ S3 ) @ ( groups6464643781859351333omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6287_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: complex > complex > $o,S3: set_int,H: int > complex,G2: int > complex] :
% 8.64/4.87 ( ( R2 @ one_one_complex @ one_one_complex )
% 8.64/4.87 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ S3 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups7440179247065528705omplex @ H @ S3 ) @ ( groups7440179247065528705omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6288_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: complex > complex > $o,S3: set_complex,H: complex > complex,G2: complex > complex] :
% 8.64/4.87 ( ( R2 @ one_one_complex @ one_one_complex )
% 8.64/4.87 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_times_complex @ X15 @ Y15 ) @ ( times_times_complex @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups3708469109370488835omplex @ H @ S3 ) @ ( groups3708469109370488835omplex @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6289_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: real > real > $o,S3: set_nat,H: nat > real,G2: nat > real] :
% 8.64/4.87 ( ( R2 @ one_one_real @ one_one_real )
% 8.64/4.87 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite_finite_nat @ S3 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups129246275422532515t_real @ H @ S3 ) @ ( groups129246275422532515t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6290_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: real > real > $o,S3: set_int,H: int > real,G2: int > real] :
% 8.64/4.87 ( ( R2 @ one_one_real @ one_one_real )
% 8.64/4.87 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite_finite_int @ S3 )
% 8.64/4.87 => ( ! [X3: int] :
% 8.64/4.87 ( ( member_int @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups2316167850115554303t_real @ H @ S3 ) @ ( groups2316167850115554303t_real @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6291_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: real > real > $o,S3: set_complex,H: complex > real,G2: complex > real] :
% 8.64/4.87 ( ( R2 @ one_one_real @ one_one_real )
% 8.64/4.87 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_times_real @ X15 @ Y15 ) @ ( times_times_real @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.87 => ( ! [X3: complex] :
% 8.64/4.87 ( ( member_complex @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups766887009212190081x_real @ H @ S3 ) @ ( groups766887009212190081x_real @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6292_prod_Orelated,axiom,
% 8.64/4.87 ! [R2: rat > rat > $o,S3: set_nat,H: nat > rat,G2: nat > rat] :
% 8.64/4.87 ( ( R2 @ one_one_rat @ one_one_rat )
% 8.64/4.87 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 8.64/4.87 ( ( ( R2 @ X15 @ X23 )
% 8.64/4.87 & ( R2 @ Y15 @ Y23 ) )
% 8.64/4.87 => ( R2 @ ( times_times_rat @ X15 @ Y15 ) @ ( times_times_rat @ X23 @ Y23 ) ) )
% 8.64/4.87 => ( ( finite_finite_nat @ S3 )
% 8.64/4.87 => ( ! [X3: nat] :
% 8.64/4.87 ( ( member_nat @ X3 @ S3 )
% 8.64/4.87 => ( R2 @ ( H @ X3 ) @ ( G2 @ X3 ) ) )
% 8.64/4.87 => ( R2 @ ( groups73079841787564623at_rat @ H @ S3 ) @ ( groups73079841787564623at_rat @ G2 @ S3 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6293_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_real,X: real,G2: real > real] :
% 8.64/4.87 ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ( ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( groups1681761925125756287l_real @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6294_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_nat,X: nat,G2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( ( member_nat @ X @ A4 )
% 8.64/4.87 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.87 = ( groups129246275422532515t_real @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_nat @ X @ A4 )
% 8.64/4.87 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6295_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_int,X: int,G2: int > real] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( groups2316167850115554303t_real @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6296_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_complex,X: complex,G2: complex > real] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( ( member_complex @ X @ A4 )
% 8.64/4.87 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.87 = ( groups766887009212190081x_real @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_complex @ X @ A4 )
% 8.64/4.87 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.87 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6297_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_real,X: real,G2: real > rat] :
% 8.64/4.87 ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ( ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( groups4061424788464935467al_rat @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6298_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 8.64/4.87 ( ( finite_finite_nat @ A4 )
% 8.64/4.87 => ( ( ( member_nat @ X @ A4 )
% 8.64/4.87 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.87 = ( groups73079841787564623at_rat @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_nat @ X @ A4 )
% 8.64/4.87 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6299_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_int,X: int,G2: int > rat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6300_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.87 => ( ( ( member_complex @ X @ A4 )
% 8.64/4.87 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.87 = ( groups225925009352817453ex_rat @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_complex @ X @ A4 )
% 8.64/4.87 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.87 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6301_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_real,X: real,G2: real > nat] :
% 8.64/4.87 ( ( finite_finite_real @ A4 )
% 8.64/4.87 => ( ( ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( groups4696554848551431203al_nat @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_real @ X @ A4 )
% 8.64/4.87 => ( ( groups4696554848551431203al_nat @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.87 = ( times_times_nat @ ( G2 @ X ) @ ( groups4696554848551431203al_nat @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6302_prod_Oinsert__if,axiom,
% 8.64/4.87 ! [A4: set_int,X: int,G2: int > nat] :
% 8.64/4.87 ( ( finite_finite_int @ A4 )
% 8.64/4.87 => ( ( ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) )
% 8.64/4.87 & ( ~ ( member_int @ X @ A4 )
% 8.64/4.87 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.87 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6303_ivl__disj__int__one_I4_J,axiom,
% 8.64/4.87 ! [L: nat,U: nat] :
% 8.64/4.87 ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 8.64/4.87 = bot_bot_set_nat ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6304_ivl__disj__int__one_I4_J,axiom,
% 8.64/4.87 ! [L: int,U: int] :
% 8.64/4.87 ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 8.64/4.87 = bot_bot_set_int ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6305_ivl__disj__int__one_I4_J,axiom,
% 8.64/4.87 ! [L: real,U: real] :
% 8.64/4.87 ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ L ) @ ( set_or1222579329274155063t_real @ L @ U ) )
% 8.64/4.87 = bot_bot_set_real ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6306_prod_OatLeastAtMost__rev,axiom,
% 8.64/4.87 ! [G2: nat > int,N: nat,M2: nat] :
% 8.64/4.87 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 8.64/4.87 = ( groups705719431365010083at_int
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6307_prod_OatLeastAtMost__rev,axiom,
% 8.64/4.87 ! [G2: nat > nat,N: nat,M2: nat] :
% 8.64/4.87 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ N @ M2 ) )
% 8.64/4.87 = ( groups708209901874060359at_nat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ ( plus_plus_nat @ M2 @ N ) @ I ) )
% 8.64/4.87 @ ( set_or1269000886237332187st_nat @ N @ M2 ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6308_sum_Onat__diff__reindex,axiom,
% 8.64/4.87 ! [G2: nat > nat,N: nat] :
% 8.64/4.87 ( ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.87 = ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6309_sum_Onat__diff__reindex,axiom,
% 8.64/4.87 ! [G2: nat > real,N: nat] :
% 8.64/4.87 ( ( groups6591440286371151544t_real
% 8.64/4.87 @ ^ [I: nat] : ( G2 @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.87 = ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6310_sum__diff__distrib,axiom,
% 8.64/4.87 ! [Q: nat > nat,P2: nat > nat,N: nat] :
% 8.64/4.87 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P2 @ X3 ) )
% 8.64/4.87 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P2 @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 8.64/4.87 = ( groups3542108847815614940at_nat
% 8.64/4.87 @ ^ [X4: nat] : ( minus_minus_nat @ ( P2 @ X4 ) @ ( Q @ X4 ) )
% 8.64/4.87 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6311_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_real,I2: real,F2: real > code_integer] :
% 8.64/4.87 ( ( finite_finite_real @ I5 )
% 8.64/4.87 => ( ( member_real @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ I5 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups6225526099057966256nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6312_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_nat,I2: nat,F2: nat > code_integer] :
% 8.64/4.87 ( ( finite_finite_nat @ I5 )
% 8.64/4.87 => ( ( member_nat @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ I5 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6313_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_int,I2: int,F2: int > code_integer] :
% 8.64/4.87 ( ( finite_finite_int @ I5 )
% 8.64/4.87 => ( ( member_int @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ I5 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6314_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_complex,I2: complex,F2: complex > code_integer] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.87 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ I5 )
% 8.64/4.87 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups8682486955453173170nteger @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6315_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_real,I2: real,F2: real > real] :
% 8.64/4.87 ( ( finite_finite_real @ I5 )
% 8.64/4.87 => ( ( member_real @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ I5 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_less_real @ one_one_real @ ( groups1681761925125756287l_real @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6316_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_nat,I2: nat,F2: nat > real] :
% 8.64/4.87 ( ( finite_finite_nat @ I5 )
% 8.64/4.87 => ( ( member_nat @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: nat] :
% 8.64/4.87 ( ( member_nat @ I3 @ I5 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_less_real @ one_one_real @ ( groups129246275422532515t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6317_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_int,I2: int,F2: int > real] :
% 8.64/4.87 ( ( finite_finite_int @ I5 )
% 8.64/4.87 => ( ( member_int @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: int] :
% 8.64/4.87 ( ( member_int @ I3 @ I5 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_less_real @ one_one_real @ ( groups2316167850115554303t_real @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6318_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_complex,I2: complex,F2: complex > real] :
% 8.64/4.87 ( ( finite3207457112153483333omplex @ I5 )
% 8.64/4.87 => ( ( member_complex @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_less_real @ one_one_real @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: complex] :
% 8.64/4.87 ( ( member_complex @ I3 @ I5 )
% 8.64/4.87 => ( ord_less_eq_real @ one_one_real @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_less_real @ one_one_real @ ( groups766887009212190081x_real @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6319_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_real,I2: real,F2: real > rat] :
% 8.64/4.87 ( ( finite_finite_real @ I5 )
% 8.64/4.87 => ( ( member_real @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) )
% 8.64/4.87 => ( ! [I3: real] :
% 8.64/4.87 ( ( member_real @ I3 @ I5 )
% 8.64/4.87 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I3 ) ) )
% 8.64/4.87 => ( ord_less_rat @ one_one_rat @ ( groups4061424788464935467al_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.87
% 8.64/4.87 thf(fact_6320_less__1__prod2,axiom,
% 8.64/4.87 ! [I5: set_nat,I2: nat,F2: nat > rat] :
% 8.64/4.87 ( ( finite_finite_nat @ I5 )
% 8.64/4.87 => ( ( member_nat @ I2 @ I5 )
% 8.64/4.87 => ( ( ord_less_rat @ one_one_rat @ ( F2 @ I2 ) )
% 8.64/4.88 => ( ! [I3: nat] :
% 8.64/4.88 ( ( member_nat @ I3 @ I5 )
% 8.64/4.88 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ I3 ) ) )
% 8.64/4.88 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F2 @ I5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6321_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_int,A4: set_int,G2: int > real] :
% 8.64/4.88 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6322_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_complex,A4: set_complex,G2: complex > real] :
% 8.64/4.88 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6323_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_int,A4: set_int,G2: int > rat] :
% 8.64/4.88 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6324_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_complex,A4: set_complex,G2: complex > rat] :
% 8.64/4.88 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6325_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_int,A4: set_int,G2: int > nat] :
% 8.64/4.88 ( ( ord_less_eq_set_int @ B5 @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6326_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_complex,A4: set_complex,G2: complex > nat] :
% 8.64/4.88 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6327_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_complex,A4: set_complex,G2: complex > int] :
% 8.64/4.88 ( ( ord_le211207098394363844omplex @ B5 @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups858564598930262913ex_int @ G2 @ A4 )
% 8.64/4.88 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6328_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_nat,A4: set_nat,G2: nat > real] :
% 8.64/4.88 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6329_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_nat,A4: set_nat,G2: nat > rat] :
% 8.64/4.88 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6330_prod_Osubset__diff,axiom,
% 8.64/4.88 ! [B5: set_nat,A4: set_nat,G2: nat > int] :
% 8.64/4.88 ( ( ord_less_eq_set_nat @ B5 @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups705719431365010083at_int @ G2 @ A4 )
% 8.64/4.88 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6331_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6332_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6333_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6334_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6335_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6336_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6337_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6338_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6339_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ A4 ) @ ( groups858564598930262913ex_int @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6340_prod_Ounion__inter,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > int] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) )
% 8.64/4.88 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ A4 ) @ ( groups705719431365010083at_int @ G2 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6341_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_int,G2: int > real,B5: set_int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6342_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_complex,G2: complex > real,B5: set_complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6343_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_nat,G2: nat > real,B5: set_nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6344_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_int,G2: int > rat,B5: set_int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6345_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_complex,G2: complex > rat,B5: set_complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6346_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_nat,G2: nat > rat,B5: set_nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6347_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_int,G2: int > nat,B5: set_int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6348_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_complex,G2: complex > nat,B5: set_complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6349_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_complex,G2: complex > int,B5: set_complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups858564598930262913ex_int @ G2 @ A4 )
% 8.64/4.88 = ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6350_prod_OInt__Diff,axiom,
% 8.64/4.88 ! [A4: set_nat,G2: nat > int,B5: set_nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups705719431365010083at_int @ G2 @ A4 )
% 8.64/4.88 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6351_prod_OatLeast0__atMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6352_prod_OatLeast0__atMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6353_prod_OatLeast0__atMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6354_prod_OatLeast0__atMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6355_prod_OatLeast__Suc__atMost,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > real] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ M2 ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6356_prod_OatLeast__Suc__atMost,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > rat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ M2 ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6357_prod_OatLeast__Suc__atMost,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > int] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_int @ ( G2 @ M2 ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6358_prod_OatLeast__Suc__atMost,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ M2 ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6359_prod_Onat__ivl__Suc_H,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > real] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ ( suc @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6360_prod_Onat__ivl__Suc_H,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > rat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ ( suc @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6361_prod_Onat__ivl__Suc_H,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > int] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.88 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_int @ ( G2 @ ( suc @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6362_prod_Onat__ivl__Suc_H,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( suc @ N ) )
% 8.64/4.88 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ ( suc @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6363_Iio__Int__singleton,axiom,
% 8.64/4.88 ! [X: real,K2: real] :
% 8.64/4.88 ( ( ( ord_less_real @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 8.64/4.88 = ( insert_real @ X @ bot_bot_set_real ) ) )
% 8.64/4.88 & ( ~ ( ord_less_real @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_real @ ( set_or5984915006950818249n_real @ K2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 8.64/4.88 = bot_bot_set_real ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6364_Iio__Int__singleton,axiom,
% 8.64/4.88 ! [X: rat,K2: rat] :
% 8.64/4.88 ( ( ( ord_less_rat @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 8.64/4.88 = ( insert_rat @ X @ bot_bot_set_rat ) ) )
% 8.64/4.88 & ( ~ ( ord_less_rat @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_rat @ ( set_ord_lessThan_rat @ K2 ) @ ( insert_rat @ X @ bot_bot_set_rat ) )
% 8.64/4.88 = bot_bot_set_rat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6365_Iio__Int__singleton,axiom,
% 8.64/4.88 ! [X: num,K2: num] :
% 8.64/4.88 ( ( ( ord_less_num @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 8.64/4.88 = ( insert_num @ X @ bot_bot_set_num ) ) )
% 8.64/4.88 & ( ~ ( ord_less_num @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_num @ ( set_ord_lessThan_num @ K2 ) @ ( insert_num @ X @ bot_bot_set_num ) )
% 8.64/4.88 = bot_bot_set_num ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6366_Iio__Int__singleton,axiom,
% 8.64/4.88 ! [X: int,K2: int] :
% 8.64/4.88 ( ( ( ord_less_int @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 8.64/4.88 = ( insert_int @ X @ bot_bot_set_int ) ) )
% 8.64/4.88 & ( ~ ( ord_less_int @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ K2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 8.64/4.88 = bot_bot_set_int ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6367_Iio__Int__singleton,axiom,
% 8.64/4.88 ! [X: nat,K2: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 8.64/4.88 = ( insert_nat @ X @ bot_bot_set_nat ) ) )
% 8.64/4.88 & ( ~ ( ord_less_nat @ X @ K2 )
% 8.64/4.88 => ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ K2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 8.64/4.88 = bot_bot_set_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6368_prod_OSuc__reindex__ivl,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > real] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ M2 )
% 8.64/4.88 @ ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6369_prod_OSuc__reindex__ivl,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > rat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ M2 )
% 8.64/4.88 @ ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6370_prod_OSuc__reindex__ivl,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > int] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_int @ ( G2 @ M2 )
% 8.64/4.88 @ ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6371_prod_OSuc__reindex__ivl,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( G2 @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ M2 )
% 8.64/4.88 @ ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6372_sum_OlessThan__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6373_sum_OlessThan__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6374_sum_OlessThan__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6375_sum_OlessThan__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6376_sum__lessThan__telescope_H,axiom,
% 8.64/4.88 ! [F2: nat > rat,M2: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [N4: nat] : ( minus_minus_rat @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6377_sum__lessThan__telescope_H,axiom,
% 8.64/4.88 ! [F2: nat > int,M2: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [N4: nat] : ( minus_minus_int @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6378_sum__lessThan__telescope_H,axiom,
% 8.64/4.88 ! [F2: nat > real,M2: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ N4 ) @ ( F2 @ ( suc @ N4 ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( minus_minus_real @ ( F2 @ zero_zero_nat ) @ ( F2 @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6379_sum__lessThan__telescope,axiom,
% 8.64/4.88 ! [F2: nat > rat,M2: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [N4: nat] : ( minus_minus_rat @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( minus_minus_rat @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6380_sum__lessThan__telescope,axiom,
% 8.64/4.88 ! [F2: nat > int,M2: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [N4: nat] : ( minus_minus_int @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( minus_minus_int @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6381_sum__lessThan__telescope,axiom,
% 8.64/4.88 ! [F2: nat > real,M2: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ ( suc @ N4 ) ) @ ( F2 @ N4 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( minus_minus_real @ ( F2 @ M2 ) @ ( F2 @ zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6382_sumr__diff__mult__const2,axiom,
% 8.64/4.88 ! [F2: nat > rat,N: nat,R3: rat] :
% 8.64/4.88 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R3 ) )
% 8.64/4.88 = ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ I ) @ R3 )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6383_sumr__diff__mult__const2,axiom,
% 8.64/4.88 ! [F2: nat > int,N: nat,R3: int] :
% 8.64/4.88 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R3 ) )
% 8.64/4.88 = ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ I ) @ R3 )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6384_sumr__diff__mult__const2,axiom,
% 8.64/4.88 ! [F2: nat > real,N: nat,R3: real] :
% 8.64/4.88 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R3 ) )
% 8.64/4.88 = ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ I ) @ R3 )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6385_sum_OatLeast1__atMost__eq,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.88 = ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6386_sum_OatLeast1__atMost__eq,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.88 = ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [K3: nat] : ( G2 @ ( suc @ K3 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6387_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > real,G2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ! [I3: complex] :
% 8.64/4.88 ( ( member_complex @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_complex )
% 8.64/4.88 => ( ord_less_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6388_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > real,G2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ! [I3: nat] :
% 8.64/4.88 ( ( member_nat @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_nat )
% 8.64/4.88 => ( ord_less_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6389_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > real,G2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ! [I3: int] :
% 8.64/4.88 ( ( member_int @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_int )
% 8.64/4.88 => ( ord_less_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6390_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > real,G2: real > real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ! [I3: real] :
% 8.64/4.88 ( ( member_real @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_real @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_real )
% 8.64/4.88 => ( ord_less_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6391_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > rat,G2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ! [I3: complex] :
% 8.64/4.88 ( ( member_complex @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_complex )
% 8.64/4.88 => ( ord_less_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6392_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > rat,G2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ! [I3: nat] :
% 8.64/4.88 ( ( member_nat @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_nat )
% 8.64/4.88 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6393_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > rat,G2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ! [I3: int] :
% 8.64/4.88 ( ( member_int @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_int )
% 8.64/4.88 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6394_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > rat,G2: real > rat] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ! [I3: real] :
% 8.64/4.88 ( ( member_real @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_rat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_real )
% 8.64/4.88 => ( ord_less_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6395_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > nat,G2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ! [I3: complex] :
% 8.64/4.88 ( ( member_complex @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_complex )
% 8.64/4.88 => ( ord_less_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6396_prod__mono__strict,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > nat,G2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ! [I3: int] :
% 8.64/4.88 ( ( member_int @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_nat @ ( F2 @ I3 ) @ ( G2 @ I3 ) ) ) )
% 8.64/4.88 => ( ( A4 != bot_bot_set_int )
% 8.64/4.88 => ( ord_less_nat @ ( groups1707563613775114915nt_nat @ F2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6397_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_complex,X: complex,G2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( member_complex @ X @ A4 )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6398_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_int,X: int,G2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( member_int @ X @ A4 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6399_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_real,X: real,G2: real > real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( member_real @ X @ A4 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6400_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_nat,X: nat,G2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( member_nat @ X @ A4 )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ A4 )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6401_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_complex,X: complex,G2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( member_complex @ X @ A4 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6402_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_int,X: int,G2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( member_int @ X @ A4 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6403_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_real,X: real,G2: real > rat] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( member_real @ X @ A4 )
% 8.64/4.88 => ( ( groups4061424788464935467al_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6404_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_nat,X: nat,G2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( member_nat @ X @ A4 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6405_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_complex,X: complex,G2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( member_complex @ X @ A4 )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ X ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6406_prod_Oremove,axiom,
% 8.64/4.88 ! [A4: set_int,X: int,G2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( member_int @ X @ A4 )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat @ G2 @ A4 )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6407_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_complex,G2: complex > real,X: complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6408_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_int,G2: int > real,X: int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6409_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_real,G2: real > real,X: real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups1681761925125756287l_real @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6410_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_nat,G2: nat > real,X: nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ X ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6411_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_complex,G2: complex > rat,X: complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6412_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_int,G2: int > rat,X: int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6413_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_real,G2: real > rat,X: real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups4061424788464935467al_rat @ G2 @ ( insert_real @ X @ A4 ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups4061424788464935467al_rat @ G2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6414_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_nat,G2: nat > rat,X: nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ ( insert_nat @ X @ A4 ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ X ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6415_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_complex,G2: complex > nat,X: complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat @ G2 @ ( insert_complex @ X @ A4 ) )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ X ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6416_prod_Oinsert__remove,axiom,
% 8.64/4.88 ! [A4: set_int,G2: int > nat,X: int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat @ G2 @ ( insert_int @ X @ A4 ) )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ X ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6417_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > code_integer] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ! [X3: int] :
% 8.64/4.88 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_Code_integer ) )
% 8.64/4.88 => ( ( groups3827104343326376752nteger @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G2 @ A4 ) @ ( groups3827104343326376752nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6418_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > code_integer] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ! [X3: complex] :
% 8.64/4.88 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_Code_integer ) )
% 8.64/4.88 => ( ( groups8682486955453173170nteger @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( groups8682486955453173170nteger @ G2 @ A4 ) @ ( groups8682486955453173170nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6419_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > complex] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ! [X3: int] :
% 8.64/4.88 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_complex ) )
% 8.64/4.88 => ( ( groups7440179247065528705omplex @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_complex @ ( groups7440179247065528705omplex @ G2 @ A4 ) @ ( groups7440179247065528705omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6420_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ! [X3: complex] :
% 8.64/4.88 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_complex ) )
% 8.64/4.88 => ( ( groups3708469109370488835omplex @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_complex @ ( groups3708469109370488835omplex @ G2 @ A4 ) @ ( groups3708469109370488835omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6421_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > code_integer] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ! [X3: nat] :
% 8.64/4.88 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_Code_integer ) )
% 8.64/4.88 => ( ( groups3455450783089532116nteger @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G2 @ A4 ) @ ( groups3455450783089532116nteger @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6422_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > complex] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ! [X3: nat] :
% 8.64/4.88 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_complex ) )
% 8.64/4.88 => ( ( groups6464643781859351333omplex @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_complex @ ( groups6464643781859351333omplex @ G2 @ A4 ) @ ( groups6464643781859351333omplex @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6423_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ! [X3: int] :
% 8.64/4.88 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_real ) )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6424_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ! [X3: complex] :
% 8.64/4.88 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_real ) )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6425_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ! [X3: nat] :
% 8.64/4.88 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_real ) )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6426_prod_Ounion__inter__neutral,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ! [X3: int] :
% 8.64/4.88 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.88 => ( ( G2 @ X3 )
% 8.64/4.88 = one_one_rat ) )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6427_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_complex )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( groups766887009212190081x_real @ G2 @ A4 ) @ ( groups766887009212190081x_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6428_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_nat )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ A4 ) @ ( groups129246275422532515t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6429_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_int )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ A4 ) @ ( groups2316167850115554303t_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6430_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_real,B5: set_real,G2: real > real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( finite_finite_real @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_real @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_real )
% 8.64/4.88 => ( ( groups1681761925125756287l_real @ G2 @ ( sup_sup_set_real @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( groups1681761925125756287l_real @ G2 @ A4 ) @ ( groups1681761925125756287l_real @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6431_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_complex )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ A4 ) @ ( groups225925009352817453ex_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6432_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_nat @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_nat )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ A4 ) @ ( groups73079841787564623at_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6433_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_int )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ A4 ) @ ( groups1072433553688619179nt_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6434_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_real,B5: set_real,G2: real > rat] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( finite_finite_real @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_real @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_real )
% 8.64/4.88 => ( ( groups4061424788464935467al_rat @ G2 @ ( sup_sup_set_real @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( groups4061424788464935467al_rat @ G2 @ A4 ) @ ( groups4061424788464935467al_rat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6435_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_complex @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_complex )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ A4 ) @ ( groups861055069439313189ex_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6436_prod_Ounion__disjoint,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( ( inf_inf_set_int @ A4 @ B5 )
% 8.64/4.88 = bot_bot_set_int )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ A4 ) @ ( groups1707563613775114915nt_nat @ G2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6437_binomial__maximum_H,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K2 ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6438_binomial__mono,axiom,
% 8.64/4.88 ! [K2: nat,K6: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ K6 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 8.64/4.88 => ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6439_binomial__antimono,axiom,
% 8.64/4.88 ! [K2: nat,K6: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ K6 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K2 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K6 @ N )
% 8.64/4.88 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6440_binomial__maximum,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6441_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( times_times_real @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups2316167850115554303t_real @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6442_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( times_times_real @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups766887009212190081x_real @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6443_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_real @ ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups129246275422532515t_real @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6444_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6445_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( times_times_rat @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6446_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups73079841787564623at_rat @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6447_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,G2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat @ G2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_nat @ ( times_times_nat @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ A4 @ B5 ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( minus_minus_set_int @ B5 @ A4 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6448_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_nat @ ( times_times_nat @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups861055069439313189ex_nat @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6449_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,G2: complex > int] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( groups858564598930262913ex_int @ G2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_int @ ( times_times_int @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ A4 @ B5 ) ) @ ( groups858564598930262913ex_int @ G2 @ ( minus_811609699411566653omplex @ B5 @ A4 ) ) ) @ ( groups858564598930262913ex_int @ G2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6450_prod_Ounion__diff2,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,G2: nat > int] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ( groups705719431365010083at_int @ G2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( times_times_int @ ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ A4 @ B5 ) ) @ ( groups705719431365010083at_int @ G2 @ ( minus_minus_set_nat @ B5 @ A4 ) ) ) @ ( groups705719431365010083at_int @ G2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6451_prod_Oub__add__nat,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > real,P: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6452_prod_Oub__add__nat,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > rat,P: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6453_prod_Oub__add__nat,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > int,P: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.88 => ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.88 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6454_prod_Oub__add__nat,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,G2: nat > nat,P: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ ( plus_plus_nat @ N @ one_one_nat ) )
% 8.64/4.88 => ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ ( plus_plus_nat @ N @ P ) ) )
% 8.64/4.88 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) @ ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6455_fold__atLeastAtMost__nat_Osimps,axiom,
% 8.64/4.88 ( set_fo2584398358068434914at_nat
% 8.64/4.88 = ( ^ [F4: nat > nat > nat,A5: nat,B4: nat,Acc2: nat] : ( if_nat @ ( ord_less_nat @ B4 @ A5 ) @ Acc2 @ ( set_fo2584398358068434914at_nat @ F4 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B4 @ ( F4 @ A5 @ Acc2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6456_fold__atLeastAtMost__nat_Oelims,axiom,
% 8.64/4.88 ! [X: nat > nat > nat,Xa2: nat,Xb: nat,Xc: nat,Y: nat] :
% 8.64/4.88 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa2 @ Xb @ Xc )
% 8.64/4.88 = Y )
% 8.64/4.88 => ( ( ( ord_less_nat @ Xb @ Xa2 )
% 8.64/4.88 => ( Y = Xc ) )
% 8.64/4.88 & ( ~ ( ord_less_nat @ Xb @ Xa2 )
% 8.64/4.88 => ( Y
% 8.64/4.88 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa2 @ one_one_nat ) @ Xb @ ( X @ Xa2 @ Xc ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6457_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_complex,A: complex,B: complex > real,C2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.88 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups766887009212190081x_real
% 8.64/4.88 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups766887009212190081x_real
% 8.64/4.88 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups766887009212190081x_real @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6458_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_int,A: int,B: int > real,C2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ S3 )
% 8.64/4.88 => ( ( ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real
% 8.64/4.88 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real
% 8.64/4.88 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups2316167850115554303t_real @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6459_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_real,A: real,B: real > real,C2: real > real] :
% 8.64/4.88 ( ( finite_finite_real @ S3 )
% 8.64/4.88 => ( ( ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real
% 8.64/4.88 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real
% 8.64/4.88 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups1681761925125756287l_real @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6460_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_nat,A: nat,B: nat > real,C2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ S3 )
% 8.64/4.88 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups129246275422532515t_real @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6461_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_complex,A: complex,B: complex > rat,C2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.88 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat
% 8.64/4.88 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_rat @ ( B @ A ) @ ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat
% 8.64/4.88 @ ^ [K3: complex] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups225925009352817453ex_rat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6462_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_int,A: int,B: int > rat,C2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ S3 )
% 8.64/4.88 => ( ( ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat
% 8.64/4.88 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_rat @ ( B @ A ) @ ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat
% 8.64/4.88 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups1072433553688619179nt_rat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6463_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_real,A: real,B: real > rat,C2: real > rat] :
% 8.64/4.88 ( ( finite_finite_real @ S3 )
% 8.64/4.88 => ( ( ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups4061424788464935467al_rat
% 8.64/4.88 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_rat @ ( B @ A ) @ ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups4061424788464935467al_rat
% 8.64/4.88 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups4061424788464935467al_rat @ C2 @ ( minus_minus_set_real @ S3 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6464_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_nat,A: nat,B: nat > rat,C2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ S3 )
% 8.64/4.88 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_rat @ ( B @ A ) @ ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups73079841787564623at_rat @ C2 @ ( minus_minus_set_nat @ S3 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6465_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_complex,A: complex,B: complex > nat,C2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.88 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat
% 8.64/4.88 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_nat @ ( B @ A ) @ ( groups861055069439313189ex_nat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups861055069439313189ex_nat
% 8.64/4.88 @ ^ [K3: complex] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups861055069439313189ex_nat @ C2 @ ( minus_811609699411566653omplex @ S3 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6466_prod_Odelta__remove,axiom,
% 8.64/4.88 ! [S3: set_int,A: int,B: int > nat,C2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ S3 )
% 8.64/4.88 => ( ( ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat
% 8.64/4.88 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_nat @ ( B @ A ) @ ( groups1707563613775114915nt_nat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups1707563613775114915nt_nat
% 8.64/4.88 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ ( C2 @ K3 ) )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( groups1707563613775114915nt_nat @ C2 @ ( minus_minus_set_int @ S3 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6467_power__diff__1__eq,axiom,
% 8.64/4.88 ! [X: code_integer,N: nat] :
% 8.64/4.88 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N ) @ one_one_Code_integer )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6468_power__diff__1__eq,axiom,
% 8.64/4.88 ! [X: complex,N: nat] :
% 8.64/4.88 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 8.64/4.88 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6469_power__diff__1__eq,axiom,
% 8.64/4.88 ! [X: rat,N: nat] :
% 8.64/4.88 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 8.64/4.88 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6470_power__diff__1__eq,axiom,
% 8.64/4.88 ! [X: int,N: nat] :
% 8.64/4.88 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 8.64/4.88 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6471_power__diff__1__eq,axiom,
% 8.64/4.88 ! [X: real,N: nat] :
% 8.64/4.88 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 8.64/4.88 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6472_one__diff__power__eq,axiom,
% 8.64/4.88 ! [X: code_integer,N: nat] :
% 8.64/4.88 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6473_one__diff__power__eq,axiom,
% 8.64/4.88 ! [X: complex,N: nat] :
% 8.64/4.88 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 8.64/4.88 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6474_one__diff__power__eq,axiom,
% 8.64/4.88 ! [X: rat,N: nat] :
% 8.64/4.88 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 8.64/4.88 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6475_one__diff__power__eq,axiom,
% 8.64/4.88 ! [X: int,N: nat] :
% 8.64/4.88 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 8.64/4.88 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6476_one__diff__power__eq,axiom,
% 8.64/4.88 ! [X: real,N: nat] :
% 8.64/4.88 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 8.64/4.88 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6477_geometric__sum,axiom,
% 8.64/4.88 ! [X: complex,N: nat] :
% 8.64/4.88 ( ( X != one_one_complex )
% 8.64/4.88 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6478_geometric__sum,axiom,
% 8.64/4.88 ! [X: rat,N: nat] :
% 8.64/4.88 ( ( X != one_one_rat )
% 8.64/4.88 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6479_geometric__sum,axiom,
% 8.64/4.88 ! [X: real,N: nat] :
% 8.64/4.88 ( ( X != one_one_real )
% 8.64/4.88 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6480_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_real,A4: set_real,F2: real > code_integer] :
% 8.64/4.88 ( ( finite_finite_real @ B5 )
% 8.64/4.88 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: real] :
% 8.64/4.88 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: real] :
% 8.64/4.88 ( ( member_real @ A3 @ A4 )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ ( groups6225526099057966256nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6481_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_int,A4: set_int,F2: int > code_integer] :
% 8.64/4.88 ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: int] :
% 8.64/4.88 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: int] :
% 8.64/4.88 ( ( member_int @ A3 @ A4 )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ ( groups3827104343326376752nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6482_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_complex,A4: set_complex,F2: complex > code_integer] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: complex] :
% 8.64/4.88 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: complex] :
% 8.64/4.88 ( ( member_complex @ A3 @ A4 )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ ( groups8682486955453173170nteger @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6483_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_real,A4: set_real,F2: real > real] :
% 8.64/4.88 ( ( finite_finite_real @ B5 )
% 8.64/4.88 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: real] :
% 8.64/4.88 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: real] :
% 8.64/4.88 ( ( member_real @ A3 @ A4 )
% 8.64/4.88 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( groups1681761925125756287l_real @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6484_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_int,A4: set_int,F2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: int] :
% 8.64/4.88 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: int] :
% 8.64/4.88 ( ( member_int @ A3 @ A4 )
% 8.64/4.88 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6485_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_complex,A4: set_complex,F2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: complex] :
% 8.64/4.88 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_less_eq_real @ one_one_real @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: complex] :
% 8.64/4.88 ( ( member_complex @ A3 @ A4 )
% 8.64/4.88 => ( ord_less_eq_real @ zero_zero_real @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6486_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_real,A4: set_real,F2: real > rat] :
% 8.64/4.88 ( ( finite_finite_real @ B5 )
% 8.64/4.88 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: real] :
% 8.64/4.88 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: real] :
% 8.64/4.88 ( ( member_real @ A3 @ A4 )
% 8.64/4.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( groups4061424788464935467al_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6487_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_int,A4: set_int,F2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ( ord_less_eq_set_int @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: int] :
% 8.64/4.88 ( ( member_int @ B3 @ ( minus_minus_set_int @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: int] :
% 8.64/4.88 ( ( member_int @ A3 @ A4 )
% 8.64/4.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6488_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_complex,A4: set_complex,F2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ( ord_le211207098394363844omplex @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: complex] :
% 8.64/4.88 ( ( member_complex @ B3 @ ( minus_811609699411566653omplex @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_less_eq_rat @ one_one_rat @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: complex] :
% 8.64/4.88 ( ( member_complex @ A3 @ A4 )
% 8.64/4.88 => ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_less_eq_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6489_prod__mono2,axiom,
% 8.64/4.88 ! [B5: set_real,A4: set_real,F2: real > int] :
% 8.64/4.88 ( ( finite_finite_real @ B5 )
% 8.64/4.88 => ( ( ord_less_eq_set_real @ A4 @ B5 )
% 8.64/4.88 => ( ! [B3: real] :
% 8.64/4.88 ( ( member_real @ B3 @ ( minus_minus_set_real @ B5 @ A4 ) )
% 8.64/4.88 => ( ord_less_eq_int @ one_one_int @ ( F2 @ B3 ) ) )
% 8.64/4.88 => ( ! [A3: real] :
% 8.64/4.88 ( ( member_real @ A3 @ A4 )
% 8.64/4.88 => ( ord_less_eq_int @ zero_zero_int @ ( F2 @ A3 ) ) )
% 8.64/4.88 => ( ord_less_eq_int @ ( groups4694064378042380927al_int @ F2 @ A4 ) @ ( groups4694064378042380927al_int @ F2 @ B5 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6490_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > code_integer,N: code_integer,K2: nat] :
% 8.64/4.88 ( ! [I3: real] :
% 8.64/4.88 ( ( member_real @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ ( groups6225526099057966256nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6491_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > code_integer,N: code_integer,K2: nat] :
% 8.64/4.88 ( ! [I3: nat] :
% 8.64/4.88 ( ( member_nat @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6492_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > code_integer,N: code_integer,K2: nat] :
% 8.64/4.88 ( ! [I3: complex] :
% 8.64/4.88 ( ( member_complex @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ ( groups8682486955453173170nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6493_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > code_integer,N: code_integer,K2: nat] :
% 8.64/4.88 ( ! [I3: int] :
% 8.64/4.88 ( ( member_int @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_le3102999989581377725nteger @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ N )
% 8.64/4.88 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F2 @ A4 ) @ ( power_8256067586552552935nteger @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6494_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > real,N: real,K2: nat] :
% 8.64/4.88 ( ! [I3: real] :
% 8.64/4.88 ( ( member_real @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_less_eq_real @ one_one_real @ N )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6495_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > real,N: real,K2: nat] :
% 8.64/4.88 ( ! [I3: nat] :
% 8.64/4.88 ( ( member_nat @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_less_eq_real @ one_one_real @ N )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6496_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > real,N: real,K2: nat] :
% 8.64/4.88 ( ! [I3: complex] :
% 8.64/4.88 ( ( member_complex @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_complex @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_less_eq_real @ one_one_real @ N )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6497_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > real,N: real,K2: nat] :
% 8.64/4.88 ( ! [I3: int] :
% 8.64/4.88 ( ( member_int @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_eq_real @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_int @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_less_eq_real @ one_one_real @ N )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( power_power_real @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6498_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > rat,N: rat,K2: nat] :
% 8.64/4.88 ( ! [I3: real] :
% 8.64/4.88 ( ( member_real @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_real @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 8.64/4.88 => ( ord_less_eq_rat @ ( groups4061424788464935467al_rat @ F2 @ A4 ) @ ( power_power_rat @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6499_prod__le__power,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > rat,N: rat,K2: nat] :
% 8.64/4.88 ( ! [I3: nat] :
% 8.64/4.88 ( ( member_nat @ I3 @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F2 @ I3 ) )
% 8.64/4.88 & ( ord_less_eq_rat @ ( F2 @ I3 ) @ N ) ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A4 ) @ K2 )
% 8.64/4.88 => ( ( ord_less_eq_rat @ one_one_rat @ N )
% 8.64/4.88 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( power_power_rat @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6500_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,F2: int > complex] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ! [X3: int] :
% 8.64/4.88 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_complex ) )
% 8.64/4.88 => ( ( groups7440179247065528705omplex @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups7440179247065528705omplex @ F2 @ A4 ) @ ( groups7440179247065528705omplex @ F2 @ B5 ) ) @ ( groups7440179247065528705omplex @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6501_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,F2: complex > complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ! [X3: complex] :
% 8.64/4.88 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_complex ) )
% 8.64/4.88 => ( ( groups3708469109370488835omplex @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups3708469109370488835omplex @ F2 @ A4 ) @ ( groups3708469109370488835omplex @ F2 @ B5 ) ) @ ( groups3708469109370488835omplex @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6502_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,F2: nat > complex] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ! [X3: nat] :
% 8.64/4.88 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_complex ) )
% 8.64/4.88 => ( ( groups6464643781859351333omplex @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups6464643781859351333omplex @ F2 @ A4 ) @ ( groups6464643781859351333omplex @ F2 @ B5 ) ) @ ( groups6464643781859351333omplex @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6503_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,F2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ! [X3: int] :
% 8.64/4.88 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_real ) )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( divide_divide_real @ ( times_times_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( groups2316167850115554303t_real @ F2 @ B5 ) ) @ ( groups2316167850115554303t_real @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6504_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,F2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ! [X3: complex] :
% 8.64/4.88 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_real ) )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( divide_divide_real @ ( times_times_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( groups766887009212190081x_real @ F2 @ B5 ) ) @ ( groups766887009212190081x_real @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6505_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,F2: nat > real] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ! [X3: nat] :
% 8.64/4.88 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_real ) )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( divide_divide_real @ ( times_times_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( groups129246275422532515t_real @ F2 @ B5 ) ) @ ( groups129246275422532515t_real @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6506_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_int,B5: set_int,F2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( finite_finite_int @ B5 )
% 8.64/4.88 => ( ! [X3: int] :
% 8.64/4.88 ( ( member_int @ X3 @ ( inf_inf_set_int @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_rat ) )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ F2 @ ( sup_sup_set_int @ A4 @ B5 ) )
% 8.64/4.88 = ( divide_divide_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( groups1072433553688619179nt_rat @ F2 @ B5 ) ) @ ( groups1072433553688619179nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6507_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_complex,B5: set_complex,F2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( finite3207457112153483333omplex @ B5 )
% 8.64/4.88 => ( ! [X3: complex] :
% 8.64/4.88 ( ( member_complex @ X3 @ ( inf_inf_set_complex @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_rat ) )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ F2 @ ( sup_sup_set_complex @ A4 @ B5 ) )
% 8.64/4.88 = ( divide_divide_rat @ ( times_times_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( groups225925009352817453ex_rat @ F2 @ B5 ) ) @ ( groups225925009352817453ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6508_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_nat,B5: set_nat,F2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( finite_finite_nat @ B5 )
% 8.64/4.88 => ( ! [X3: nat] :
% 8.64/4.88 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_rat ) )
% 8.64/4.88 => ( ( groups73079841787564623at_rat @ F2 @ ( sup_sup_set_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( divide_divide_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ F2 @ A4 ) @ ( groups73079841787564623at_rat @ F2 @ B5 ) ) @ ( groups73079841787564623at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6509_prod__Un,axiom,
% 8.64/4.88 ! [A4: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat,F2: product_prod_nat_nat > complex] :
% 8.64/4.88 ( ( finite6177210948735845034at_nat @ A4 )
% 8.64/4.88 => ( ( finite6177210948735845034at_nat @ B5 )
% 8.64/4.88 => ( ! [X3: product_prod_nat_nat] :
% 8.64/4.88 ( ( member8440522571783428010at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) )
% 8.64/4.88 => ( ( F2 @ X3 )
% 8.64/4.88 != zero_zero_complex ) )
% 8.64/4.88 => ( ( groups8110221916422527690omplex @ F2 @ ( sup_su6327502436637775413at_nat @ A4 @ B5 ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( groups8110221916422527690omplex @ F2 @ A4 ) @ ( groups8110221916422527690omplex @ F2 @ B5 ) ) @ ( groups8110221916422527690omplex @ F2 @ ( inf_in2572325071724192079at_nat @ A4 @ B5 ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6510_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > complex,A: complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_complex )
% 8.64/4.88 => ( ( ( member_complex @ A @ A4 )
% 8.64/4.88 => ( ( groups3708469109370488835omplex @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( groups3708469109370488835omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ A4 )
% 8.64/4.88 => ( ( groups3708469109370488835omplex @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.64/4.88 = ( groups3708469109370488835omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6511_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > complex,A: int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_complex )
% 8.64/4.88 => ( ( ( member_int @ A @ A4 )
% 8.64/4.88 => ( ( groups7440179247065528705omplex @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( groups7440179247065528705omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ A4 )
% 8.64/4.88 => ( ( groups7440179247065528705omplex @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.64/4.88 = ( groups7440179247065528705omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6512_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > complex,A: real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_complex )
% 8.64/4.88 => ( ( ( member_real @ A @ A4 )
% 8.64/4.88 => ( ( groups713298508707869441omplex @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( groups713298508707869441omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_real @ A @ A4 )
% 8.64/4.88 => ( ( groups713298508707869441omplex @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.64/4.88 = ( groups713298508707869441omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6513_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > complex,A: nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_complex )
% 8.64/4.88 => ( ( ( member_nat @ A @ A4 )
% 8.64/4.88 => ( ( groups6464643781859351333omplex @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( groups6464643781859351333omplex @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_nat @ A @ A4 )
% 8.64/4.88 => ( ( groups6464643781859351333omplex @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.64/4.88 = ( groups6464643781859351333omplex @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6514_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > real,A: complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_real )
% 8.64/4.88 => ( ( ( member_complex @ A @ A4 )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.64/4.88 = ( divide_divide_real @ ( groups766887009212190081x_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ A4 )
% 8.64/4.88 => ( ( groups766887009212190081x_real @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.64/4.88 = ( groups766887009212190081x_real @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6515_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > real,A: int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_real )
% 8.64/4.88 => ( ( ( member_int @ A @ A4 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.64/4.88 = ( divide_divide_real @ ( groups2316167850115554303t_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ A4 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.64/4.88 = ( groups2316167850115554303t_real @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6516_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > real,A: real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_real )
% 8.64/4.88 => ( ( ( member_real @ A @ A4 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.64/4.88 = ( divide_divide_real @ ( groups1681761925125756287l_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_real @ A @ A4 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real @ F2 @ ( minus_minus_set_real @ A4 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 8.64/4.88 = ( groups1681761925125756287l_real @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6517_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > real,A: nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_real )
% 8.64/4.88 => ( ( ( member_nat @ A @ A4 )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.64/4.88 = ( divide_divide_real @ ( groups129246275422532515t_real @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_nat @ A @ A4 )
% 8.64/4.88 => ( ( groups129246275422532515t_real @ F2 @ ( minus_minus_set_nat @ A4 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 8.64/4.88 = ( groups129246275422532515t_real @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6518_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > rat,A: complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_rat )
% 8.64/4.88 => ( ( ( member_complex @ A @ A4 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.64/4.88 = ( divide_divide_rat @ ( groups225925009352817453ex_rat @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ A4 )
% 8.64/4.88 => ( ( groups225925009352817453ex_rat @ F2 @ ( minus_811609699411566653omplex @ A4 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 8.64/4.88 = ( groups225925009352817453ex_rat @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6519_prod__diff1,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > rat,A: int] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( ( F2 @ A )
% 8.64/4.88 != zero_zero_rat )
% 8.64/4.88 => ( ( ( member_int @ A @ A4 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.64/4.88 = ( divide_divide_rat @ ( groups1072433553688619179nt_rat @ F2 @ A4 ) @ ( F2 @ A ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ A4 )
% 8.64/4.88 => ( ( groups1072433553688619179nt_rat @ F2 @ ( minus_minus_set_int @ A4 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 8.64/4.88 = ( groups1072433553688619179nt_rat @ F2 @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6520_binomial__less__binomial__Suc,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ K2 @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.88 => ( ord_less_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6521_binomial__strict__antimono,axiom,
% 8.64/4.88 ! [K2: nat,K6: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ K2 @ K6 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K6 @ N )
% 8.64/4.88 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6522_binomial__strict__mono,axiom,
% 8.64/4.88 ! [K2: nat,K6: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ K2 @ K6 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 8.64/4.88 => ( ord_less_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6523_central__binomial__odd,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.88 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.88 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6524_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_real,A: real,B: real > complex,C2: complex] :
% 8.64/4.88 ( ( finite_finite_real @ S3 )
% 8.64/4.88 => ( ( ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups713298508707869441omplex
% 8.64/4.88 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups713298508707869441omplex
% 8.64/4.88 @ ^ [K3: real] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_complex @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6525_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_nat,A: nat,B: nat > complex,C2: complex] :
% 8.64/4.88 ( ( finite_finite_nat @ S3 )
% 8.64/4.88 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups6464643781859351333omplex
% 8.64/4.88 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups6464643781859351333omplex
% 8.64/4.88 @ ^ [K3: nat] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_complex @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6526_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_int,A: int,B: int > complex,C2: complex] :
% 8.64/4.88 ( ( finite_finite_int @ S3 )
% 8.64/4.88 => ( ( ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups7440179247065528705omplex
% 8.64/4.88 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_int @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups7440179247065528705omplex
% 8.64/4.88 @ ^ [K3: int] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_complex @ C2 @ ( finite_card_int @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6527_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_complex,A: complex,B: complex > complex,C2: complex] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.88 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups3708469109370488835omplex
% 8.64/4.88 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_complex @ ( B @ A ) @ ( power_power_complex @ C2 @ ( minus_minus_nat @ ( finite_card_complex @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups3708469109370488835omplex
% 8.64/4.88 @ ^ [K3: complex] : ( if_complex @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_complex @ C2 @ ( finite_card_complex @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6528_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_real,A: real,B: real > real,C2: real] :
% 8.64/4.88 ( ( finite_finite_real @ S3 )
% 8.64/4.88 => ( ( ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real
% 8.64/4.88 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups1681761925125756287l_real
% 8.64/4.88 @ ^ [K3: real] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_real @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6529_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_nat,A: nat,B: nat > real,C2: real] :
% 8.64/4.88 ( ( finite_finite_nat @ S3 )
% 8.64/4.88 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [K3: nat] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_real @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6530_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_int,A: int,B: int > real,C2: real] :
% 8.64/4.88 ( ( finite_finite_int @ S3 )
% 8.64/4.88 => ( ( ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real
% 8.64/4.88 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_int @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_int @ A @ S3 )
% 8.64/4.88 => ( ( groups2316167850115554303t_real
% 8.64/4.88 @ ^ [K3: int] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_real @ C2 @ ( finite_card_int @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6531_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_complex,A: complex,B: complex > real,C2: real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ S3 )
% 8.64/4.88 => ( ( ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups766887009212190081x_real
% 8.64/4.88 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_real @ ( B @ A ) @ ( power_power_real @ C2 @ ( minus_minus_nat @ ( finite_card_complex @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_complex @ A @ S3 )
% 8.64/4.88 => ( ( groups766887009212190081x_real
% 8.64/4.88 @ ^ [K3: complex] : ( if_real @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_real @ C2 @ ( finite_card_complex @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6532_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_real,A: real,B: real > rat,C2: rat] :
% 8.64/4.88 ( ( finite_finite_real @ S3 )
% 8.64/4.88 => ( ( ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups4061424788464935467al_rat
% 8.64/4.88 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C2 @ ( minus_minus_nat @ ( finite_card_real @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_real @ A @ S3 )
% 8.64/4.88 => ( ( groups4061424788464935467al_rat
% 8.64/4.88 @ ^ [K3: real] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_rat @ C2 @ ( finite_card_real @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6533_prod__gen__delta,axiom,
% 8.64/4.88 ! [S3: set_nat,A: nat,B: nat > rat,C2: rat] :
% 8.64/4.88 ( ( finite_finite_nat @ S3 )
% 8.64/4.88 => ( ( ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( times_times_rat @ ( B @ A ) @ ( power_power_rat @ C2 @ ( minus_minus_nat @ ( finite_card_nat @ S3 ) @ one_one_nat ) ) ) ) )
% 8.64/4.88 & ( ~ ( member_nat @ A @ S3 )
% 8.64/4.88 => ( ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ C2 )
% 8.64/4.88 @ S3 )
% 8.64/4.88 = ( power_power_rat @ C2 @ ( finite_card_nat @ S3 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6534_pochhammer__Suc__prod,axiom,
% 8.64/4.88 ! [A: rat,N: nat] :
% 8.64/4.88 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6535_pochhammer__Suc__prod,axiom,
% 8.64/4.88 ! [A: real,N: nat] :
% 8.64/4.88 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6536_pochhammer__Suc__prod,axiom,
% 8.64/4.88 ! [A: int,N: nat] :
% 8.64/4.88 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6537_pochhammer__Suc__prod,axiom,
% 8.64/4.88 ! [A: nat,N: nat] :
% 8.64/4.88 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6538_sum__gp__strict,axiom,
% 8.64/4.88 ! [X: complex,N: nat] :
% 8.64/4.88 ( ( ( X = one_one_complex )
% 8.64/4.88 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( semiri8010041392384452111omplex @ N ) ) )
% 8.64/4.88 & ( ( X != one_one_complex )
% 8.64/4.88 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6539_sum__gp__strict,axiom,
% 8.64/4.88 ! [X: rat,N: nat] :
% 8.64/4.88 ( ( ( X = one_one_rat )
% 8.64/4.88 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( semiri681578069525770553at_rat @ N ) ) )
% 8.64/4.88 & ( ( X != one_one_rat )
% 8.64/4.88 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6540_sum__gp__strict,axiom,
% 8.64/4.88 ! [X: real,N: nat] :
% 8.64/4.88 ( ( ( X = one_one_real )
% 8.64/4.88 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( semiri5074537144036343181t_real @ N ) ) )
% 8.64/4.88 & ( ( X != one_one_real )
% 8.64/4.88 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6541_lemma__termdiff1,axiom,
% 8.64/4.88 ! [Z3: complex,H: complex,M2: nat] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_complex @ Z3 @ P5 ) ) @ ( power_power_complex @ Z3 @ M2 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z3 @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_complex @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6542_lemma__termdiff1,axiom,
% 8.64/4.88 ! [Z3: rat,H: rat,M2: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_rat @ Z3 @ P5 ) ) @ ( power_power_rat @ Z3 @ M2 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z3 @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_rat @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6543_lemma__termdiff1,axiom,
% 8.64/4.88 ! [Z3: int,H: int,M2: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_int @ Z3 @ P5 ) ) @ ( power_power_int @ Z3 @ M2 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z3 @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_int @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6544_lemma__termdiff1,axiom,
% 8.64/4.88 ! [Z3: real,H: real,M2: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_real @ Z3 @ P5 ) ) @ ( power_power_real @ Z3 @ M2 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) )
% 8.64/4.88 = ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z3 @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z3 @ H ) @ ( minus_minus_nat @ M2 @ P5 ) ) @ ( power_power_real @ Z3 @ ( minus_minus_nat @ M2 @ P5 ) ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6545_diff__power__eq__sum,axiom,
% 8.64/4.88 ! [X: complex,N: nat,Y: complex] :
% 8.64/4.88 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6546_diff__power__eq__sum,axiom,
% 8.64/4.88 ! [X: rat,N: nat,Y: rat] :
% 8.64/4.88 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6547_diff__power__eq__sum,axiom,
% 8.64/4.88 ! [X: int,N: nat,Y: int] :
% 8.64/4.88 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6548_diff__power__eq__sum,axiom,
% 8.64/4.88 ! [X: real,N: nat,Y: real] :
% 8.64/4.88 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P5 ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6549_power__diff__sumr2,axiom,
% 8.64/4.88 ! [X: complex,N: nat,Y: complex] :
% 8.64/4.88 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 8.64/4.88 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_complex @ X @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6550_power__diff__sumr2,axiom,
% 8.64/4.88 ! [X: rat,N: nat,Y: rat] :
% 8.64/4.88 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 8.64/4.88 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_rat @ X @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6551_power__diff__sumr2,axiom,
% 8.64/4.88 ! [X: int,N: nat,Y: int] :
% 8.64/4.88 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 8.64/4.88 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_int @ X @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6552_power__diff__sumr2,axiom,
% 8.64/4.88 ! [X: real,N: nat,Y: real] :
% 8.64/4.88 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 8.64/4.88 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I ) ) ) @ ( power_power_real @ X @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6553_real__sum__nat__ivl__bounded2,axiom,
% 8.64/4.88 ! [N: nat,F2: nat > rat,K5: rat,K2: nat] :
% 8.64/4.88 ( ! [P7: nat] :
% 8.64/4.88 ( ( ord_less_nat @ P7 @ N )
% 8.64/4.88 => ( ord_less_eq_rat @ ( F2 @ P7 ) @ K5 ) )
% 8.64/4.88 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 8.64/4.88 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6554_real__sum__nat__ivl__bounded2,axiom,
% 8.64/4.88 ! [N: nat,F2: nat > int,K5: int,K2: nat] :
% 8.64/4.88 ( ! [P7: nat] :
% 8.64/4.88 ( ( ord_less_nat @ P7 @ N )
% 8.64/4.88 => ( ord_less_eq_int @ ( F2 @ P7 ) @ K5 ) )
% 8.64/4.88 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 8.64/4.88 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6555_real__sum__nat__ivl__bounded2,axiom,
% 8.64/4.88 ! [N: nat,F2: nat > nat,K5: nat,K2: nat] :
% 8.64/4.88 ( ! [P7: nat] :
% 8.64/4.88 ( ( ord_less_nat @ P7 @ N )
% 8.64/4.88 => ( ord_less_eq_nat @ ( F2 @ P7 ) @ K5 ) )
% 8.64/4.88 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 8.64/4.88 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6556_real__sum__nat__ivl__bounded2,axiom,
% 8.64/4.88 ! [N: nat,F2: nat > real,K5: real,K2: nat] :
% 8.64/4.88 ( ! [P7: nat] :
% 8.64/4.88 ( ( ord_less_nat @ P7 @ N )
% 8.64/4.88 => ( ord_less_eq_real @ ( F2 @ P7 ) @ K5 ) )
% 8.64/4.88 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 8.64/4.88 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6557_prod_Oin__pairs,axiom,
% 8.64/4.88 ! [G2: nat > real,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups129246275422532515t_real @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.88 = ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6558_prod_Oin__pairs,axiom,
% 8.64/4.88 ! [G2: nat > rat,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups73079841787564623at_rat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.88 = ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6559_prod_Oin__pairs,axiom,
% 8.64/4.88 ! [G2: nat > int,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.88 = ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6560_prod_Oin__pairs,axiom,
% 8.64/4.88 ! [G2: nat > nat,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups708209901874060359at_nat @ G2 @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ M2 @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6561_sum__atLeastAtMost__code,axiom,
% 8.64/4.88 ! [F2: nat > complex,A: nat,B: nat] :
% 8.64/4.88 ( ( groups2073611262835488442omplex @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.88 = ( set_fo1517530859248394432omplex
% 8.64/4.88 @ ^ [A5: nat] : ( plus_plus_complex @ ( F2 @ A5 ) )
% 8.64/4.88 @ A
% 8.64/4.88 @ B
% 8.64/4.88 @ zero_zero_complex ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6562_sum__atLeastAtMost__code,axiom,
% 8.64/4.88 ! [F2: nat > rat,A: nat,B: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.88 = ( set_fo1949268297981939178at_rat
% 8.64/4.88 @ ^ [A5: nat] : ( plus_plus_rat @ ( F2 @ A5 ) )
% 8.64/4.88 @ A
% 8.64/4.88 @ B
% 8.64/4.88 @ zero_zero_rat ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6563_sum__atLeastAtMost__code,axiom,
% 8.64/4.88 ! [F2: nat > int,A: nat,B: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.88 = ( set_fo2581907887559384638at_int
% 8.64/4.88 @ ^ [A5: nat] : ( plus_plus_int @ ( F2 @ A5 ) )
% 8.64/4.88 @ A
% 8.64/4.88 @ B
% 8.64/4.88 @ zero_zero_int ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6564_sum__atLeastAtMost__code,axiom,
% 8.64/4.88 ! [F2: nat > nat,A: nat,B: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.88 = ( set_fo2584398358068434914at_nat
% 8.64/4.88 @ ^ [A5: nat] : ( plus_plus_nat @ ( F2 @ A5 ) )
% 8.64/4.88 @ A
% 8.64/4.88 @ B
% 8.64/4.88 @ zero_zero_nat ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6565_sum__atLeastAtMost__code,axiom,
% 8.64/4.88 ! [F2: nat > real,A: nat,B: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.88 = ( set_fo3111899725591712190t_real
% 8.64/4.88 @ ^ [A5: nat] : ( plus_plus_real @ ( F2 @ A5 ) )
% 8.64/4.88 @ A
% 8.64/4.88 @ B
% 8.64/4.88 @ zero_zero_real ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6566_pochhammer__Suc__prod__rev,axiom,
% 8.64/4.88 ! [A: rat,N: nat] :
% 8.64/4.88 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6567_pochhammer__Suc__prod__rev,axiom,
% 8.64/4.88 ! [A: real,N: nat] :
% 8.64/4.88 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ I ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6568_pochhammer__Suc__prod__rev,axiom,
% 8.64/4.88 ! [A: int,N: nat] :
% 8.64/4.88 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6569_pochhammer__Suc__prod__rev,axiom,
% 8.64/4.88 ! [A: nat,N: nat] :
% 8.64/4.88 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6570_one__diff__power__eq_H,axiom,
% 8.64/4.88 ! [X: code_integer,N: nat] :
% 8.64/4.88 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 8.64/4.88 @ ( groups7501900531339628137nteger
% 8.64/4.88 @ ^ [I: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6571_one__diff__power__eq_H,axiom,
% 8.64/4.88 ! [X: complex,N: nat] :
% 8.64/4.88 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 8.64/4.88 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6572_one__diff__power__eq_H,axiom,
% 8.64/4.88 ! [X: rat,N: nat] :
% 8.64/4.88 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 8.64/4.88 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6573_one__diff__power__eq_H,axiom,
% 8.64/4.88 ! [X: int,N: nat] :
% 8.64/4.88 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 8.64/4.88 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6574_one__diff__power__eq_H,axiom,
% 8.64/4.88 ! [X: real,N: nat] :
% 8.64/4.88 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 8.64/4.88 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6575_sum__split__even__odd,axiom,
% 8.64/4.88 ! [F2: nat > real,G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( F2 @ I ) @ ( G2 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.88 = ( plus_plus_real
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( F2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ one_one_nat ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6576_zero__less__binomial__iff,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K2 ) )
% 8.64/4.88 = ( ord_less_eq_nat @ K2 @ N ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6577_choose__two,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.88 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6578_binomial__n__0,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( binomial @ N @ zero_zero_nat )
% 8.64/4.88 = one_one_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6579_binomial__Suc__Suc,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( binomial @ ( suc @ N ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_nat @ ( binomial @ N @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6580_binomial__eq__0__iff,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( ( binomial @ N @ K2 )
% 8.64/4.88 = zero_zero_nat )
% 8.64/4.88 = ( ord_less_nat @ N @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6581_binomial__1,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 8.64/4.88 = N ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6582_binomial__0__Suc,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( binomial @ zero_zero_nat @ ( suc @ K2 ) )
% 8.64/4.88 = zero_zero_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6583_binomial__Suc__n,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( binomial @ ( suc @ N ) @ N )
% 8.64/4.88 = ( suc @ N ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6584_prod__pos__nat__iff,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F2 @ A4 ) )
% 8.64/4.88 = ( ! [X4: int] :
% 8.64/4.88 ( ( member_int @ X4 @ A4 )
% 8.64/4.88 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6585_prod__pos__nat__iff,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( ord_less_nat @ zero_zero_nat @ ( groups861055069439313189ex_nat @ F2 @ A4 ) )
% 8.64/4.88 = ( ! [X4: complex] :
% 8.64/4.88 ( ( member_complex @ X4 @ A4 )
% 8.64/4.88 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6586_prod__pos__nat__iff,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F2 @ A4 ) )
% 8.64/4.88 = ( ! [X4: nat] :
% 8.64/4.88 ( ( member_nat @ X4 @ A4 )
% 8.64/4.88 => ( ord_less_nat @ zero_zero_nat @ ( F2 @ X4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6587_prod__int__eq,axiom,
% 8.64/4.88 ! [I2: nat,J2: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 8.64/4.88 = ( groups1705073143266064639nt_int
% 8.64/4.88 @ ^ [X4: int] : X4
% 8.64/4.88 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6588_prod__int__plus__eq,axiom,
% 8.64/4.88 ! [I2: nat,J2: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J2 ) ) )
% 8.64/4.88 = ( groups1705073143266064639nt_int
% 8.64/4.88 @ ^ [X4: int] : X4
% 8.64/4.88 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6589_binomial__eq__0,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ N @ K2 )
% 8.64/4.88 => ( ( binomial @ N @ K2 )
% 8.64/4.88 = zero_zero_nat ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6590_Suc__times__binomial,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( times_times_nat @ ( suc @ K2 ) @ ( binomial @ ( suc @ N ) @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6591_Suc__times__binomial__eq,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) )
% 8.64/4.88 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K2 ) ) @ ( suc @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6592_binomial__symmetric,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ( binomial @ N @ K2 )
% 8.64/4.88 = ( binomial @ N @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6593_choose__mult__lemma,axiom,
% 8.64/4.88 ! [M2: nat,R3: nat,K2: nat] :
% 8.64/4.88 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R3 ) @ K2 ) @ ( plus_plus_nat @ M2 @ K2 ) ) @ ( binomial @ ( plus_plus_nat @ M2 @ K2 ) @ K2 ) )
% 8.64/4.88 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M2 @ R3 ) @ K2 ) @ K2 ) @ ( binomial @ ( plus_plus_nat @ M2 @ R3 ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6594_binomial__le__pow,axiom,
% 8.64/4.88 ! [R3: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ R3 @ N )
% 8.64/4.88 => ( ord_less_eq_nat @ ( binomial @ N @ R3 ) @ ( power_power_nat @ N @ R3 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6595_zero__less__binomial,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6596_Suc__times__binomial__add,axiom,
% 8.64/4.88 ! [A: nat,B: nat] :
% 8.64/4.88 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 8.64/4.88 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6597_binomial__Suc__Suc__eq__times,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( binomial @ ( suc @ N ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K2 ) ) @ ( suc @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6598_choose__mult,axiom,
% 8.64/4.88 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ M2 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( times_times_nat @ ( binomial @ N @ M2 ) @ ( binomial @ M2 @ K2 ) )
% 8.64/4.88 = ( times_times_nat @ ( binomial @ N @ K2 ) @ ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6599_binomial__absorb__comp,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( times_times_nat @ ( minus_minus_nat @ N @ K2 ) @ ( binomial @ N @ K2 ) )
% 8.64/4.88 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6600_binomial__absorption,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( times_times_nat @ ( suc @ K2 ) @ ( binomial @ N @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6601_sum__bounds__lt__plus1,axiom,
% 8.64/4.88 ! [F2: nat > nat,Mm: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [K3: nat] : ( F2 @ ( suc @ K3 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ Mm ) )
% 8.64/4.88 = ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6602_sum__bounds__lt__plus1,axiom,
% 8.64/4.88 ! [F2: nat > real,Mm: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [K3: nat] : ( F2 @ ( suc @ K3 ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ Mm ) )
% 8.64/4.88 = ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6603_binomial__ge__n__over__k__pow__k,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6604_binomial__ge__n__over__k__pow__k,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6605_binomial__le__pow2,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6606_choose__reduce__nat,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.88 => ( ( binomial @ N @ K2 )
% 8.64/4.88 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6607_times__binomial__minus1__eq,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.88 => ( ( times_times_nat @ K2 @ ( binomial @ N @ K2 ) )
% 8.64/4.88 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6608_binomial__addition__formula,axiom,
% 8.64/4.88 ! [N: nat,K2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( binomial @ N @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K2 ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6609_choose__odd__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] :
% 8.64/4.88 ( if_rat
% 8.64/4.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 8.64/4.88 @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) )
% 8.64/4.88 @ zero_zero_rat )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6610_choose__odd__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] :
% 8.64/4.88 ( if_complex
% 8.64/4.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 8.64/4.88 @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) )
% 8.64/4.88 @ zero_zero_complex )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6611_choose__odd__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] :
% 8.64/4.88 ( if_int
% 8.64/4.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 8.64/4.88 @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) )
% 8.64/4.88 @ zero_zero_int )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6612_choose__odd__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] :
% 8.64/4.88 ( if_real
% 8.64/4.88 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I )
% 8.64/4.88 @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) )
% 8.64/4.88 @ zero_zero_real )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6613_choose__even__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) @ zero_zero_rat )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6614_choose__even__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) @ zero_zero_complex )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6615_choose__even__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) @ zero_zero_int )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6616_choose__even__sum,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.88 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) @ zero_zero_real )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6617_card__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_list_nat,K2: nat] :
% 8.64/4.88 ( ( finite8100373058378681591st_nat @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_list_nat @ A4 ) )
% 8.64/4.88 => ( ( finite7325466520557071688st_nat
% 8.64/4.88 @ ( collec5989764272469232197st_nat
% 8.64/4.88 @ ^ [Xs: list_list_nat] :
% 8.64/4.88 ( ( ( size_s3023201423986296836st_nat @ Xs )
% 8.64/4.88 = K2 )
% 8.64/4.88 & ( distinct_list_nat @ Xs )
% 8.64/4.88 & ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [X4: nat] : X4
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6618_card__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_set_nat,K2: nat] :
% 8.64/4.88 ( ( finite1152437895449049373et_nat @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_set_nat @ A4 ) )
% 8.64/4.88 => ( ( finite5631907774883551598et_nat
% 8.64/4.88 @ ( collect_list_set_nat
% 8.64/4.88 @ ^ [Xs: list_set_nat] :
% 8.64/4.88 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 8.64/4.88 = K2 )
% 8.64/4.88 & ( distinct_set_nat @ Xs )
% 8.64/4.88 & ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [X4: nat] : X4
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6619_card__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,K2: nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_complex @ A4 ) )
% 8.64/4.88 => ( ( finite5120063068150530198omplex
% 8.64/4.88 @ ( collect_list_complex
% 8.64/4.88 @ ^ [Xs: list_complex] :
% 8.64/4.88 ( ( ( size_s3451745648224563538omplex @ Xs )
% 8.64/4.88 = K2 )
% 8.64/4.88 & ( distinct_complex @ Xs )
% 8.64/4.88 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [X4: nat] : X4
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_complex @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6620_card__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_VEBT_VEBT,K2: nat] :
% 8.64/4.88 ( ( finite5795047828879050333T_VEBT @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 8.64/4.88 => ( ( finite5915292604075114978T_VEBT
% 8.64/4.88 @ ( collec5608196760682091941T_VEBT
% 8.64/4.88 @ ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.88 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.64/4.88 = K2 )
% 8.64/4.88 & ( distinct_VEBT_VEBT @ Xs )
% 8.64/4.88 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [X4: nat] : X4
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6621_card__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_o,K2: nat] :
% 8.64/4.88 ( ( finite_finite_o @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_o @ A4 ) )
% 8.64/4.88 => ( ( finite_card_list_o
% 8.64/4.88 @ ( collect_list_o
% 8.64/4.88 @ ^ [Xs: list_o] :
% 8.64/4.88 ( ( ( size_size_list_o @ Xs )
% 8.64/4.88 = K2 )
% 8.64/4.88 & ( distinct_o @ Xs )
% 8.64/4.88 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [X4: nat] : X4
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_o @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_o @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6622_card__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_int,K2: nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_int @ A4 ) )
% 8.64/4.88 => ( ( finite_card_list_int
% 8.64/4.88 @ ( collect_list_int
% 8.64/4.88 @ ^ [Xs: list_int] :
% 8.64/4.88 ( ( ( size_size_list_int @ Xs )
% 8.64/4.88 = K2 )
% 8.64/4.88 & ( distinct_int @ Xs )
% 8.64/4.88 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [X4: nat] : X4
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_int @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6623_card__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_nat,K2: nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ ( finite_card_nat @ A4 ) )
% 8.64/4.88 => ( ( finite_card_list_nat
% 8.64/4.88 @ ( collect_list_nat
% 8.64/4.88 @ ^ [Xs: list_nat] :
% 8.64/4.88 ( ( ( size_size_list_nat @ Xs )
% 8.64/4.88 = K2 )
% 8.64/4.88 & ( distinct_nat @ Xs )
% 8.64/4.88 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [X4: nat] : X4
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_nat @ A4 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6624_gchoose__row__sum__weighted,axiom,
% 8.64/4.88 ! [R3: complex,M2: nat] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R3 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 8.64/4.88 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M2 ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R3 @ ( suc @ M2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6625_gchoose__row__sum__weighted,axiom,
% 8.64/4.88 ! [R3: rat,M2: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 8.64/4.88 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M2 ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6626_gchoose__row__sum__weighted,axiom,
% 8.64/4.88 ! [R3: real,M2: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R3 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M2 ) )
% 8.64/4.88 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R3 @ ( suc @ M2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6627_vebt__buildup_Opelims,axiom,
% 8.64/4.88 ! [X: nat,Y: vEBT_VEBT] :
% 8.64/4.88 ( ( ( vEBT_vebt_buildup @ X )
% 8.64/4.88 = Y )
% 8.64/4.88 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 8.64/4.88 => ( ( ( X = zero_zero_nat )
% 8.64/4.88 => ( ( Y
% 8.64/4.88 = ( vEBT_Leaf @ $false @ $false ) )
% 8.64/4.88 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 8.64/4.88 => ( ( ( X
% 8.64/4.88 = ( suc @ zero_zero_nat ) )
% 8.64/4.88 => ( ( Y
% 8.64/4.88 = ( vEBT_Leaf @ $false @ $false ) )
% 8.64/4.88 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 8.64/4.88 => ~ ! [Va: nat] :
% 8.64/4.88 ( ( X
% 8.64/4.88 = ( suc @ ( suc @ Va ) ) )
% 8.64/4.88 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 8.64/4.88 => ( Y
% 8.64/4.88 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 8.64/4.88 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 8.64/4.88 => ( Y
% 8.64/4.88 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 8.64/4.88 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va ) ) ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6628_flip__bit__0,axiom,
% 8.64/4.88 ! [A: nat] :
% 8.64/4.88 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 8.64/4.88 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6629_flip__bit__0,axiom,
% 8.64/4.88 ! [A: int] :
% 8.64/4.88 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 8.64/4.88 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6630_flip__bit__0,axiom,
% 8.64/4.88 ! [A: code_integer] :
% 8.64/4.88 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 8.64/4.88 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6631_atMost__eq__iff,axiom,
% 8.64/4.88 ! [X: nat,Y: nat] :
% 8.64/4.88 ( ( ( set_ord_atMost_nat @ X )
% 8.64/4.88 = ( set_ord_atMost_nat @ Y ) )
% 8.64/4.88 = ( X = Y ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6632_atMost__iff,axiom,
% 8.64/4.88 ! [I2: real,K2: real] :
% 8.64/4.88 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K2 ) )
% 8.64/4.88 = ( ord_less_eq_real @ I2 @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6633_atMost__iff,axiom,
% 8.64/4.88 ! [I2: set_nat,K2: set_nat] :
% 8.64/4.88 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K2 ) )
% 8.64/4.88 = ( ord_less_eq_set_nat @ I2 @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6634_atMost__iff,axiom,
% 8.64/4.88 ! [I2: rat,K2: rat] :
% 8.64/4.88 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K2 ) )
% 8.64/4.88 = ( ord_less_eq_rat @ I2 @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6635_atMost__iff,axiom,
% 8.64/4.88 ! [I2: num,K2: num] :
% 8.64/4.88 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K2 ) )
% 8.64/4.88 = ( ord_less_eq_num @ I2 @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6636_atMost__iff,axiom,
% 8.64/4.88 ! [I2: int,K2: int] :
% 8.64/4.88 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K2 ) )
% 8.64/4.88 = ( ord_less_eq_int @ I2 @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6637_atMost__iff,axiom,
% 8.64/4.88 ! [I2: nat,K2: nat] :
% 8.64/4.88 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K2 ) )
% 8.64/4.88 = ( ord_less_eq_nat @ I2 @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6638_of__bool__less__eq__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 8.64/4.88 = ( P2
% 8.64/4.88 => Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6639_of__bool__less__eq__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 8.64/4.88 = ( P2
% 8.64/4.88 => Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6640_of__bool__less__eq__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 8.64/4.88 = ( P2
% 8.64/4.88 => Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6641_of__bool__less__eq__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) )
% 8.64/4.88 = ( P2
% 8.64/4.88 => Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6642_of__bool__eq_I1_J,axiom,
% 8.64/4.88 ( ( zero_n1201886186963655149omplex @ $false )
% 8.64/4.88 = zero_zero_complex ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6643_of__bool__eq_I1_J,axiom,
% 8.64/4.88 ( ( zero_n3304061248610475627l_real @ $false )
% 8.64/4.88 = zero_zero_real ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6644_of__bool__eq_I1_J,axiom,
% 8.64/4.88 ( ( zero_n2052037380579107095ol_rat @ $false )
% 8.64/4.88 = zero_zero_rat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6645_of__bool__eq_I1_J,axiom,
% 8.64/4.88 ( ( zero_n2687167440665602831ol_nat @ $false )
% 8.64/4.88 = zero_zero_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6646_of__bool__eq_I1_J,axiom,
% 8.64/4.88 ( ( zero_n2684676970156552555ol_int @ $false )
% 8.64/4.88 = zero_zero_int ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6647_of__bool__eq_I1_J,axiom,
% 8.64/4.88 ( ( zero_n356916108424825756nteger @ $false )
% 8.64/4.88 = zero_z3403309356797280102nteger ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6648_of__bool__eq__0__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n1201886186963655149omplex @ P2 )
% 8.64/4.88 = zero_zero_complex )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6649_of__bool__eq__0__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n3304061248610475627l_real @ P2 )
% 8.64/4.88 = zero_zero_real )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6650_of__bool__eq__0__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n2052037380579107095ol_rat @ P2 )
% 8.64/4.88 = zero_zero_rat )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6651_of__bool__eq__0__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 8.64/4.88 = zero_zero_nat )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6652_of__bool__eq__0__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 8.64/4.88 = zero_zero_int )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6653_of__bool__eq__0__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n356916108424825756nteger @ P2 )
% 8.64/4.88 = zero_z3403309356797280102nteger )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6654_of__bool__less__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P2 ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 8.64/4.88 = ( ~ P2
% 8.64/4.88 & Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6655_of__bool__less__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 8.64/4.88 = ( ~ P2
% 8.64/4.88 & Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6656_of__bool__less__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 8.64/4.88 = ( ~ P2
% 8.64/4.88 & Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6657_of__bool__less__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 8.64/4.88 = ( ~ P2
% 8.64/4.88 & Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6658_of__bool__less__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) )
% 8.64/4.88 = ( ~ P2
% 8.64/4.88 & Q ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6659_of__bool__eq__1__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n1201886186963655149omplex @ P2 )
% 8.64/4.88 = one_one_complex )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6660_of__bool__eq__1__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n3304061248610475627l_real @ P2 )
% 8.64/4.88 = one_one_real )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6661_of__bool__eq__1__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 8.64/4.88 = one_one_nat )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6662_of__bool__eq__1__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 8.64/4.88 = one_one_int )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6663_of__bool__eq__1__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ( zero_n356916108424825756nteger @ P2 )
% 8.64/4.88 = one_one_Code_integer )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6664_of__bool__eq_I2_J,axiom,
% 8.64/4.88 ( ( zero_n1201886186963655149omplex @ $true )
% 8.64/4.88 = one_one_complex ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6665_of__bool__eq_I2_J,axiom,
% 8.64/4.88 ( ( zero_n3304061248610475627l_real @ $true )
% 8.64/4.88 = one_one_real ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6666_of__bool__eq_I2_J,axiom,
% 8.64/4.88 ( ( zero_n2687167440665602831ol_nat @ $true )
% 8.64/4.88 = one_one_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6667_of__bool__eq_I2_J,axiom,
% 8.64/4.88 ( ( zero_n2684676970156552555ol_int @ $true )
% 8.64/4.88 = one_one_int ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6668_of__bool__eq_I2_J,axiom,
% 8.64/4.88 ( ( zero_n356916108424825756nteger @ $true )
% 8.64/4.88 = one_one_Code_integer ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6669_of__nat__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 8.64/4.88 = ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6670_of__nat__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 8.64/4.88 = ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6671_of__nat__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 8.64/4.88 = ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6672_of__nat__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 8.64/4.88 = ( zero_n356916108424825756nteger @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6673_of__bool__or__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n2687167440665602831ol_nat
% 8.64/4.88 @ ( P2
% 8.64/4.88 | Q ) )
% 8.64/4.88 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6674_of__bool__or__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n2684676970156552555ol_int
% 8.64/4.88 @ ( P2
% 8.64/4.88 | Q ) )
% 8.64/4.88 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6675_of__bool__or__iff,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n356916108424825756nteger
% 8.64/4.88 @ ( P2
% 8.64/4.88 | Q ) )
% 8.64/4.88 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6676_finite__atMost,axiom,
% 8.64/4.88 ! [K2: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6677_zero__less__of__bool__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P2 ) )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6678_zero__less__of__bool__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6679_zero__less__of__bool__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6680_zero__less__of__bool__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6681_zero__less__of__bool__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) )
% 8.64/4.88 = P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6682_atMost__subset__iff,axiom,
% 8.64/4.88 ! [X: set_nat,Y: set_nat] :
% 8.64/4.88 ( ( ord_le6893508408891458716et_nat @ ( set_or4236626031148496127et_nat @ X ) @ ( set_or4236626031148496127et_nat @ Y ) )
% 8.64/4.88 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6683_atMost__subset__iff,axiom,
% 8.64/4.88 ! [X: rat,Y: rat] :
% 8.64/4.88 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 8.64/4.88 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6684_atMost__subset__iff,axiom,
% 8.64/4.88 ! [X: num,Y: num] :
% 8.64/4.88 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 8.64/4.88 = ( ord_less_eq_num @ X @ Y ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6685_atMost__subset__iff,axiom,
% 8.64/4.88 ! [X: int,Y: int] :
% 8.64/4.88 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 8.64/4.88 = ( ord_less_eq_int @ X @ Y ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6686_atMost__subset__iff,axiom,
% 8.64/4.88 ! [X: nat,Y: nat] :
% 8.64/4.88 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 8.64/4.88 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6687_of__bool__less__one__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P2 ) @ one_one_real )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6688_of__bool__less__one__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6689_of__bool__less__one__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6690_of__bool__less__one__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6691_of__bool__less__one__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer )
% 8.64/4.88 = ~ P2 ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6692_of__bool__not__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( zero_n1201886186963655149omplex @ ~ P2 )
% 8.64/4.88 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6693_of__bool__not__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( zero_n3304061248610475627l_real @ ~ P2 )
% 8.64/4.88 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6694_of__bool__not__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( zero_n2052037380579107095ol_rat @ ~ P2 )
% 8.64/4.88 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6695_of__bool__not__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( zero_n2684676970156552555ol_int @ ~ P2 )
% 8.64/4.88 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6696_of__bool__not__iff,axiom,
% 8.64/4.88 ! [P2: $o] :
% 8.64/4.88 ( ( zero_n356916108424825756nteger @ ~ P2 )
% 8.64/4.88 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6697_Suc__0__mod__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.88 = ( zero_n2687167440665602831ol_nat
% 8.64/4.88 @ ( N
% 8.64/4.88 != ( suc @ zero_zero_nat ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6698_gbinomial__0_I2_J,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K2 ) )
% 8.64/4.88 = zero_zero_complex ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6699_gbinomial__0_I2_J,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K2 ) )
% 8.64/4.88 = zero_zero_real ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6700_gbinomial__0_I2_J,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K2 ) )
% 8.64/4.88 = zero_zero_rat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6701_gbinomial__0_I2_J,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K2 ) )
% 8.64/4.88 = zero_zero_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6702_gbinomial__0_I2_J,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K2 ) )
% 8.64/4.88 = zero_zero_int ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6703_gbinomial__0_I1_J,axiom,
% 8.64/4.88 ! [A: code_integer] :
% 8.64/4.88 ( ( gbinom8545251970709558553nteger @ A @ zero_zero_nat )
% 8.64/4.88 = one_one_Code_integer ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6704_gbinomial__0_I1_J,axiom,
% 8.64/4.88 ! [A: complex] :
% 8.64/4.88 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 8.64/4.88 = one_one_complex ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6705_gbinomial__0_I1_J,axiom,
% 8.64/4.88 ! [A: real] :
% 8.64/4.88 ( ( gbinomial_real @ A @ zero_zero_nat )
% 8.64/4.88 = one_one_real ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6706_gbinomial__0_I1_J,axiom,
% 8.64/4.88 ! [A: nat] :
% 8.64/4.88 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 8.64/4.88 = one_one_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6707_gbinomial__0_I1_J,axiom,
% 8.64/4.88 ! [A: int] :
% 8.64/4.88 ( ( gbinomial_int @ A @ zero_zero_nat )
% 8.64/4.88 = one_one_int ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6708_card__atMost,axiom,
% 8.64/4.88 ! [U: nat] :
% 8.64/4.88 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 8.64/4.88 = ( suc @ U ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6709_Icc__subset__Iic__iff,axiom,
% 8.64/4.88 ! [L: set_nat,H: set_nat,H3: set_nat] :
% 8.64/4.88 ( ( ord_le6893508408891458716et_nat @ ( set_or4548717258645045905et_nat @ L @ H ) @ ( set_or4236626031148496127et_nat @ H3 ) )
% 8.64/4.88 = ( ~ ( ord_less_eq_set_nat @ L @ H )
% 8.64/4.88 | ( ord_less_eq_set_nat @ H @ H3 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6710_Icc__subset__Iic__iff,axiom,
% 8.64/4.88 ! [L: rat,H: rat,H3: rat] :
% 8.64/4.88 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H3 ) )
% 8.64/4.88 = ( ~ ( ord_less_eq_rat @ L @ H )
% 8.64/4.88 | ( ord_less_eq_rat @ H @ H3 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6711_Icc__subset__Iic__iff,axiom,
% 8.64/4.88 ! [L: num,H: num,H3: num] :
% 8.64/4.88 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H3 ) )
% 8.64/4.88 = ( ~ ( ord_less_eq_num @ L @ H )
% 8.64/4.88 | ( ord_less_eq_num @ H @ H3 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6712_Icc__subset__Iic__iff,axiom,
% 8.64/4.88 ! [L: nat,H: nat,H3: nat] :
% 8.64/4.88 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H3 ) )
% 8.64/4.88 = ( ~ ( ord_less_eq_nat @ L @ H )
% 8.64/4.88 | ( ord_less_eq_nat @ H @ H3 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6713_Icc__subset__Iic__iff,axiom,
% 8.64/4.88 ! [L: int,H: int,H3: int] :
% 8.64/4.88 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H3 ) )
% 8.64/4.88 = ( ~ ( ord_less_eq_int @ L @ H )
% 8.64/4.88 | ( ord_less_eq_int @ H @ H3 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6714_Icc__subset__Iic__iff,axiom,
% 8.64/4.88 ! [L: real,H: real,H3: real] :
% 8.64/4.88 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H ) @ ( set_ord_atMost_real @ H3 ) )
% 8.64/4.88 = ( ~ ( ord_less_eq_real @ L @ H )
% 8.64/4.88 | ( ord_less_eq_real @ H @ H3 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6715_sum_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6716_sum_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6717_sum_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6718_sum_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6719_prod_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_real @ ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6720_prod_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_rat @ ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6721_prod_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_int @ ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6722_prod_OatMost__Suc,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_nat @ ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) ) @ ( G2 @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6723_atMost__0,axiom,
% 8.64/4.88 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 8.64/4.88 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6724_distinct__swap,axiom,
% 8.64/4.88 ! [I2: nat,Xs2: list_VEBT_VEBT,J2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.88 => ( ( distinct_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs2 @ I2 @ ( nth_VEBT_VEBT @ Xs2 @ J2 ) ) @ J2 @ ( nth_VEBT_VEBT @ Xs2 @ I2 ) ) )
% 8.64/4.88 = ( distinct_VEBT_VEBT @ Xs2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6725_distinct__swap,axiom,
% 8.64/4.88 ! [I2: nat,Xs2: list_o,J2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.88 => ( ( distinct_o @ ( list_update_o @ ( list_update_o @ Xs2 @ I2 @ ( nth_o @ Xs2 @ J2 ) ) @ J2 @ ( nth_o @ Xs2 @ I2 ) ) )
% 8.64/4.88 = ( distinct_o @ Xs2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6726_distinct__swap,axiom,
% 8.64/4.88 ! [I2: nat,Xs2: list_nat,J2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.88 => ( ( distinct_nat @ ( list_update_nat @ ( list_update_nat @ Xs2 @ I2 @ ( nth_nat @ Xs2 @ J2 ) ) @ J2 @ ( nth_nat @ Xs2 @ I2 ) ) )
% 8.64/4.88 = ( distinct_nat @ Xs2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6727_distinct__swap,axiom,
% 8.64/4.88 ! [I2: nat,Xs2: list_int,J2: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.88 => ( ( distinct_int @ ( list_update_int @ ( list_update_int @ Xs2 @ I2 @ ( nth_int @ Xs2 @ J2 ) ) @ J2 @ ( nth_int @ Xs2 @ I2 ) ) )
% 8.64/4.88 = ( distinct_int @ Xs2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6728_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > real,P2: real > $o] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups8097168146408367636l_real
% 8.64/4.88 @ ^ [X4: real] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups8097168146408367636l_real @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6729_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > real,P2: int > $o] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups8778361861064173332t_real
% 8.64/4.88 @ ^ [X4: int] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups8778361861064173332t_real @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6730_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > real,P2: complex > $o] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups5808333547571424918x_real
% 8.64/4.88 @ ^ [X4: complex] : ( times_times_real @ ( F2 @ X4 ) @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups5808333547571424918x_real @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6731_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > rat,P2: real > $o] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups1300246762558778688al_rat
% 8.64/4.88 @ ^ [X4: real] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups1300246762558778688al_rat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6732_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > rat,P2: int > $o] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups3906332499630173760nt_rat
% 8.64/4.88 @ ^ [X4: int] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6733_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > rat,P2: complex > $o] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups5058264527183730370ex_rat
% 8.64/4.88 @ ^ [X4: complex] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups5058264527183730370ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6734_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_nat,F2: nat > rat,P2: nat > $o] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [X4: nat] : ( times_times_rat @ ( F2 @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6735_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_real,F2: real > nat,P2: real > $o] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups1935376822645274424al_nat
% 8.64/4.88 @ ^ [X4: real] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups1935376822645274424al_nat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6736_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_int,F2: int > nat,P2: int > $o] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups4541462559716669496nt_nat
% 8.64/4.88 @ ^ [X4: int] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6737_sum__mult__of__bool__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,F2: complex > nat,P2: complex > $o] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups5693394587270226106ex_nat
% 8.64/4.88 @ ^ [X4: complex] : ( times_times_nat @ ( F2 @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups5693394587270226106ex_nat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6738_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_real,P2: real > $o,F2: real > real] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups8097168146408367636l_real
% 8.64/4.88 @ ^ [X4: real] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups8097168146408367636l_real @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6739_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_int,P2: int > $o,F2: int > real] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups8778361861064173332t_real
% 8.64/4.88 @ ^ [X4: int] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups8778361861064173332t_real @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6740_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,P2: complex > $o,F2: complex > real] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups5808333547571424918x_real
% 8.64/4.88 @ ^ [X4: complex] : ( times_times_real @ ( zero_n3304061248610475627l_real @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups5808333547571424918x_real @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6741_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_real,P2: real > $o,F2: real > rat] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups1300246762558778688al_rat
% 8.64/4.88 @ ^ [X4: real] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups1300246762558778688al_rat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6742_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_int,P2: int > $o,F2: int > rat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups3906332499630173760nt_rat
% 8.64/4.88 @ ^ [X4: int] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups3906332499630173760nt_rat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6743_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,P2: complex > $o,F2: complex > rat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups5058264527183730370ex_rat
% 8.64/4.88 @ ^ [X4: complex] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups5058264527183730370ex_rat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6744_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_nat,P2: nat > $o,F2: nat > rat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [X4: nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups2906978787729119204at_rat @ F2 @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6745_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_real,P2: real > $o,F2: real > nat] :
% 8.64/4.88 ( ( finite_finite_real @ A4 )
% 8.64/4.88 => ( ( groups1935376822645274424al_nat
% 8.64/4.88 @ ^ [X4: real] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups1935376822645274424al_nat @ F2 @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6746_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_int,P2: int > $o,F2: int > nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( ( groups4541462559716669496nt_nat
% 8.64/4.88 @ ^ [X4: int] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups4541462559716669496nt_nat @ F2 @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6747_sum__of__bool__mult__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,P2: complex > $o,F2: complex > nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( ( groups5693394587270226106ex_nat
% 8.64/4.88 @ ^ [X4: complex] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P2 @ X4 ) ) @ ( F2 @ X4 ) )
% 8.64/4.88 @ A4 )
% 8.64/4.88 = ( groups5693394587270226106ex_nat @ F2 @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6748_of__bool__half__eq__0,axiom,
% 8.64/4.88 ! [B: $o] :
% 8.64/4.88 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.88 = zero_zero_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6749_of__bool__half__eq__0,axiom,
% 8.64/4.88 ! [B: $o] :
% 8.64/4.88 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.88 = zero_zero_int ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6750_of__bool__half__eq__0,axiom,
% 8.64/4.88 ! [B: $o] :
% 8.64/4.88 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.88 = zero_z3403309356797280102nteger ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6751_finite__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_complex,N: nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.88 => ( finite8712137658972009173omplex
% 8.64/4.88 @ ( collect_list_complex
% 8.64/4.88 @ ^ [Xs: list_complex] :
% 8.64/4.88 ( ( ( size_s3451745648224563538omplex @ Xs )
% 8.64/4.88 = N )
% 8.64/4.88 & ( distinct_complex @ Xs )
% 8.64/4.88 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6752_finite__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_VEBT_VEBT,N: nat] :
% 8.64/4.88 ( ( finite5795047828879050333T_VEBT @ A4 )
% 8.64/4.88 => ( finite3004134309566078307T_VEBT
% 8.64/4.88 @ ( collec5608196760682091941T_VEBT
% 8.64/4.88 @ ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.88 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.64/4.88 = N )
% 8.64/4.88 & ( distinct_VEBT_VEBT @ Xs )
% 8.64/4.88 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6753_finite__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_o,N: nat] :
% 8.64/4.88 ( ( finite_finite_o @ A4 )
% 8.64/4.88 => ( finite_finite_list_o
% 8.64/4.88 @ ( collect_list_o
% 8.64/4.88 @ ^ [Xs: list_o] :
% 8.64/4.88 ( ( ( size_size_list_o @ Xs )
% 8.64/4.88 = N )
% 8.64/4.88 & ( distinct_o @ Xs )
% 8.64/4.88 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6754_finite__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_int,N: nat] :
% 8.64/4.88 ( ( finite_finite_int @ A4 )
% 8.64/4.88 => ( finite3922522038869484883st_int
% 8.64/4.88 @ ( collect_list_int
% 8.64/4.88 @ ^ [Xs: list_int] :
% 8.64/4.88 ( ( ( size_size_list_int @ Xs )
% 8.64/4.88 = N )
% 8.64/4.88 & ( distinct_int @ Xs )
% 8.64/4.88 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6755_finite__lists__distinct__length__eq,axiom,
% 8.64/4.88 ! [A4: set_nat,N: nat] :
% 8.64/4.88 ( ( finite_finite_nat @ A4 )
% 8.64/4.88 => ( finite8100373058378681591st_nat
% 8.64/4.88 @ ( collect_list_nat
% 8.64/4.88 @ ^ [Xs: list_nat] :
% 8.64/4.88 ( ( ( size_size_list_nat @ Xs )
% 8.64/4.88 = N )
% 8.64/4.88 & ( distinct_nat @ Xs )
% 8.64/4.88 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6756_one__div__2__pow__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6757_one__div__2__pow__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6758_one__div__2__pow__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6759_bits__1__div__exp,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6760_bits__1__div__exp,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6761_bits__1__div__exp,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6762_one__mod__2__pow__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6763_one__mod__2__pow__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6764_one__mod__2__pow__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6765_one__mod__2__pow__eq,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6766_of__bool__eq__iff,axiom,
% 8.64/4.88 ! [P: $o,Q2: $o] :
% 8.64/4.88 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 8.64/4.88 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 8.64/4.88 = ( P = Q2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6767_of__bool__eq__iff,axiom,
% 8.64/4.88 ! [P: $o,Q2: $o] :
% 8.64/4.88 ( ( ( zero_n2684676970156552555ol_int @ P )
% 8.64/4.88 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 8.64/4.88 = ( P = Q2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6768_of__bool__eq__iff,axiom,
% 8.64/4.88 ! [P: $o,Q2: $o] :
% 8.64/4.88 ( ( ( zero_n356916108424825756nteger @ P )
% 8.64/4.88 = ( zero_n356916108424825756nteger @ Q2 ) )
% 8.64/4.88 = ( P = Q2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6769_of__bool__conj,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n3304061248610475627l_real
% 8.64/4.88 @ ( P2
% 8.64/4.88 & Q ) )
% 8.64/4.88 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P2 ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6770_of__bool__conj,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n2052037380579107095ol_rat
% 8.64/4.88 @ ( P2
% 8.64/4.88 & Q ) )
% 8.64/4.88 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6771_of__bool__conj,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n2687167440665602831ol_nat
% 8.64/4.88 @ ( P2
% 8.64/4.88 & Q ) )
% 8.64/4.88 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6772_of__bool__conj,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n2684676970156552555ol_int
% 8.64/4.88 @ ( P2
% 8.64/4.88 & Q ) )
% 8.64/4.88 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6773_of__bool__conj,axiom,
% 8.64/4.88 ! [P2: $o,Q: $o] :
% 8.64/4.88 ( ( zero_n356916108424825756nteger
% 8.64/4.88 @ ( P2
% 8.64/4.88 & Q ) )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P2 ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6774_not__empty__eq__Iic__eq__empty,axiom,
% 8.64/4.88 ! [H: int] :
% 8.64/4.88 ( bot_bot_set_int
% 8.64/4.88 != ( set_ord_atMost_int @ H ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6775_not__empty__eq__Iic__eq__empty,axiom,
% 8.64/4.88 ! [H: real] :
% 8.64/4.88 ( bot_bot_set_real
% 8.64/4.88 != ( set_ord_atMost_real @ H ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6776_not__empty__eq__Iic__eq__empty,axiom,
% 8.64/4.88 ! [H: nat] :
% 8.64/4.88 ( bot_bot_set_nat
% 8.64/4.88 != ( set_ord_atMost_nat @ H ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6777_infinite__Iic,axiom,
% 8.64/4.88 ! [A: int] :
% 8.64/4.88 ~ ( finite_finite_int @ ( set_ord_atMost_int @ A ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6778_not__Iic__eq__Icc,axiom,
% 8.64/4.88 ! [H3: int,L: int,H: int] :
% 8.64/4.88 ( ( set_ord_atMost_int @ H3 )
% 8.64/4.88 != ( set_or1266510415728281911st_int @ L @ H ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6779_not__Iic__eq__Icc,axiom,
% 8.64/4.88 ! [H3: real,L: real,H: real] :
% 8.64/4.88 ( ( set_ord_atMost_real @ H3 )
% 8.64/4.88 != ( set_or1222579329274155063t_real @ L @ H ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6780_atMost__def,axiom,
% 8.64/4.88 ( set_ord_atMost_real
% 8.64/4.88 = ( ^ [U2: real] :
% 8.64/4.88 ( collect_real
% 8.64/4.88 @ ^ [X4: real] : ( ord_less_eq_real @ X4 @ U2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6781_atMost__def,axiom,
% 8.64/4.88 ( set_or4236626031148496127et_nat
% 8.64/4.88 = ( ^ [U2: set_nat] :
% 8.64/4.88 ( collect_set_nat
% 8.64/4.88 @ ^ [X4: set_nat] : ( ord_less_eq_set_nat @ X4 @ U2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6782_atMost__def,axiom,
% 8.64/4.88 ( set_ord_atMost_rat
% 8.64/4.88 = ( ^ [U2: rat] :
% 8.64/4.88 ( collect_rat
% 8.64/4.88 @ ^ [X4: rat] : ( ord_less_eq_rat @ X4 @ U2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6783_atMost__def,axiom,
% 8.64/4.88 ( set_ord_atMost_num
% 8.64/4.88 = ( ^ [U2: num] :
% 8.64/4.88 ( collect_num
% 8.64/4.88 @ ^ [X4: num] : ( ord_less_eq_num @ X4 @ U2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6784_atMost__def,axiom,
% 8.64/4.88 ( set_ord_atMost_int
% 8.64/4.88 = ( ^ [U2: int] :
% 8.64/4.88 ( collect_int
% 8.64/4.88 @ ^ [X4: int] : ( ord_less_eq_int @ X4 @ U2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6785_atMost__def,axiom,
% 8.64/4.88 ( set_ord_atMost_nat
% 8.64/4.88 = ( ^ [U2: nat] :
% 8.64/4.88 ( collect_nat
% 8.64/4.88 @ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6786_zero__less__eq__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6787_zero__less__eq__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6788_zero__less__eq__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6789_zero__less__eq__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6790_zero__less__eq__of__bool,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6791_of__bool__less__eq__one,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P2 ) @ one_one_real ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6792_of__bool__less__eq__one,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) @ one_one_rat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6793_of__bool__less__eq__one,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P2 ) @ one_one_nat ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6794_of__bool__less__eq__one,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P2 ) @ one_one_int ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6795_of__bool__less__eq__one,axiom,
% 8.64/4.88 ! [P2: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P2 ) @ one_one_Code_integer ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6796_of__bool__def,axiom,
% 8.64/4.88 ( zero_n1201886186963655149omplex
% 8.64/4.88 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6797_of__bool__def,axiom,
% 8.64/4.88 ( zero_n3304061248610475627l_real
% 8.64/4.88 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6798_of__bool__def,axiom,
% 8.64/4.88 ( zero_n2052037380579107095ol_rat
% 8.64/4.88 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6799_of__bool__def,axiom,
% 8.64/4.88 ( zero_n2687167440665602831ol_nat
% 8.64/4.88 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6800_of__bool__def,axiom,
% 8.64/4.88 ( zero_n2684676970156552555ol_int
% 8.64/4.88 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6801_of__bool__def,axiom,
% 8.64/4.88 ( zero_n356916108424825756nteger
% 8.64/4.88 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6802_split__of__bool,axiom,
% 8.64/4.88 ! [P2: complex > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n1201886186963655149omplex @ P ) )
% 8.64/4.88 = ( ( P
% 8.64/4.88 => ( P2 @ one_one_complex ) )
% 8.64/4.88 & ( ~ P
% 8.64/4.88 => ( P2 @ zero_zero_complex ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6803_split__of__bool,axiom,
% 8.64/4.88 ! [P2: real > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n3304061248610475627l_real @ P ) )
% 8.64/4.88 = ( ( P
% 8.64/4.88 => ( P2 @ one_one_real ) )
% 8.64/4.88 & ( ~ P
% 8.64/4.88 => ( P2 @ zero_zero_real ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6804_split__of__bool,axiom,
% 8.64/4.88 ! [P2: rat > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P ) )
% 8.64/4.88 = ( ( P
% 8.64/4.88 => ( P2 @ one_one_rat ) )
% 8.64/4.88 & ( ~ P
% 8.64/4.88 => ( P2 @ zero_zero_rat ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6805_split__of__bool,axiom,
% 8.64/4.88 ! [P2: nat > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.64/4.88 = ( ( P
% 8.64/4.88 => ( P2 @ one_one_nat ) )
% 8.64/4.88 & ( ~ P
% 8.64/4.88 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6806_split__of__bool,axiom,
% 8.64/4.88 ! [P2: int > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 8.64/4.88 = ( ( P
% 8.64/4.88 => ( P2 @ one_one_int ) )
% 8.64/4.88 & ( ~ P
% 8.64/4.88 => ( P2 @ zero_zero_int ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6807_split__of__bool,axiom,
% 8.64/4.88 ! [P2: code_integer > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n356916108424825756nteger @ P ) )
% 8.64/4.88 = ( ( P
% 8.64/4.88 => ( P2 @ one_one_Code_integer ) )
% 8.64/4.88 & ( ~ P
% 8.64/4.88 => ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6808_split__of__bool__asm,axiom,
% 8.64/4.88 ! [P2: complex > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n1201886186963655149omplex @ P ) )
% 8.64/4.88 = ( ~ ( ( P
% 8.64/4.88 & ~ ( P2 @ one_one_complex ) )
% 8.64/4.88 | ( ~ P
% 8.64/4.88 & ~ ( P2 @ zero_zero_complex ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6809_split__of__bool__asm,axiom,
% 8.64/4.88 ! [P2: real > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n3304061248610475627l_real @ P ) )
% 8.64/4.88 = ( ~ ( ( P
% 8.64/4.88 & ~ ( P2 @ one_one_real ) )
% 8.64/4.88 | ( ~ P
% 8.64/4.88 & ~ ( P2 @ zero_zero_real ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6810_split__of__bool__asm,axiom,
% 8.64/4.88 ! [P2: rat > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n2052037380579107095ol_rat @ P ) )
% 8.64/4.88 = ( ~ ( ( P
% 8.64/4.88 & ~ ( P2 @ one_one_rat ) )
% 8.64/4.88 | ( ~ P
% 8.64/4.88 & ~ ( P2 @ zero_zero_rat ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6811_split__of__bool__asm,axiom,
% 8.64/4.88 ! [P2: nat > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n2687167440665602831ol_nat @ P ) )
% 8.64/4.88 = ( ~ ( ( P
% 8.64/4.88 & ~ ( P2 @ one_one_nat ) )
% 8.64/4.88 | ( ~ P
% 8.64/4.88 & ~ ( P2 @ zero_zero_nat ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6812_split__of__bool__asm,axiom,
% 8.64/4.88 ! [P2: int > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n2684676970156552555ol_int @ P ) )
% 8.64/4.88 = ( ~ ( ( P
% 8.64/4.88 & ~ ( P2 @ one_one_int ) )
% 8.64/4.88 | ( ~ P
% 8.64/4.88 & ~ ( P2 @ zero_zero_int ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6813_split__of__bool__asm,axiom,
% 8.64/4.88 ! [P2: code_integer > $o,P: $o] :
% 8.64/4.88 ( ( P2 @ ( zero_n356916108424825756nteger @ P ) )
% 8.64/4.88 = ( ~ ( ( P
% 8.64/4.88 & ~ ( P2 @ one_one_Code_integer ) )
% 8.64/4.88 | ( ~ P
% 8.64/4.88 & ~ ( P2 @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6814_atMost__atLeast0,axiom,
% 8.64/4.88 ( set_ord_atMost_nat
% 8.64/4.88 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6815_lessThan__Suc__atMost,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( set_ord_lessThan_nat @ ( suc @ K2 ) )
% 8.64/4.88 = ( set_ord_atMost_nat @ K2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6816_atMost__Suc,axiom,
% 8.64/4.88 ! [K2: nat] :
% 8.64/4.88 ( ( set_ord_atMost_nat @ ( suc @ K2 ) )
% 8.64/4.88 = ( insert_nat @ ( suc @ K2 ) @ ( set_ord_atMost_nat @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6817_not__Iic__le__Icc,axiom,
% 8.64/4.88 ! [H: int,L3: int,H3: int] :
% 8.64/4.88 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6818_not__Iic__le__Icc,axiom,
% 8.64/4.88 ! [H: real,L3: real,H3: real] :
% 8.64/4.88 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6819_nth__eq__iff__index__eq,axiom,
% 8.64/4.88 ! [Xs2: list_VEBT_VEBT,I2: nat,J2: nat] :
% 8.64/4.88 ( ( distinct_VEBT_VEBT @ Xs2 )
% 8.64/4.88 => ( ( ord_less_nat @ I2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.88 => ( ( ( nth_VEBT_VEBT @ Xs2 @ I2 )
% 8.64/4.88 = ( nth_VEBT_VEBT @ Xs2 @ J2 ) )
% 8.64/4.88 = ( I2 = J2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6820_nth__eq__iff__index__eq,axiom,
% 8.64/4.88 ! [Xs2: list_o,I2: nat,J2: nat] :
% 8.64/4.88 ( ( distinct_o @ Xs2 )
% 8.64/4.88 => ( ( ord_less_nat @ I2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.88 => ( ( ( nth_o @ Xs2 @ I2 )
% 8.64/4.88 = ( nth_o @ Xs2 @ J2 ) )
% 8.64/4.88 = ( I2 = J2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6821_nth__eq__iff__index__eq,axiom,
% 8.64/4.88 ! [Xs2: list_nat,I2: nat,J2: nat] :
% 8.64/4.88 ( ( distinct_nat @ Xs2 )
% 8.64/4.88 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.88 => ( ( ( nth_nat @ Xs2 @ I2 )
% 8.64/4.88 = ( nth_nat @ Xs2 @ J2 ) )
% 8.64/4.88 = ( I2 = J2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6822_nth__eq__iff__index__eq,axiom,
% 8.64/4.88 ! [Xs2: list_int,I2: nat,J2: nat] :
% 8.64/4.88 ( ( distinct_int @ Xs2 )
% 8.64/4.88 => ( ( ord_less_nat @ I2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.88 => ( ( ord_less_nat @ J2 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.88 => ( ( ( nth_int @ Xs2 @ I2 )
% 8.64/4.88 = ( nth_int @ Xs2 @ J2 ) )
% 8.64/4.88 = ( I2 = J2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6823_distinct__conv__nth,axiom,
% 8.64/4.88 ( distinct_VEBT_VEBT
% 8.64/4.88 = ( ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.88 ! [I: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.64/4.88 => ! [J: nat] :
% 8.64/4.88 ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 8.64/4.88 => ( ( I != J )
% 8.64/4.88 => ( ( nth_VEBT_VEBT @ Xs @ I )
% 8.64/4.88 != ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6824_distinct__conv__nth,axiom,
% 8.64/4.88 ( distinct_o
% 8.64/4.88 = ( ^ [Xs: list_o] :
% 8.64/4.88 ! [I: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 8.64/4.88 => ! [J: nat] :
% 8.64/4.88 ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 8.64/4.88 => ( ( I != J )
% 8.64/4.88 => ( ( nth_o @ Xs @ I )
% 8.64/4.88 != ( nth_o @ Xs @ J ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6825_distinct__conv__nth,axiom,
% 8.64/4.88 ( distinct_nat
% 8.64/4.88 = ( ^ [Xs: list_nat] :
% 8.64/4.88 ! [I: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 8.64/4.88 => ! [J: nat] :
% 8.64/4.88 ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 8.64/4.88 => ( ( I != J )
% 8.64/4.88 => ( ( nth_nat @ Xs @ I )
% 8.64/4.88 != ( nth_nat @ Xs @ J ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6826_distinct__conv__nth,axiom,
% 8.64/4.88 ( distinct_int
% 8.64/4.88 = ( ^ [Xs: list_int] :
% 8.64/4.88 ! [I: nat] :
% 8.64/4.88 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 8.64/4.88 => ! [J: nat] :
% 8.64/4.88 ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 8.64/4.88 => ( ( I != J )
% 8.64/4.88 => ( ( nth_int @ Xs @ I )
% 8.64/4.88 != ( nth_int @ Xs @ J ) ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6827_card__distinct,axiom,
% 8.64/4.88 ! [Xs2: list_complex] :
% 8.64/4.88 ( ( ( finite_card_complex @ ( set_complex2 @ Xs2 ) )
% 8.64/4.88 = ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.64/4.88 => ( distinct_complex @ Xs2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6828_card__distinct,axiom,
% 8.64/4.88 ! [Xs2: list_list_nat] :
% 8.64/4.88 ( ( ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) )
% 8.64/4.88 = ( size_s3023201423986296836st_nat @ Xs2 ) )
% 8.64/4.88 => ( distinct_list_nat @ Xs2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6829_card__distinct,axiom,
% 8.64/4.88 ! [Xs2: list_set_nat] :
% 8.64/4.88 ( ( ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) )
% 8.64/4.88 = ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.64/4.88 => ( distinct_set_nat @ Xs2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6830_card__distinct,axiom,
% 8.64/4.88 ! [Xs2: list_VEBT_VEBT] :
% 8.64/4.88 ( ( ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.64/4.88 = ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.88 => ( distinct_VEBT_VEBT @ Xs2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6831_card__distinct,axiom,
% 8.64/4.88 ! [Xs2: list_o] :
% 8.64/4.88 ( ( ( finite_card_o @ ( set_o2 @ Xs2 ) )
% 8.64/4.88 = ( size_size_list_o @ Xs2 ) )
% 8.64/4.88 => ( distinct_o @ Xs2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6832_card__distinct,axiom,
% 8.64/4.88 ! [Xs2: list_nat] :
% 8.64/4.88 ( ( ( finite_card_nat @ ( set_nat2 @ Xs2 ) )
% 8.64/4.88 = ( size_size_list_nat @ Xs2 ) )
% 8.64/4.88 => ( distinct_nat @ Xs2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6833_card__distinct,axiom,
% 8.64/4.88 ! [Xs2: list_int] :
% 8.64/4.88 ( ( ( finite_card_int @ ( set_int2 @ Xs2 ) )
% 8.64/4.88 = ( size_size_list_int @ Xs2 ) )
% 8.64/4.88 => ( distinct_int @ Xs2 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6834_distinct__card,axiom,
% 8.64/4.88 ! [Xs2: list_complex] :
% 8.64/4.88 ( ( distinct_complex @ Xs2 )
% 8.64/4.88 => ( ( finite_card_complex @ ( set_complex2 @ Xs2 ) )
% 8.64/4.88 = ( size_s3451745648224563538omplex @ Xs2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6835_distinct__card,axiom,
% 8.64/4.88 ! [Xs2: list_list_nat] :
% 8.64/4.88 ( ( distinct_list_nat @ Xs2 )
% 8.64/4.88 => ( ( finite_card_list_nat @ ( set_list_nat2 @ Xs2 ) )
% 8.64/4.88 = ( size_s3023201423986296836st_nat @ Xs2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6836_distinct__card,axiom,
% 8.64/4.88 ! [Xs2: list_set_nat] :
% 8.64/4.88 ( ( distinct_set_nat @ Xs2 )
% 8.64/4.88 => ( ( finite_card_set_nat @ ( set_set_nat2 @ Xs2 ) )
% 8.64/4.88 = ( size_s3254054031482475050et_nat @ Xs2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6837_distinct__card,axiom,
% 8.64/4.88 ! [Xs2: list_VEBT_VEBT] :
% 8.64/4.88 ( ( distinct_VEBT_VEBT @ Xs2 )
% 8.64/4.88 => ( ( finite7802652506058667612T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.64/4.88 = ( size_s6755466524823107622T_VEBT @ Xs2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6838_distinct__card,axiom,
% 8.64/4.88 ! [Xs2: list_o] :
% 8.64/4.88 ( ( distinct_o @ Xs2 )
% 8.64/4.88 => ( ( finite_card_o @ ( set_o2 @ Xs2 ) )
% 8.64/4.88 = ( size_size_list_o @ Xs2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6839_distinct__card,axiom,
% 8.64/4.88 ! [Xs2: list_nat] :
% 8.64/4.88 ( ( distinct_nat @ Xs2 )
% 8.64/4.88 => ( ( finite_card_nat @ ( set_nat2 @ Xs2 ) )
% 8.64/4.88 = ( size_size_list_nat @ Xs2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6840_distinct__card,axiom,
% 8.64/4.88 ! [Xs2: list_int] :
% 8.64/4.88 ( ( distinct_int @ Xs2 )
% 8.64/4.88 => ( ( finite_card_int @ ( set_int2 @ Xs2 ) )
% 8.64/4.88 = ( size_size_list_int @ Xs2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6841_gbinomial__Suc__Suc,axiom,
% 8.64/4.88 ! [A: complex,K2: nat] :
% 8.64/4.88 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K2 ) @ ( gbinomial_complex @ A @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6842_gbinomial__Suc__Suc,axiom,
% 8.64/4.88 ! [A: real,K2: nat] :
% 8.64/4.88 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_real @ ( gbinomial_real @ A @ K2 ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6843_gbinomial__Suc__Suc,axiom,
% 8.64/4.88 ! [A: rat,K2: nat] :
% 8.64/4.88 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6844_gbinomial__of__nat__symmetric,axiom,
% 8.64/4.88 ! [K2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ K2 )
% 8.64/4.88 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6845_Iic__subset__Iio__iff,axiom,
% 8.64/4.88 ! [A: real,B: real] :
% 8.64/4.88 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 8.64/4.88 = ( ord_less_real @ A @ B ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6846_Iic__subset__Iio__iff,axiom,
% 8.64/4.88 ! [A: rat,B: rat] :
% 8.64/4.88 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 8.64/4.88 = ( ord_less_rat @ A @ B ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6847_Iic__subset__Iio__iff,axiom,
% 8.64/4.88 ! [A: num,B: num] :
% 8.64/4.88 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 8.64/4.88 = ( ord_less_num @ A @ B ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6848_Iic__subset__Iio__iff,axiom,
% 8.64/4.88 ! [A: int,B: int] :
% 8.64/4.88 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 8.64/4.88 = ( ord_less_int @ A @ B ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6849_Iic__subset__Iio__iff,axiom,
% 8.64/4.88 ! [A: nat,B: nat] :
% 8.64/4.88 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 8.64/4.88 = ( ord_less_nat @ A @ B ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6850_sum__choose__upper,axiom,
% 8.64/4.88 ! [M2: nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [K3: nat] : ( binomial @ K3 @ M2 )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( binomial @ ( suc @ N ) @ ( suc @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6851_distinct__Ex1,axiom,
% 8.64/4.88 ! [Xs2: list_complex,X: complex] :
% 8.64/4.88 ( ( distinct_complex @ Xs2 )
% 8.64/4.88 => ( ( member_complex @ X @ ( set_complex2 @ Xs2 ) )
% 8.64/4.88 => ? [X3: nat] :
% 8.64/4.88 ( ( ord_less_nat @ X3 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.64/4.88 & ( ( nth_complex @ Xs2 @ X3 )
% 8.64/4.88 = X )
% 8.64/4.88 & ! [Y6: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ Y6 @ ( size_s3451745648224563538omplex @ Xs2 ) )
% 8.64/4.88 & ( ( nth_complex @ Xs2 @ Y6 )
% 8.64/4.88 = X ) )
% 8.64/4.88 => ( Y6 = X3 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6852_distinct__Ex1,axiom,
% 8.64/4.88 ! [Xs2: list_real,X: real] :
% 8.64/4.88 ( ( distinct_real @ Xs2 )
% 8.64/4.88 => ( ( member_real @ X @ ( set_real2 @ Xs2 ) )
% 8.64/4.88 => ? [X3: nat] :
% 8.64/4.88 ( ( ord_less_nat @ X3 @ ( size_size_list_real @ Xs2 ) )
% 8.64/4.88 & ( ( nth_real @ Xs2 @ X3 )
% 8.64/4.88 = X )
% 8.64/4.88 & ! [Y6: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_real @ Xs2 ) )
% 8.64/4.88 & ( ( nth_real @ Xs2 @ Y6 )
% 8.64/4.88 = X ) )
% 8.64/4.88 => ( Y6 = X3 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6853_distinct__Ex1,axiom,
% 8.64/4.88 ! [Xs2: list_set_nat,X: set_nat] :
% 8.64/4.88 ( ( distinct_set_nat @ Xs2 )
% 8.64/4.88 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs2 ) )
% 8.64/4.88 => ? [X3: nat] :
% 8.64/4.88 ( ( ord_less_nat @ X3 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.64/4.88 & ( ( nth_set_nat @ Xs2 @ X3 )
% 8.64/4.88 = X )
% 8.64/4.88 & ! [Y6: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ Y6 @ ( size_s3254054031482475050et_nat @ Xs2 ) )
% 8.64/4.88 & ( ( nth_set_nat @ Xs2 @ Y6 )
% 8.64/4.88 = X ) )
% 8.64/4.88 => ( Y6 = X3 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6854_distinct__Ex1,axiom,
% 8.64/4.88 ! [Xs2: list_VEBT_VEBT,X: vEBT_VEBT] :
% 8.64/4.88 ( ( distinct_VEBT_VEBT @ Xs2 )
% 8.64/4.88 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs2 ) )
% 8.64/4.88 => ? [X3: nat] :
% 8.64/4.88 ( ( ord_less_nat @ X3 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.88 & ( ( nth_VEBT_VEBT @ Xs2 @ X3 )
% 8.64/4.88 = X )
% 8.64/4.88 & ! [Y6: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ Y6 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.88 & ( ( nth_VEBT_VEBT @ Xs2 @ Y6 )
% 8.64/4.88 = X ) )
% 8.64/4.88 => ( Y6 = X3 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6855_distinct__Ex1,axiom,
% 8.64/4.88 ! [Xs2: list_o,X: $o] :
% 8.64/4.88 ( ( distinct_o @ Xs2 )
% 8.64/4.88 => ( ( member_o @ X @ ( set_o2 @ Xs2 ) )
% 8.64/4.88 => ? [X3: nat] :
% 8.64/4.88 ( ( ord_less_nat @ X3 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.88 & ( ( nth_o @ Xs2 @ X3 )
% 8.64/4.88 = X )
% 8.64/4.88 & ! [Y6: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.88 & ( ( nth_o @ Xs2 @ Y6 )
% 8.64/4.88 = X ) )
% 8.64/4.88 => ( Y6 = X3 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6856_distinct__Ex1,axiom,
% 8.64/4.88 ! [Xs2: list_nat,X: nat] :
% 8.64/4.88 ( ( distinct_nat @ Xs2 )
% 8.64/4.88 => ( ( member_nat @ X @ ( set_nat2 @ Xs2 ) )
% 8.64/4.88 => ? [X3: nat] :
% 8.64/4.88 ( ( ord_less_nat @ X3 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.88 & ( ( nth_nat @ Xs2 @ X3 )
% 8.64/4.88 = X )
% 8.64/4.88 & ! [Y6: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.88 & ( ( nth_nat @ Xs2 @ Y6 )
% 8.64/4.88 = X ) )
% 8.64/4.88 => ( Y6 = X3 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6857_distinct__Ex1,axiom,
% 8.64/4.88 ! [Xs2: list_int,X: int] :
% 8.64/4.88 ( ( distinct_int @ Xs2 )
% 8.64/4.88 => ( ( member_int @ X @ ( set_int2 @ Xs2 ) )
% 8.64/4.88 => ? [X3: nat] :
% 8.64/4.88 ( ( ord_less_nat @ X3 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.88 & ( ( nth_int @ Xs2 @ X3 )
% 8.64/4.88 = X )
% 8.64/4.88 & ! [Y6: nat] :
% 8.64/4.88 ( ( ( ord_less_nat @ Y6 @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.88 & ( ( nth_int @ Xs2 @ Y6 )
% 8.64/4.88 = X ) )
% 8.64/4.88 => ( Y6 = X3 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6858_gbinomial__partial__sum__poly__xpos,axiom,
% 8.64/4.88 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A ) @ one_one_complex ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6859_gbinomial__partial__sum__poly__xpos,axiom,
% 8.64/4.88 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A ) @ one_one_rat ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6860_gbinomial__partial__sum__poly__xpos,axiom,
% 8.64/4.88 ! [M2: nat,A: real,X: real,Y: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A ) @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6861_gbinomial__addition__formula,axiom,
% 8.64/4.88 ! [A: complex,K2: nat] :
% 8.64/4.88 ( ( gbinomial_complex @ A @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6862_gbinomial__addition__formula,axiom,
% 8.64/4.88 ! [A: real,K2: nat] :
% 8.64/4.88 ( ( gbinomial_real @ A @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K2 ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6863_gbinomial__addition__formula,axiom,
% 8.64/4.88 ! [A: rat,K2: nat] :
% 8.64/4.88 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 8.64/4.88 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6864_gbinomial__absorb__comp,axiom,
% 8.64/4.88 ! [A: complex,K2: nat] :
% 8.64/4.88 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( gbinomial_complex @ A @ K2 ) )
% 8.64/4.88 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6865_gbinomial__absorb__comp,axiom,
% 8.64/4.88 ! [A: rat,K2: nat] :
% 8.64/4.88 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( gbinomial_rat @ A @ K2 ) )
% 8.64/4.88 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6866_gbinomial__absorb__comp,axiom,
% 8.64/4.88 ! [A: real,K2: nat] :
% 8.64/4.88 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( gbinomial_real @ A @ K2 ) )
% 8.64/4.88 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6867_gbinomial__ge__n__over__k__pow__k,axiom,
% 8.64/4.88 ! [K2: nat,A: real] :
% 8.64/4.88 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K2 ) @ A )
% 8.64/4.88 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6868_gbinomial__ge__n__over__k__pow__k,axiom,
% 8.64/4.88 ! [K2: nat,A: rat] :
% 8.64/4.88 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K2 ) @ A )
% 8.64/4.88 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6869_gbinomial__mult__1_H,axiom,
% 8.64/4.88 ! [A: rat,K2: nat] :
% 8.64/4.88 ( ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ A )
% 8.64/4.88 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6870_gbinomial__mult__1_H,axiom,
% 8.64/4.88 ! [A: real,K2: nat] :
% 8.64/4.88 ( ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ A )
% 8.64/4.88 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6871_gbinomial__mult__1,axiom,
% 8.64/4.88 ! [A: rat,K2: nat] :
% 8.64/4.88 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K2 ) )
% 8.64/4.88 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K2 ) @ ( gbinomial_rat @ A @ K2 ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6872_gbinomial__mult__1,axiom,
% 8.64/4.88 ! [A: real,K2: nat] :
% 8.64/4.88 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K2 ) )
% 8.64/4.88 = ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ K2 ) @ ( gbinomial_real @ A @ K2 ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6873_sum_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6874_sum_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6875_sum_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6876_sum_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6877_sum__telescope,axiom,
% 8.64/4.88 ! [F2: nat > rat,I2: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( minus_minus_rat @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ I2 ) )
% 8.64/4.88 = ( minus_minus_rat @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6878_sum__telescope,axiom,
% 8.64/4.88 ! [F2: nat > int,I2: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( minus_minus_int @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ I2 ) )
% 8.64/4.88 = ( minus_minus_int @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6879_sum__telescope,axiom,
% 8.64/4.88 ! [F2: nat > real,I2: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( minus_minus_real @ ( F2 @ I ) @ ( F2 @ ( suc @ I ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ I2 ) )
% 8.64/4.88 = ( minus_minus_real @ ( F2 @ zero_zero_nat ) @ ( F2 @ ( suc @ I2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6880_polyfun__eq__coeffs,axiom,
% 8.64/4.88 ! [C2: nat > complex,N: nat,D: nat > complex] :
% 8.64/4.88 ( ( ! [X4: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( D @ I ) @ ( power_power_complex @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) )
% 8.64/4.88 = ( ! [I: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ I @ N )
% 8.64/4.88 => ( ( C2 @ I )
% 8.64/4.88 = ( D @ I ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6881_polyfun__eq__coeffs,axiom,
% 8.64/4.88 ! [C2: nat > real,N: nat,D: nat > real] :
% 8.64/4.88 ( ( ! [X4: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( D @ I ) @ ( power_power_real @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) )
% 8.64/4.88 = ( ! [I: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ I @ N )
% 8.64/4.88 => ( ( C2 @ I )
% 8.64/4.88 = ( D @ I ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6882_prod_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6883_prod_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6884_prod_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6885_prod_OatMost__Suc__shift,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ N ) ) )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6886_sum_Onested__swap_H,axiom,
% 8.64/4.88 ! [A: nat > nat > nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [I: nat] : ( groups3542108847815614940at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [J: nat] :
% 8.64/4.88 ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [I: nat] : ( A @ I @ J )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6887_sum_Onested__swap_H,axiom,
% 8.64/4.88 ! [A: nat > nat > real,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( groups6591440286371151544t_real @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [J: nat] :
% 8.64/4.88 ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( A @ I @ J )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6888_ivl__disj__un__one_I4_J,axiom,
% 8.64/4.88 ! [L: rat,U: rat] :
% 8.64/4.88 ( ( ord_less_eq_rat @ L @ U )
% 8.64/4.88 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 8.64/4.88 = ( set_ord_atMost_rat @ U ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6889_ivl__disj__un__one_I4_J,axiom,
% 8.64/4.88 ! [L: num,U: num] :
% 8.64/4.88 ( ( ord_less_eq_num @ L @ U )
% 8.64/4.88 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or7049704709247886629st_num @ L @ U ) )
% 8.64/4.88 = ( set_ord_atMost_num @ U ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6890_ivl__disj__un__one_I4_J,axiom,
% 8.64/4.88 ! [L: nat,U: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ L @ U )
% 8.64/4.88 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 8.64/4.88 = ( set_ord_atMost_nat @ U ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6891_ivl__disj__un__one_I4_J,axiom,
% 8.64/4.88 ! [L: int,U: int] :
% 8.64/4.88 ( ( ord_less_eq_int @ L @ U )
% 8.64/4.88 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 8.64/4.88 = ( set_ord_atMost_int @ U ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6892_ivl__disj__un__one_I4_J,axiom,
% 8.64/4.88 ! [L: real,U: real] :
% 8.64/4.88 ( ( ord_less_eq_real @ L @ U )
% 8.64/4.88 => ( ( sup_sup_set_real @ ( set_or5984915006950818249n_real @ L ) @ ( set_or1222579329274155063t_real @ L @ U ) )
% 8.64/4.88 = ( set_ord_atMost_real @ U ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6893_ivl__disj__un__singleton_I2_J,axiom,
% 8.64/4.88 ! [U: int] :
% 8.64/4.88 ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ U ) @ ( insert_int @ U @ bot_bot_set_int ) )
% 8.64/4.88 = ( set_ord_atMost_int @ U ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6894_ivl__disj__un__singleton_I2_J,axiom,
% 8.64/4.88 ! [U: real] :
% 8.64/4.88 ( ( sup_sup_set_real @ ( set_or5984915006950818249n_real @ U ) @ ( insert_real @ U @ bot_bot_set_real ) )
% 8.64/4.88 = ( set_ord_atMost_real @ U ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6895_ivl__disj__un__singleton_I2_J,axiom,
% 8.64/4.88 ! [U: nat] :
% 8.64/4.88 ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ U ) @ ( insert_nat @ U @ bot_bot_set_nat ) )
% 8.64/4.88 = ( set_ord_atMost_nat @ U ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6896_prod_Onested__swap_H,axiom,
% 8.64/4.88 ! [A: nat > nat > int,N: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( groups705719431365010083at_int @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [J: nat] :
% 8.64/4.88 ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( A @ I @ J )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6897_prod_Onested__swap_H,axiom,
% 8.64/4.88 ! [A: nat > nat > nat,N: nat] :
% 8.64/4.88 ( ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( groups708209901874060359at_nat @ ( A @ I ) @ ( set_ord_lessThan_nat @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [J: nat] :
% 8.64/4.88 ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( A @ I @ J )
% 8.64/4.88 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6898_sum__choose__lower,axiom,
% 8.64/4.88 ! [R3: nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K3 ) @ K3 )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N ) ) @ N ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6899_Suc__times__gbinomial,axiom,
% 8.64/4.88 ! [K2: nat,A: complex] :
% 8.64/4.88 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6900_Suc__times__gbinomial,axiom,
% 8.64/4.88 ! [K2: nat,A: rat] :
% 8.64/4.88 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6901_Suc__times__gbinomial,axiom,
% 8.64/4.88 ! [K2: nat,A: real] :
% 8.64/4.88 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6902_gbinomial__absorption,axiom,
% 8.64/4.88 ! [K2: nat,A: complex] :
% 8.64/4.88 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) @ ( gbinomial_complex @ A @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6903_gbinomial__absorption,axiom,
% 8.64/4.88 ! [K2: nat,A: rat] :
% 8.64/4.88 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) @ ( gbinomial_rat @ A @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6904_gbinomial__absorption,axiom,
% 8.64/4.88 ! [K2: nat,A: real] :
% 8.64/4.88 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) @ ( gbinomial_real @ A @ ( suc @ K2 ) ) )
% 8.64/4.88 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6905_gbinomial__trinomial__revision,axiom,
% 8.64/4.88 ! [K2: nat,M2: nat,A: rat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ M2 )
% 8.64/4.88 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M2 ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M2 ) @ K2 ) )
% 8.64/4.88 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6906_gbinomial__trinomial__revision,axiom,
% 8.64/4.88 ! [K2: nat,M2: nat,A: real] :
% 8.64/4.88 ( ( ord_less_eq_nat @ K2 @ M2 )
% 8.64/4.88 => ( ( times_times_real @ ( gbinomial_real @ A @ M2 ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M2 ) @ K2 ) )
% 8.64/4.88 = ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( minus_minus_nat @ M2 @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6907_zero__polynom__imp__zero__coeffs,axiom,
% 8.64/4.88 ! [C2: nat > complex,N: nat,K2: nat] :
% 8.64/4.88 ( ! [W: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ W @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_complex )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ( C2 @ K2 )
% 8.64/4.88 = zero_zero_complex ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6908_zero__polynom__imp__zero__coeffs,axiom,
% 8.64/4.88 ! [C2: nat > real,N: nat,K2: nat] :
% 8.64/4.88 ( ! [W: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ W @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_real )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ( C2 @ K2 )
% 8.64/4.88 = zero_zero_real ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6909_polyfun__eq__0,axiom,
% 8.64/4.88 ! [C2: nat > complex,N: nat] :
% 8.64/4.88 ( ( ! [X4: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_complex ) )
% 8.64/4.88 = ( ! [I: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ I @ N )
% 8.64/4.88 => ( ( C2 @ I )
% 8.64/4.88 = zero_zero_complex ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6910_polyfun__eq__0,axiom,
% 8.64/4.88 ! [C2: nat > real,N: nat] :
% 8.64/4.88 ( ( ! [X4: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_real ) )
% 8.64/4.88 = ( ! [I: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ I @ N )
% 8.64/4.88 => ( ( C2 @ I )
% 8.64/4.88 = zero_zero_real ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6911_sum_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_rat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6912_sum_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_int @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6913_sum_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_nat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6914_sum_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_real @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6915_sum__up__index__split,axiom,
% 8.64/4.88 ! [F2: nat > rat,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.88 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups2906978787729119204at_rat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6916_sum__up__index__split,axiom,
% 8.64/4.88 ! [F2: nat > int,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups3539618377306564664at_int @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.88 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3539618377306564664at_int @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6917_sum__up__index__split,axiom,
% 8.64/4.88 ! [F2: nat > nat,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.88 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups3542108847815614940at_nat @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6918_sum__up__index__split,axiom,
% 8.64/4.88 ! [F2: nat > real,M2: nat,N: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ F2 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) )
% 8.64/4.88 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_atMost_nat @ M2 ) ) @ ( groups6591440286371151544t_real @ F2 @ ( set_or1269000886237332187st_nat @ ( suc @ M2 ) @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6919_prod_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > real,N: nat] :
% 8.64/4.88 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_real @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups129246275422532515t_real
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6920_prod_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > rat,N: nat] :
% 8.64/4.88 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_rat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups73079841787564623at_rat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6921_prod_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > int,N: nat] :
% 8.64/4.88 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_int @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups705719431365010083at_int
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6922_prod_OatMost__shift,axiom,
% 8.64/4.88 ! [G2: nat > nat,N: nat] :
% 8.64/4.88 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_nat @ ( G2 @ zero_zero_nat )
% 8.64/4.88 @ ( groups708209901874060359at_nat
% 8.64/4.88 @ ^ [I: nat] : ( G2 @ ( suc @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6923_gbinomial__r__part__sum,axiom,
% 8.64/4.88 ! [M2: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M2 ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6924_gbinomial__r__part__sum,axiom,
% 8.64/4.88 ! [M2: nat] :
% 8.64/4.88 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M2 ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6925_gbinomial__r__part__sum,axiom,
% 8.64/4.88 ! [M2: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real @ ( gbinomial_real @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ one_one_real ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6926_sum__choose__diagonal,axiom,
% 8.64/4.88 ! [M2: nat,N: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N @ K3 ) @ ( minus_minus_nat @ M2 @ K3 ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( binomial @ ( suc @ N ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6927_vandermonde,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,R3: nat] :
% 8.64/4.88 ( ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M2 @ K3 ) @ ( binomial @ N @ ( minus_minus_nat @ R3 @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ R3 ) )
% 8.64/4.88 = ( binomial @ ( plus_plus_nat @ M2 @ N ) @ R3 ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6928_bits__induct,axiom,
% 8.64/4.88 ! [P2: nat > $o,A: nat] :
% 8.64/4.88 ( ! [A3: nat] :
% 8.64/4.88 ( ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.88 = A3 )
% 8.64/4.88 => ( P2 @ A3 ) )
% 8.64/4.88 => ( ! [A3: nat,B3: $o] :
% 8.64/4.88 ( ( P2 @ A3 )
% 8.64/4.88 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.88 = A3 )
% 8.64/4.88 => ( P2 @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B3 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 8.64/4.88 => ( P2 @ A ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6929_bits__induct,axiom,
% 8.64/4.88 ! [P2: int > $o,A: int] :
% 8.64/4.88 ( ! [A3: int] :
% 8.64/4.88 ( ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.88 = A3 )
% 8.64/4.88 => ( P2 @ A3 ) )
% 8.64/4.88 => ( ! [A3: int,B3: $o] :
% 8.64/4.88 ( ( P2 @ A3 )
% 8.64/4.88 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.88 = A3 )
% 8.64/4.88 => ( P2 @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B3 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 8.64/4.88 => ( P2 @ A ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6930_bits__induct,axiom,
% 8.64/4.88 ! [P2: code_integer > $o,A: code_integer] :
% 8.64/4.88 ( ! [A3: code_integer] :
% 8.64/4.88 ( ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.88 = A3 )
% 8.64/4.88 => ( P2 @ A3 ) )
% 8.64/4.88 => ( ! [A3: code_integer,B3: $o] :
% 8.64/4.88 ( ( P2 @ A3 )
% 8.64/4.88 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 8.64/4.88 = A3 )
% 8.64/4.88 => ( P2 @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B3 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) ) ) ) )
% 8.64/4.88 => ( P2 @ A ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6931_gbinomial__partial__row__sum,axiom,
% 8.64/4.88 ! [A: complex,M2: nat] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ one_one_complex ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6932_gbinomial__partial__row__sum,axiom,
% 8.64/4.88 ! [A: rat,M2: nat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6933_gbinomial__partial__row__sum,axiom,
% 8.64/4.88 ! [A: real,M2: nat] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.88 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ one_one_real ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ A @ ( plus_plus_nat @ M2 @ one_one_nat ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6934_gbinomial__factors,axiom,
% 8.64/4.88 ! [A: complex,K2: nat] :
% 8.64/4.88 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) ) @ ( gbinomial_complex @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6935_gbinomial__factors,axiom,
% 8.64/4.88 ! [A: rat,K2: nat] :
% 8.64/4.88 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) @ ( gbinomial_rat @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6936_gbinomial__factors,axiom,
% 8.64/4.88 ! [A: real,K2: nat] :
% 8.64/4.88 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) ) @ ( gbinomial_real @ A @ K2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6937_gbinomial__rec,axiom,
% 8.64/4.88 ! [A: complex,K2: nat] :
% 8.64/4.88 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( times_times_complex @ ( gbinomial_complex @ A @ K2 ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6938_gbinomial__rec,axiom,
% 8.64/4.88 ! [A: rat,K2: nat] :
% 8.64/4.88 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( times_times_rat @ ( gbinomial_rat @ A @ K2 ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6939_gbinomial__rec,axiom,
% 8.64/4.88 ! [A: real,K2: nat] :
% 8.64/4.88 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K2 ) )
% 8.64/4.88 = ( times_times_real @ ( gbinomial_real @ A @ K2 ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K2 ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6940_sum__gp__basic,axiom,
% 8.64/4.88 ! [X: code_integer,N: nat] :
% 8.64/4.88 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6941_sum__gp__basic,axiom,
% 8.64/4.88 ! [X: complex,N: nat] :
% 8.64/4.88 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6942_sum__gp__basic,axiom,
% 8.64/4.88 ! [X: rat,N: nat] :
% 8.64/4.88 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6943_sum__gp__basic,axiom,
% 8.64/4.88 ! [X: int,N: nat] :
% 8.64/4.88 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6944_sum__gp__basic,axiom,
% 8.64/4.88 ! [X: real,N: nat] :
% 8.64/4.88 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.88 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6945_polyfun__finite__roots,axiom,
% 8.64/4.88 ! [C2: nat > complex,N: nat] :
% 8.64/4.88 ( ( finite3207457112153483333omplex
% 8.64/4.88 @ ( collect_complex
% 8.64/4.88 @ ^ [X4: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_complex ) ) )
% 8.64/4.88 = ( ? [I: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ I @ N )
% 8.64/4.88 & ( ( C2 @ I )
% 8.64/4.88 != zero_zero_complex ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6946_polyfun__finite__roots,axiom,
% 8.64/4.88 ! [C2: nat > real,N: nat] :
% 8.64/4.88 ( ( finite_finite_real
% 8.64/4.88 @ ( collect_real
% 8.64/4.88 @ ^ [X4: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_real ) ) )
% 8.64/4.88 = ( ? [I: nat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ I @ N )
% 8.64/4.88 & ( ( C2 @ I )
% 8.64/4.88 != zero_zero_real ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6947_polyfun__roots__finite,axiom,
% 8.64/4.88 ! [C2: nat > complex,K2: nat,N: nat] :
% 8.64/4.88 ( ( ( C2 @ K2 )
% 8.64/4.88 != zero_zero_complex )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( finite3207457112153483333omplex
% 8.64/4.88 @ ( collect_complex
% 8.64/4.88 @ ^ [Z4: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_complex ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6948_polyfun__roots__finite,axiom,
% 8.64/4.88 ! [C2: nat > real,K2: nat,N: nat] :
% 8.64/4.88 ( ( ( C2 @ K2 )
% 8.64/4.88 != zero_zero_real )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( finite_finite_real
% 8.64/4.88 @ ( collect_real
% 8.64/4.88 @ ^ [Z4: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6949_polyfun__roots__card,axiom,
% 8.64/4.88 ! [C2: nat > complex,K2: nat,N: nat] :
% 8.64/4.88 ( ( ( C2 @ K2 )
% 8.64/4.88 != zero_zero_complex )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ord_less_eq_nat
% 8.64/4.88 @ ( finite_card_complex
% 8.64/4.88 @ ( collect_complex
% 8.64/4.88 @ ^ [Z4: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_complex ) ) )
% 8.64/4.88 @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6950_polyfun__roots__card,axiom,
% 8.64/4.88 ! [C2: nat > real,K2: nat,N: nat] :
% 8.64/4.88 ( ( ( C2 @ K2 )
% 8.64/4.88 != zero_zero_real )
% 8.64/4.88 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.88 => ( ord_less_eq_nat
% 8.64/4.88 @ ( finite_card_real
% 8.64/4.88 @ ( collect_real
% 8.64/4.88 @ ^ [Z4: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_real ) ) )
% 8.64/4.88 @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6951_polyfun__linear__factor__root,axiom,
% 8.64/4.88 ! [C2: nat > complex,A: complex,N: nat] :
% 8.64/4.88 ( ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_complex )
% 8.64/4.88 => ~ ! [B3: nat > complex] :
% 8.64/4.88 ~ ! [Z5: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( B3 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6952_polyfun__linear__factor__root,axiom,
% 8.64/4.88 ! [C2: nat > rat,A: rat,N: nat] :
% 8.64/4.88 ( ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_rat )
% 8.64/4.88 => ~ ! [B3: nat > rat] :
% 8.64/4.88 ~ ! [Z5: rat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( B3 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6953_polyfun__linear__factor__root,axiom,
% 8.64/4.88 ! [C2: nat > int,A: int,N: nat] :
% 8.64/4.88 ( ( ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_int )
% 8.64/4.88 => ~ ! [B3: nat > int] :
% 8.64/4.88 ~ ! [Z5: int] :
% 8.64/4.88 ( ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( B3 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6954_polyfun__linear__factor__root,axiom,
% 8.64/4.88 ! [C2: nat > real,A: real,N: nat] :
% 8.64/4.88 ( ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = zero_zero_real )
% 8.64/4.88 => ~ ! [B3: nat > real] :
% 8.64/4.88 ~ ! [Z5: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( B3 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6955_polyfun__linear__factor,axiom,
% 8.64/4.88 ! [C2: nat > complex,N: nat,A: complex] :
% 8.64/4.88 ? [B3: nat > complex] :
% 8.64/4.88 ! [Z5: complex] :
% 8.64/4.88 ( ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_complex
% 8.64/4.88 @ ( times_times_complex @ ( minus_minus_complex @ Z5 @ A )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( B3 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 8.64/4.88 @ ( groups2073611262835488442omplex
% 8.64/4.88 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6956_polyfun__linear__factor,axiom,
% 8.64/4.88 ! [C2: nat > rat,N: nat,A: rat] :
% 8.64/4.88 ? [B3: nat > rat] :
% 8.64/4.88 ! [Z5: rat] :
% 8.64/4.88 ( ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_rat
% 8.64/4.88 @ ( times_times_rat @ ( minus_minus_rat @ Z5 @ A )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( B3 @ I ) @ ( power_power_rat @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 8.64/4.88 @ ( groups2906978787729119204at_rat
% 8.64/4.88 @ ^ [I: nat] : ( times_times_rat @ ( C2 @ I ) @ ( power_power_rat @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6957_polyfun__linear__factor,axiom,
% 8.64/4.88 ! [C2: nat > int,N: nat,A: int] :
% 8.64/4.88 ? [B3: nat > int] :
% 8.64/4.88 ! [Z5: int] :
% 8.64/4.88 ( ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_int
% 8.64/4.88 @ ( times_times_int @ ( minus_minus_int @ Z5 @ A )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( B3 @ I ) @ ( power_power_int @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 8.64/4.88 @ ( groups3539618377306564664at_int
% 8.64/4.88 @ ^ [I: nat] : ( times_times_int @ ( C2 @ I ) @ ( power_power_int @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6958_polyfun__linear__factor,axiom,
% 8.64/4.88 ! [C2: nat > real,N: nat,A: real] :
% 8.64/4.88 ? [B3: nat > real] :
% 8.64/4.88 ! [Z5: real] :
% 8.64/4.88 ( ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.88 = ( plus_plus_real
% 8.64/4.88 @ ( times_times_real @ ( minus_minus_real @ Z5 @ A )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( B3 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 8.64/4.88 @ ( set_ord_lessThan_nat @ N ) ) )
% 8.64/4.88 @ ( groups6591440286371151544t_real
% 8.64/4.88 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ A @ I ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6959_sum__power__shift,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,X: complex] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_complex @ ( power_power_complex @ X @ M2 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6960_sum__power__shift,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,X: rat] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_rat @ ( power_power_rat @ X @ M2 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6961_sum__power__shift,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,X: int] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_int @ ( power_power_int @ X @ M2 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6962_sum__power__shift,axiom,
% 8.64/4.88 ! [M2: nat,N: nat,X: real] :
% 8.64/4.88 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.88 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M2 @ N ) )
% 8.64/4.88 = ( times_times_real @ ( power_power_real @ X @ M2 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6963_binomial,axiom,
% 8.64/4.88 ! [A: nat,B: nat,N: nat] :
% 8.64/4.88 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 8.64/4.88 = ( groups3542108847815614940at_nat
% 8.64/4.88 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.88 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6964_atLeast1__atMost__eq__remove0,axiom,
% 8.64/4.88 ! [N: nat] :
% 8.64/4.88 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.88 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6965_exp__mod__exp,axiom,
% 8.64/4.88 ! [M2: nat,N: nat] :
% 8.64/4.88 ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M2 @ N ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6966_exp__mod__exp,axiom,
% 8.64/4.88 ! [M2: nat,N: nat] :
% 8.64/4.88 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6967_exp__mod__exp,axiom,
% 8.64/4.88 ! [M2: nat,N: nat] :
% 8.64/4.88 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M2 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6968_exp__mod__exp,axiom,
% 8.64/4.88 ! [M2: nat,N: nat] :
% 8.64/4.88 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.88 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M2 @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6969_gbinomial__reduce__nat,axiom,
% 8.64/4.88 ! [K2: nat,A: complex] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.88 => ( ( gbinomial_complex @ A @ K2 )
% 8.64/4.88 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K2 ) ) ) ) ).
% 8.64/4.88
% 8.64/4.88 thf(fact_6970_gbinomial__reduce__nat,axiom,
% 8.64/4.88 ! [K2: nat,A: real] :
% 8.64/4.88 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.88 => ( ( gbinomial_real @ A @ K2 )
% 8.64/4.89 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6971_gbinomial__reduce__nat,axiom,
% 8.64/4.89 ! [K2: nat,A: rat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.89 => ( ( gbinomial_rat @ A @ K2 )
% 8.64/4.89 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6972_sum_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > rat,N: nat] :
% 8.64/4.89 ( ( groups2906978787729119204at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( plus_plus_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6973_sum_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > int,N: nat] :
% 8.64/4.89 ( ( groups3539618377306564664at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( plus_plus_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6974_sum_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > nat,N: nat] :
% 8.64/4.89 ( ( groups3542108847815614940at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [I: nat] : ( plus_plus_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6975_sum_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > real,N: nat] :
% 8.64/4.89 ( ( groups6591440286371151544t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( plus_plus_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6976_polyfun__rootbound,axiom,
% 8.64/4.89 ! [C2: nat > complex,K2: nat,N: nat] :
% 8.64/4.89 ( ( ( C2 @ K2 )
% 8.64/4.89 != zero_zero_complex )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.89 => ( ( finite3207457112153483333omplex
% 8.64/4.89 @ ( collect_complex
% 8.64/4.89 @ ^ [Z4: complex] :
% 8.64/4.89 ( ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_complex ) ) )
% 8.64/4.89 & ( ord_less_eq_nat
% 8.64/4.89 @ ( finite_card_complex
% 8.64/4.89 @ ( collect_complex
% 8.64/4.89 @ ^ [Z4: complex] :
% 8.64/4.89 ( ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z4 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_complex ) ) )
% 8.64/4.89 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6977_polyfun__rootbound,axiom,
% 8.64/4.89 ! [C2: nat > real,K2: nat,N: nat] :
% 8.64/4.89 ( ( ( C2 @ K2 )
% 8.64/4.89 != zero_zero_real )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.89 => ( ( finite_finite_real
% 8.64/4.89 @ ( collect_real
% 8.64/4.89 @ ^ [Z4: real] :
% 8.64/4.89 ( ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_real ) ) )
% 8.64/4.89 & ( ord_less_eq_nat
% 8.64/4.89 @ ( finite_card_real
% 8.64/4.89 @ ( collect_real
% 8.64/4.89 @ ^ [Z4: real] :
% 8.64/4.89 ( ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z4 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_real ) ) )
% 8.64/4.89 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6978_polynomial__product,axiom,
% 8.64/4.89 ! [M2: nat,A: nat > complex,N: nat,B: nat > complex,X: complex] :
% 8.64/4.89 ( ! [I3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ M2 @ I3 )
% 8.64/4.89 => ( ( A @ I3 )
% 8.64/4.89 = zero_zero_complex ) )
% 8.64/4.89 => ( ! [J3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ J3 )
% 8.64/4.89 => ( ( B @ J3 )
% 8.64/4.89 = zero_zero_complex ) )
% 8.64/4.89 => ( ( times_times_complex
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [J: nat] : ( times_times_complex @ ( B @ J ) @ ( power_power_complex @ X @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [R: nat] :
% 8.64/4.89 ( times_times_complex
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ R ) )
% 8.64/4.89 @ ( power_power_complex @ X @ R ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6979_polynomial__product,axiom,
% 8.64/4.89 ! [M2: nat,A: nat > rat,N: nat,B: nat > rat,X: rat] :
% 8.64/4.89 ( ! [I3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ M2 @ I3 )
% 8.64/4.89 => ( ( A @ I3 )
% 8.64/4.89 = zero_zero_rat ) )
% 8.64/4.89 => ( ! [J3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ J3 )
% 8.64/4.89 => ( ( B @ J3 )
% 8.64/4.89 = zero_zero_rat ) )
% 8.64/4.89 => ( ( times_times_rat
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [J: nat] : ( times_times_rat @ ( B @ J ) @ ( power_power_rat @ X @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [R: nat] :
% 8.64/4.89 ( times_times_rat
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ R ) )
% 8.64/4.89 @ ( power_power_rat @ X @ R ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6980_polynomial__product,axiom,
% 8.64/4.89 ! [M2: nat,A: nat > int,N: nat,B: nat > int,X: int] :
% 8.64/4.89 ( ! [I3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ M2 @ I3 )
% 8.64/4.89 => ( ( A @ I3 )
% 8.64/4.89 = zero_zero_int ) )
% 8.64/4.89 => ( ! [J3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ J3 )
% 8.64/4.89 => ( ( B @ J3 )
% 8.64/4.89 = zero_zero_int ) )
% 8.64/4.89 => ( ( times_times_int
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [J: nat] : ( times_times_int @ ( B @ J ) @ ( power_power_int @ X @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [R: nat] :
% 8.64/4.89 ( times_times_int
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ R ) )
% 8.64/4.89 @ ( power_power_int @ X @ R ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6981_polynomial__product,axiom,
% 8.64/4.89 ! [M2: nat,A: nat > real,N: nat,B: nat > real,X: real] :
% 8.64/4.89 ( ! [I3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ M2 @ I3 )
% 8.64/4.89 => ( ( A @ I3 )
% 8.64/4.89 = zero_zero_real ) )
% 8.64/4.89 => ( ! [J3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ J3 )
% 8.64/4.89 => ( ( B @ J3 )
% 8.64/4.89 = zero_zero_real ) )
% 8.64/4.89 => ( ( times_times_real
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [J: nat] : ( times_times_real @ ( B @ J ) @ ( power_power_real @ X @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [R: nat] :
% 8.64/4.89 ( times_times_real
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ R ) )
% 8.64/4.89 @ ( power_power_real @ X @ R ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6982_prod_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > real,N: nat] :
% 8.64/4.89 ( ( groups129246275422532515t_real @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups129246275422532515t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6983_prod_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > rat,N: nat] :
% 8.64/4.89 ( ( groups73079841787564623at_rat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups73079841787564623at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6984_prod_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > int,N: nat] :
% 8.64/4.89 ( ( groups705719431365010083at_int @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups705719431365010083at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6985_prod_Oin__pairs__0,axiom,
% 8.64/4.89 ! [G2: nat > nat,N: nat] :
% 8.64/4.89 ( ( groups708209901874060359at_nat @ G2 @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_nat @ ( G2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) @ ( G2 @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6986_polyfun__eq__const,axiom,
% 8.64/4.89 ! [C2: nat > complex,N: nat,K2: complex] :
% 8.64/4.89 ( ( ! [X4: complex] :
% 8.64/4.89 ( ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ X4 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = K2 ) )
% 8.64/4.89 = ( ( ( C2 @ zero_zero_nat )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ! [X4: nat] :
% 8.64/4.89 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 8.64/4.89 => ( ( C2 @ X4 )
% 8.64/4.89 = zero_zero_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6987_polyfun__eq__const,axiom,
% 8.64/4.89 ! [C2: nat > real,N: nat,K2: real] :
% 8.64/4.89 ( ( ! [X4: real] :
% 8.64/4.89 ( ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ X4 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = K2 ) )
% 8.64/4.89 = ( ( ( C2 @ zero_zero_nat )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ! [X4: nat] :
% 8.64/4.89 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) )
% 8.64/4.89 => ( ( C2 @ X4 )
% 8.64/4.89 = zero_zero_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6988_binomial__ring,axiom,
% 8.64/4.89 ! [A: complex,B: complex,N: nat] :
% 8.64/4.89 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N )
% 8.64/4.89 = ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6989_binomial__ring,axiom,
% 8.64/4.89 ! [A: rat,B: rat,N: nat] :
% 8.64/4.89 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 8.64/4.89 = ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6990_binomial__ring,axiom,
% 8.64/4.89 ! [A: int,B: int,N: nat] :
% 8.64/4.89 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N )
% 8.64/4.89 = ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6991_binomial__ring,axiom,
% 8.64/4.89 ! [A: nat,B: nat,N: nat] :
% 8.64/4.89 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 8.64/4.89 = ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6992_binomial__ring,axiom,
% 8.64/4.89 ! [A: real,B: real,N: nat] :
% 8.64/4.89 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N )
% 8.64/4.89 = ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6993_pochhammer__binomial__sum,axiom,
% 8.64/4.89 ! [A: rat,B: rat,N: nat] :
% 8.64/4.89 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N )
% 8.64/4.89 = ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6994_pochhammer__binomial__sum,axiom,
% 8.64/4.89 ! [A: int,B: int,N: nat] :
% 8.64/4.89 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N )
% 8.64/4.89 = ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6995_pochhammer__binomial__sum,axiom,
% 8.64/4.89 ! [A: real,B: real,N: nat] :
% 8.64/4.89 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N )
% 8.64/4.89 = ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6996_polynomial__product__nat,axiom,
% 8.64/4.89 ! [M2: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 8.64/4.89 ( ! [I3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ M2 @ I3 )
% 8.64/4.89 => ( ( A @ I3 )
% 8.64/4.89 = zero_zero_nat ) )
% 8.64/4.89 => ( ! [J3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ J3 )
% 8.64/4.89 => ( ( B @ J3 )
% 8.64/4.89 = zero_zero_nat ) )
% 8.64/4.89 => ( ( times_times_nat
% 8.64/4.89 @ ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_nat @ ( A @ I ) @ ( power_power_nat @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.89 @ ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [J: nat] : ( times_times_nat @ ( B @ J ) @ ( power_power_nat @ X @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [R: nat] :
% 8.64/4.89 ( times_times_nat
% 8.64/4.89 @ ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R @ K3 ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ R ) )
% 8.64/4.89 @ ( power_power_nat @ X @ R ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M2 @ N ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6997_choose__square__sum,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6998_set__update__distinct,axiom,
% 8.64/4.89 ! [Xs2: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 8.64/4.89 ( ( distinct_VEBT_VEBT @ Xs2 )
% 8.64/4.89 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 8.64/4.89 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs2 @ N @ X ) )
% 8.64/4.89 = ( insert_VEBT_VEBT @ X @ ( minus_5127226145743854075T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ ( insert_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs2 @ N ) @ bot_bo8194388402131092736T_VEBT ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_6999_set__update__distinct,axiom,
% 8.64/4.89 ! [Xs2: list_o,N: nat,X: $o] :
% 8.64/4.89 ( ( distinct_o @ Xs2 )
% 8.64/4.89 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs2 ) )
% 8.64/4.89 => ( ( set_o2 @ ( list_update_o @ Xs2 @ N @ X ) )
% 8.64/4.89 = ( insert_o @ X @ ( minus_minus_set_o @ ( set_o2 @ Xs2 ) @ ( insert_o @ ( nth_o @ Xs2 @ N ) @ bot_bot_set_o ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7000_set__update__distinct,axiom,
% 8.64/4.89 ! [Xs2: list_int,N: nat,X: int] :
% 8.64/4.89 ( ( distinct_int @ Xs2 )
% 8.64/4.89 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs2 ) )
% 8.64/4.89 => ( ( set_int2 @ ( list_update_int @ Xs2 @ N @ X ) )
% 8.64/4.89 = ( insert_int @ X @ ( minus_minus_set_int @ ( set_int2 @ Xs2 ) @ ( insert_int @ ( nth_int @ Xs2 @ N ) @ bot_bot_set_int ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7001_set__update__distinct,axiom,
% 8.64/4.89 ! [Xs2: list_real,N: nat,X: real] :
% 8.64/4.89 ( ( distinct_real @ Xs2 )
% 8.64/4.89 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs2 ) )
% 8.64/4.89 => ( ( set_real2 @ ( list_update_real @ Xs2 @ N @ X ) )
% 8.64/4.89 = ( insert_real @ X @ ( minus_minus_set_real @ ( set_real2 @ Xs2 ) @ ( insert_real @ ( nth_real @ Xs2 @ N ) @ bot_bot_set_real ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7002_set__update__distinct,axiom,
% 8.64/4.89 ! [Xs2: list_P6011104703257516679at_nat,N: nat,X: product_prod_nat_nat] :
% 8.64/4.89 ( ( distin6923225563576452346at_nat @ Xs2 )
% 8.64/4.89 => ( ( ord_less_nat @ N @ ( size_s5460976970255530739at_nat @ Xs2 ) )
% 8.64/4.89 => ( ( set_Pr5648618587558075414at_nat @ ( list_u6180841689913720943at_nat @ Xs2 @ N @ X ) )
% 8.64/4.89 = ( insert8211810215607154385at_nat @ X @ ( minus_1356011639430497352at_nat @ ( set_Pr5648618587558075414at_nat @ Xs2 ) @ ( insert8211810215607154385at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs2 @ N ) @ bot_bo2099793752762293965at_nat ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7003_set__update__distinct,axiom,
% 8.64/4.89 ! [Xs2: list_nat,N: nat,X: nat] :
% 8.64/4.89 ( ( distinct_nat @ Xs2 )
% 8.64/4.89 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs2 ) )
% 8.64/4.89 => ( ( set_nat2 @ ( list_update_nat @ Xs2 @ N @ X ) )
% 8.64/4.89 = ( insert_nat @ X @ ( minus_minus_set_nat @ ( set_nat2 @ Xs2 ) @ ( insert_nat @ ( nth_nat @ Xs2 @ N ) @ bot_bot_set_nat ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7004_sum_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > complex,H: nat > complex] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_complex @ ( J = K2 ) @ zero_zero_complex @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7005_sum_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > rat,H: nat > rat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_rat @ ( J = K2 ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [J: nat] : ( if_rat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7006_sum_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > int,H: nat > int] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_int @ ( J = K2 ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7007_sum_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > nat,H: nat > nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_nat @ ( J = K2 ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7008_sum_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > real,H: nat > real] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_real @ ( J = K2 ) @ zero_zero_real @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7009_prod_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > code_integer,H: nat > code_integer] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups3455450783089532116nteger
% 8.64/4.89 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_Code_integer @ ( J = K2 ) @ one_one_Code_integer @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups3455450783089532116nteger
% 8.64/4.89 @ ^ [J: nat] : ( if_Code_integer @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7010_prod_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > complex,H: nat > complex] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups6464643781859351333omplex
% 8.64/4.89 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_complex @ ( J = K2 ) @ one_one_complex @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups6464643781859351333omplex
% 8.64/4.89 @ ^ [J: nat] : ( if_complex @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7011_prod_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > real,H: nat > real] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups129246275422532515t_real
% 8.64/4.89 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_real @ ( J = K2 ) @ one_one_real @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups129246275422532515t_real
% 8.64/4.89 @ ^ [J: nat] : ( if_real @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7012_prod_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > int,H: nat > int] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups705719431365010083at_int
% 8.64/4.89 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_int @ ( J = K2 ) @ one_one_int @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups705719431365010083at_int
% 8.64/4.89 @ ^ [J: nat] : ( if_int @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7013_prod_Ozero__middle,axiom,
% 8.64/4.89 ! [P: nat,K2: nat,G2: nat > nat,H: nat > nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ P )
% 8.64/4.89 => ( ( ord_less_eq_nat @ K2 @ P )
% 8.64/4.89 => ( ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( if_nat @ ( J = K2 ) @ one_one_nat @ ( H @ ( minus_minus_nat @ J @ ( suc @ zero_zero_nat ) ) ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ P ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [J: nat] : ( if_nat @ ( ord_less_nat @ J @ K2 ) @ ( G2 @ J ) @ ( H @ J ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7014_gbinomial__sum__up__index,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [J: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J ) @ K2 )
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.89 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7015_gbinomial__sum__up__index,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [J: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J ) @ K2 )
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.89 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7016_gbinomial__sum__up__index,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [J: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J ) @ K2 )
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 8.64/4.89 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7017_exp__div__exp__eq,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( times_times_nat
% 8.64/4.89 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.89 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 )
% 8.64/4.89 != zero_zero_nat )
% 8.64/4.89 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 8.64/4.89 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7018_exp__div__exp__eq,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( times_times_int
% 8.64/4.89 @ ( zero_n2684676970156552555ol_int
% 8.64/4.89 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M2 )
% 8.64/4.89 != zero_zero_int )
% 8.64/4.89 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 8.64/4.89 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7019_exp__div__exp__eq,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( times_3573771949741848930nteger
% 8.64/4.89 @ ( zero_n356916108424825756nteger
% 8.64/4.89 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M2 )
% 8.64/4.89 != zero_z3403309356797280102nteger )
% 8.64/4.89 & ( ord_less_eq_nat @ N @ M2 ) ) )
% 8.64/4.89 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7020_gbinomial__absorption_H,axiom,
% 8.64/4.89 ! [K2: nat,A: complex] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.89 => ( ( gbinomial_complex @ A @ K2 )
% 8.64/4.89 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7021_gbinomial__absorption_H,axiom,
% 8.64/4.89 ! [K2: nat,A: rat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.89 => ( ( gbinomial_rat @ A @ K2 )
% 8.64/4.89 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7022_gbinomial__absorption_H,axiom,
% 8.64/4.89 ! [K2: nat,A: real] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.89 => ( ( gbinomial_real @ A @ K2 )
% 8.64/4.89 = ( times_times_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( minus_minus_nat @ K2 @ one_one_nat ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7023_sum__gp0,axiom,
% 8.64/4.89 ! [X: complex,N: nat] :
% 8.64/4.89 ( ( ( X = one_one_complex )
% 8.64/4.89 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 8.64/4.89 & ( ( X != one_one_complex )
% 8.64/4.89 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7024_sum__gp0,axiom,
% 8.64/4.89 ! [X: rat,N: nat] :
% 8.64/4.89 ( ( ( X = one_one_rat )
% 8.64/4.89 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 8.64/4.89 & ( ( X != one_one_rat )
% 8.64/4.89 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7025_sum__gp0,axiom,
% 8.64/4.89 ! [X: real,N: nat] :
% 8.64/4.89 ( ( ( X = one_one_real )
% 8.64/4.89 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) )
% 8.64/4.89 & ( ( X != one_one_real )
% 8.64/4.89 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7026_polyfun__diff__alt,axiom,
% 8.64/4.89 ! [N: nat,A: nat > complex,X: complex,Y: complex] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_complex
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_complex @ Y @ K3 ) ) @ ( power_power_complex @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7027_polyfun__diff__alt,axiom,
% 8.64/4.89 ! [N: nat,A: nat > rat,X: rat,Y: rat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_rat
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_rat @ Y @ K3 ) ) @ ( power_power_rat @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7028_polyfun__diff__alt,axiom,
% 8.64/4.89 ! [N: nat,A: nat > int,X: int,Y: int] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_int
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_int @ Y @ K3 ) ) @ ( power_power_int @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7029_polyfun__diff__alt,axiom,
% 8.64/4.89 ! [N: nat,A: nat > real,X: real,Y: real] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_real
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( A @ ( plus_plus_nat @ ( plus_plus_nat @ J @ K3 ) @ one_one_nat ) ) @ ( power_power_real @ Y @ K3 ) ) @ ( power_power_real @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ J ) ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7030_binomial__r__part__sum,axiom,
% 8.64/4.89 ! [M2: nat] :
% 8.64/4.89 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.89 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7031_choose__linear__sum,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( groups3542108847815614940at_nat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_nat @ I @ ( binomial @ N @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7032_card__lists__length__le,axiom,
% 8.64/4.89 ! [A4: set_list_nat,N: nat] :
% 8.64/4.89 ( ( finite8100373058378681591st_nat @ A4 )
% 8.64/4.89 => ( ( finite7325466520557071688st_nat
% 8.64/4.89 @ ( collec5989764272469232197st_nat
% 8.64/4.89 @ ^ [Xs: list_list_nat] :
% 8.64/4.89 ( ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 )
% 8.64/4.89 & ( ord_less_eq_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_list_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7033_card__lists__length__le,axiom,
% 8.64/4.89 ! [A4: set_set_nat,N: nat] :
% 8.64/4.89 ( ( finite1152437895449049373et_nat @ A4 )
% 8.64/4.89 => ( ( finite5631907774883551598et_nat
% 8.64/4.89 @ ( collect_list_set_nat
% 8.64/4.89 @ ^ [Xs: list_set_nat] :
% 8.64/4.89 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 )
% 8.64/4.89 & ( ord_less_eq_nat @ ( size_s3254054031482475050et_nat @ Xs ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_set_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7034_card__lists__length__le,axiom,
% 8.64/4.89 ! [A4: set_complex,N: nat] :
% 8.64/4.89 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.89 => ( ( finite5120063068150530198omplex
% 8.64/4.89 @ ( collect_list_complex
% 8.64/4.89 @ ^ [Xs: list_complex] :
% 8.64/4.89 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 )
% 8.64/4.89 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_complex @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7035_card__lists__length__le,axiom,
% 8.64/4.89 ! [A4: set_VEBT_VEBT,N: nat] :
% 8.64/4.89 ( ( finite5795047828879050333T_VEBT @ A4 )
% 8.64/4.89 => ( ( finite5915292604075114978T_VEBT
% 8.64/4.89 @ ( collec5608196760682091941T_VEBT
% 8.64/4.89 @ ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.89 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 )
% 8.64/4.89 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite7802652506058667612T_VEBT @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7036_card__lists__length__le,axiom,
% 8.64/4.89 ! [A4: set_o,N: nat] :
% 8.64/4.89 ( ( finite_finite_o @ A4 )
% 8.64/4.89 => ( ( finite_card_list_o
% 8.64/4.89 @ ( collect_list_o
% 8.64/4.89 @ ^ [Xs: list_o] :
% 8.64/4.89 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 )
% 8.64/4.89 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_o @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7037_card__lists__length__le,axiom,
% 8.64/4.89 ! [A4: set_int,N: nat] :
% 8.64/4.89 ( ( finite_finite_int @ A4 )
% 8.64/4.89 => ( ( finite_card_list_int
% 8.64/4.89 @ ( collect_list_int
% 8.64/4.89 @ ^ [Xs: list_int] :
% 8.64/4.89 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 )
% 8.64/4.89 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_int @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7038_card__lists__length__le,axiom,
% 8.64/4.89 ! [A4: set_nat,N: nat] :
% 8.64/4.89 ( ( finite_finite_nat @ A4 )
% 8.64/4.89 => ( ( finite_card_list_nat
% 8.64/4.89 @ ( collect_list_nat
% 8.64/4.89 @ ^ [Xs: list_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 )
% 8.64/4.89 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ N ) ) ) )
% 8.64/4.89 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( finite_card_nat @ A4 ) ) @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7039_polyfun__extremal__lemma,axiom,
% 8.64/4.89 ! [E: real,C2: nat > complex,N: nat] :
% 8.64/4.89 ( ( ord_less_real @ zero_zero_real @ E )
% 8.64/4.89 => ? [M8: real] :
% 8.64/4.89 ! [Z5: complex] :
% 8.64/4.89 ( ( ord_less_eq_real @ M8 @ ( real_V1022390504157884413omplex @ Z5 ) )
% 8.64/4.89 => ( ord_less_eq_real
% 8.64/4.89 @ ( real_V1022390504157884413omplex
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( C2 @ I ) @ ( power_power_complex @ Z5 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 @ ( times_times_real @ E @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7040_polyfun__extremal__lemma,axiom,
% 8.64/4.89 ! [E: real,C2: nat > real,N: nat] :
% 8.64/4.89 ( ( ord_less_real @ zero_zero_real @ E )
% 8.64/4.89 => ? [M8: real] :
% 8.64/4.89 ! [Z5: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ M8 @ ( real_V7735802525324610683m_real @ Z5 ) )
% 8.64/4.89 => ( ord_less_eq_real
% 8.64/4.89 @ ( real_V7735802525324610683m_real
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( C2 @ I ) @ ( power_power_real @ Z5 @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 @ ( times_times_real @ E @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z5 ) @ ( suc @ N ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7041_polyfun__diff,axiom,
% 8.64/4.89 ! [N: nat,A: nat > complex,X: complex,Y: complex] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_complex
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( times_times_complex
% 8.64/4.89 @ ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( A @ I ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.89 @ ( power_power_complex @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7042_polyfun__diff,axiom,
% 8.64/4.89 ! [N: nat,A: nat > rat,X: rat,Y: rat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_rat
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( times_times_rat
% 8.64/4.89 @ ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.89 @ ( power_power_rat @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7043_polyfun__diff,axiom,
% 8.64/4.89 ! [N: nat,A: nat > int,X: int,Y: int] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_int
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( times_times_int
% 8.64/4.89 @ ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( A @ I ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.89 @ ( power_power_int @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7044_polyfun__diff,axiom,
% 8.64/4.89 ! [N: nat,A: nat > real,X: real,Y: real] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.89 => ( ( minus_minus_real
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ X @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ I ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) ) )
% 8.64/4.89 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [J: nat] :
% 8.64/4.89 ( times_times_real
% 8.64/4.89 @ ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( A @ I ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ one_one_nat ) ) )
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( suc @ J ) @ N ) )
% 8.64/4.89 @ ( power_power_real @ X @ J ) )
% 8.64/4.89 @ ( set_ord_lessThan_nat @ N ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7045_card__lists__distinct__length__eq_H,axiom,
% 8.64/4.89 ! [K2: nat,A4: set_complex] :
% 8.64/4.89 ( ( ord_less_nat @ K2 @ ( finite_card_complex @ A4 ) )
% 8.64/4.89 => ( ( finite5120063068150530198omplex
% 8.64/4.89 @ ( collect_list_complex
% 8.64/4.89 @ ^ [Xs: list_complex] :
% 8.64/4.89 ( ( ( size_s3451745648224563538omplex @ Xs )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ( distinct_complex @ Xs )
% 8.64/4.89 & ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [X4: nat] : X4
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_complex @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_complex @ A4 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7046_card__lists__distinct__length__eq_H,axiom,
% 8.64/4.89 ! [K2: nat,A4: set_list_nat] :
% 8.64/4.89 ( ( ord_less_nat @ K2 @ ( finite_card_list_nat @ A4 ) )
% 8.64/4.89 => ( ( finite7325466520557071688st_nat
% 8.64/4.89 @ ( collec5989764272469232197st_nat
% 8.64/4.89 @ ^ [Xs: list_list_nat] :
% 8.64/4.89 ( ( ( size_s3023201423986296836st_nat @ Xs )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ( distinct_list_nat @ Xs )
% 8.64/4.89 & ( ord_le6045566169113846134st_nat @ ( set_list_nat2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [X4: nat] : X4
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_list_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_list_nat @ A4 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7047_card__lists__distinct__length__eq_H,axiom,
% 8.64/4.89 ! [K2: nat,A4: set_set_nat] :
% 8.64/4.89 ( ( ord_less_nat @ K2 @ ( finite_card_set_nat @ A4 ) )
% 8.64/4.89 => ( ( finite5631907774883551598et_nat
% 8.64/4.89 @ ( collect_list_set_nat
% 8.64/4.89 @ ^ [Xs: list_set_nat] :
% 8.64/4.89 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ( distinct_set_nat @ Xs )
% 8.64/4.89 & ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [X4: nat] : X4
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_set_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_set_nat @ A4 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7048_card__lists__distinct__length__eq_H,axiom,
% 8.64/4.89 ! [K2: nat,A4: set_VEBT_VEBT] :
% 8.64/4.89 ( ( ord_less_nat @ K2 @ ( finite7802652506058667612T_VEBT @ A4 ) )
% 8.64/4.89 => ( ( finite5915292604075114978T_VEBT
% 8.64/4.89 @ ( collec5608196760682091941T_VEBT
% 8.64/4.89 @ ^ [Xs: list_VEBT_VEBT] :
% 8.64/4.89 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ( distinct_VEBT_VEBT @ Xs )
% 8.64/4.89 & ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [X4: nat] : X4
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite7802652506058667612T_VEBT @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite7802652506058667612T_VEBT @ A4 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7049_card__lists__distinct__length__eq_H,axiom,
% 8.64/4.89 ! [K2: nat,A4: set_o] :
% 8.64/4.89 ( ( ord_less_nat @ K2 @ ( finite_card_o @ A4 ) )
% 8.64/4.89 => ( ( finite_card_list_o
% 8.64/4.89 @ ( collect_list_o
% 8.64/4.89 @ ^ [Xs: list_o] :
% 8.64/4.89 ( ( ( size_size_list_o @ Xs )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ( distinct_o @ Xs )
% 8.64/4.89 & ( ord_less_eq_set_o @ ( set_o2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [X4: nat] : X4
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_o @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_o @ A4 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7050_card__lists__distinct__length__eq_H,axiom,
% 8.64/4.89 ! [K2: nat,A4: set_int] :
% 8.64/4.89 ( ( ord_less_nat @ K2 @ ( finite_card_int @ A4 ) )
% 8.64/4.89 => ( ( finite_card_list_int
% 8.64/4.89 @ ( collect_list_int
% 8.64/4.89 @ ^ [Xs: list_int] :
% 8.64/4.89 ( ( ( size_size_list_int @ Xs )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ( distinct_int @ Xs )
% 8.64/4.89 & ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [X4: nat] : X4
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_int @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_int @ A4 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7051_card__lists__distinct__length__eq_H,axiom,
% 8.64/4.89 ! [K2: nat,A4: set_nat] :
% 8.64/4.89 ( ( ord_less_nat @ K2 @ ( finite_card_nat @ A4 ) )
% 8.64/4.89 => ( ( finite_card_list_nat
% 8.64/4.89 @ ( collect_list_nat
% 8.64/4.89 @ ^ [Xs: list_nat] :
% 8.64/4.89 ( ( ( size_size_list_nat @ Xs )
% 8.64/4.89 = K2 )
% 8.64/4.89 & ( distinct_nat @ Xs )
% 8.64/4.89 & ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A4 ) ) ) )
% 8.64/4.89 = ( groups708209901874060359at_nat
% 8.64/4.89 @ ^ [X4: nat] : X4
% 8.64/4.89 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ ( minus_minus_nat @ ( finite_card_nat @ A4 ) @ K2 ) @ one_one_nat ) @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7052_Divides_Oadjust__div__eq,axiom,
% 8.64/4.89 ! [Q2: int,R3: int] :
% 8.64/4.89 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.89 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7053_list__decode_Opinduct,axiom,
% 8.64/4.89 ! [A0: nat,P2: nat > $o] :
% 8.64/4.89 ( ( accp_nat @ nat_list_decode_rel @ A0 )
% 8.64/4.89 => ( ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 8.64/4.89 => ( P2 @ zero_zero_nat ) )
% 8.64/4.89 => ( ! [N3: nat] :
% 8.64/4.89 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) )
% 8.64/4.89 => ( ! [X5: nat,Y6: nat] :
% 8.64/4.89 ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 8.64/4.89 = ( nat_prod_decode @ N3 ) )
% 8.64/4.89 => ( P2 @ Y6 ) )
% 8.64/4.89 => ( P2 @ ( suc @ N3 ) ) ) )
% 8.64/4.89 => ( P2 @ A0 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7054_gbinomial__code,axiom,
% 8.64/4.89 ( gbinomial_complex
% 8.64/4.89 = ( ^ [A5: complex,K3: nat] :
% 8.64/4.89 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 8.64/4.89 @ ( divide1717551699836669952omplex
% 8.64/4.89 @ ( set_fo1517530859248394432omplex
% 8.64/4.89 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A5 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 8.64/4.89 @ zero_zero_nat
% 8.64/4.89 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 8.64/4.89 @ one_one_complex )
% 8.64/4.89 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7055_gbinomial__code,axiom,
% 8.64/4.89 ( gbinomial_rat
% 8.64/4.89 = ( ^ [A5: rat,K3: nat] :
% 8.64/4.89 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 8.64/4.89 @ ( divide_divide_rat
% 8.64/4.89 @ ( set_fo1949268297981939178at_rat
% 8.64/4.89 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 8.64/4.89 @ zero_zero_nat
% 8.64/4.89 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 8.64/4.89 @ one_one_rat )
% 8.64/4.89 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7056_gbinomial__code,axiom,
% 8.64/4.89 ( gbinomial_real
% 8.64/4.89 = ( ^ [A5: real,K3: nat] :
% 8.64/4.89 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 8.64/4.89 @ ( divide_divide_real
% 8.64/4.89 @ ( set_fo3111899725591712190t_real
% 8.64/4.89 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A5 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 8.64/4.89 @ zero_zero_nat
% 8.64/4.89 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 8.64/4.89 @ one_one_real )
% 8.64/4.89 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7057_choose__alternating__sum,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.89 => ( ( groups2073611262835488442omplex
% 8.64/4.89 @ ^ [I: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7058_choose__alternating__sum,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.89 => ( ( groups7501900531339628137nteger
% 8.64/4.89 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7059_choose__alternating__sum,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.89 => ( ( groups2906978787729119204at_rat
% 8.64/4.89 @ ^ [I: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7060_choose__alternating__sum,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.89 => ( ( groups3539618377306564664at_int
% 8.64/4.89 @ ^ [I: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7061_choose__alternating__sum,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.89 => ( ( groups6591440286371151544t_real
% 8.64/4.89 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) )
% 8.64/4.89 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.89 = zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7062_signed__take__bit__Suc,axiom,
% 8.64/4.89 ! [N: nat,A: int] :
% 8.64/4.89 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 8.64/4.89 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7063_set__decode__0,axiom,
% 8.64/4.89 ! [X: nat] :
% 8.64/4.89 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 8.64/4.89 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7064_add_Oinverse__inverse,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7065_add_Oinverse__inverse,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7066_add_Oinverse__inverse,axiom,
% 8.64/4.89 ! [A: complex] :
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7067_add_Oinverse__inverse,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7068_add_Oinverse__inverse,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7069_neg__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ A )
% 8.64/4.89 = ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( A = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7070_neg__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ A )
% 8.64/4.89 = ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( A = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7071_neg__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ A )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( A = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7072_neg__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ A )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( A = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7073_neg__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ A )
% 8.64/4.89 = ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( A = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7074_of__nat__id,axiom,
% 8.64/4.89 ( semiri1316708129612266289at_nat
% 8.64/4.89 = ( ^ [N4: nat] : N4 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7075_compl__le__compl__iff,axiom,
% 8.64/4.89 ! [X: set_nat,Y: set_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) )
% 8.64/4.89 = ( ord_less_eq_set_nat @ Y @ X ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7076_neg__le__iff__le,axiom,
% 8.64/4.89 ! [B: real,A: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( ord_less_eq_real @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7077_neg__le__iff__le,axiom,
% 8.64/4.89 ! [B: code_integer,A: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7078_neg__le__iff__le,axiom,
% 8.64/4.89 ! [B: rat,A: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( ord_less_eq_rat @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7079_neg__le__iff__le,axiom,
% 8.64/4.89 ! [B: int,A: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( ord_less_eq_int @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7080_neg__equal__zero,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ A )
% 8.64/4.89 = A )
% 8.64/4.89 = ( A = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7081_neg__equal__zero,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ A )
% 8.64/4.89 = A )
% 8.64/4.89 = ( A = zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7082_neg__equal__zero,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ A )
% 8.64/4.89 = A )
% 8.64/4.89 = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7083_neg__equal__zero,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ A )
% 8.64/4.89 = A )
% 8.64/4.89 = ( A = zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7084_equal__neg__zero,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( A = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7085_equal__neg__zero,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( A = zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7086_equal__neg__zero,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7087_equal__neg__zero,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( A = zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7088_neg__equal__0__iff__equal,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ A )
% 8.64/4.89 = zero_zero_int )
% 8.64/4.89 = ( A = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7089_neg__equal__0__iff__equal,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ A )
% 8.64/4.89 = zero_zero_real )
% 8.64/4.89 = ( A = zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7090_neg__equal__0__iff__equal,axiom,
% 8.64/4.89 ! [A: complex] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ A )
% 8.64/4.89 = zero_zero_complex )
% 8.64/4.89 = ( A = zero_zero_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7091_neg__equal__0__iff__equal,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ A )
% 8.64/4.89 = zero_z3403309356797280102nteger )
% 8.64/4.89 = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7092_neg__equal__0__iff__equal,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ A )
% 8.64/4.89 = zero_zero_rat )
% 8.64/4.89 = ( A = zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7093_neg__0__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( zero_zero_int
% 8.64/4.89 = ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( zero_zero_int = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7094_neg__0__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( zero_zero_real
% 8.64/4.89 = ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( zero_zero_real = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7095_neg__0__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: complex] :
% 8.64/4.89 ( ( zero_zero_complex
% 8.64/4.89 = ( uminus1482373934393186551omplex @ A ) )
% 8.64/4.89 = ( zero_zero_complex = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7096_neg__0__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( zero_z3403309356797280102nteger
% 8.64/4.89 = ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( zero_z3403309356797280102nteger = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7097_neg__0__equal__iff__equal,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( zero_zero_rat
% 8.64/4.89 = ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( zero_zero_rat = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7098_add_Oinverse__neutral,axiom,
% 8.64/4.89 ( ( uminus_uminus_int @ zero_zero_int )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7099_add_Oinverse__neutral,axiom,
% 8.64/4.89 ( ( uminus_uminus_real @ zero_zero_real )
% 8.64/4.89 = zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7100_add_Oinverse__neutral,axiom,
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 8.64/4.89 = zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7101_add_Oinverse__neutral,axiom,
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7102_add_Oinverse__neutral,axiom,
% 8.64/4.89 ( ( uminus_uminus_rat @ zero_zero_rat )
% 8.64/4.89 = zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7103_neg__less__iff__less,axiom,
% 8.64/4.89 ! [B: int,A: int] :
% 8.64/4.89 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( ord_less_int @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7104_neg__less__iff__less,axiom,
% 8.64/4.89 ! [B: real,A: real] :
% 8.64/4.89 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( ord_less_real @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7105_neg__less__iff__less,axiom,
% 8.64/4.89 ! [B: code_integer,A: code_integer] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7106_neg__less__iff__less,axiom,
% 8.64/4.89 ! [B: rat,A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( ord_less_rat @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7107_neg__numeral__eq__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( M2 = N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7108_neg__numeral__eq__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( M2 = N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7109_neg__numeral__eq__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.64/4.89 = ( M2 = N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7110_neg__numeral__eq__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( M2 = N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7111_neg__numeral__eq__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( M2 = N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7112_mult__minus__right,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7113_mult__minus__right,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7114_mult__minus__right,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7115_mult__minus__right,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7116_mult__minus__right,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7117_minus__mult__minus,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( times_times_int @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7118_minus__mult__minus,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( times_times_real @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7119_minus__mult__minus,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( times_times_complex @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7120_minus__mult__minus,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7121_minus__mult__minus,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( times_times_rat @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7122_mult__minus__left,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7123_mult__minus__left,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 8.64/4.89 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7124_mult__minus__left,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7125_mult__minus__left,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7126_mult__minus__left,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7127_add__minus__cancel,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7128_add__minus__cancel,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7129_add__minus__cancel,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7130_add__minus__cancel,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7131_add__minus__cancel,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7132_minus__add__cancel,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7133_minus__add__cancel,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7134_minus__add__cancel,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7135_minus__add__cancel,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7136_minus__add__cancel,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 8.64/4.89 = B ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7137_minus__add__distrib,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.64/4.89 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7138_minus__add__distrib,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 8.64/4.89 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7139_minus__add__distrib,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 8.64/4.89 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7140_minus__add__distrib,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7141_minus__add__distrib,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.64/4.89 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7142_minus__diff__eq,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 8.64/4.89 = ( minus_minus_int @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7143_minus__diff__eq,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 8.64/4.89 = ( minus_minus_real @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7144_minus__diff__eq,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 8.64/4.89 = ( minus_minus_complex @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7145_minus__diff__eq,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.64/4.89 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7146_minus__diff__eq,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 8.64/4.89 = ( minus_minus_rat @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7147_dvd__minus__iff,axiom,
% 8.64/4.89 ! [X: int,Y: int] :
% 8.64/4.89 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 8.64/4.89 = ( dvd_dvd_int @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7148_dvd__minus__iff,axiom,
% 8.64/4.89 ! [X: real,Y: real] :
% 8.64/4.89 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 8.64/4.89 = ( dvd_dvd_real @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7149_dvd__minus__iff,axiom,
% 8.64/4.89 ! [X: complex,Y: complex] :
% 8.64/4.89 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 8.64/4.89 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7150_dvd__minus__iff,axiom,
% 8.64/4.89 ! [X: code_integer,Y: code_integer] :
% 8.64/4.89 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 8.64/4.89 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7151_dvd__minus__iff,axiom,
% 8.64/4.89 ! [X: rat,Y: rat] :
% 8.64/4.89 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 8.64/4.89 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7152_minus__dvd__iff,axiom,
% 8.64/4.89 ! [X: int,Y: int] :
% 8.64/4.89 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 8.64/4.89 = ( dvd_dvd_int @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7153_minus__dvd__iff,axiom,
% 8.64/4.89 ! [X: real,Y: real] :
% 8.64/4.89 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 8.64/4.89 = ( dvd_dvd_real @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7154_minus__dvd__iff,axiom,
% 8.64/4.89 ! [X: complex,Y: complex] :
% 8.64/4.89 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 8.64/4.89 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7155_minus__dvd__iff,axiom,
% 8.64/4.89 ! [X: code_integer,Y: code_integer] :
% 8.64/4.89 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 8.64/4.89 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7156_minus__dvd__iff,axiom,
% 8.64/4.89 ! [X: rat,Y: rat] :
% 8.64/4.89 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 8.64/4.89 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7157_negative__eq__positive,axiom,
% 8.64/4.89 ! [N: nat,M2: nat] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.89 = ( semiri1314217659103216013at_int @ M2 ) )
% 8.64/4.89 = ( ( N = zero_zero_nat )
% 8.64/4.89 & ( M2 = zero_zero_nat ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7158_signed__take__bit__of__0,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7159_set__decode__inverse,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( nat_set_encode @ ( nat_set_decode @ N ) )
% 8.64/4.89 = N ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7160_neg__less__eq__nonneg,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 8.64/4.89 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7161_neg__less__eq__nonneg,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.64/4.89 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7162_neg__less__eq__nonneg,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.64/4.89 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7163_neg__less__eq__nonneg,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 8.64/4.89 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7164_less__eq__neg__nonpos,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7165_less__eq__neg__nonpos,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7166_less__eq__neg__nonpos,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7167_less__eq__neg__nonpos,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7168_neg__le__0__iff__le,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 8.64/4.89 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7169_neg__le__0__iff__le,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 8.64/4.89 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7170_neg__le__0__iff__le,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 8.64/4.89 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7171_neg__le__0__iff__le,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 8.64/4.89 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7172_neg__0__le__iff__le,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7173_neg__0__le__iff__le,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7174_neg__0__le__iff__le,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7175_neg__0__le__iff__le,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7176_less__neg__neg,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7177_less__neg__neg,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7178_less__neg__neg,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7179_less__neg__neg,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7180_neg__less__pos,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 8.64/4.89 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7181_neg__less__pos,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 8.64/4.89 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7182_neg__less__pos,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.64/4.89 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7183_neg__less__pos,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.64/4.89 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7184_neg__0__less__iff__less,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7185_neg__0__less__iff__less,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7186_neg__0__less__iff__less,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7187_neg__0__less__iff__less,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7188_neg__less__0__iff__less,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 8.64/4.89 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7189_neg__less__0__iff__less,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 8.64/4.89 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7190_neg__less__0__iff__less,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 8.64/4.89 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7191_neg__less__0__iff__less,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 8.64/4.89 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7192_add_Oright__inverse,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7193_add_Oright__inverse,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 8.64/4.89 = zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7194_add_Oright__inverse,axiom,
% 8.64/4.89 ! [A: complex] :
% 8.64/4.89 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 8.64/4.89 = zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7195_add_Oright__inverse,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7196_add_Oright__inverse,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 8.64/4.89 = zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7197_ab__left__minus,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7198_ab__left__minus,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 8.64/4.89 = zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7199_ab__left__minus,axiom,
% 8.64/4.89 ! [A: complex] :
% 8.64/4.89 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 8.64/4.89 = zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7200_ab__left__minus,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7201_ab__left__minus,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.64/4.89 = zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7202_verit__minus__simplify_I3_J,axiom,
% 8.64/4.89 ! [B: int] :
% 8.64/4.89 ( ( minus_minus_int @ zero_zero_int @ B )
% 8.64/4.89 = ( uminus_uminus_int @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7203_verit__minus__simplify_I3_J,axiom,
% 8.64/4.89 ! [B: real] :
% 8.64/4.89 ( ( minus_minus_real @ zero_zero_real @ B )
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7204_verit__minus__simplify_I3_J,axiom,
% 8.64/4.89 ! [B: complex] :
% 8.64/4.89 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7205_verit__minus__simplify_I3_J,axiom,
% 8.64/4.89 ! [B: code_integer] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7206_verit__minus__simplify_I3_J,axiom,
% 8.64/4.89 ! [B: rat] :
% 8.64/4.89 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7207_diff__0,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( minus_minus_int @ zero_zero_int @ A )
% 8.64/4.89 = ( uminus_uminus_int @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7208_diff__0,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( minus_minus_real @ zero_zero_real @ A )
% 8.64/4.89 = ( uminus_uminus_real @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7209_diff__0,axiom,
% 8.64/4.89 ! [A: complex] :
% 8.64/4.89 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7210_diff__0,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7211_diff__0,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 8.64/4.89 = ( uminus_uminus_rat @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7212_add__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7213_add__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M2 ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7214_add__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7215_add__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7216_add__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M2 ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7217_mult__minus1__right,axiom,
% 8.64/4.89 ! [Z3: int] :
% 8.64/4.89 ( ( times_times_int @ Z3 @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = ( uminus_uminus_int @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7218_mult__minus1__right,axiom,
% 8.64/4.89 ! [Z3: real] :
% 8.64/4.89 ( ( times_times_real @ Z3 @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( uminus_uminus_real @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7219_mult__minus1__right,axiom,
% 8.64/4.89 ! [Z3: complex] :
% 8.64/4.89 ( ( times_times_complex @ Z3 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7220_mult__minus1__right,axiom,
% 8.64/4.89 ! [Z3: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ Z3 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7221_mult__minus1__right,axiom,
% 8.64/4.89 ! [Z3: rat] :
% 8.64/4.89 ( ( times_times_rat @ Z3 @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( uminus_uminus_rat @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7222_mult__minus1,axiom,
% 8.64/4.89 ! [Z3: int] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z3 )
% 8.64/4.89 = ( uminus_uminus_int @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7223_mult__minus1,axiom,
% 8.64/4.89 ! [Z3: real] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z3 )
% 8.64/4.89 = ( uminus_uminus_real @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7224_mult__minus1,axiom,
% 8.64/4.89 ! [Z3: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z3 )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7225_mult__minus1,axiom,
% 8.64/4.89 ! [Z3: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z3 )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7226_mult__minus1,axiom,
% 8.64/4.89 ! [Z3: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z3 )
% 8.64/4.89 = ( uminus_uminus_rat @ Z3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7227_diff__minus__eq__add,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( plus_plus_int @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7228_diff__minus__eq__add,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( plus_plus_real @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7229_diff__minus__eq__add,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( plus_plus_complex @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7230_diff__minus__eq__add,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7231_diff__minus__eq__add,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( plus_plus_rat @ A @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7232_uminus__add__conv__diff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = ( minus_minus_int @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7233_uminus__add__conv__diff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 8.64/4.89 = ( minus_minus_real @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7234_uminus__add__conv__diff,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.64/4.89 = ( minus_minus_complex @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7235_uminus__add__conv__diff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.64/4.89 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7236_uminus__add__conv__diff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.64/4.89 = ( minus_minus_rat @ B @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7237_fact__0,axiom,
% 8.64/4.89 ( ( semiri3624122377584611663nteger @ zero_zero_nat )
% 8.64/4.89 = one_one_Code_integer ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7238_fact__0,axiom,
% 8.64/4.89 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 8.64/4.89 = one_one_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7239_fact__0,axiom,
% 8.64/4.89 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 8.64/4.89 = one_one_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7240_fact__0,axiom,
% 8.64/4.89 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 8.64/4.89 = one_one_nat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7241_fact__0,axiom,
% 8.64/4.89 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 8.64/4.89 = one_one_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7242_negative__zless,axiom,
% 8.64/4.89 ! [N: nat,M2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ ( semiri1314217659103216013at_int @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7243_signed__take__bit__Suc__1,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ one_one_Code_integer )
% 8.64/4.89 = one_one_Code_integer ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7244_signed__take__bit__Suc__1,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 8.64/4.89 = one_one_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7245_dbl__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7246_dbl__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7247_dbl__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7248_dbl__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7249_dbl__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7250_dbl__inc__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7251_dbl__inc__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7252_dbl__inc__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7253_dbl__inc__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7254_dbl__inc__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7255_set__decode__zero,axiom,
% 8.64/4.89 ( ( nat_set_decode @ zero_zero_nat )
% 8.64/4.89 = bot_bot_set_nat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7256_set__encode__inverse,axiom,
% 8.64/4.89 ! [A4: set_nat] :
% 8.64/4.89 ( ( finite_finite_nat @ A4 )
% 8.64/4.89 => ( ( nat_set_decode @ ( nat_set_encode @ A4 ) )
% 8.64/4.89 = A4 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7257_add__neg__numeral__special_I7_J,axiom,
% 8.64/4.89 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7258_add__neg__numeral__special_I7_J,axiom,
% 8.64/4.89 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7259_add__neg__numeral__special_I7_J,axiom,
% 8.64/4.89 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7260_add__neg__numeral__special_I7_J,axiom,
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7261_add__neg__numeral__special_I7_J,axiom,
% 8.64/4.89 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7262_add__neg__numeral__special_I8_J,axiom,
% 8.64/4.89 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7263_add__neg__numeral__special_I8_J,axiom,
% 8.64/4.89 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 8.64/4.89 = zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7264_add__neg__numeral__special_I8_J,axiom,
% 8.64/4.89 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 8.64/4.89 = zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7265_add__neg__numeral__special_I8_J,axiom,
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7266_add__neg__numeral__special_I8_J,axiom,
% 8.64/4.89 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 8.64/4.89 = zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7267_diff__numeral__special_I12_J,axiom,
% 8.64/4.89 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7268_diff__numeral__special_I12_J,axiom,
% 8.64/4.89 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7269_diff__numeral__special_I12_J,axiom,
% 8.64/4.89 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7270_diff__numeral__special_I12_J,axiom,
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7271_diff__numeral__special_I12_J,axiom,
% 8.64/4.89 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7272_neg__one__eq__numeral__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ one_one_int )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7273_neg__one__eq__numeral__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ one_one_real )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7274_neg__one__eq__numeral__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7275_neg__one__eq__numeral__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7276_neg__one__eq__numeral__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ one_one_rat )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7277_numeral__eq__neg__one__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7278_numeral__eq__neg__one__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 8.64/4.89 = ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7279_numeral__eq__neg__one__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7280_numeral__eq__neg__one__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7281_numeral__eq__neg__one__iff,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 8.64/4.89 = ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( N = one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7282_left__minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat,A: int] :
% 8.64/4.89 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7283_left__minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat,A: real] :
% 8.64/4.89 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7284_left__minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat,A: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7285_left__minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat,A: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7286_left__minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat,A: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 8.64/4.89 = A ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7287_minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 8.64/4.89 = one_one_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7288_minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 8.64/4.89 = one_one_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7289_minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 8.64/4.89 = one_one_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7290_minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 8.64/4.89 = one_one_Code_integer ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7291_minus__one__mult__self,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 8.64/4.89 = one_one_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7292_mod__minus1__right,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7293_mod__minus1__right,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7294_max__number__of_I2_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 = ( numeral_numeral_real @ U ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7295_max__number__of_I2_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7296_max__number__of_I2_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7297_max__number__of_I2_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 = ( numeral_numeral_int @ U ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7298_max__number__of_I3_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.89 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.89 = ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.89 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V2 ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7299_max__number__of_I3_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 8.64/4.89 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 8.64/4.89 = ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 8.64/4.89 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V2 ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7300_max__number__of_I3_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.89 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.89 = ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.89 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V2 ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7301_max__number__of_I3_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.89 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.89 = ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.89 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V2 ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7302_max__number__of_I4_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7303_max__number__of_I4_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7304_max__number__of_I4_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7305_max__number__of_I4_J,axiom,
% 8.64/4.89 ! [U: num,V2: num] :
% 8.64/4.89 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) ) )
% 8.64/4.89 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7306_fact__Suc__0,axiom,
% 8.64/4.89 ( ( semiri3624122377584611663nteger @ ( suc @ zero_zero_nat ) )
% 8.64/4.89 = one_one_Code_integer ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7307_fact__Suc__0,axiom,
% 8.64/4.89 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 8.64/4.89 = one_one_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7308_fact__Suc__0,axiom,
% 8.64/4.89 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 8.64/4.89 = one_one_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7309_fact__Suc__0,axiom,
% 8.64/4.89 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 8.64/4.89 = one_one_nat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7310_fact__Suc__0,axiom,
% 8.64/4.89 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 8.64/4.89 = one_one_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7311_fact__Suc,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri773545260158071498ct_rat @ ( suc @ N ) )
% 8.64/4.89 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7312_fact__Suc,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri1406184849735516958ct_int @ ( suc @ N ) )
% 8.64/4.89 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7313_fact__Suc,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri1408675320244567234ct_nat @ ( suc @ N ) )
% 8.64/4.89 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7314_fact__Suc,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri2265585572941072030t_real @ ( suc @ N ) )
% 8.64/4.89 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7315_diff__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7316_diff__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7317_diff__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7318_diff__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7319_diff__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7320_diff__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_int @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7321_diff__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_real @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7322_diff__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.64/4.89 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7323_diff__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7324_diff__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7325_mult__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7326_mult__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7327_mult__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M2 ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7328_mult__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7329_mult__neg__numeral__simps_I3_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7330_mult__neg__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7331_mult__neg__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7332_mult__neg__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( numera6690914467698888265omplex @ N ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7333_mult__neg__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7334_mult__neg__numeral__simps_I2_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7335_mult__neg__numeral__simps_I1_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_int @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7336_mult__neg__numeral__simps_I1_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_real @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7337_mult__neg__numeral__simps_I1_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.64/4.89 = ( numera6690914467698888265omplex @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7338_mult__neg__numeral__simps_I1_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( numera6620942414471956472nteger @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7339_mult__neg__numeral__simps_I1_J,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_rat @ ( times_times_num @ M2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7340_semiring__norm_I172_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: int] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7341_semiring__norm_I172_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: real] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7342_semiring__norm_I172_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7343_semiring__norm_I172_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7344_semiring__norm_I172_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7345_semiring__norm_I171_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: int] :
% 8.64/4.89 ( ( times_times_int @ ( numeral_numeral_int @ V2 ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7346_semiring__norm_I171_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: real] :
% 8.64/4.89 ( ( times_times_real @ ( numeral_numeral_real @ V2 ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7347_semiring__norm_I171_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V2 ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7348_semiring__norm_I171_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V2 ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7349_semiring__norm_I171_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( numeral_numeral_rat @ V2 ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 8.64/4.89 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7350_semiring__norm_I170_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: int] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Y ) )
% 8.64/4.89 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7351_semiring__norm_I170_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: real] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V2 ) ) @ ( times_times_real @ ( numeral_numeral_real @ W2 ) @ Y ) )
% 8.64/4.89 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7352_semiring__norm_I170_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V2 ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ Y ) )
% 8.64/4.89 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7353_semiring__norm_I170_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V2 ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Y ) )
% 8.64/4.89 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7354_semiring__norm_I170_J,axiom,
% 8.64/4.89 ! [V2: num,W2: num,Y: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V2 ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Y ) )
% 8.64/4.89 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V2 @ W2 ) ) ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7355_neg__numeral__le__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7356_neg__numeral__le__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7357_neg__numeral__le__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7358_neg__numeral__le__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( ord_less_eq_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7359_neg__numeral__less__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( ord_less_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7360_neg__numeral__less__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( ord_less_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7361_neg__numeral__less__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( ord_less_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7362_neg__numeral__less__iff,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( ord_less_num @ N @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7363_dbl__dec__simps_I2_J,axiom,
% 8.64/4.89 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7364_dbl__dec__simps_I2_J,axiom,
% 8.64/4.89 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 8.64/4.89 = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7365_dbl__dec__simps_I2_J,axiom,
% 8.64/4.89 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7366_dbl__dec__simps_I2_J,axiom,
% 8.64/4.89 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7367_dbl__dec__simps_I2_J,axiom,
% 8.64/4.89 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 8.64/4.89 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7368_not__neg__one__le__neg__numeral__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7369_not__neg__one__le__neg__numeral__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7370_not__neg__one__le__neg__numeral__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7371_not__neg__one__le__neg__numeral__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7372_divide__le__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [B: real,W2: num,A: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 8.64/4.89 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7373_divide__le__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [B: rat,W2: num,A: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 8.64/4.89 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7374_le__divide__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [A: real,B: real,W2: num] :
% 8.64/4.89 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 8.64/4.89 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7375_le__divide__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [A: rat,B: rat,W2: num] :
% 8.64/4.89 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.64/4.89 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7376_divide__eq__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [B: real,W2: num,A: real] :
% 8.64/4.89 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.89 = A )
% 8.64/4.89 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.89 != zero_zero_real )
% 8.64/4.89 => ( B
% 8.64/4.89 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) )
% 8.64/4.89 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.89 = zero_zero_real )
% 8.64/4.89 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7377_divide__eq__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [B: complex,W2: num,A: complex] :
% 8.64/4.89 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 8.64/4.89 = A )
% 8.64/4.89 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.89 != zero_zero_complex )
% 8.64/4.89 => ( B
% 8.64/4.89 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) )
% 8.64/4.89 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.89 = zero_zero_complex )
% 8.64/4.89 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7378_divide__eq__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [B: rat,W2: num,A: rat] :
% 8.64/4.89 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.89 = A )
% 8.64/4.89 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.89 != zero_zero_rat )
% 8.64/4.89 => ( B
% 8.64/4.89 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 8.64/4.89 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.89 = zero_zero_rat )
% 8.64/4.89 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7379_eq__divide__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [A: real,B: real,W2: num] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 8.64/4.89 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.89 != zero_zero_real )
% 8.64/4.89 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.89 = zero_zero_real )
% 8.64/4.89 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7380_eq__divide__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [A: complex,B: complex,W2: num] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) )
% 8.64/4.89 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.89 != zero_zero_complex )
% 8.64/4.89 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.89 = zero_zero_complex )
% 8.64/4.89 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7381_eq__divide__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [A: rat,B: rat,W2: num] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.64/4.89 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.89 != zero_zero_rat )
% 8.64/4.89 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.89 = zero_zero_rat )
% 8.64/4.89 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7382_neg__numeral__less__neg__one__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7383_neg__numeral__less__neg__one__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7384_neg__numeral__less__neg__one__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7385_neg__numeral__less__neg__one__iff,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( M2 != one ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7386_less__divide__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [A: real,B: real,W2: num] :
% 8.64/4.89 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) )
% 8.64/4.89 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7387_less__divide__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [A: rat,B: rat,W2: num] :
% 8.64/4.89 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 8.64/4.89 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7388_divide__less__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [B: real,W2: num,A: real] :
% 8.64/4.89 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ A )
% 8.64/4.89 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7389_divide__less__eq__numeral1_I2_J,axiom,
% 8.64/4.89 ! [B: rat,W2: num,A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 8.64/4.89 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7390_dbl__dec__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7391_dbl__dec__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7392_dbl__dec__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7393_dbl__dec__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7394_dbl__dec__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7395_dbl__inc__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7396_dbl__inc__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7397_dbl__inc__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K2 ) ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7398_dbl__inc__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K2 ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7399_dbl__inc__simps_I1_J,axiom,
% 8.64/4.89 ! [K2: num] :
% 8.64/4.89 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K2 ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7400_signed__take__bit__Suc__minus__bit0,axiom,
% 8.64/4.89 ! [N: nat,K2: num] :
% 8.64/4.89 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 8.64/4.89 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7401_signed__take__bit__Suc__bit0,axiom,
% 8.64/4.89 ! [N: nat,K2: num] :
% 8.64/4.89 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) )
% 8.64/4.89 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7402_add__neg__numeral__special_I9_J,axiom,
% 8.64/4.89 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7403_add__neg__numeral__special_I9_J,axiom,
% 8.64/4.89 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7404_add__neg__numeral__special_I9_J,axiom,
% 8.64/4.89 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7405_add__neg__numeral__special_I9_J,axiom,
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7406_add__neg__numeral__special_I9_J,axiom,
% 8.64/4.89 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7407_diff__numeral__special_I11_J,axiom,
% 8.64/4.89 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7408_diff__numeral__special_I11_J,axiom,
% 8.64/4.89 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7409_diff__numeral__special_I11_J,axiom,
% 8.64/4.89 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7410_diff__numeral__special_I11_J,axiom,
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7411_diff__numeral__special_I11_J,axiom,
% 8.64/4.89 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7412_diff__numeral__special_I10_J,axiom,
% 8.64/4.89 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7413_diff__numeral__special_I10_J,axiom,
% 8.64/4.89 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7414_diff__numeral__special_I10_J,axiom,
% 8.64/4.89 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7415_diff__numeral__special_I10_J,axiom,
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7416_diff__numeral__special_I10_J,axiom,
% 8.64/4.89 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7417_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.64/4.89 ! [A: int,N: nat] :
% 8.64/4.89 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7418_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.64/4.89 ! [A: real,N: nat] :
% 8.64/4.89 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7419_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.64/4.89 ! [A: complex,N: nat] :
% 8.64/4.89 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7420_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.64/4.89 ! [A: code_integer,N: nat] :
% 8.64/4.89 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7421_Power_Oring__1__class_Opower__minus__even,axiom,
% 8.64/4.89 ! [A: rat,N: nat] :
% 8.64/4.89 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7422_diff__numeral__special_I4_J,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7423_diff__numeral__special_I4_J,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7424_diff__numeral__special_I4_J,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) ) @ one_one_complex )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7425_diff__numeral__special_I4_J,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7426_diff__numeral__special_I4_J,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M2 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7427_diff__numeral__special_I3_J,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7428_diff__numeral__special_I3_J,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7429_diff__numeral__special_I3_J,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 8.64/4.89 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7430_diff__numeral__special_I3_J,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.89 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7431_diff__numeral__special_I3_J,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.89 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7432_set__decode__Suc,axiom,
% 8.64/4.89 ! [N: nat,X: nat] :
% 8.64/4.89 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 8.64/4.89 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7433_dbl__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7434_dbl__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7435_dbl__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7436_dbl__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7437_dbl__simps_I4_J,axiom,
% 8.64/4.89 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7438_power__minus1__even,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = one_one_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7439_power__minus1__even,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = one_one_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7440_power__minus1__even,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = one_one_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7441_power__minus1__even,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = one_one_Code_integer ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7442_power__minus1__even,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.89 = one_one_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7443_signed__take__bit__0,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7444_signed__take__bit__0,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 8.64/4.89 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7445_equation__minus__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7446_equation__minus__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7447_equation__minus__iff,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7448_equation__minus__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7449_equation__minus__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7450_minus__equation__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( uminus_uminus_int @ B )
% 8.64/4.89 = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7451_minus__equation__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( uminus_uminus_real @ B )
% 8.64/4.89 = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7452_minus__equation__iff,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( uminus1482373934393186551omplex @ B )
% 8.64/4.89 = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7453_minus__equation__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( uminus1351360451143612070nteger @ B )
% 8.64/4.89 = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7454_minus__equation__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( uminus_uminus_rat @ B )
% 8.64/4.89 = A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7455_fact__mono__nat,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7456_fact__ge__self,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7457_fact__nonzero,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri5044797733671781792omplex @ N )
% 8.64/4.89 != zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7458_fact__nonzero,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri773545260158071498ct_rat @ N )
% 8.64/4.89 != zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7459_fact__nonzero,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri1406184849735516958ct_int @ N )
% 8.64/4.89 != zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7460_fact__nonzero,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri1408675320244567234ct_nat @ N )
% 8.64/4.89 != zero_zero_nat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7461_fact__nonzero,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( semiri2265585572941072030t_real @ N )
% 8.64/4.89 != zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7462_compl__le__swap2,axiom,
% 8.64/4.89 ! [Y: set_nat,X: set_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ X )
% 8.64/4.89 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7463_compl__le__swap1,axiom,
% 8.64/4.89 ! [Y: set_nat,X: set_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) )
% 8.64/4.89 => ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7464_compl__mono,axiom,
% 8.64/4.89 ! [X: set_nat,Y: set_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ X @ Y )
% 8.64/4.89 => ( ord_less_eq_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ ( uminus5710092332889474511et_nat @ X ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7465_le__imp__neg__le,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ A @ B )
% 8.64/4.89 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7466_le__imp__neg__le,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.64/4.89 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7467_le__imp__neg__le,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.89 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7468_le__imp__neg__le,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ A @ B )
% 8.64/4.89 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7469_minus__le__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 8.64/4.89 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7470_minus__le__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.64/4.89 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7471_minus__le__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.64/4.89 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7472_minus__le__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7473_le__minus__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7474_le__minus__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7475_le__minus__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7476_le__minus__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7477_less__minus__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7478_less__minus__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7479_less__minus__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7480_less__minus__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7481_minus__less__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7482_minus__less__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 8.64/4.89 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7483_minus__less__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.64/4.89 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7484_minus__less__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.64/4.89 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7485_neg__numeral__neq__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) )
% 8.64/4.89 != ( numeral_numeral_int @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7486_neg__numeral__neq__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) )
% 8.64/4.89 != ( numeral_numeral_real @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7487_neg__numeral__neq__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M2 ) )
% 8.64/4.89 != ( numera6690914467698888265omplex @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7488_neg__numeral__neq__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) )
% 8.64/4.89 != ( numera6620942414471956472nteger @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7489_neg__numeral__neq__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) )
% 8.64/4.89 != ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7490_numeral__neq__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( numeral_numeral_int @ M2 )
% 8.64/4.89 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7491_numeral__neq__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( numeral_numeral_real @ M2 )
% 8.64/4.89 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7492_numeral__neq__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( numera6690914467698888265omplex @ M2 )
% 8.64/4.89 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7493_numeral__neq__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( numera6620942414471956472nteger @ M2 )
% 8.64/4.89 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7494_numeral__neq__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ( ( numeral_numeral_rat @ M2 )
% 8.64/4.89 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7495_minus__mult__commute,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7496_minus__mult__commute,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 8.64/4.89 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7497_minus__mult__commute,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.64/4.89 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7498_minus__mult__commute,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.64/4.89 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7499_minus__mult__commute,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.64/4.89 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7500_square__eq__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( times_times_int @ A @ A )
% 8.64/4.89 = ( times_times_int @ B @ B ) )
% 8.64/4.89 = ( ( A = B )
% 8.64/4.89 | ( A
% 8.64/4.89 = ( uminus_uminus_int @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7501_square__eq__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ( times_times_real @ A @ A )
% 8.64/4.89 = ( times_times_real @ B @ B ) )
% 8.64/4.89 = ( ( A = B )
% 8.64/4.89 | ( A
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7502_square__eq__iff,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( ( times_times_complex @ A @ A )
% 8.64/4.89 = ( times_times_complex @ B @ B ) )
% 8.64/4.89 = ( ( A = B )
% 8.64/4.89 | ( A
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7503_square__eq__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ( times_3573771949741848930nteger @ A @ A )
% 8.64/4.89 = ( times_3573771949741848930nteger @ B @ B ) )
% 8.64/4.89 = ( ( A = B )
% 8.64/4.89 | ( A
% 8.64/4.89 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7504_square__eq__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ( times_times_rat @ A @ A )
% 8.64/4.89 = ( times_times_rat @ B @ B ) )
% 8.64/4.89 = ( ( A = B )
% 8.64/4.89 | ( A
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7505_is__num__normalize_I8_J,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.64/4.89 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7506_is__num__normalize_I8_J,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 8.64/4.89 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7507_is__num__normalize_I8_J,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 8.64/4.89 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7508_is__num__normalize_I8_J,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7509_is__num__normalize_I8_J,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.64/4.89 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7510_group__cancel_Oneg1,axiom,
% 8.64/4.89 ! [A4: int,K2: int,A: int] :
% 8.64/4.89 ( ( A4
% 8.64/4.89 = ( plus_plus_int @ K2 @ A ) )
% 8.64/4.89 => ( ( uminus_uminus_int @ A4 )
% 8.64/4.89 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7511_group__cancel_Oneg1,axiom,
% 8.64/4.89 ! [A4: real,K2: real,A: real] :
% 8.64/4.89 ( ( A4
% 8.64/4.89 = ( plus_plus_real @ K2 @ A ) )
% 8.64/4.89 => ( ( uminus_uminus_real @ A4 )
% 8.64/4.89 = ( plus_plus_real @ ( uminus_uminus_real @ K2 ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7512_group__cancel_Oneg1,axiom,
% 8.64/4.89 ! [A4: complex,K2: complex,A: complex] :
% 8.64/4.89 ( ( A4
% 8.64/4.89 = ( plus_plus_complex @ K2 @ A ) )
% 8.64/4.89 => ( ( uminus1482373934393186551omplex @ A4 )
% 8.64/4.89 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K2 ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7513_group__cancel_Oneg1,axiom,
% 8.64/4.89 ! [A4: code_integer,K2: code_integer,A: code_integer] :
% 8.64/4.89 ( ( A4
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ K2 @ A ) )
% 8.64/4.89 => ( ( uminus1351360451143612070nteger @ A4 )
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7514_group__cancel_Oneg1,axiom,
% 8.64/4.89 ! [A4: rat,K2: rat,A: rat] :
% 8.64/4.89 ( ( A4
% 8.64/4.89 = ( plus_plus_rat @ K2 @ A ) )
% 8.64/4.89 => ( ( uminus_uminus_rat @ A4 )
% 8.64/4.89 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7515_add_Oinverse__distrib__swap,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 8.64/4.89 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7516_add_Oinverse__distrib__swap,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 8.64/4.89 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7517_add_Oinverse__distrib__swap,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 8.64/4.89 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7518_add_Oinverse__distrib__swap,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7519_add_Oinverse__distrib__swap,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 8.64/4.89 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7520_one__neq__neg__one,axiom,
% 8.64/4.89 ( one_one_int
% 8.64/4.89 != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7521_one__neq__neg__one,axiom,
% 8.64/4.89 ( one_one_real
% 8.64/4.89 != ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7522_one__neq__neg__one,axiom,
% 8.64/4.89 ( one_one_complex
% 8.64/4.89 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7523_one__neq__neg__one,axiom,
% 8.64/4.89 ( one_one_Code_integer
% 8.64/4.89 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7524_one__neq__neg__one,axiom,
% 8.64/4.89 ( one_one_rat
% 8.64/4.89 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7525_minus__diff__commute,axiom,
% 8.64/4.89 ! [B: int,A: int] :
% 8.64/4.89 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 8.64/4.89 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7526_minus__diff__commute,axiom,
% 8.64/4.89 ! [B: real,A: real] :
% 8.64/4.89 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 8.64/4.89 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7527_minus__diff__commute,axiom,
% 8.64/4.89 ! [B: complex,A: complex] :
% 8.64/4.89 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 8.64/4.89 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7528_minus__diff__commute,axiom,
% 8.64/4.89 ! [B: code_integer,A: code_integer] :
% 8.64/4.89 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 8.64/4.89 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7529_minus__diff__commute,axiom,
% 8.64/4.89 ! [B: rat,A: rat] :
% 8.64/4.89 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 8.64/4.89 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7530_signed__take__bit__mult,axiom,
% 8.64/4.89 ! [N: nat,K2: int,L: int] :
% 8.64/4.89 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K2 ) @ ( bit_ri631733984087533419it_int @ N @ L ) ) )
% 8.64/4.89 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K2 @ L ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7531_fact__less__mono__nat,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.89 => ( ( ord_less_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7532_fact__ge__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7533_fact__ge__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7534_fact__ge__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7535_fact__ge__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7536_fact__not__neg,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N ) @ zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7537_fact__not__neg,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N ) @ zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7538_fact__not__neg,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N ) @ zero_zero_nat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7539_fact__not__neg,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N ) @ zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7540_fact__gt__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7541_fact__gt__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7542_fact__gt__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7543_fact__gt__zero,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7544_finite__set__decode,axiom,
% 8.64/4.89 ! [N: nat] : ( finite_finite_nat @ ( nat_set_decode @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7545_fact__ge__1,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7546_fact__ge__1,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7547_fact__ge__1,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7548_fact__ge__1,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7549_fact__ge__1,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7550_neg__numeral__le__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7551_neg__numeral__le__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7552_neg__numeral__le__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7553_neg__numeral__le__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7554_not__numeral__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7555_not__numeral__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7556_not__numeral__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7557_not__numeral__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7558_zero__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( zero_zero_int
% 8.64/4.89 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7559_zero__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( zero_zero_real
% 8.64/4.89 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7560_zero__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( zero_zero_complex
% 8.64/4.89 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7561_zero__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( zero_z3403309356797280102nteger
% 8.64/4.89 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7562_zero__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( zero_zero_rat
% 8.64/4.89 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7563_not__numeral__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7564_not__numeral__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7565_not__numeral__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7566_not__numeral__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] :
% 8.64/4.89 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7567_neg__numeral__less__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7568_neg__numeral__less__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( numeral_numeral_real @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7569_neg__numeral__less__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7570_neg__numeral__less__numeral,axiom,
% 8.64/4.89 ! [M2: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7571_le__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7572_le__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7573_le__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7574_le__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7575_le__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7576_le__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7577_le__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7578_le__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7579_add__eq__0__iff,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( plus_plus_int @ A @ B )
% 8.64/4.89 = zero_zero_int )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7580_add__eq__0__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ( plus_plus_real @ A @ B )
% 8.64/4.89 = zero_zero_real )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7581_add__eq__0__iff,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( ( plus_plus_complex @ A @ B )
% 8.64/4.89 = zero_zero_complex )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7582_add__eq__0__iff,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.64/4.89 = zero_z3403309356797280102nteger )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7583_add__eq__0__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ( plus_plus_rat @ A @ B )
% 8.64/4.89 = zero_zero_rat )
% 8.64/4.89 = ( B
% 8.64/4.89 = ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7584_ab__group__add__class_Oab__left__minus,axiom,
% 8.64/4.89 ! [A: int] :
% 8.64/4.89 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 8.64/4.89 = zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7585_ab__group__add__class_Oab__left__minus,axiom,
% 8.64/4.89 ! [A: real] :
% 8.64/4.89 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 8.64/4.89 = zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7586_ab__group__add__class_Oab__left__minus,axiom,
% 8.64/4.89 ! [A: complex] :
% 8.64/4.89 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 8.64/4.89 = zero_zero_complex ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7587_ab__group__add__class_Oab__left__minus,axiom,
% 8.64/4.89 ! [A: code_integer] :
% 8.64/4.89 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7588_ab__group__add__class_Oab__left__minus,axiom,
% 8.64/4.89 ! [A: rat] :
% 8.64/4.89 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 8.64/4.89 = zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7589_add_Oinverse__unique,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( plus_plus_int @ A @ B )
% 8.64/4.89 = zero_zero_int )
% 8.64/4.89 => ( ( uminus_uminus_int @ A )
% 8.64/4.89 = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7590_add_Oinverse__unique,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ( plus_plus_real @ A @ B )
% 8.64/4.89 = zero_zero_real )
% 8.64/4.89 => ( ( uminus_uminus_real @ A )
% 8.64/4.89 = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7591_add_Oinverse__unique,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( ( plus_plus_complex @ A @ B )
% 8.64/4.89 = zero_zero_complex )
% 8.64/4.89 => ( ( uminus1482373934393186551omplex @ A )
% 8.64/4.89 = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7592_add_Oinverse__unique,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.64/4.89 = zero_z3403309356797280102nteger )
% 8.64/4.89 => ( ( uminus1351360451143612070nteger @ A )
% 8.64/4.89 = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7593_add_Oinverse__unique,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ( plus_plus_rat @ A @ B )
% 8.64/4.89 = zero_zero_rat )
% 8.64/4.89 => ( ( uminus_uminus_rat @ A )
% 8.64/4.89 = B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7594_eq__neg__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( ( plus_plus_int @ A @ B )
% 8.64/4.89 = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7595_eq__neg__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( ( plus_plus_real @ A @ B )
% 8.64/4.89 = zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7596_eq__neg__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( ( plus_plus_complex @ A @ B )
% 8.64/4.89 = zero_zero_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7597_eq__neg__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7598_eq__neg__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( ( plus_plus_rat @ A @ B )
% 8.64/4.89 = zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7599_neg__eq__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( uminus_uminus_int @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( plus_plus_int @ A @ B )
% 8.64/4.89 = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7600_neg__eq__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( plus_plus_real @ A @ B )
% 8.64/4.89 = zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7601_neg__eq__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( plus_plus_complex @ A @ B )
% 8.64/4.89 = zero_zero_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7602_neg__eq__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: code_integer,B: code_integer] :
% 8.64/4.89 ( ( ( uminus1351360451143612070nteger @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7603_neg__eq__iff__add__eq__0,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ A )
% 8.64/4.89 = B )
% 8.64/4.89 = ( ( plus_plus_rat @ A @ B )
% 8.64/4.89 = zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7604_zero__neq__neg__one,axiom,
% 8.64/4.89 ( zero_zero_int
% 8.64/4.89 != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7605_zero__neq__neg__one,axiom,
% 8.64/4.89 ( zero_zero_real
% 8.64/4.89 != ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7606_zero__neq__neg__one,axiom,
% 8.64/4.89 ( zero_zero_complex
% 8.64/4.89 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7607_zero__neq__neg__one,axiom,
% 8.64/4.89 ( zero_z3403309356797280102nteger
% 8.64/4.89 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7608_zero__neq__neg__one,axiom,
% 8.64/4.89 ( zero_zero_rat
% 8.64/4.89 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7609_less__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7610_less__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7611_less__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7612_less__minus__one__simps_I4_J,axiom,
% 8.64/4.89 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7613_less__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7614_less__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7615_less__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7616_less__minus__one__simps_I2_J,axiom,
% 8.64/4.89 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7617_numeral__times__minus__swap,axiom,
% 8.64/4.89 ! [W2: num,X: int] :
% 8.64/4.89 ( ( times_times_int @ ( numeral_numeral_int @ W2 ) @ ( uminus_uminus_int @ X ) )
% 8.64/4.89 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7618_numeral__times__minus__swap,axiom,
% 8.64/4.89 ! [W2: num,X: real] :
% 8.64/4.89 ( ( times_times_real @ ( numeral_numeral_real @ W2 ) @ ( uminus_uminus_real @ X ) )
% 8.64/4.89 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7619_numeral__times__minus__swap,axiom,
% 8.64/4.89 ! [W2: num,X: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W2 ) @ ( uminus1482373934393186551omplex @ X ) )
% 8.64/4.89 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7620_numeral__times__minus__swap,axiom,
% 8.64/4.89 ! [W2: num,X: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ ( uminus1351360451143612070nteger @ X ) )
% 8.64/4.89 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7621_numeral__times__minus__swap,axiom,
% 8.64/4.89 ! [W2: num,X: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ ( uminus_uminus_rat @ X ) )
% 8.64/4.89 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7622_nonzero__minus__divide__divide,axiom,
% 8.64/4.89 ! [B: real,A: real] :
% 8.64/4.89 ( ( B != zero_zero_real )
% 8.64/4.89 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( divide_divide_real @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7623_nonzero__minus__divide__divide,axiom,
% 8.64/4.89 ! [B: complex,A: complex] :
% 8.64/4.89 ( ( B != zero_zero_complex )
% 8.64/4.89 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7624_nonzero__minus__divide__divide,axiom,
% 8.64/4.89 ! [B: rat,A: rat] :
% 8.64/4.89 ( ( B != zero_zero_rat )
% 8.64/4.89 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( divide_divide_rat @ A @ B ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7625_nonzero__minus__divide__right,axiom,
% 8.64/4.89 ! [B: real,A: real] :
% 8.64/4.89 ( ( B != zero_zero_real )
% 8.64/4.89 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 8.64/4.89 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7626_nonzero__minus__divide__right,axiom,
% 8.64/4.89 ! [B: complex,A: complex] :
% 8.64/4.89 ( ( B != zero_zero_complex )
% 8.64/4.89 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.64/4.89 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7627_nonzero__minus__divide__right,axiom,
% 8.64/4.89 ! [B: rat,A: rat] :
% 8.64/4.89 ( ( B != zero_zero_rat )
% 8.64/4.89 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.64/4.89 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7628_one__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( one_one_int
% 8.64/4.89 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7629_one__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( one_one_real
% 8.64/4.89 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7630_one__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( one_one_complex
% 8.64/4.89 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7631_one__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( one_one_Code_integer
% 8.64/4.89 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7632_one__neq__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( one_one_rat
% 8.64/4.89 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7633_numeral__neq__neg__one,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( numeral_numeral_int @ N )
% 8.64/4.89 != ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7634_numeral__neq__neg__one,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( numeral_numeral_real @ N )
% 8.64/4.89 != ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7635_numeral__neq__neg__one,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( numera6690914467698888265omplex @ N )
% 8.64/4.89 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7636_numeral__neq__neg__one,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( numera6620942414471956472nteger @ N )
% 8.64/4.89 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7637_numeral__neq__neg__one,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ( ( numeral_numeral_rat @ N )
% 8.64/4.89 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7638_square__eq__1__iff,axiom,
% 8.64/4.89 ! [X: int] :
% 8.64/4.89 ( ( ( times_times_int @ X @ X )
% 8.64/4.89 = one_one_int )
% 8.64/4.89 = ( ( X = one_one_int )
% 8.64/4.89 | ( X
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7639_square__eq__1__iff,axiom,
% 8.64/4.89 ! [X: real] :
% 8.64/4.89 ( ( ( times_times_real @ X @ X )
% 8.64/4.89 = one_one_real )
% 8.64/4.89 = ( ( X = one_one_real )
% 8.64/4.89 | ( X
% 8.64/4.89 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7640_square__eq__1__iff,axiom,
% 8.64/4.89 ! [X: complex] :
% 8.64/4.89 ( ( ( times_times_complex @ X @ X )
% 8.64/4.89 = one_one_complex )
% 8.64/4.89 = ( ( X = one_one_complex )
% 8.64/4.89 | ( X
% 8.64/4.89 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7641_square__eq__1__iff,axiom,
% 8.64/4.89 ! [X: code_integer] :
% 8.64/4.89 ( ( ( times_3573771949741848930nteger @ X @ X )
% 8.64/4.89 = one_one_Code_integer )
% 8.64/4.89 = ( ( X = one_one_Code_integer )
% 8.64/4.89 | ( X
% 8.64/4.89 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7642_square__eq__1__iff,axiom,
% 8.64/4.89 ! [X: rat] :
% 8.64/4.89 ( ( ( times_times_rat @ X @ X )
% 8.64/4.89 = one_one_rat )
% 8.64/4.89 = ( ( X = one_one_rat )
% 8.64/4.89 | ( X
% 8.64/4.89 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7643_fact__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7644_fact__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7645_fact__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7646_fact__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7647_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_int
% 8.64/4.89 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7648_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_real
% 8.64/4.89 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7649_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_complex
% 8.64/4.89 = ( ^ [A5: complex,B4: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7650_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_8373710615458151222nteger
% 8.64/4.89 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7651_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_rat
% 8.64/4.89 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7652_diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_int
% 8.64/4.89 = ( ^ [A5: int,B4: int] : ( plus_plus_int @ A5 @ ( uminus_uminus_int @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7653_diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_real
% 8.64/4.89 = ( ^ [A5: real,B4: real] : ( plus_plus_real @ A5 @ ( uminus_uminus_real @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7654_diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_complex
% 8.64/4.89 = ( ^ [A5: complex,B4: complex] : ( plus_plus_complex @ A5 @ ( uminus1482373934393186551omplex @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7655_diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_8373710615458151222nteger
% 8.64/4.89 = ( ^ [A5: code_integer,B4: code_integer] : ( plus_p5714425477246183910nteger @ A5 @ ( uminus1351360451143612070nteger @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7656_diff__conv__add__uminus,axiom,
% 8.64/4.89 ( minus_minus_rat
% 8.64/4.89 = ( ^ [A5: rat,B4: rat] : ( plus_plus_rat @ A5 @ ( uminus_uminus_rat @ B4 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7657_group__cancel_Osub2,axiom,
% 8.64/4.89 ! [B5: int,K2: int,B: int,A: int] :
% 8.64/4.89 ( ( B5
% 8.64/4.89 = ( plus_plus_int @ K2 @ B ) )
% 8.64/4.89 => ( ( minus_minus_int @ A @ B5 )
% 8.64/4.89 = ( plus_plus_int @ ( uminus_uminus_int @ K2 ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7658_group__cancel_Osub2,axiom,
% 8.64/4.89 ! [B5: real,K2: real,B: real,A: real] :
% 8.64/4.89 ( ( B5
% 8.64/4.89 = ( plus_plus_real @ K2 @ B ) )
% 8.64/4.89 => ( ( minus_minus_real @ A @ B5 )
% 8.64/4.89 = ( plus_plus_real @ ( uminus_uminus_real @ K2 ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7659_group__cancel_Osub2,axiom,
% 8.64/4.89 ! [B5: complex,K2: complex,B: complex,A: complex] :
% 8.64/4.89 ( ( B5
% 8.64/4.89 = ( plus_plus_complex @ K2 @ B ) )
% 8.64/4.89 => ( ( minus_minus_complex @ A @ B5 )
% 8.64/4.89 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K2 ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7660_group__cancel_Osub2,axiom,
% 8.64/4.89 ! [B5: code_integer,K2: code_integer,B: code_integer,A: code_integer] :
% 8.64/4.89 ( ( B5
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ K2 @ B ) )
% 8.64/4.89 => ( ( minus_8373710615458151222nteger @ A @ B5 )
% 8.64/4.89 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K2 ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7661_group__cancel_Osub2,axiom,
% 8.64/4.89 ! [B5: rat,K2: rat,B: rat,A: rat] :
% 8.64/4.89 ( ( B5
% 8.64/4.89 = ( plus_plus_rat @ K2 @ B ) )
% 8.64/4.89 => ( ( minus_minus_rat @ A @ B5 )
% 8.64/4.89 = ( plus_plus_rat @ ( uminus_uminus_rat @ K2 ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7662_dvd__neg__div,axiom,
% 8.64/4.89 ! [B: int,A: int] :
% 8.64/4.89 ( ( dvd_dvd_int @ B @ A )
% 8.64/4.89 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7663_dvd__neg__div,axiom,
% 8.64/4.89 ! [B: real,A: real] :
% 8.64/4.89 ( ( dvd_dvd_real @ B @ A )
% 8.64/4.89 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 8.64/4.89 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7664_dvd__neg__div,axiom,
% 8.64/4.89 ! [B: complex,A: complex] :
% 8.64/4.89 ( ( dvd_dvd_complex @ B @ A )
% 8.64/4.89 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7665_dvd__neg__div,axiom,
% 8.64/4.89 ! [B: code_integer,A: code_integer] :
% 8.64/4.89 ( ( dvd_dvd_Code_integer @ B @ A )
% 8.64/4.89 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7666_dvd__neg__div,axiom,
% 8.64/4.89 ! [B: rat,A: rat] :
% 8.64/4.89 ( ( dvd_dvd_rat @ B @ A )
% 8.64/4.89 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7667_dvd__div__neg,axiom,
% 8.64/4.89 ! [B: int,A: int] :
% 8.64/4.89 ( ( dvd_dvd_int @ B @ A )
% 8.64/4.89 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7668_dvd__div__neg,axiom,
% 8.64/4.89 ! [B: real,A: real] :
% 8.64/4.89 ( ( dvd_dvd_real @ B @ A )
% 8.64/4.89 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 8.64/4.89 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7669_dvd__div__neg,axiom,
% 8.64/4.89 ! [B: complex,A: complex] :
% 8.64/4.89 ( ( dvd_dvd_complex @ B @ A )
% 8.64/4.89 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7670_dvd__div__neg,axiom,
% 8.64/4.89 ! [B: code_integer,A: code_integer] :
% 8.64/4.89 ( ( dvd_dvd_Code_integer @ B @ A )
% 8.64/4.89 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7671_dvd__div__neg,axiom,
% 8.64/4.89 ! [B: rat,A: rat] :
% 8.64/4.89 ( ( dvd_dvd_rat @ B @ A )
% 8.64/4.89 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 8.64/4.89 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7672_fact__dvd,axiom,
% 8.64/4.89 ! [N: nat,M2: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.89 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7673_fact__dvd,axiom,
% 8.64/4.89 ! [N: nat,M2: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.89 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7674_fact__dvd,axiom,
% 8.64/4.89 ! [N: nat,M2: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.89 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7675_real__minus__mult__self__le,axiom,
% 8.64/4.89 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7676_int__of__nat__induct,axiom,
% 8.64/4.89 ! [P2: int > $o,Z3: int] :
% 8.64/4.89 ( ! [N3: nat] : ( P2 @ ( semiri1314217659103216013at_int @ N3 ) )
% 8.64/4.89 => ( ! [N3: nat] : ( P2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 8.64/4.89 => ( P2 @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7677_int__cases,axiom,
% 8.64/4.89 ! [Z3: int] :
% 8.64/4.89 ( ! [N3: nat] :
% 8.64/4.89 ( Z3
% 8.64/4.89 != ( semiri1314217659103216013at_int @ N3 ) )
% 8.64/4.89 => ~ ! [N3: nat] :
% 8.64/4.89 ( Z3
% 8.64/4.89 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7678_zmult__eq__1__iff,axiom,
% 8.64/4.89 ! [M2: int,N: int] :
% 8.64/4.89 ( ( ( times_times_int @ M2 @ N )
% 8.64/4.89 = one_one_int )
% 8.64/4.89 = ( ( ( M2 = one_one_int )
% 8.64/4.89 & ( N = one_one_int ) )
% 8.64/4.89 | ( ( M2
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.89 & ( N
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7679_pos__zmult__eq__1__iff__lemma,axiom,
% 8.64/4.89 ! [M2: int,N: int] :
% 8.64/4.89 ( ( ( times_times_int @ M2 @ N )
% 8.64/4.89 = one_one_int )
% 8.64/4.89 => ( ( M2 = one_one_int )
% 8.64/4.89 | ( M2
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7680_zmod__zminus1__not__zero,axiom,
% 8.64/4.89 ! [K2: int,L: int] :
% 8.64/4.89 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K2 ) @ L )
% 8.64/4.89 != zero_zero_int )
% 8.64/4.89 => ( ( modulo_modulo_int @ K2 @ L )
% 8.64/4.89 != zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7681_zmod__zminus2__not__zero,axiom,
% 8.64/4.89 ! [K2: int,L: int] :
% 8.64/4.89 ( ( ( modulo_modulo_int @ K2 @ ( uminus_uminus_int @ L ) )
% 8.64/4.89 != zero_zero_int )
% 8.64/4.89 => ( ( modulo_modulo_int @ K2 @ L )
% 8.64/4.89 != zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7682_pochhammer__same,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ N )
% 8.64/4.89 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7683_pochhammer__same,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ N )
% 8.64/4.89 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( semiri3624122377584611663nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7684_pochhammer__same,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ N )
% 8.64/4.89 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7685_pochhammer__same,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ N )
% 8.64/4.89 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7686_pochhammer__same,axiom,
% 8.64/4.89 ! [N: nat] :
% 8.64/4.89 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ N )
% 8.64/4.89 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7687_fact__ge__Suc__0__nat,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7688_dvd__fact,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 8.64/4.89 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( dvd_dvd_nat @ M2 @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7689_not__zero__le__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7690_not__zero__le__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7691_not__zero__le__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7692_not__zero__le__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7693_neg__numeral__le__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7694_neg__numeral__le__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7695_neg__numeral__le__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7696_neg__numeral__le__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7697_not__zero__less__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7698_not__zero__less__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7699_not__zero__less__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7700_not__zero__less__neg__numeral,axiom,
% 8.64/4.89 ! [N: num] :
% 8.64/4.89 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7701_neg__numeral__less__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7702_neg__numeral__less__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7703_neg__numeral__less__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7704_neg__numeral__less__zero,axiom,
% 8.64/4.89 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7705_le__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7706_le__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7707_le__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7708_le__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7709_le__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7710_le__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7711_le__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7712_le__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7713_less__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7714_less__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7715_less__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7716_less__minus__one__simps_I1_J,axiom,
% 8.64/4.89 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7717_less__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7718_less__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7719_less__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7720_less__minus__one__simps_I3_J,axiom,
% 8.64/4.89 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7721_not__one__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7722_not__one__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7723_not__one__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7724_not__one__le__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7725_not__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7726_not__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7727_not__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7728_not__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7729_neg__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7730_neg__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7731_neg__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7732_neg__numeral__le__neg__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7733_neg__one__le__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7734_neg__one__le__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7735_neg__one__le__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7736_neg__one__le__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7737_neg__numeral__le__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7738_neg__numeral__le__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7739_neg__numeral__le__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7740_neg__numeral__le__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7741_gbinomial__pochhammer,axiom,
% 8.64/4.89 ( gbinomial_complex
% 8.64/4.89 = ( ^ [A5: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A5 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7742_gbinomial__pochhammer,axiom,
% 8.64/4.89 ( gbinomial_rat
% 8.64/4.89 = ( ^ [A5: rat,K3: nat] : ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ A5 ) @ K3 ) ) @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7743_gbinomial__pochhammer,axiom,
% 8.64/4.89 ( gbinomial_real
% 8.64/4.89 = ( ^ [A5: real,K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ A5 ) @ K3 ) ) @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7744_neg__numeral__less__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ one_one_int ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7745_neg__numeral__less__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) @ one_one_real ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7746_neg__numeral__less__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) @ one_one_Code_integer ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7747_neg__numeral__less__one,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) @ one_one_rat ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7748_neg__one__less__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7749_neg__one__less__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7750_neg__one__less__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7751_neg__one__less__numeral,axiom,
% 8.64/4.89 ! [M2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7752_not__numeral__less__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7753_not__numeral__less__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_real @ ( numeral_numeral_real @ M2 ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7754_not__numeral__less__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7755_not__numeral__less__neg__one,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M2 ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7756_not__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7757_not__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7758_not__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7759_not__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7760_not__neg__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7761_not__neg__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7762_not__neg__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7763_not__neg__one__less__neg__numeral,axiom,
% 8.64/4.89 ! [M2: num] :
% 8.64/4.89 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7764_eq__minus__divide__eq,axiom,
% 8.64/4.89 ! [A: real,B: real,C2: real] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_real )
% 8.64/4.89 => ( ( times_times_real @ A @ C2 )
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_real )
% 8.64/4.89 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7765_eq__minus__divide__eq,axiom,
% 8.64/4.89 ! [A: complex,B: complex,C2: complex] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C2 ) ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.89 => ( ( times_times_complex @ A @ C2 )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_complex )
% 8.64/4.89 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7766_eq__minus__divide__eq,axiom,
% 8.64/4.89 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.89 ( ( A
% 8.64/4.89 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.89 => ( ( times_times_rat @ A @ C2 )
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_rat )
% 8.64/4.89 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7767_minus__divide__eq__eq,axiom,
% 8.64/4.89 ! [B: real,C2: real,A: real] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.89 = A )
% 8.64/4.89 = ( ( ( C2 != zero_zero_real )
% 8.64/4.89 => ( ( uminus_uminus_real @ B )
% 8.64/4.89 = ( times_times_real @ A @ C2 ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_real )
% 8.64/4.89 => ( A = zero_zero_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7768_minus__divide__eq__eq,axiom,
% 8.64/4.89 ! [B: complex,C2: complex,A: complex] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.89 = A )
% 8.64/4.89 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.89 => ( ( uminus1482373934393186551omplex @ B )
% 8.64/4.89 = ( times_times_complex @ A @ C2 ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_complex )
% 8.64/4.89 => ( A = zero_zero_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7769_minus__divide__eq__eq,axiom,
% 8.64/4.89 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.89 = A )
% 8.64/4.89 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.89 => ( ( uminus_uminus_rat @ B )
% 8.64/4.89 = ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_rat )
% 8.64/4.89 => ( A = zero_zero_rat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7770_nonzero__neg__divide__eq__eq,axiom,
% 8.64/4.89 ! [B: real,A: real,C2: real] :
% 8.64/4.89 ( ( B != zero_zero_real )
% 8.64/4.89 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 8.64/4.89 = C2 )
% 8.64/4.89 = ( ( uminus_uminus_real @ A )
% 8.64/4.89 = ( times_times_real @ C2 @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7771_nonzero__neg__divide__eq__eq,axiom,
% 8.64/4.89 ! [B: complex,A: complex,C2: complex] :
% 8.64/4.89 ( ( B != zero_zero_complex )
% 8.64/4.89 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.64/4.89 = C2 )
% 8.64/4.89 = ( ( uminus1482373934393186551omplex @ A )
% 8.64/4.89 = ( times_times_complex @ C2 @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7772_nonzero__neg__divide__eq__eq,axiom,
% 8.64/4.89 ! [B: rat,A: rat,C2: rat] :
% 8.64/4.89 ( ( B != zero_zero_rat )
% 8.64/4.89 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 8.64/4.89 = C2 )
% 8.64/4.89 = ( ( uminus_uminus_rat @ A )
% 8.64/4.89 = ( times_times_rat @ C2 @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7773_nonzero__neg__divide__eq__eq2,axiom,
% 8.64/4.89 ! [B: real,C2: real,A: real] :
% 8.64/4.89 ( ( B != zero_zero_real )
% 8.64/4.89 => ( ( C2
% 8.64/4.89 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 8.64/4.89 = ( ( times_times_real @ C2 @ B )
% 8.64/4.89 = ( uminus_uminus_real @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7774_nonzero__neg__divide__eq__eq2,axiom,
% 8.64/4.89 ! [B: complex,C2: complex,A: complex] :
% 8.64/4.89 ( ( B != zero_zero_complex )
% 8.64/4.89 => ( ( C2
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.64/4.89 = ( ( times_times_complex @ C2 @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7775_nonzero__neg__divide__eq__eq2,axiom,
% 8.64/4.89 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.89 ( ( B != zero_zero_rat )
% 8.64/4.89 => ( ( C2
% 8.64/4.89 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 8.64/4.89 = ( ( times_times_rat @ C2 @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7776_mult__1s__ring__1_I1_J,axiom,
% 8.64/4.89 ! [B: int] :
% 8.64/4.89 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 8.64/4.89 = ( uminus_uminus_int @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7777_mult__1s__ring__1_I1_J,axiom,
% 8.64/4.89 ! [B: real] :
% 8.64/4.89 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7778_mult__1s__ring__1_I1_J,axiom,
% 8.64/4.89 ! [B: complex] :
% 8.64/4.89 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7779_mult__1s__ring__1_I1_J,axiom,
% 8.64/4.89 ! [B: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7780_mult__1s__ring__1_I1_J,axiom,
% 8.64/4.89 ! [B: rat] :
% 8.64/4.89 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7781_mult__1s__ring__1_I2_J,axiom,
% 8.64/4.89 ! [B: int] :
% 8.64/4.89 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 8.64/4.89 = ( uminus_uminus_int @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7782_mult__1s__ring__1_I2_J,axiom,
% 8.64/4.89 ! [B: real] :
% 8.64/4.89 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7783_mult__1s__ring__1_I2_J,axiom,
% 8.64/4.89 ! [B: complex] :
% 8.64/4.89 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7784_mult__1s__ring__1_I2_J,axiom,
% 8.64/4.89 ! [B: code_integer] :
% 8.64/4.89 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7785_mult__1s__ring__1_I2_J,axiom,
% 8.64/4.89 ! [B: rat] :
% 8.64/4.89 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7786_divide__eq__minus__1__iff,axiom,
% 8.64/4.89 ! [A: real,B: real] :
% 8.64/4.89 ( ( ( divide_divide_real @ A @ B )
% 8.64/4.89 = ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.89 = ( ( B != zero_zero_real )
% 8.64/4.89 & ( A
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7787_divide__eq__minus__1__iff,axiom,
% 8.64/4.89 ! [A: complex,B: complex] :
% 8.64/4.89 ( ( ( divide1717551699836669952omplex @ A @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.89 = ( ( B != zero_zero_complex )
% 8.64/4.89 & ( A
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7788_divide__eq__minus__1__iff,axiom,
% 8.64/4.89 ! [A: rat,B: rat] :
% 8.64/4.89 ( ( ( divide_divide_rat @ A @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.89 = ( ( B != zero_zero_rat )
% 8.64/4.89 & ( A
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7789_uminus__numeral__One,axiom,
% 8.64/4.89 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 8.64/4.89 = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7790_uminus__numeral__One,axiom,
% 8.64/4.89 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 8.64/4.89 = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7791_uminus__numeral__One,axiom,
% 8.64/4.89 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7792_uminus__numeral__One,axiom,
% 8.64/4.89 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 8.64/4.89 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7793_uminus__numeral__One,axiom,
% 8.64/4.89 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 8.64/4.89 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7794_fact__less__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.89 => ( ( ord_less_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M2 ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7795_fact__less__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.89 => ( ( ord_less_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M2 ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7796_fact__less__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.89 => ( ( ord_less_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7797_fact__less__mono,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.89 => ( ( ord_less_nat @ M2 @ N )
% 8.64/4.89 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M2 ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7798_power__minus,axiom,
% 8.64/4.89 ! [A: int,N: nat] :
% 8.64/4.89 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 8.64/4.89 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7799_power__minus,axiom,
% 8.64/4.89 ! [A: real,N: nat] :
% 8.64/4.89 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 8.64/4.89 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7800_power__minus,axiom,
% 8.64/4.89 ! [A: complex,N: nat] :
% 8.64/4.89 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 8.64/4.89 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7801_power__minus,axiom,
% 8.64/4.89 ! [A: code_integer,N: nat] :
% 8.64/4.89 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 8.64/4.89 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7802_power__minus,axiom,
% 8.64/4.89 ! [A: rat,N: nat] :
% 8.64/4.89 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 8.64/4.89 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7803_inf__shunt,axiom,
% 8.64/4.89 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 8.64/4.89 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 8.64/4.89 = bot_bo2099793752762293965at_nat )
% 8.64/4.89 = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7804_inf__shunt,axiom,
% 8.64/4.89 ! [X: set_int,Y: set_int] :
% 8.64/4.89 ( ( ( inf_inf_set_int @ X @ Y )
% 8.64/4.89 = bot_bot_set_int )
% 8.64/4.89 = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7805_inf__shunt,axiom,
% 8.64/4.89 ! [X: set_real,Y: set_real] :
% 8.64/4.89 ( ( ( inf_inf_set_real @ X @ Y )
% 8.64/4.89 = bot_bot_set_real )
% 8.64/4.89 = ( ord_less_eq_set_real @ X @ ( uminus612125837232591019t_real @ Y ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7806_inf__shunt,axiom,
% 8.64/4.89 ! [X: set_nat,Y: set_nat] :
% 8.64/4.89 ( ( ( inf_inf_set_nat @ X @ Y )
% 8.64/4.89 = bot_bot_set_nat )
% 8.64/4.89 = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7807_fact__fact__dvd__fact,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ N ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7808_fact__fact__dvd__fact,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ N ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7809_fact__fact__dvd__fact,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ N ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7810_fact__fact__dvd__fact,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K2 @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7811_fact__mod,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1406184849735516958ct_int @ M2 ) )
% 8.64/4.89 = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7812_fact__mod,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N ) @ ( semiri2447717529341329178atural @ M2 ) )
% 8.64/4.89 = zero_z2226904508553997617atural ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7813_fact__mod,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.89 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ M2 ) )
% 8.64/4.89 = zero_zero_nat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7814_sup__neg__inf,axiom,
% 8.64/4.89 ! [P: set_Pr1261947904930325089at_nat,Q2: set_Pr1261947904930325089at_nat,R3: set_Pr1261947904930325089at_nat] :
% 8.64/4.89 ( ( ord_le3146513528884898305at_nat @ P @ ( sup_su6327502436637775413at_nat @ Q2 @ R3 ) )
% 8.64/4.89 = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P @ ( uminus6524753893492686040at_nat @ Q2 ) ) @ R3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7815_sup__neg__inf,axiom,
% 8.64/4.89 ! [P: set_nat,Q2: set_nat,R3: set_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ P @ ( sup_sup_set_nat @ Q2 @ R3 ) )
% 8.64/4.89 = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P @ ( uminus5710092332889474511et_nat @ Q2 ) ) @ R3 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7816_shunt2,axiom,
% 8.64/4.89 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 8.64/4.89 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z3 )
% 8.64/4.89 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7817_shunt2,axiom,
% 8.64/4.89 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z3 )
% 8.64/4.89 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7818_shunt1,axiom,
% 8.64/4.89 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z3: set_Pr1261947904930325089at_nat] :
% 8.64/4.89 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z3 )
% 8.64/4.89 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7819_shunt1,axiom,
% 8.64/4.89 ! [X: set_nat,Y: set_nat,Z3: set_nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z3 )
% 8.64/4.89 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7820_fact__le__power,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7821_fact__le__power,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7822_fact__le__power,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7823_fact__le__power,axiom,
% 8.64/4.89 ! [N: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7824_int__cases4,axiom,
% 8.64/4.89 ! [M2: int] :
% 8.64/4.89 ( ! [N3: nat] :
% 8.64/4.89 ( M2
% 8.64/4.89 != ( semiri1314217659103216013at_int @ N3 ) )
% 8.64/4.89 => ~ ! [N3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.64/4.89 => ( M2
% 8.64/4.89 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7825_int__zle__neg,axiom,
% 8.64/4.89 ! [N: nat,M2: nat] :
% 8.64/4.89 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 8.64/4.89 = ( ( N = zero_zero_nat )
% 8.64/4.89 & ( M2 = zero_zero_nat ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7826_zmod__zminus1__eq__if,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.89 = zero_zero_int )
% 8.64/4.89 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = zero_zero_int ) )
% 8.64/4.89 & ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.89 != zero_zero_int )
% 8.64/4.89 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.89 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7827_zmod__zminus2__eq__if,axiom,
% 8.64/4.89 ! [A: int,B: int] :
% 8.64/4.89 ( ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.89 = zero_zero_int )
% 8.64/4.89 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = zero_zero_int ) )
% 8.64/4.89 & ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.89 != zero_zero_int )
% 8.64/4.89 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.89 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7828_fact__div__fact__le__pow,axiom,
% 8.64/4.89 ! [R3: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ R3 @ N )
% 8.64/4.89 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R3 ) ) ) @ ( power_power_nat @ N @ R3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7829_binomial__fact__lemma,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.89 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( binomial @ N @ K2 ) )
% 8.64/4.89 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7830_subset__decode__imp__le,axiom,
% 8.64/4.89 ! [M2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M2 ) @ ( nat_set_decode @ N ) )
% 8.64/4.89 => ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7831_less__minus__divide__eq,axiom,
% 8.64/4.89 ! [A: real,B: real,C2: real] :
% 8.64/4.89 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 8.64/4.89 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.89 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 8.64/4.89 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.89 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.89 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.89 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.89 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7832_less__minus__divide__eq,axiom,
% 8.64/4.89 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.89 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 8.64/4.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.89 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 8.64/4.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.89 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.89 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.89 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.89 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7833_minus__divide__less__eq,axiom,
% 8.64/4.89 ! [B: real,C2: real,A: real] :
% 8.64/4.89 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 8.64/4.89 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.89 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.89 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.89 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.89 => ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 8.64/4.89 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.89 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7834_minus__divide__less__eq,axiom,
% 8.64/4.89 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 8.64/4.89 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.89 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.89 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.89 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.89 => ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 8.64/4.89 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.89 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7835_neg__less__minus__divide__eq,axiom,
% 8.64/4.89 ! [C2: real,A: real,B: real] :
% 8.64/4.89 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.89 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 8.64/4.89 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7836_neg__less__minus__divide__eq,axiom,
% 8.64/4.89 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.89 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.89 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 8.64/4.89 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7837_neg__minus__divide__less__eq,axiom,
% 8.64/4.89 ! [C2: real,B: real,A: real] :
% 8.64/4.89 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.89 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 8.64/4.89 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7838_neg__minus__divide__less__eq,axiom,
% 8.64/4.89 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.89 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 8.64/4.89 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7839_pos__less__minus__divide__eq,axiom,
% 8.64/4.89 ! [C2: real,A: real,B: real] :
% 8.64/4.89 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.89 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 8.64/4.89 = ( ord_less_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7840_pos__less__minus__divide__eq,axiom,
% 8.64/4.89 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.89 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.89 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 8.64/4.89 = ( ord_less_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7841_pos__minus__divide__less__eq,axiom,
% 8.64/4.89 ! [C2: real,B: real,A: real] :
% 8.64/4.89 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.89 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 8.64/4.89 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7842_pos__minus__divide__less__eq,axiom,
% 8.64/4.89 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.89 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.89 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 8.64/4.89 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7843_eq__divide__eq__numeral_I2_J,axiom,
% 8.64/4.89 ! [W2: num,B: real,C2: real] :
% 8.64/4.89 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.89 = ( divide_divide_real @ B @ C2 ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_real )
% 8.64/4.89 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( C2 = zero_zero_real )
% 8.64/4.89 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.89 = zero_zero_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7844_eq__divide__eq__numeral_I2_J,axiom,
% 8.64/4.89 ! [W2: num,B: complex,C2: complex] :
% 8.64/4.89 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.89 = ( divide1717551699836669952omplex @ B @ C2 ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.89 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C2 )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( C2 = zero_zero_complex )
% 8.64/4.89 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.89 = zero_zero_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7845_eq__divide__eq__numeral_I2_J,axiom,
% 8.64/4.89 ! [W2: num,B: rat,C2: rat] :
% 8.64/4.89 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.89 = ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.89 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( C2 = zero_zero_rat )
% 8.64/4.89 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.89 = zero_zero_rat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7846_divide__eq__eq__numeral_I2_J,axiom,
% 8.64/4.89 ! [B: real,C2: real,W2: num] :
% 8.64/4.89 ( ( ( divide_divide_real @ B @ C2 )
% 8.64/4.89 = ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_real )
% 8.64/4.89 => ( B
% 8.64/4.89 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_real )
% 8.64/4.89 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) )
% 8.64/4.89 = zero_zero_real ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7847_divide__eq__eq__numeral_I2_J,axiom,
% 8.64/4.89 ! [B: complex,C2: complex,W2: num] :
% 8.64/4.89 ( ( ( divide1717551699836669952omplex @ B @ C2 )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_complex )
% 8.64/4.89 => ( B
% 8.64/4.89 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) ) @ C2 ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_complex )
% 8.64/4.89 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W2 ) )
% 8.64/4.89 = zero_zero_complex ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7848_divide__eq__eq__numeral_I2_J,axiom,
% 8.64/4.89 ! [B: rat,C2: rat,W2: num] :
% 8.64/4.89 ( ( ( divide_divide_rat @ B @ C2 )
% 8.64/4.89 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.89 = ( ( ( C2 != zero_zero_rat )
% 8.64/4.89 => ( B
% 8.64/4.89 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 8.64/4.89 & ( ( C2 = zero_zero_rat )
% 8.64/4.89 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 8.64/4.89 = zero_zero_rat ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7849_add__divide__eq__if__simps_I3_J,axiom,
% 8.64/4.89 ! [Z3: real,A: real,B: real] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_real )
% 8.64/4.89 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_real )
% 8.64/4.89 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7850_add__divide__eq__if__simps_I3_J,axiom,
% 8.64/4.89 ! [Z3: complex,A: complex,B: complex] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_complex )
% 8.64/4.89 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_complex )
% 8.64/4.89 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7851_add__divide__eq__if__simps_I3_J,axiom,
% 8.64/4.89 ! [Z3: rat,A: rat,B: rat] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_rat )
% 8.64/4.89 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 8.64/4.89 = B ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_rat )
% 8.64/4.89 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7852_minus__divide__add__eq__iff,axiom,
% 8.64/4.89 ! [Z3: real,X: real,Y: real] :
% 8.64/4.89 ( ( Z3 != zero_zero_real )
% 8.64/4.89 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 8.64/4.89 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7853_minus__divide__add__eq__iff,axiom,
% 8.64/4.89 ! [Z3: complex,X: complex,Y: complex] :
% 8.64/4.89 ( ( Z3 != zero_zero_complex )
% 8.64/4.89 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 8.64/4.89 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7854_minus__divide__add__eq__iff,axiom,
% 8.64/4.89 ! [Z3: rat,X: rat,Y: rat] :
% 8.64/4.89 ( ( Z3 != zero_zero_rat )
% 8.64/4.89 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z3 ) ) @ Y )
% 8.64/4.89 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7855_signed__take__bit__int__greater__eq,axiom,
% 8.64/4.89 ! [K2: int,N: nat] :
% 8.64/4.89 ( ( ord_less_int @ K2 @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.89 => ( ord_less_eq_int @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K2 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7856_add__divide__eq__if__simps_I6_J,axiom,
% 8.64/4.89 ! [Z3: real,A: real,B: real] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_real )
% 8.64/4.89 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_real )
% 8.64/4.89 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7857_add__divide__eq__if__simps_I6_J,axiom,
% 8.64/4.89 ! [Z3: complex,A: complex,B: complex] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_complex )
% 8.64/4.89 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_complex )
% 8.64/4.89 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7858_add__divide__eq__if__simps_I6_J,axiom,
% 8.64/4.89 ! [Z3: rat,A: rat,B: rat] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_rat )
% 8.64/4.89 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_rat )
% 8.64/4.89 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z3 ) ) @ B )
% 8.64/4.89 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7859_add__divide__eq__if__simps_I5_J,axiom,
% 8.64/4.89 ! [Z3: real,A: real,B: real] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_real )
% 8.64/4.89 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 8.64/4.89 = ( uminus_uminus_real @ B ) ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_real )
% 8.64/4.89 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z3 ) @ B )
% 8.64/4.89 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7860_add__divide__eq__if__simps_I5_J,axiom,
% 8.64/4.89 ! [Z3: complex,A: complex,B: complex] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_complex )
% 8.64/4.89 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 8.64/4.89 = ( uminus1482373934393186551omplex @ B ) ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_complex )
% 8.64/4.89 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z3 ) @ B )
% 8.64/4.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7861_add__divide__eq__if__simps_I5_J,axiom,
% 8.64/4.89 ! [Z3: rat,A: rat,B: rat] :
% 8.64/4.89 ( ( ( Z3 = zero_zero_rat )
% 8.64/4.89 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 8.64/4.89 = ( uminus_uminus_rat @ B ) ) )
% 8.64/4.89 & ( ( Z3 != zero_zero_rat )
% 8.64/4.89 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z3 ) @ B )
% 8.64/4.89 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z3 ) ) @ Z3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7862_minus__divide__diff__eq__iff,axiom,
% 8.64/4.89 ! [Z3: real,X: real,Y: real] :
% 8.64/4.89 ( ( Z3 != zero_zero_real )
% 8.64/4.89 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z3 ) ) @ Y )
% 8.64/4.89 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7863_minus__divide__diff__eq__iff,axiom,
% 8.64/4.89 ! [Z3: complex,X: complex,Y: complex] :
% 8.64/4.89 ( ( Z3 != zero_zero_complex )
% 8.64/4.89 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z3 ) ) @ Y )
% 8.64/4.89 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7864_minus__divide__diff__eq__iff,axiom,
% 8.64/4.89 ! [Z3: rat,X: rat,Y: rat] :
% 8.64/4.89 ( ( Z3 != zero_zero_rat )
% 8.64/4.89 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z3 ) ) @ Y )
% 8.64/4.89 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z3 ) ) @ Z3 ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7865_choose__dvd,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.89 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7866_choose__dvd,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.89 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri1406184849735516958ct_int @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7867_choose__dvd,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.89 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7868_choose__dvd,axiom,
% 8.64/4.89 ! [K2: nat,N: nat] :
% 8.64/4.89 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.89 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7869_int__cases3,axiom,
% 8.64/4.89 ! [K2: int] :
% 8.64/4.89 ( ( K2 != zero_zero_int )
% 8.64/4.89 => ( ! [N3: nat] :
% 8.64/4.89 ( ( K2
% 8.64/4.89 = ( semiri1314217659103216013at_int @ N3 ) )
% 8.64/4.89 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 8.64/4.89 => ~ ! [N3: nat] :
% 8.64/4.89 ( ( K2
% 8.64/4.89 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 8.64/4.89 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7870_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ K2 )
% 8.64/4.89 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_complex ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7871_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ K2 )
% 8.64/4.89 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 8.64/4.89 = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7872_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ K2 )
% 8.64/4.89 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_rat ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7873_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ K2 )
% 8.64/4.89 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_real ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7874_pochhammer__of__nat__eq__0__lemma,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ord_less_nat @ N @ K2 )
% 8.64/4.89 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_int ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7875_pochhammer__of__nat__eq__0__iff,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_complex )
% 8.64/4.89 = ( ord_less_nat @ N @ K2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7876_pochhammer__of__nat__eq__0__iff,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 8.64/4.89 = zero_z3403309356797280102nteger )
% 8.64/4.89 = ( ord_less_nat @ N @ K2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7877_pochhammer__of__nat__eq__0__iff,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_rat )
% 8.64/4.89 = ( ord_less_nat @ N @ K2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7878_pochhammer__of__nat__eq__0__iff,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_real )
% 8.64/4.89 = ( ord_less_nat @ N @ K2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7879_pochhammer__of__nat__eq__0__iff,axiom,
% 8.64/4.89 ! [N: nat,K2: nat] :
% 8.64/4.89 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 8.64/4.89 = zero_zero_int )
% 8.64/4.89 = ( ord_less_nat @ N @ K2 ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7880_pochhammer__eq__0__iff,axiom,
% 8.64/4.89 ! [A: complex,N: nat] :
% 8.64/4.89 ( ( ( comm_s2602460028002588243omplex @ A @ N )
% 8.64/4.89 = zero_zero_complex )
% 8.64/4.89 = ( ? [K3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ K3 @ N )
% 8.64/4.89 & ( A
% 8.64/4.89 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7881_pochhammer__eq__0__iff,axiom,
% 8.64/4.89 ! [A: rat,N: nat] :
% 8.64/4.89 ( ( ( comm_s4028243227959126397er_rat @ A @ N )
% 8.64/4.89 = zero_zero_rat )
% 8.64/4.89 = ( ? [K3: nat] :
% 8.64/4.89 ( ( ord_less_nat @ K3 @ N )
% 8.64/4.89 & ( A
% 8.64/4.89 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 8.64/4.89
% 8.64/4.89 thf(fact_7882_pochhammer__eq__0__iff,axiom,
% 8.64/4.89 ! [A: real,N: nat] :
% 8.64/4.89 ( ( ( comm_s7457072308508201937r_real @ A @ N )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( ? [K3: nat] :
% 8.64/4.90 ( ( ord_less_nat @ K3 @ N )
% 8.64/4.90 & ( A
% 8.64/4.90 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7883_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ K2 )
% 8.64/4.90 != zero_zero_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7884_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N ) ) @ K2 )
% 8.64/4.90 != zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7885_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ K2 )
% 8.64/4.90 != zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7886_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ K2 )
% 8.64/4.90 != zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7887_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ K2 )
% 8.64/4.90 != zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7888_not__zle__0__negative,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7889_negD,axiom,
% 8.64/4.90 ! [X: int] :
% 8.64/4.90 ( ( ord_less_int @ X @ zero_zero_int )
% 8.64/4.90 => ? [N3: nat] :
% 8.64/4.90 ( X
% 8.64/4.90 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7890_negative__zless__0,axiom,
% 8.64/4.90 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7891_div__eq__minus1,axiom,
% 8.64/4.90 ! [B: int] :
% 8.64/4.90 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.90 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 8.64/4.90 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7892_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_real,P2: real > $o,H: real > real,G2: real > real] :
% 8.64/4.90 ( ( finite_finite_real @ A4 )
% 8.64/4.90 => ( ( groups1681761925125756287l_real
% 8.64/4.90 @ ^ [X4: real] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_real @ ( groups1681761925125756287l_real @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups1681761925125756287l_real @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7893_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_int,P2: int > $o,H: int > real,G2: int > real] :
% 8.64/4.90 ( ( finite_finite_int @ A4 )
% 8.64/4.90 => ( ( groups2316167850115554303t_real
% 8.64/4.90 @ ^ [X4: int] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_real @ ( groups2316167850115554303t_real @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups2316167850115554303t_real @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7894_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_complex,P2: complex > $o,H: complex > real,G2: complex > real] :
% 8.64/4.90 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.90 => ( ( groups766887009212190081x_real
% 8.64/4.90 @ ^ [X4: complex] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_real @ ( groups766887009212190081x_real @ H @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) @ ( groups766887009212190081x_real @ G2 @ ( inf_inf_set_complex @ A4 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7895_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_nat,P2: nat > $o,H: nat > real,G2: nat > real] :
% 8.64/4.90 ( ( finite_finite_nat @ A4 )
% 8.64/4.90 => ( ( groups129246275422532515t_real
% 8.64/4.90 @ ^ [X4: nat] : ( if_real @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_real @ ( groups129246275422532515t_real @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups129246275422532515t_real @ G2 @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7896_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_real,P2: real > $o,H: real > rat,G2: real > rat] :
% 8.64/4.90 ( ( finite_finite_real @ A4 )
% 8.64/4.90 => ( ( groups4061424788464935467al_rat
% 8.64/4.90 @ ^ [X4: real] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_rat @ ( groups4061424788464935467al_rat @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups4061424788464935467al_rat @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7897_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_int,P2: int > $o,H: int > rat,G2: int > rat] :
% 8.64/4.90 ( ( finite_finite_int @ A4 )
% 8.64/4.90 => ( ( groups1072433553688619179nt_rat
% 8.64/4.90 @ ^ [X4: int] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1072433553688619179nt_rat @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7898_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_complex,P2: complex > $o,H: complex > rat,G2: complex > rat] :
% 8.64/4.90 ( ( finite3207457112153483333omplex @ A4 )
% 8.64/4.90 => ( ( groups225925009352817453ex_rat
% 8.64/4.90 @ ^ [X4: complex] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_rat @ ( groups225925009352817453ex_rat @ H @ ( inf_inf_set_complex @ A4 @ ( collect_complex @ P2 ) ) ) @ ( groups225925009352817453ex_rat @ G2 @ ( inf_inf_set_complex @ A4 @ ( uminus8566677241136511917omplex @ ( collect_complex @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7899_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_nat,P2: nat > $o,H: nat > rat,G2: nat > rat] :
% 8.64/4.90 ( ( finite_finite_nat @ A4 )
% 8.64/4.90 => ( ( groups73079841787564623at_rat
% 8.64/4.90 @ ^ [X4: nat] : ( if_rat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_rat @ ( groups73079841787564623at_rat @ H @ ( inf_inf_set_nat @ A4 @ ( collect_nat @ P2 ) ) ) @ ( groups73079841787564623at_rat @ G2 @ ( inf_inf_set_nat @ A4 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7900_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_real,P2: real > $o,H: real > nat,G2: real > nat] :
% 8.64/4.90 ( ( finite_finite_real @ A4 )
% 8.64/4.90 => ( ( groups4696554848551431203al_nat
% 8.64/4.90 @ ^ [X4: real] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_nat @ ( groups4696554848551431203al_nat @ H @ ( inf_inf_set_real @ A4 @ ( collect_real @ P2 ) ) ) @ ( groups4696554848551431203al_nat @ G2 @ ( inf_inf_set_real @ A4 @ ( uminus612125837232591019t_real @ ( collect_real @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7901_prod_OIf__cases,axiom,
% 8.64/4.90 ! [A4: set_int,P2: int > $o,H: int > nat,G2: int > nat] :
% 8.64/4.90 ( ( finite_finite_int @ A4 )
% 8.64/4.90 => ( ( groups1707563613775114915nt_nat
% 8.64/4.90 @ ^ [X4: int] : ( if_nat @ ( P2 @ X4 ) @ ( H @ X4 ) @ ( G2 @ X4 ) )
% 8.64/4.90 @ A4 )
% 8.64/4.90 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ H @ ( inf_inf_set_int @ A4 @ ( collect_int @ P2 ) ) ) @ ( groups1707563613775114915nt_nat @ G2 @ ( inf_inf_set_int @ A4 @ ( uminus1532241313380277803et_int @ ( collect_int @ P2 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7902_binomial__altdef__nat,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( binomial @ N @ K2 )
% 8.64/4.90 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7903_le__minus__divide__eq,axiom,
% 8.64/4.90 ! [A: real,B: real,C2: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 8.64/4.90 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7904_le__minus__divide__eq,axiom,
% 8.64/4.90 ! [A: rat,B: rat,C2: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 8.64/4.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7905_minus__divide__le__eq,axiom,
% 8.64/4.90 ! [B: real,C2: real,A: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 8.64/4.90 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7906_minus__divide__le__eq,axiom,
% 8.64/4.90 ! [B: rat,C2: rat,A: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 8.64/4.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7907_neg__le__minus__divide__eq,axiom,
% 8.64/4.90 ! [C2: real,A: real,B: real] :
% 8.64/4.90 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 8.64/4.90 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7908_neg__le__minus__divide__eq,axiom,
% 8.64/4.90 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 8.64/4.90 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7909_neg__minus__divide__le__eq,axiom,
% 8.64/4.90 ! [C2: real,B: real,A: real] :
% 8.64/4.90 ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 8.64/4.90 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7910_neg__minus__divide__le__eq,axiom,
% 8.64/4.90 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.90 ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 8.64/4.90 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7911_pos__le__minus__divide__eq,axiom,
% 8.64/4.90 ! [C2: real,A: real,B: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) )
% 8.64/4.90 = ( ord_less_eq_real @ ( times_times_real @ A @ C2 ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7912_pos__le__minus__divide__eq,axiom,
% 8.64/4.90 ! [C2: rat,A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) )
% 8.64/4.90 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C2 ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7913_pos__minus__divide__le__eq,axiom,
% 8.64/4.90 ! [C2: real,B: real,A: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C2 ) ) @ A )
% 8.64/4.90 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7914_pos__minus__divide__le__eq,axiom,
% 8.64/4.90 ! [C2: rat,B: rat,A: rat] :
% 8.64/4.90 ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C2 ) ) @ A )
% 8.64/4.90 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7915_divide__less__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [B: real,C2: real,W2: num] :
% 8.64/4.90 ( ( ord_less_real @ ( divide_divide_real @ B @ C2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.90 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7916_divide__less__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [B: rat,C2: rat,W2: num] :
% 8.64/4.90 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7917_less__divide__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [W2: num,B: real,C2: real] :
% 8.64/4.90 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.90 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7918_less__divide__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [W2: num,B: rat,C2: rat] :
% 8.64/4.90 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7919_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K2 ) )
% 8.64/4.90 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7920_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K2 ) )
% 8.64/4.90 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7921_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K2 ) )
% 8.64/4.90 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7922_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K2 ) )
% 8.64/4.90 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7923_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K2 ) )
% 8.64/4.90 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7924_neg__int__cases,axiom,
% 8.64/4.90 ! [K2: int] :
% 8.64/4.90 ( ( ord_less_int @ K2 @ zero_zero_int )
% 8.64/4.90 => ~ ! [N3: nat] :
% 8.64/4.90 ( ( K2
% 8.64/4.90 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 8.64/4.90 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7925_minus__mod__int__eq,axiom,
% 8.64/4.90 ! [L: int,K2: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 8.64/4.90 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K2 ) @ L )
% 8.64/4.90 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K2 @ one_one_int ) @ L ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7926_zmod__minus1,axiom,
% 8.64/4.90 ! [B: int] :
% 8.64/4.90 ( ( ord_less_int @ zero_zero_int @ B )
% 8.64/4.90 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 8.64/4.90 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7927_zdiv__zminus1__eq__if,axiom,
% 8.64/4.90 ! [B: int,A: int] :
% 8.64/4.90 ( ( B != zero_zero_int )
% 8.64/4.90 => ( ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.90 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 8.64/4.90 & ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.90 != zero_zero_int )
% 8.64/4.90 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.90 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7928_zdiv__zminus2__eq__if,axiom,
% 8.64/4.90 ! [B: int,A: int] :
% 8.64/4.90 ( ( B != zero_zero_int )
% 8.64/4.90 => ( ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.90 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 8.64/4.90 & ( ( ( modulo_modulo_int @ A @ B )
% 8.64/4.90 != zero_zero_int )
% 8.64/4.90 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 8.64/4.90 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7929_fact__eq__fact__times,axiom,
% 8.64/4.90 ! [N: nat,M2: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.90 => ( ( semiri1408675320244567234ct_nat @ M2 )
% 8.64/4.90 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 8.64/4.90 @ ( groups708209901874060359at_nat
% 8.64/4.90 @ ^ [X4: nat] : X4
% 8.64/4.90 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7930_signed__take__bit__rec,axiom,
% 8.64/4.90 ( bit_ri6519982836138164636nteger
% 8.64/4.90 = ( ^ [N4: nat,A5: code_integer] : ( if_Code_integer @ ( N4 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7931_signed__take__bit__rec,axiom,
% 8.64/4.90 ( bit_ri631733984087533419it_int
% 8.64/4.90 = ( ^ [N4: nat,A5: int] : ( if_int @ ( N4 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N4 @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7932_square__fact__le__2__fact,axiom,
% 8.64/4.90 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7933_zminus1__lemma,axiom,
% 8.64/4.90 ! [A: int,B: int,Q2: int,R3: int] :
% 8.64/4.90 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R3 ) )
% 8.64/4.90 => ( ( B != zero_zero_int )
% 8.64/4.90 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7934_divide__le__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [B: real,C2: real,W2: num] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C2 ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) )
% 8.64/4.90 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7935_divide__le__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [B: rat,C2: rat,W2: num] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C2 ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 8.64/4.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7936_le__divide__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [W2: num,B: real,C2: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ ( divide_divide_real @ B @ C2 ) )
% 8.64/4.90 = ( ( ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ zero_zero_real @ C2 )
% 8.64/4.90 => ( ( ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_real @ C2 @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W2 ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7937_le__divide__eq__numeral_I2_J,axiom,
% 8.64/4.90 ! [W2: num,B: rat,C2: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C2 ) )
% 8.64/4.90 = ( ( ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) @ B ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ zero_zero_rat @ C2 )
% 8.64/4.90 => ( ( ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_rat @ C2 @ zero_zero_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7938_square__le__1,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.64/4.90 => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.64/4.90 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7939_square__le__1,axiom,
% 8.64/4.90 ! [X: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 8.64/4.90 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7940_square__le__1,axiom,
% 8.64/4.90 ! [X: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 8.64/4.90 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 8.64/4.90 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7941_square__le__1,axiom,
% 8.64/4.90 ! [X: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 8.64/4.90 => ( ( ord_less_eq_int @ X @ one_one_int )
% 8.64/4.90 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7942_minus__power__mult__self,axiom,
% 8.64/4.90 ! [A: int,N: nat] :
% 8.64/4.90 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 8.64/4.90 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7943_minus__power__mult__self,axiom,
% 8.64/4.90 ! [A: real,N: nat] :
% 8.64/4.90 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 8.64/4.90 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7944_minus__power__mult__self,axiom,
% 8.64/4.90 ! [A: complex,N: nat] :
% 8.64/4.90 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 8.64/4.90 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7945_minus__power__mult__self,axiom,
% 8.64/4.90 ! [A: code_integer,N: nat] :
% 8.64/4.90 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 8.64/4.90 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7946_minus__power__mult__self,axiom,
% 8.64/4.90 ! [A: rat,N: nat] :
% 8.64/4.90 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 8.64/4.90 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7947_fact__num__eq__if,axiom,
% 8.64/4.90 ( semiri3624122377584611663nteger
% 8.64/4.90 = ( ^ [M6: nat] : ( if_Code_integer @ ( M6 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M6 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7948_fact__num__eq__if,axiom,
% 8.64/4.90 ( semiri5044797733671781792omplex
% 8.64/4.90 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7949_fact__num__eq__if,axiom,
% 8.64/4.90 ( semiri773545260158071498ct_rat
% 8.64/4.90 = ( ^ [M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M6 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7950_fact__num__eq__if,axiom,
% 8.64/4.90 ( semiri1406184849735516958ct_int
% 8.64/4.90 = ( ^ [M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7951_fact__num__eq__if,axiom,
% 8.64/4.90 ( semiri1408675320244567234ct_nat
% 8.64/4.90 = ( ^ [M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M6 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7952_fact__num__eq__if,axiom,
% 8.64/4.90 ( semiri2265585572941072030t_real
% 8.64/4.90 = ( ^ [M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M6 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7953_fact__code,axiom,
% 8.64/4.90 ( semiri1406184849735516958ct_int
% 8.64/4.90 = ( ^ [N4: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7954_fact__code,axiom,
% 8.64/4.90 ( semiri1408675320244567234ct_nat
% 8.64/4.90 = ( ^ [N4: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7955_fact__code,axiom,
% 8.64/4.90 ( semiri2265585572941072030t_real
% 8.64/4.90 = ( ^ [N4: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 @ one_one_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7956_fact__reduce,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ( semiri773545260158071498ct_rat @ N )
% 8.64/4.90 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7957_fact__reduce,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ( semiri1406184849735516958ct_int @ N )
% 8.64/4.90 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7958_fact__reduce,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ( semiri1408675320244567234ct_nat @ N )
% 8.64/4.90 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7959_fact__reduce,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ( semiri2265585572941072030t_real @ N )
% 8.64/4.90 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7960_pochhammer__absorb__comp,axiom,
% 8.64/4.90 ! [R3: complex,K2: nat] :
% 8.64/4.90 ( ( times_times_complex @ ( minus_minus_complex @ R3 @ ( semiri8010041392384452111omplex @ K2 ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R3 ) @ K2 ) )
% 8.64/4.90 = ( times_times_complex @ R3 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R3 ) @ one_one_complex ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7961_pochhammer__absorb__comp,axiom,
% 8.64/4.90 ! [R3: code_integer,K2: nat] :
% 8.64/4.90 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K2 ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K2 ) )
% 8.64/4.90 = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7962_pochhammer__absorb__comp,axiom,
% 8.64/4.90 ! [R3: rat,K2: nat] :
% 8.64/4.90 ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K2 ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K2 ) )
% 8.64/4.90 = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7963_pochhammer__absorb__comp,axiom,
% 8.64/4.90 ! [R3: real,K2: nat] :
% 8.64/4.90 ( ( times_times_real @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R3 ) @ K2 ) )
% 8.64/4.90 = ( times_times_real @ R3 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R3 ) @ one_one_real ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7964_pochhammer__absorb__comp,axiom,
% 8.64/4.90 ! [R3: int,K2: nat] :
% 8.64/4.90 ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K2 ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K2 ) )
% 8.64/4.90 = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7965_gbinomial__index__swap,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N ) ) @ one_one_complex ) @ K2 ) )
% 8.64/4.90 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7966_gbinomial__index__swap,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N ) ) @ one_one_rat ) @ K2 ) )
% 8.64/4.90 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7967_gbinomial__index__swap,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ one_one_real ) @ K2 ) )
% 8.64/4.90 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7968_gbinomial__negated__upper,axiom,
% 8.64/4.90 ( gbinomial_complex
% 8.64/4.90 = ( ^ [A5: complex,K3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ K3 ) @ A5 ) @ one_one_complex ) @ K3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7969_gbinomial__negated__upper,axiom,
% 8.64/4.90 ( gbinomial_rat
% 8.64/4.90 = ( ^ [A5: rat,K3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ K3 ) @ A5 ) @ one_one_rat ) @ K3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7970_gbinomial__negated__upper,axiom,
% 8.64/4.90 ( gbinomial_real
% 8.64/4.90 = ( ^ [A5: real,K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( gbinomial_real @ ( minus_minus_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ K3 ) @ A5 ) @ one_one_real ) @ K3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7971_binomial__fact,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) )
% 8.64/4.90 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7972_binomial__fact,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) )
% 8.64/4.90 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7973_binomial__fact,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) )
% 8.64/4.90 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7974_fact__binomial,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K2 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ K2 ) ) )
% 8.64/4.90 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7975_fact__binomial,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K2 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ K2 ) ) )
% 8.64/4.90 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7976_fact__binomial,axiom,
% 8.64/4.90 ! [K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ K2 @ N )
% 8.64/4.90 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K2 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ K2 ) ) )
% 8.64/4.90 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ K2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7977_Bernoulli__inequality,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 8.64/4.90 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7978_fact__div__fact,axiom,
% 8.64/4.90 ! [N: nat,M2: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.90 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M2 ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 8.64/4.90 = ( groups708209901874060359at_nat
% 8.64/4.90 @ ^ [X4: nat] : X4
% 8.64/4.90 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7979_power__minus1__odd,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.90 = ( uminus_uminus_int @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7980_power__minus1__odd,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.90 = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7981_power__minus1__odd,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.90 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7982_power__minus1__odd,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.90 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7983_power__minus1__odd,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.90 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7984_gbinomial__minus,axiom,
% 8.64/4.90 ! [A: complex,K2: nat] :
% 8.64/4.90 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K2 )
% 8.64/4.90 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7985_gbinomial__minus,axiom,
% 8.64/4.90 ! [A: rat,K2: nat] :
% 8.64/4.90 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K2 )
% 8.64/4.90 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7986_gbinomial__minus,axiom,
% 8.64/4.90 ! [A: real,K2: nat] :
% 8.64/4.90 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K2 )
% 8.64/4.90 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7987_signed__take__bit__int__less__eq,axiom,
% 8.64/4.90 ! [N: nat,K2: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K2 )
% 8.64/4.90 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7988_pochhammer__minus_H,axiom,
% 8.64/4.90 ! [B: complex,K2: nat] :
% 8.64/4.90 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 )
% 8.64/4.90 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7989_pochhammer__minus_H,axiom,
% 8.64/4.90 ! [B: code_integer,K2: nat] :
% 8.64/4.90 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 )
% 8.64/4.90 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7990_pochhammer__minus_H,axiom,
% 8.64/4.90 ! [B: rat,K2: nat] :
% 8.64/4.90 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 )
% 8.64/4.90 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7991_pochhammer__minus_H,axiom,
% 8.64/4.90 ! [B: real,K2: nat] :
% 8.64/4.90 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 )
% 8.64/4.90 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7992_pochhammer__minus_H,axiom,
% 8.64/4.90 ! [B: int,K2: nat] :
% 8.64/4.90 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 )
% 8.64/4.90 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7993_pochhammer__minus,axiom,
% 8.64/4.90 ! [B: complex,K2: nat] :
% 8.64/4.90 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K2 )
% 8.64/4.90 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K2 ) ) @ one_one_complex ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7994_pochhammer__minus,axiom,
% 8.64/4.90 ! [B: code_integer,K2: nat] :
% 8.64/4.90 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K2 )
% 8.64/4.90 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K2 ) ) @ one_one_Code_integer ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7995_pochhammer__minus,axiom,
% 8.64/4.90 ! [B: rat,K2: nat] :
% 8.64/4.90 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K2 )
% 8.64/4.90 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K2 ) ) @ one_one_rat ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7996_pochhammer__minus,axiom,
% 8.64/4.90 ! [B: real,K2: nat] :
% 8.64/4.90 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K2 )
% 8.64/4.90 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K2 ) ) @ one_one_real ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7997_pochhammer__minus,axiom,
% 8.64/4.90 ! [B: int,K2: nat] :
% 8.64/4.90 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K2 )
% 8.64/4.90 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K2 ) ) @ one_one_int ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7998_int__bit__induct,axiom,
% 8.64/4.90 ! [P2: int > $o,K2: int] :
% 8.64/4.90 ( ( P2 @ zero_zero_int )
% 8.64/4.90 => ( ( P2 @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.90 => ( ! [K: int] :
% 8.64/4.90 ( ( P2 @ K )
% 8.64/4.90 => ( ( K != zero_zero_int )
% 8.64/4.90 => ( P2 @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.90 => ( ! [K: int] :
% 8.64/4.90 ( ( P2 @ K )
% 8.64/4.90 => ( ( K
% 8.64/4.90 != ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.90 => ( P2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 8.64/4.90 => ( P2 @ K2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_7999_gbinomial__sum__lower__neg,axiom,
% 8.64/4.90 ! [A: complex,M2: nat] :
% 8.64/4.90 ( ( groups2073611262835488442omplex
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.90 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8000_gbinomial__sum__lower__neg,axiom,
% 8.64/4.90 ! [A: rat,M2: nat] :
% 8.64/4.90 ( ( groups2906978787729119204at_rat
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.90 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8001_gbinomial__sum__lower__neg,axiom,
% 8.64/4.90 ! [A: real,M2: nat] :
% 8.64/4.90 ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.90 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M2 ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8002_gbinomial__Suc,axiom,
% 8.64/4.90 ! [A: complex,K2: nat] :
% 8.64/4.90 ( ( gbinomial_complex @ A @ ( suc @ K2 ) )
% 8.64/4.90 = ( divide1717551699836669952omplex
% 8.64/4.90 @ ( groups6464643781859351333omplex
% 8.64/4.90 @ ^ [I: nat] : ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ I ) )
% 8.64/4.90 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 8.64/4.90 @ ( semiri5044797733671781792omplex @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8003_gbinomial__Suc,axiom,
% 8.64/4.90 ! [A: rat,K2: nat] :
% 8.64/4.90 ( ( gbinomial_rat @ A @ ( suc @ K2 ) )
% 8.64/4.90 = ( divide_divide_rat
% 8.64/4.90 @ ( groups73079841787564623at_rat
% 8.64/4.90 @ ^ [I: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I ) )
% 8.64/4.90 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 8.64/4.90 @ ( semiri773545260158071498ct_rat @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8004_gbinomial__Suc,axiom,
% 8.64/4.90 ! [A: real,K2: nat] :
% 8.64/4.90 ( ( gbinomial_real @ A @ ( suc @ K2 ) )
% 8.64/4.90 = ( divide_divide_real
% 8.64/4.90 @ ( groups129246275422532515t_real
% 8.64/4.90 @ ^ [I: nat] : ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ I ) )
% 8.64/4.90 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 8.64/4.90 @ ( semiri2265585572941072030t_real @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8005_gbinomial__Suc,axiom,
% 8.64/4.90 ! [A: int,K2: nat] :
% 8.64/4.90 ( ( gbinomial_int @ A @ ( suc @ K2 ) )
% 8.64/4.90 = ( divide_divide_int
% 8.64/4.90 @ ( groups705719431365010083at_int
% 8.64/4.90 @ ^ [I: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I ) )
% 8.64/4.90 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 8.64/4.90 @ ( semiri1406184849735516958ct_int @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8006_gbinomial__Suc,axiom,
% 8.64/4.90 ! [A: nat,K2: nat] :
% 8.64/4.90 ( ( gbinomial_nat @ A @ ( suc @ K2 ) )
% 8.64/4.90 = ( divide_divide_nat
% 8.64/4.90 @ ( groups708209901874060359at_nat
% 8.64/4.90 @ ^ [I: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I ) )
% 8.64/4.90 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K2 ) )
% 8.64/4.90 @ ( semiri1408675320244567234ct_nat @ ( suc @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8007_gbinomial__partial__sum__poly,axiom,
% 8.64/4.90 ! [M2: nat,A: complex,X: complex,Y: complex] :
% 8.64/4.90 ( ( groups2073611262835488442omplex
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M2 ) @ A ) @ K3 ) @ ( power_power_complex @ X @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.90 = ( groups2073611262835488442omplex
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8008_gbinomial__partial__sum__poly,axiom,
% 8.64/4.90 ! [M2: nat,A: rat,X: rat,Y: rat] :
% 8.64/4.90 ( ( groups2906978787729119204at_rat
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M2 ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.90 = ( groups2906978787729119204at_rat
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8009_gbinomial__partial__sum__poly,axiom,
% 8.64/4.90 ! [M2: nat,A: real,X: real,Y: real] :
% 8.64/4.90 ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M2 ) @ A ) @ K3 ) @ ( power_power_real @ X @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) )
% 8.64/4.90 = ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_nat @ M2 @ K3 ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8010_root__polyfun,axiom,
% 8.64/4.90 ! [N: nat,Z3: int,A: int] :
% 8.64/4.90 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.90 => ( ( ( power_power_int @ Z3 @ N )
% 8.64/4.90 = A )
% 8.64/4.90 = ( ( groups3539618377306564664at_int
% 8.64/4.90 @ ^ [I: nat] : ( times_times_int @ ( if_int @ ( I = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I = N ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z3 @ I ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8011_root__polyfun,axiom,
% 8.64/4.90 ! [N: nat,Z3: complex,A: complex] :
% 8.64/4.90 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.90 => ( ( ( power_power_complex @ Z3 @ N )
% 8.64/4.90 = A )
% 8.64/4.90 = ( ( groups2073611262835488442omplex
% 8.64/4.90 @ ^ [I: nat] : ( times_times_complex @ ( if_complex @ ( I = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I = N ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z3 @ I ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_complex ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8012_root__polyfun,axiom,
% 8.64/4.90 ! [N: nat,Z3: code_integer,A: code_integer] :
% 8.64/4.90 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.90 => ( ( ( power_8256067586552552935nteger @ Z3 @ N )
% 8.64/4.90 = A )
% 8.64/4.90 = ( ( groups7501900531339628137nteger
% 8.64/4.90 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I = N ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z3 @ I ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_z3403309356797280102nteger ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8013_root__polyfun,axiom,
% 8.64/4.90 ! [N: nat,Z3: rat,A: rat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.90 => ( ( ( power_power_rat @ Z3 @ N )
% 8.64/4.90 = A )
% 8.64/4.90 = ( ( groups2906978787729119204at_rat
% 8.64/4.90 @ ^ [I: nat] : ( times_times_rat @ ( if_rat @ ( I = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I = N ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z3 @ I ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_rat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8014_root__polyfun,axiom,
% 8.64/4.90 ! [N: nat,Z3: real,A: real] :
% 8.64/4.90 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 8.64/4.90 => ( ( ( power_power_real @ Z3 @ N )
% 8.64/4.90 = A )
% 8.64/4.90 = ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [I: nat] : ( times_times_real @ ( if_real @ ( I = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I = N ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z3 @ I ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_real ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8015_set__decode__plus__power__2,axiom,
% 8.64/4.90 ! [N: nat,Z3: nat] :
% 8.64/4.90 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z3 ) )
% 8.64/4.90 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z3 ) )
% 8.64/4.90 = ( insert_nat @ N @ ( nat_set_decode @ Z3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8016_choose__alternating__linear__sum,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( N != one_one_nat )
% 8.64/4.90 => ( ( groups2073611262835488442omplex
% 8.64/4.90 @ ^ [I: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I ) @ ( semiri8010041392384452111omplex @ I ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N @ I ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8017_choose__alternating__linear__sum,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( N != one_one_nat )
% 8.64/4.90 => ( ( groups7501900531339628137nteger
% 8.64/4.90 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I ) @ ( semiri4939895301339042750nteger @ I ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N @ I ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8018_choose__alternating__linear__sum,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( N != one_one_nat )
% 8.64/4.90 => ( ( groups2906978787729119204at_rat
% 8.64/4.90 @ ^ [I: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I ) @ ( semiri681578069525770553at_rat @ I ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N @ I ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8019_choose__alternating__linear__sum,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( N != one_one_nat )
% 8.64/4.90 => ( ( groups3539618377306564664at_int
% 8.64/4.90 @ ^ [I: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I ) @ ( semiri1314217659103216013at_int @ I ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N @ I ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8020_choose__alternating__linear__sum,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( N != one_one_nat )
% 8.64/4.90 => ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [I: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( semiri5074537144036343181t_real @ I ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N @ I ) ) )
% 8.64/4.90 @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.90 = zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8021_set__decode__def,axiom,
% 8.64/4.90 ( nat_set_decode
% 8.64/4.90 = ( ^ [X4: nat] :
% 8.64/4.90 ( collect_nat
% 8.64/4.90 @ ^ [N4: nat] :
% 8.64/4.90 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8022_fact__double,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri5044797733671781792omplex @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8023_fact__double,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.90 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri773545260158071498ct_rat @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8024_fact__double,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8025_binomial__code,axiom,
% 8.64/4.90 ( binomial
% 8.64/4.90 = ( ^ [N4: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N4 @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N4 @ ( minus_minus_nat @ N4 @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N4 @ K3 ) @ one_one_nat ) @ N4 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8026_Maclaurin__lemma,axiom,
% 8.64/4.90 ! [H: real,F2: real > real,J2: nat > real,N: nat] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ H )
% 8.64/4.90 => ? [B8: real] :
% 8.64/4.90 ( ( F2 @ H )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J2 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8027_Maclaurin__zero,axiom,
% 8.64/4.90 ! [X: real,N: nat,Diff: nat > complex > real] :
% 8.64/4.90 ( ( X = zero_zero_real )
% 8.64/4.90 => ( ( N != zero_zero_nat )
% 8.64/4.90 => ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8028_Maclaurin__zero,axiom,
% 8.64/4.90 ! [X: real,N: nat,Diff: nat > real > real] :
% 8.64/4.90 ( ( X = zero_zero_real )
% 8.64/4.90 => ( ( N != zero_zero_nat )
% 8.64/4.90 => ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8029_Maclaurin__zero,axiom,
% 8.64/4.90 ! [X: real,N: nat,Diff: nat > rat > real] :
% 8.64/4.90 ( ( X = zero_zero_real )
% 8.64/4.90 => ( ( N != zero_zero_nat )
% 8.64/4.90 => ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8030_Maclaurin__zero,axiom,
% 8.64/4.90 ! [X: real,N: nat,Diff: nat > nat > real] :
% 8.64/4.90 ( ( X = zero_zero_real )
% 8.64/4.90 => ( ( N != zero_zero_nat )
% 8.64/4.90 => ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8031_Maclaurin__zero,axiom,
% 8.64/4.90 ! [X: real,N: nat,Diff: nat > int > real] :
% 8.64/4.90 ( ( X = zero_zero_real )
% 8.64/4.90 => ( ( N != zero_zero_nat )
% 8.64/4.90 => ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8032_sin__coeff__def,axiom,
% 8.64/4.90 ( sin_coeff
% 8.64/4.90 = ( ^ [N4: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8033_fact__diff__Suc,axiom,
% 8.64/4.90 ! [N: nat,M2: nat] :
% 8.64/4.90 ( ( ord_less_nat @ N @ ( suc @ M2 ) )
% 8.64/4.90 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) )
% 8.64/4.90 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M2 ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M2 @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8034_sin__paired,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( sums_real
% 8.64/4.90 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 8.64/4.90 @ ( sin_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8035_and__int_Osimps,axiom,
% 8.64/4.90 ( bit_se725231765392027082nd_int
% 8.64/4.90 = ( ^ [K3: int,L2: int] :
% 8.64/4.90 ( if_int
% 8.64/4.90 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.64/4.90 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.64/4.90 @ ( uminus_uminus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 8.64/4.90 @ ( plus_plus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 8.64/4.90 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8036_sin__zero,axiom,
% 8.64/4.90 ( ( sin_complex @ zero_zero_complex )
% 8.64/4.90 = zero_zero_complex ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8037_sin__zero,axiom,
% 8.64/4.90 ( ( sin_real @ zero_zero_real )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8038_bit_Oconj__zero__right,axiom,
% 8.64/4.90 ! [X: int] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8039_bit_Oconj__zero__left,axiom,
% 8.64/4.90 ! [X: int] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8040_zero__and__eq,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8041_zero__and__eq,axiom,
% 8.64/4.90 ! [A: nat] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8042_and__zero__eq,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8043_and__zero__eq,axiom,
% 8.64/4.90 ! [A: nat] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8044_sin__coeff__0,axiom,
% 8.64/4.90 ( ( sin_coeff @ zero_zero_nat )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8045_and__numerals_I5_J,axiom,
% 8.64/4.90 ! [X: num] :
% 8.64/4.90 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ one_one_Code_integer )
% 8.64/4.90 = zero_z3403309356797280102nteger ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8046_and__numerals_I5_J,axiom,
% 8.64/4.90 ! [X: num] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8047_and__numerals_I5_J,axiom,
% 8.64/4.90 ! [X: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8048_and__numerals_I1_J,axiom,
% 8.64/4.90 ! [Y: num] :
% 8.64/4.90 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 8.64/4.90 = zero_z3403309356797280102nteger ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8049_and__numerals_I1_J,axiom,
% 8.64/4.90 ! [Y: num] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8050_and__numerals_I1_J,axiom,
% 8.64/4.90 ! [Y: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8051_and__numerals_I3_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 8.64/4.90 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8052_and__numerals_I3_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.64/4.90 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8053_and__int__rec,axiom,
% 8.64/4.90 ( bit_se725231765392027082nd_int
% 8.64/4.90 = ( ^ [K3: int,L2: int] :
% 8.64/4.90 ( plus_plus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 8.64/4.90 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8054_and__int__unfold,axiom,
% 8.64/4.90 ( bit_se725231765392027082nd_int
% 8.64/4.90 = ( ^ [K3: int,L2: int] :
% 8.64/4.90 ( if_int
% 8.64/4.90 @ ( ( K3 = zero_zero_int )
% 8.64/4.90 | ( L2 = zero_zero_int ) )
% 8.64/4.90 @ zero_zero_int
% 8.64/4.90 @ ( if_int
% 8.64/4.90 @ ( K3
% 8.64/4.90 = ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.90 @ L2
% 8.64/4.90 @ ( if_int
% 8.64/4.90 @ ( L2
% 8.64/4.90 = ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.90 @ K3
% 8.64/4.90 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8055_and__int_Oelims,axiom,
% 8.64/4.90 ! [X: int,Xa2: int,Y: int] :
% 8.64/4.90 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 8.64/4.90 = Y )
% 8.64/4.90 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.64/4.90 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.64/4.90 => ( Y
% 8.64/4.90 = ( uminus_uminus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 8.64/4.90 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.64/4.90 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.64/4.90 => ( Y
% 8.64/4.90 = ( plus_plus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 8.64/4.90 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8056_Maclaurin__sin__expansion3,axiom,
% 8.64/4.90 ! [N: nat,X: real] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ? [T6: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.64/4.90 & ( ord_less_real @ T6 @ X )
% 8.64/4.90 & ( ( sin_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8057_Maclaurin__sin__expansion4,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ? [T6: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.64/4.90 & ( ord_less_eq_real @ T6 @ X )
% 8.64/4.90 & ( ( sin_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8058_sumr__cos__zero__one,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8059_sin__cos__npi,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8060_Maclaurin__sin__expansion,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ? [T6: real] :
% 8.64/4.90 ( ( sin_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8061_signed__take__bit__Suc__minus__bit1,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8062_semiring__norm_I15_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit0 @ N ) )
% 8.64/4.90 = ( bit0 @ ( times_times_num @ ( bit1 @ M2 ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8063_semiring__norm_I14_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( times_times_num @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( bit0 @ ( times_times_num @ M2 @ ( bit1 @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8064_cos__coeff__0,axiom,
% 8.64/4.90 ( ( cos_coeff @ zero_zero_nat )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8065_dbl__inc__simps_I5_J,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K2 ) )
% 8.64/4.90 = ( numera6690914467698888265omplex @ ( bit1 @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8066_dbl__inc__simps_I5_J,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K2 ) )
% 8.64/4.90 = ( numeral_numeral_real @ ( bit1 @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8067_dbl__inc__simps_I5_J,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K2 ) )
% 8.64/4.90 = ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8068_and__nat__numerals_I1_J,axiom,
% 8.64/4.90 ! [Y: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8069_and__nat__numerals_I3_J,axiom,
% 8.64/4.90 ! [X: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8070_zdiv__numeral__Bit1,axiom,
% 8.64/4.90 ! [V2: num,W2: num] :
% 8.64/4.90 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 8.64/4.90 = ( divide_divide_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8071_semiring__norm_I16_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( times_times_num @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M2 @ N ) @ ( bit0 @ ( times_times_num @ M2 @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8072_and__nat__numerals_I4_J,axiom,
% 8.64/4.90 ! [X: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.64/4.90 = one_one_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8073_and__nat__numerals_I2_J,axiom,
% 8.64/4.90 ! [Y: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.64/4.90 = one_one_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8074_sin__npi2,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8075_sin__npi,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8076_dbl__inc__simps_I3_J,axiom,
% 8.64/4.90 ( ( neg_nu5831290666863070958nteger @ one_one_Code_integer )
% 8.64/4.90 = ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8077_dbl__inc__simps_I3_J,axiom,
% 8.64/4.90 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 8.64/4.90 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8078_dbl__inc__simps_I3_J,axiom,
% 8.64/4.90 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 8.64/4.90 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8079_dbl__inc__simps_I3_J,axiom,
% 8.64/4.90 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 8.64/4.90 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8080_and__numerals_I4_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 8.64/4.90 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8081_and__numerals_I4_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.64/4.90 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8082_and__numerals_I6_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 8.64/4.90 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8083_and__numerals_I6_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.64/4.90 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8084_Suc__0__and__eq,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.90 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8085_and__Suc__0__eq,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.64/4.90 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8086_div__Suc__eq__div__add3,axiom,
% 8.64/4.90 ! [M2: nat,N: nat] :
% 8.64/4.90 ( ( divide_divide_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 8.64/4.90 = ( divide_divide_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8087_Suc__div__eq__add3__div__numeral,axiom,
% 8.64/4.90 ! [M2: nat,V2: num] :
% 8.64/4.90 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 8.64/4.90 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8088_mod__Suc__eq__mod__add3,axiom,
% 8.64/4.90 ! [M2: nat,N: nat] :
% 8.64/4.90 ( ( modulo_modulo_nat @ M2 @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 8.64/4.90 = ( modulo_modulo_nat @ M2 @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8089_Suc__mod__eq__add3__mod__numeral,axiom,
% 8.64/4.90 ! [M2: nat,V2: num] :
% 8.64/4.90 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ ( numeral_numeral_nat @ V2 ) )
% 8.64/4.90 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ ( numeral_numeral_nat @ V2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8090_dbl__dec__simps_I4_J,axiom,
% 8.64/4.90 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.90 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8091_dbl__dec__simps_I4_J,axiom,
% 8.64/4.90 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.90 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8092_dbl__dec__simps_I4_J,axiom,
% 8.64/4.90 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 8.64/4.90 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8093_dbl__dec__simps_I4_J,axiom,
% 8.64/4.90 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.90 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8094_dbl__dec__simps_I4_J,axiom,
% 8.64/4.90 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.90 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8095_sin__two__pi,axiom,
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8096_sin__2pi__minus,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 8.64/4.90 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8097_sin__periodic,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.64/4.90 = ( sin_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8098_and__numerals_I7_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 8.64/4.90 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8099_and__numerals_I7_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 8.64/4.90 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8100_and__numerals_I7_J,axiom,
% 8.64/4.90 ! [X: num,Y: num] :
% 8.64/4.90 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.64/4.90 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8101_zmod__numeral__Bit1,axiom,
% 8.64/4.90 ! [V2: num,W2: num] :
% 8.64/4.90 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V2 ) ) @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V2 ) @ ( numeral_numeral_int @ W2 ) ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8102_sin__2npi,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8103_signed__take__bit__Suc__bit1,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8104_sin__3over2__pi,axiom,
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 8.64/4.90 = ( uminus_uminus_real @ one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8105_num_Oexhaust,axiom,
% 8.64/4.90 ! [Y: num] :
% 8.64/4.90 ( ( Y != one )
% 8.64/4.90 => ( ! [X23: num] :
% 8.64/4.90 ( Y
% 8.64/4.90 != ( bit0 @ X23 ) )
% 8.64/4.90 => ~ ! [X32: num] :
% 8.64/4.90 ( Y
% 8.64/4.90 != ( bit1 @ X32 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8106_numeral__Bit1,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8107_numeral__Bit1,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8108_numeral__Bit1,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numera1916890842035813515d_enat @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) @ one_on7984719198319812577d_enat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8109_numeral__Bit1,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8110_numeral__Bit1,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8111_numeral__Bit1,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8112_numeral__Bit1,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8113_eval__nat__numeral_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 8.64/4.90 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8114_cong__exp__iff__simps_I13_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num,N: num] :
% 8.64/4.90 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.90 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.64/4.90 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8115_cong__exp__iff__simps_I13_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num,N: num] :
% 8.64/4.90 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.90 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 8.64/4.90 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8116_cong__exp__iff__simps_I12_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num,N: num] :
% 8.64/4.90 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8117_cong__exp__iff__simps_I12_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num,N: num] :
% 8.64/4.90 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8118_cong__exp__iff__simps_I10_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num,N: num] :
% 8.64/4.90 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8119_cong__exp__iff__simps_I10_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num,N: num] :
% 8.64/4.90 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8120_numeral__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numera6620942414471956472nteger @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ N ) ) @ one_one_Code_integer ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8121_numeral__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8122_numeral__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numera1916890842035813515d_enat @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N ) @ ( numera1916890842035813515d_enat @ N ) ) @ one_on7984719198319812577d_enat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8123_numeral__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8124_numeral__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8125_numeral__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8126_numeral__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 8.64/4.90 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8127_power__numeral__odd,axiom,
% 8.64/4.90 ! [Z3: complex,W2: num] :
% 8.64/4.90 ( ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ Z3 @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_complex @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8128_power__numeral__odd,axiom,
% 8.64/4.90 ! [Z3: real,W2: num] :
% 8.64/4.90 ( ( power_power_real @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ Z3 @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_real @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8129_power__numeral__odd,axiom,
% 8.64/4.90 ! [Z3: rat,W2: num] :
% 8.64/4.90 ( ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 8.64/4.90 = ( times_times_rat @ ( times_times_rat @ Z3 @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_rat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8130_power__numeral__odd,axiom,
% 8.64/4.90 ! [Z3: nat,W2: num] :
% 8.64/4.90 ( ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 8.64/4.90 = ( times_times_nat @ ( times_times_nat @ Z3 @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_nat @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8131_power__numeral__odd,axiom,
% 8.64/4.90 ! [Z3: int,W2: num] :
% 8.64/4.90 ( ( power_power_int @ Z3 @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 8.64/4.90 = ( times_times_int @ ( times_times_int @ Z3 @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_int @ Z3 @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8132_cong__exp__iff__simps_I3_J,axiom,
% 8.64/4.90 ! [N: num,Q2: num] :
% 8.64/4.90 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 != zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8133_cong__exp__iff__simps_I3_J,axiom,
% 8.64/4.90 ! [N: num,Q2: num] :
% 8.64/4.90 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 != zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8134_power3__eq__cube,axiom,
% 8.64/4.90 ! [A: complex] :
% 8.64/4.90 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8135_power3__eq__cube,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8136_power3__eq__cube,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8137_power3__eq__cube,axiom,
% 8.64/4.90 ! [A: nat] :
% 8.64/4.90 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8138_power3__eq__cube,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8139_numeral__3__eq__3,axiom,
% 8.64/4.90 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 8.64/4.90 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8140_Suc3__eq__add__3,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 8.64/4.90 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8141_num_Osize_I6_J,axiom,
% 8.64/4.90 ! [X33: num] :
% 8.64/4.90 ( ( size_size_num @ ( bit1 @ X33 ) )
% 8.64/4.90 = ( plus_plus_nat @ ( size_size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8142_cong__exp__iff__simps_I7_J,axiom,
% 8.64/4.90 ! [Q2: num,N: num] :
% 8.64/4.90 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.90 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.64/4.90 = zero_zero_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8143_cong__exp__iff__simps_I7_J,axiom,
% 8.64/4.90 ! [Q2: num,N: num] :
% 8.64/4.90 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.90 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 8.64/4.90 = zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8144_cong__exp__iff__simps_I11_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num] :
% 8.64/4.90 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.90 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ Q2 ) )
% 8.64/4.90 = zero_zero_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8145_cong__exp__iff__simps_I11_J,axiom,
% 8.64/4.90 ! [M2: num,Q2: num] :
% 8.64/4.90 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 8.64/4.90 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 8.64/4.90 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ Q2 ) )
% 8.64/4.90 = zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8146_Suc__div__eq__add3__div,axiom,
% 8.64/4.90 ! [M2: nat,N: nat] :
% 8.64/4.90 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 8.64/4.90 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8147_card__3__iff,axiom,
% 8.64/4.90 ! [S3: set_complex] :
% 8.64/4.90 ( ( ( finite_card_complex @ S3 )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( ? [X4: complex,Y4: complex,Z4: complex] :
% 8.64/4.90 ( ( S3
% 8.64/4.90 = ( insert_complex @ X4 @ ( insert_complex @ Y4 @ ( insert_complex @ Z4 @ bot_bot_set_complex ) ) ) )
% 8.64/4.90 & ( X4 != Y4 )
% 8.64/4.90 & ( Y4 != Z4 )
% 8.64/4.90 & ( X4 != Z4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8148_card__3__iff,axiom,
% 8.64/4.90 ! [S3: set_list_nat] :
% 8.64/4.90 ( ( ( finite_card_list_nat @ S3 )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( ? [X4: list_nat,Y4: list_nat,Z4: list_nat] :
% 8.64/4.90 ( ( S3
% 8.64/4.90 = ( insert_list_nat @ X4 @ ( insert_list_nat @ Y4 @ ( insert_list_nat @ Z4 @ bot_bot_set_list_nat ) ) ) )
% 8.64/4.90 & ( X4 != Y4 )
% 8.64/4.90 & ( Y4 != Z4 )
% 8.64/4.90 & ( X4 != Z4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8149_card__3__iff,axiom,
% 8.64/4.90 ! [S3: set_set_nat] :
% 8.64/4.90 ( ( ( finite_card_set_nat @ S3 )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( ? [X4: set_nat,Y4: set_nat,Z4: set_nat] :
% 8.64/4.90 ( ( S3
% 8.64/4.90 = ( insert_set_nat @ X4 @ ( insert_set_nat @ Y4 @ ( insert_set_nat @ Z4 @ bot_bot_set_set_nat ) ) ) )
% 8.64/4.90 & ( X4 != Y4 )
% 8.64/4.90 & ( Y4 != Z4 )
% 8.64/4.90 & ( X4 != Z4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8150_card__3__iff,axiom,
% 8.64/4.90 ! [S3: set_nat] :
% 8.64/4.90 ( ( ( finite_card_nat @ S3 )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( ? [X4: nat,Y4: nat,Z4: nat] :
% 8.64/4.90 ( ( S3
% 8.64/4.90 = ( insert_nat @ X4 @ ( insert_nat @ Y4 @ ( insert_nat @ Z4 @ bot_bot_set_nat ) ) ) )
% 8.64/4.90 & ( X4 != Y4 )
% 8.64/4.90 & ( Y4 != Z4 )
% 8.64/4.90 & ( X4 != Z4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8151_card__3__iff,axiom,
% 8.64/4.90 ! [S3: set_int] :
% 8.64/4.90 ( ( ( finite_card_int @ S3 )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( ? [X4: int,Y4: int,Z4: int] :
% 8.64/4.90 ( ( S3
% 8.64/4.90 = ( insert_int @ X4 @ ( insert_int @ Y4 @ ( insert_int @ Z4 @ bot_bot_set_int ) ) ) )
% 8.64/4.90 & ( X4 != Y4 )
% 8.64/4.90 & ( Y4 != Z4 )
% 8.64/4.90 & ( X4 != Z4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8152_card__3__iff,axiom,
% 8.64/4.90 ! [S3: set_real] :
% 8.64/4.90 ( ( ( finite_card_real @ S3 )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 = ( ? [X4: real,Y4: real,Z4: real] :
% 8.64/4.90 ( ( S3
% 8.64/4.90 = ( insert_real @ X4 @ ( insert_real @ Y4 @ ( insert_real @ Z4 @ bot_bot_set_real ) ) ) )
% 8.64/4.90 & ( X4 != Y4 )
% 8.64/4.90 & ( Y4 != Z4 )
% 8.64/4.90 & ( X4 != Z4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8153_Suc__mod__eq__add3__mod,axiom,
% 8.64/4.90 ! [M2: nat,N: nat] :
% 8.64/4.90 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M2 ) ) ) @ N )
% 8.64/4.90 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M2 ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8154_mod__exhaust__less__4,axiom,
% 8.64/4.90 ! [M2: nat] :
% 8.64/4.90 ( ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = zero_zero_nat )
% 8.64/4.90 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = one_one_nat )
% 8.64/4.90 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.90 | ( ( modulo_modulo_nat @ M2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8155_m2pi__less__pi,axiom,
% 8.64/4.90 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8156_sin__pi__divide__n__ge__0,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( N != zero_zero_nat )
% 8.64/4.90 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8157_sin__coeff__Suc,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( sin_coeff @ ( suc @ N ) )
% 8.64/4.90 = ( divide_divide_real @ ( cos_coeff @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8158_sin__lt__zero,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_real @ pi @ X )
% 8.64/4.90 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.90 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8159_and__nat__unfold,axiom,
% 8.64/4.90 ( bit_se727722235901077358nd_nat
% 8.64/4.90 = ( ^ [M6: nat,N4: nat] :
% 8.64/4.90 ( if_nat
% 8.64/4.90 @ ( ( M6 = zero_zero_nat )
% 8.64/4.90 | ( N4 = zero_zero_nat ) )
% 8.64/4.90 @ zero_zero_nat
% 8.64/4.90 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8160_and__nat__rec,axiom,
% 8.64/4.90 ( bit_se727722235901077358nd_nat
% 8.64/4.90 = ( ^ [M6: nat,N4: nat] :
% 8.64/4.90 ( plus_plus_nat
% 8.64/4.90 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.90 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 8.64/4.90 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 8.64/4.90 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8161_sin__le__zero,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ pi @ X )
% 8.64/4.90 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.90 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8162_cos__coeff__Suc,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( cos_coeff @ ( suc @ N ) )
% 8.64/4.90 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8163_odd__mod__4__div__2,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 8.64/4.90 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8164_sin__pi__divide__n__gt__0,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8165_sin__zero__lemma,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ( sin_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 => ? [N3: nat] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8166_sin__zero__iff,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( sin_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( ? [N4: nat] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.90 | ? [N4: nat] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8167_Maclaurin__minus__cos__expansion,axiom,
% 8.64/4.90 ! [N: nat,X: real] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ( ord_less_real @ X @ zero_zero_real )
% 8.64/4.90 => ? [T6: real] :
% 8.64/4.90 ( ( ord_less_real @ X @ T6 )
% 8.64/4.90 & ( ord_less_real @ T6 @ zero_zero_real )
% 8.64/4.90 & ( ( cos_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8168_Maclaurin__cos__expansion2,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ? [T6: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.64/4.90 & ( ord_less_real @ T6 @ X )
% 8.64/4.90 & ( ( cos_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8169_Maclaurin__sin__expansion2,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ? [T6: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.90 & ( ( sin_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8170_signed__take__bit__numeral__minus__bit1,axiom,
% 8.64/4.90 ! [L: num,K2: num] :
% 8.64/4.90 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8171_divmod__algorithm__code_I8_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( ( ord_less_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M2 ) ) ) ) )
% 8.64/4.90 & ( ~ ( ord_less_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8172_divmod__algorithm__code_I8_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( ( ord_less_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) ) ) )
% 8.64/4.90 & ( ~ ( ord_less_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8173_divmod__algorithm__code_I8_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( ( ord_less_num @ M2 @ N )
% 8.64/4.90 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M2 ) ) ) ) )
% 8.64/4.90 & ( ~ ( ord_less_num @ M2 @ N )
% 8.64/4.90 => ( ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8174_divmod__algorithm__code_I7_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( ( ord_less_eq_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M2 ) ) ) ) )
% 8.64/4.90 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8175_divmod__algorithm__code_I7_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( ( ord_less_eq_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) ) ) )
% 8.64/4.90 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 8.64/4.90 => ( ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8176_divmod__algorithm__code_I7_J,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( ( ord_less_eq_num @ M2 @ N )
% 8.64/4.90 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M2 ) ) ) ) )
% 8.64/4.90 & ( ~ ( ord_less_eq_num @ M2 @ N )
% 8.64/4.90 => ( ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit1 @ N ) )
% 8.64/4.90 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M2 ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8177_abs__idempotent,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 8.64/4.90 = ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8178_abs__idempotent,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 8.64/4.90 = ( abs_abs_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8179_abs__idempotent,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 8.64/4.90 = ( abs_abs_Code_integer @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8180_abs__idempotent,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 8.64/4.90 = ( abs_abs_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8181_abs__abs,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 8.64/4.90 = ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8182_abs__abs,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 8.64/4.90 = ( abs_abs_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8183_abs__abs,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 8.64/4.90 = ( abs_abs_Code_integer @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8184_abs__abs,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 8.64/4.90 = ( abs_abs_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8185_abs__0,axiom,
% 8.64/4.90 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 8.64/4.90 = zero_z3403309356797280102nteger ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8186_abs__0,axiom,
% 8.64/4.90 ( ( abs_abs_complex @ zero_zero_complex )
% 8.64/4.90 = zero_zero_complex ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8187_abs__0,axiom,
% 8.64/4.90 ( ( abs_abs_real @ zero_zero_real )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8188_abs__0,axiom,
% 8.64/4.90 ( ( abs_abs_rat @ zero_zero_rat )
% 8.64/4.90 = zero_zero_rat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8189_abs__0,axiom,
% 8.64/4.90 ( ( abs_abs_int @ zero_zero_int )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8190_abs__0__eq,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( zero_z3403309356797280102nteger
% 8.64/4.90 = ( abs_abs_Code_integer @ A ) )
% 8.64/4.90 = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8191_abs__0__eq,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( zero_zero_real
% 8.64/4.90 = ( abs_abs_real @ A ) )
% 8.64/4.90 = ( A = zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8192_abs__0__eq,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( zero_zero_rat
% 8.64/4.90 = ( abs_abs_rat @ A ) )
% 8.64/4.90 = ( A = zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8193_abs__0__eq,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( zero_zero_int
% 8.64/4.90 = ( abs_abs_int @ A ) )
% 8.64/4.90 = ( A = zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8194_abs__eq__0,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ( abs_abs_Code_integer @ A )
% 8.64/4.90 = zero_z3403309356797280102nteger )
% 8.64/4.90 = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8195_abs__eq__0,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ( abs_abs_real @ A )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( A = zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8196_abs__eq__0,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ( abs_abs_rat @ A )
% 8.64/4.90 = zero_zero_rat )
% 8.64/4.90 = ( A = zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8197_abs__eq__0,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ( abs_abs_int @ A )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 = ( A = zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8198_abs__zero,axiom,
% 8.64/4.90 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 8.64/4.90 = zero_z3403309356797280102nteger ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8199_abs__zero,axiom,
% 8.64/4.90 ( ( abs_abs_real @ zero_zero_real )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8200_abs__zero,axiom,
% 8.64/4.90 ( ( abs_abs_rat @ zero_zero_rat )
% 8.64/4.90 = zero_zero_rat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8201_abs__zero,axiom,
% 8.64/4.90 ( ( abs_abs_int @ zero_zero_int )
% 8.64/4.90 = zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8202_abs__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 8.64/4.90 = ( numera6620942414471956472nteger @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8203_abs__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 8.64/4.90 = ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8204_abs__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 8.64/4.90 = ( numeral_numeral_real @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8205_abs__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 8.64/4.90 = ( numeral_numeral_int @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8206_abs__mult__self__eq,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 8.64/4.90 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8207_abs__mult__self__eq,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 8.64/4.90 = ( times_times_real @ A @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8208_abs__mult__self__eq,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 8.64/4.90 = ( times_times_rat @ A @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8209_abs__mult__self__eq,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 8.64/4.90 = ( times_times_int @ A @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8210_abs__add__abs,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 8.64/4.90 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8211_abs__add__abs,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 8.64/4.90 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8212_abs__add__abs,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 8.64/4.90 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8213_abs__add__abs,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8214_abs__1,axiom,
% 8.64/4.90 ( ( abs_abs_rat @ one_one_rat )
% 8.64/4.90 = one_one_rat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8215_abs__1,axiom,
% 8.64/4.90 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 8.64/4.90 = one_one_Code_integer ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8216_abs__1,axiom,
% 8.64/4.90 ( ( abs_abs_complex @ one_one_complex )
% 8.64/4.90 = one_one_complex ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8217_abs__1,axiom,
% 8.64/4.90 ( ( abs_abs_real @ one_one_real )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8218_abs__1,axiom,
% 8.64/4.90 ( ( abs_abs_int @ one_one_int )
% 8.64/4.90 = one_one_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8219_abs__minus__cancel,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 8.64/4.90 = ( abs_abs_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8220_abs__minus__cancel,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 8.64/4.90 = ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8221_abs__minus__cancel,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.90 = ( abs_abs_Code_integer @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8222_abs__minus__cancel,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 8.64/4.90 = ( abs_abs_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8223_abs__minus,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 8.64/4.90 = ( abs_abs_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8224_abs__minus,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 8.64/4.90 = ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8225_abs__minus,axiom,
% 8.64/4.90 ! [A: complex] :
% 8.64/4.90 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 8.64/4.90 = ( abs_abs_complex @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8226_abs__minus,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 8.64/4.90 = ( abs_abs_Code_integer @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8227_abs__minus,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 8.64/4.90 = ( abs_abs_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8228_dvd__abs__iff,axiom,
% 8.64/4.90 ! [M2: real,K2: real] :
% 8.64/4.90 ( ( dvd_dvd_real @ M2 @ ( abs_abs_real @ K2 ) )
% 8.64/4.90 = ( dvd_dvd_real @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8229_dvd__abs__iff,axiom,
% 8.64/4.90 ! [M2: int,K2: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ M2 @ ( abs_abs_int @ K2 ) )
% 8.64/4.90 = ( dvd_dvd_int @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8230_dvd__abs__iff,axiom,
% 8.64/4.90 ! [M2: code_integer,K2: code_integer] :
% 8.64/4.90 ( ( dvd_dvd_Code_integer @ M2 @ ( abs_abs_Code_integer @ K2 ) )
% 8.64/4.90 = ( dvd_dvd_Code_integer @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8231_dvd__abs__iff,axiom,
% 8.64/4.90 ! [M2: rat,K2: rat] :
% 8.64/4.90 ( ( dvd_dvd_rat @ M2 @ ( abs_abs_rat @ K2 ) )
% 8.64/4.90 = ( dvd_dvd_rat @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8232_abs__dvd__iff,axiom,
% 8.64/4.90 ! [M2: real,K2: real] :
% 8.64/4.90 ( ( dvd_dvd_real @ ( abs_abs_real @ M2 ) @ K2 )
% 8.64/4.90 = ( dvd_dvd_real @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8233_abs__dvd__iff,axiom,
% 8.64/4.90 ! [M2: int,K2: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ ( abs_abs_int @ M2 ) @ K2 )
% 8.64/4.90 = ( dvd_dvd_int @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8234_abs__dvd__iff,axiom,
% 8.64/4.90 ! [M2: code_integer,K2: code_integer] :
% 8.64/4.90 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M2 ) @ K2 )
% 8.64/4.90 = ( dvd_dvd_Code_integer @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8235_abs__dvd__iff,axiom,
% 8.64/4.90 ! [M2: rat,K2: rat] :
% 8.64/4.90 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M2 ) @ K2 )
% 8.64/4.90 = ( dvd_dvd_rat @ M2 @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8236_abs__of__nat,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 8.64/4.90 = ( semiri4939895301339042750nteger @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8237_abs__of__nat,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 8.64/4.90 = ( semiri681578069525770553at_rat @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8238_abs__of__nat,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.90 = ( semiri5074537144036343181t_real @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8239_abs__of__nat,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.90 = ( semiri1314217659103216013at_int @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8240_abs__bool__eq,axiom,
% 8.64/4.90 ! [P2: $o] :
% 8.64/4.90 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P2 ) )
% 8.64/4.90 = ( zero_n3304061248610475627l_real @ P2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8241_abs__bool__eq,axiom,
% 8.64/4.90 ! [P2: $o] :
% 8.64/4.90 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 8.64/4.90 = ( zero_n2052037380579107095ol_rat @ P2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8242_abs__bool__eq,axiom,
% 8.64/4.90 ! [P2: $o] :
% 8.64/4.90 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 8.64/4.90 = ( zero_n2684676970156552555ol_int @ P2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8243_abs__bool__eq,axiom,
% 8.64/4.90 ! [P2: $o] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P2 ) )
% 8.64/4.90 = ( zero_n356916108424825756nteger @ P2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8244_abs__of__nonneg,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.64/4.90 => ( ( abs_abs_Code_integer @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8245_abs__of__nonneg,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.64/4.90 => ( ( abs_abs_real @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8246_abs__of__nonneg,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.64/4.90 => ( ( abs_abs_rat @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8247_abs__of__nonneg,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.90 => ( ( abs_abs_int @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8248_abs__le__self__iff,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 8.64/4.90 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8249_abs__le__self__iff,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 8.64/4.90 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8250_abs__le__self__iff,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 8.64/4.90 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8251_abs__le__self__iff,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 8.64/4.90 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8252_abs__le__zero__iff,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 8.64/4.90 = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8253_abs__le__zero__iff,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 8.64/4.90 = ( A = zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8254_abs__le__zero__iff,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 8.64/4.90 = ( A = zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8255_abs__le__zero__iff,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 8.64/4.90 = ( A = zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8256_zero__less__abs__iff,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 8.64/4.90 = ( A != zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8257_zero__less__abs__iff,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 8.64/4.90 = ( A != zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8258_zero__less__abs__iff,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 8.64/4.90 = ( A != zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8259_zero__less__abs__iff,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 8.64/4.90 = ( A != zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8260_abs__neg__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.90 = ( numeral_numeral_int @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8261_abs__neg__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 8.64/4.90 = ( numeral_numeral_real @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8262_abs__neg__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 8.64/4.90 = ( numera6620942414471956472nteger @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8263_abs__neg__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 8.64/4.90 = ( numeral_numeral_rat @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8264_abs__neg__one,axiom,
% 8.64/4.90 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.90 = one_one_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8265_abs__neg__one,axiom,
% 8.64/4.90 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8266_abs__neg__one,axiom,
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 8.64/4.90 = one_one_Code_integer ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8267_abs__neg__one,axiom,
% 8.64/4.90 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 8.64/4.90 = one_one_rat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8268_cos__zero,axiom,
% 8.64/4.90 ( ( cos_complex @ zero_zero_complex )
% 8.64/4.90 = one_one_complex ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8269_cos__zero,axiom,
% 8.64/4.90 ( ( cos_real @ zero_zero_real )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8270_pred__numeral__simps_I1_J,axiom,
% 8.64/4.90 ( ( pred_numeral @ one )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8271_eq__numeral__Suc,axiom,
% 8.64/4.90 ! [K2: num,N: nat] :
% 8.64/4.90 ( ( ( numeral_numeral_nat @ K2 )
% 8.64/4.90 = ( suc @ N ) )
% 8.64/4.90 = ( ( pred_numeral @ K2 )
% 8.64/4.90 = N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8272_Suc__eq__numeral,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( ( suc @ N )
% 8.64/4.90 = ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( N
% 8.64/4.90 = ( pred_numeral @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8273_sum__abs,axiom,
% 8.64/4.90 ! [F2: int > int,A4: set_int] :
% 8.64/4.90 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F2 @ A4 ) )
% 8.64/4.90 @ ( groups4538972089207619220nt_int
% 8.64/4.90 @ ^ [I: int] : ( abs_abs_int @ ( F2 @ I ) )
% 8.64/4.90 @ A4 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8274_sum__abs,axiom,
% 8.64/4.90 ! [F2: nat > real,A4: set_nat] :
% 8.64/4.90 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F2 @ A4 ) )
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [I: nat] : ( abs_abs_real @ ( F2 @ I ) )
% 8.64/4.90 @ A4 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8275_divide__le__0__abs__iff,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 8.64/4.90 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.64/4.90 | ( B = zero_zero_real ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8276_divide__le__0__abs__iff,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 8.64/4.90 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.64/4.90 | ( B = zero_zero_rat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8277_zero__le__divide__abs__iff,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 8.64/4.90 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.64/4.90 | ( B = zero_zero_real ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8278_zero__le__divide__abs__iff,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 8.64/4.90 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.64/4.90 | ( B = zero_zero_rat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8279_abs__of__nonpos,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 8.64/4.90 => ( ( abs_abs_real @ A )
% 8.64/4.90 = ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8280_abs__of__nonpos,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 8.64/4.90 => ( ( abs_abs_Code_integer @ A )
% 8.64/4.90 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8281_abs__of__nonpos,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 8.64/4.90 => ( ( abs_abs_rat @ A )
% 8.64/4.90 = ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8282_abs__of__nonpos,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 8.64/4.90 => ( ( abs_abs_int @ A )
% 8.64/4.90 = ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8283_less__Suc__numeral,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( ord_less_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8284_less__numeral__Suc,axiom,
% 8.64/4.90 ! [K2: num,N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 8.64/4.90 = ( ord_less_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8285_pred__numeral__simps_I3_J,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( pred_numeral @ ( bit1 @ K2 ) )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bit0 @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8286_le__numeral__Suc,axiom,
% 8.64/4.90 ! [K2: num,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 8.64/4.90 = ( ord_less_eq_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8287_le__Suc__numeral,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8288_diff__numeral__Suc,axiom,
% 8.64/4.90 ! [K2: num,N: nat] :
% 8.64/4.90 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 8.64/4.90 = ( minus_minus_nat @ ( pred_numeral @ K2 ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8289_diff__Suc__numeral,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( minus_minus_nat @ N @ ( pred_numeral @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8290_max__Suc__numeral,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8291_max__numeral__Suc,axiom,
% 8.64/4.90 ! [K2: num,N: nat] :
% 8.64/4.90 ( ( ord_max_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 8.64/4.90 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K2 ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8292_sum__abs__ge__zero,axiom,
% 8.64/4.90 ! [F2: int > int,A4: set_int] :
% 8.64/4.90 ( ord_less_eq_int @ zero_zero_int
% 8.64/4.90 @ ( groups4538972089207619220nt_int
% 8.64/4.90 @ ^ [I: int] : ( abs_abs_int @ ( F2 @ I ) )
% 8.64/4.90 @ A4 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8293_sum__abs__ge__zero,axiom,
% 8.64/4.90 ! [F2: nat > real,A4: set_nat] :
% 8.64/4.90 ( ord_less_eq_real @ zero_zero_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [I: nat] : ( abs_abs_real @ ( F2 @ I ) )
% 8.64/4.90 @ A4 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8294_minus__numeral__div__numeral,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 8.64/4.90 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8295_numeral__div__minus__numeral,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( divide_divide_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.90 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8296_zero__less__power__abs__iff,axiom,
% 8.64/4.90 ! [A: code_integer,N: nat] :
% 8.64/4.90 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 8.64/4.90 = ( ( A != zero_z3403309356797280102nteger )
% 8.64/4.90 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8297_zero__less__power__abs__iff,axiom,
% 8.64/4.90 ! [A: real,N: nat] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 8.64/4.90 = ( ( A != zero_zero_real )
% 8.64/4.90 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8298_zero__less__power__abs__iff,axiom,
% 8.64/4.90 ! [A: rat,N: nat] :
% 8.64/4.90 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 8.64/4.90 = ( ( A != zero_zero_rat )
% 8.64/4.90 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8299_zero__less__power__abs__iff,axiom,
% 8.64/4.90 ! [A: int,N: nat] :
% 8.64/4.90 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 8.64/4.90 = ( ( A != zero_zero_int )
% 8.64/4.90 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8300_sin__cos__squared__add3,axiom,
% 8.64/4.90 ! [X: complex] :
% 8.64/4.90 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X ) @ ( cos_complex @ X ) ) @ ( times_times_complex @ ( sin_complex @ X ) @ ( sin_complex @ X ) ) )
% 8.64/4.90 = one_one_complex ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8301_sin__cos__squared__add3,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ X ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ X ) ) )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8302_dvd__numeral__simp,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M2 ) @ ( numeral_numeral_int @ N ) )
% 8.64/4.90 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8303_dvd__numeral__simp,axiom,
% 8.64/4.90 ! [M2: num,N: num] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.64/4.90 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8304_divmod__algorithm__code_I2_J,axiom,
% 8.64/4.90 ! [M2: num] :
% 8.64/4.90 ( ( unique3479559517661332726nteger @ M2 @ one )
% 8.64/4.90 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M2 ) @ zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8305_divmod__algorithm__code_I2_J,axiom,
% 8.64/4.90 ! [M2: num] :
% 8.64/4.90 ( ( unique5052692396658037445od_int @ M2 @ one )
% 8.64/4.90 = ( product_Pair_int_int @ ( numeral_numeral_int @ M2 ) @ zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8306_divmod__algorithm__code_I2_J,axiom,
% 8.64/4.90 ! [M2: num] :
% 8.64/4.90 ( ( unique5055182867167087721od_nat @ M2 @ one )
% 8.64/4.90 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M2 ) @ zero_zero_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8307_divmod__algorithm__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 8.64/4.90 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8308_divmod__algorithm__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 8.64/4.90 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8309_divmod__algorithm__code_I3_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 8.64/4.90 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8310_divmod__algorithm__code_I4_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 8.64/4.90 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8311_divmod__algorithm__code_I4_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 8.64/4.90 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8312_divmod__algorithm__code_I4_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 8.64/4.90 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8313_one__div__minus__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.90 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8314_minus__one__div__numeral,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.64/4.90 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8315_cos__two__pi,axiom,
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8316_cos__periodic,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.64/4.90 = ( cos_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8317_cos__2pi__minus,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 8.64/4.90 = ( cos_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8318_signed__take__bit__numeral__bit0,axiom,
% 8.64/4.90 ! [L: num,K2: num] :
% 8.64/4.90 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) )
% 8.64/4.90 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8319_cos__npi,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.64/4.90 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8320_cos__npi2,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.64/4.90 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8321_cos__2npi,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8322_signed__take__bit__numeral__minus__bit0,axiom,
% 8.64/4.90 ! [L: num,K2: num] :
% 8.64/4.90 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 8.64/4.90 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8323_cos__3over2__pi,axiom,
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8324_signed__take__bit__numeral__bit1,axiom,
% 8.64/4.90 ! [L: num,K2: num] :
% 8.64/4.90 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8325_cos__pi__eq__zero,axiom,
% 8.64/4.90 ! [M2: nat] :
% 8.64/4.90 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M2 ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8326_abs__ge__self,axiom,
% 8.64/4.90 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8327_abs__ge__self,axiom,
% 8.64/4.90 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8328_abs__ge__self,axiom,
% 8.64/4.90 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8329_abs__ge__self,axiom,
% 8.64/4.90 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8330_abs__le__D1,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_real @ A @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8331_abs__le__D1,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8332_abs__le__D1,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_rat @ A @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8333_abs__le__D1,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_int @ A @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8334_abs__eq__0__iff,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ( abs_abs_Code_integer @ A )
% 8.64/4.90 = zero_z3403309356797280102nteger )
% 8.64/4.90 = ( A = zero_z3403309356797280102nteger ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8335_abs__eq__0__iff,axiom,
% 8.64/4.90 ! [A: complex] :
% 8.64/4.90 ( ( ( abs_abs_complex @ A )
% 8.64/4.90 = zero_zero_complex )
% 8.64/4.90 = ( A = zero_zero_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8336_abs__eq__0__iff,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ( abs_abs_real @ A )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( A = zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8337_abs__eq__0__iff,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ( abs_abs_rat @ A )
% 8.64/4.90 = zero_zero_rat )
% 8.64/4.90 = ( A = zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8338_abs__eq__0__iff,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ( abs_abs_int @ A )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 = ( A = zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8339_abs__mult,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.64/4.90 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8340_abs__mult,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 8.64/4.90 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8341_abs__mult,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 8.64/4.90 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8342_abs__mult,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 8.64/4.90 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8343_abs__one,axiom,
% 8.64/4.90 ( ( abs_abs_rat @ one_one_rat )
% 8.64/4.90 = one_one_rat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8344_abs__one,axiom,
% 8.64/4.90 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 8.64/4.90 = one_one_Code_integer ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8345_abs__one,axiom,
% 8.64/4.90 ( ( abs_abs_real @ one_one_real )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8346_abs__one,axiom,
% 8.64/4.90 ( ( abs_abs_int @ one_one_int )
% 8.64/4.90 = one_one_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8347_abs__minus__commute,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 8.64/4.90 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8348_abs__minus__commute,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 8.64/4.90 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8349_abs__minus__commute,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 8.64/4.90 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8350_abs__minus__commute,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 8.64/4.90 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8351_abs__eq__iff,axiom,
% 8.64/4.90 ! [X: int,Y: int] :
% 8.64/4.90 ( ( ( abs_abs_int @ X )
% 8.64/4.90 = ( abs_abs_int @ Y ) )
% 8.64/4.90 = ( ( X = Y )
% 8.64/4.90 | ( X
% 8.64/4.90 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8352_abs__eq__iff,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( ( abs_abs_real @ X )
% 8.64/4.90 = ( abs_abs_real @ Y ) )
% 8.64/4.90 = ( ( X = Y )
% 8.64/4.90 | ( X
% 8.64/4.90 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8353_abs__eq__iff,axiom,
% 8.64/4.90 ! [X: code_integer,Y: code_integer] :
% 8.64/4.90 ( ( ( abs_abs_Code_integer @ X )
% 8.64/4.90 = ( abs_abs_Code_integer @ Y ) )
% 8.64/4.90 = ( ( X = Y )
% 8.64/4.90 | ( X
% 8.64/4.90 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8354_abs__eq__iff,axiom,
% 8.64/4.90 ! [X: rat,Y: rat] :
% 8.64/4.90 ( ( ( abs_abs_rat @ X )
% 8.64/4.90 = ( abs_abs_rat @ Y ) )
% 8.64/4.90 = ( ( X = Y )
% 8.64/4.90 | ( X
% 8.64/4.90 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8355_dvd__if__abs__eq,axiom,
% 8.64/4.90 ! [L: real,K2: real] :
% 8.64/4.90 ( ( ( abs_abs_real @ L )
% 8.64/4.90 = ( abs_abs_real @ K2 ) )
% 8.64/4.90 => ( dvd_dvd_real @ L @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8356_dvd__if__abs__eq,axiom,
% 8.64/4.90 ! [L: int,K2: int] :
% 8.64/4.90 ( ( ( abs_abs_int @ L )
% 8.64/4.90 = ( abs_abs_int @ K2 ) )
% 8.64/4.90 => ( dvd_dvd_int @ L @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8357_dvd__if__abs__eq,axiom,
% 8.64/4.90 ! [L: code_integer,K2: code_integer] :
% 8.64/4.90 ( ( ( abs_abs_Code_integer @ L )
% 8.64/4.90 = ( abs_abs_Code_integer @ K2 ) )
% 8.64/4.90 => ( dvd_dvd_Code_integer @ L @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8358_dvd__if__abs__eq,axiom,
% 8.64/4.90 ! [L: rat,K2: rat] :
% 8.64/4.90 ( ( ( abs_abs_rat @ L )
% 8.64/4.90 = ( abs_abs_rat @ K2 ) )
% 8.64/4.90 => ( dvd_dvd_rat @ L @ K2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8359_abs__ge__zero,axiom,
% 8.64/4.90 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8360_abs__ge__zero,axiom,
% 8.64/4.90 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8361_abs__ge__zero,axiom,
% 8.64/4.90 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8362_abs__ge__zero,axiom,
% 8.64/4.90 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8363_abs__not__less__zero,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8364_abs__not__less__zero,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8365_abs__not__less__zero,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8366_abs__not__less__zero,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8367_abs__of__pos,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 8.64/4.90 => ( ( abs_abs_Code_integer @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8368_abs__of__pos,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.90 => ( ( abs_abs_real @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8369_abs__of__pos,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ord_less_rat @ zero_zero_rat @ A )
% 8.64/4.90 => ( ( abs_abs_rat @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8370_abs__of__pos,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ord_less_int @ zero_zero_int @ A )
% 8.64/4.90 => ( ( abs_abs_int @ A )
% 8.64/4.90 = A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8371_abs__triangle__ineq,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8372_abs__triangle__ineq,axiom,
% 8.64/4.90 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8373_abs__triangle__ineq,axiom,
% 8.64/4.90 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8374_abs__triangle__ineq,axiom,
% 8.64/4.90 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8375_abs__mult__less,axiom,
% 8.64/4.90 ! [A: code_integer,C2: code_integer,B: code_integer,D: code_integer] :
% 8.64/4.90 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C2 )
% 8.64/4.90 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 8.64/4.90 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C2 @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8376_abs__mult__less,axiom,
% 8.64/4.90 ! [A: real,C2: real,B: real,D: real] :
% 8.64/4.90 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C2 )
% 8.64/4.90 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 8.64/4.90 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C2 @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8377_abs__mult__less,axiom,
% 8.64/4.90 ! [A: rat,C2: rat,B: rat,D: rat] :
% 8.64/4.90 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C2 )
% 8.64/4.90 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 8.64/4.90 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C2 @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8378_abs__mult__less,axiom,
% 8.64/4.90 ! [A: int,C2: int,B: int,D: int] :
% 8.64/4.90 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C2 )
% 8.64/4.90 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 8.64/4.90 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C2 @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8379_abs__triangle__ineq2__sym,axiom,
% 8.64/4.90 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8380_abs__triangle__ineq2__sym,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8381_abs__triangle__ineq2__sym,axiom,
% 8.64/4.90 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8382_abs__triangle__ineq2__sym,axiom,
% 8.64/4.90 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8383_abs__triangle__ineq3,axiom,
% 8.64/4.90 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8384_abs__triangle__ineq3,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8385_abs__triangle__ineq3,axiom,
% 8.64/4.90 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8386_abs__triangle__ineq3,axiom,
% 8.64/4.90 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8387_abs__triangle__ineq2,axiom,
% 8.64/4.90 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8388_abs__triangle__ineq2,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8389_abs__triangle__ineq2,axiom,
% 8.64/4.90 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8390_abs__triangle__ineq2,axiom,
% 8.64/4.90 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8391_nonzero__abs__divide,axiom,
% 8.64/4.90 ! [B: real,A: real] :
% 8.64/4.90 ( ( B != zero_zero_real )
% 8.64/4.90 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 8.64/4.90 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8392_nonzero__abs__divide,axiom,
% 8.64/4.90 ! [B: rat,A: rat] :
% 8.64/4.90 ( ( B != zero_zero_rat )
% 8.64/4.90 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 8.64/4.90 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8393_abs__leI,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ A @ B )
% 8.64/4.90 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8394_abs__leI,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.64/4.90 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8395_abs__leI,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.90 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8396_abs__leI,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ A @ B )
% 8.64/4.90 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8397_abs__le__D2,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8398_abs__le__D2,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8399_abs__le__D2,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8400_abs__le__D2,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.64/4.90 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8401_abs__le__iff,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 8.64/4.90 = ( ( ord_less_eq_real @ A @ B )
% 8.64/4.90 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8402_abs__le__iff,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.64/4.90 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 8.64/4.90 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8403_abs__le__iff,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 8.64/4.90 = ( ( ord_less_eq_rat @ A @ B )
% 8.64/4.90 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8404_abs__le__iff,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 8.64/4.90 = ( ( ord_less_eq_int @ A @ B )
% 8.64/4.90 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8405_abs__ge__minus__self,axiom,
% 8.64/4.90 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8406_abs__ge__minus__self,axiom,
% 8.64/4.90 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8407_abs__ge__minus__self,axiom,
% 8.64/4.90 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8408_abs__ge__minus__self,axiom,
% 8.64/4.90 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8409_abs__less__iff,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 8.64/4.90 = ( ( ord_less_int @ A @ B )
% 8.64/4.90 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8410_abs__less__iff,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 8.64/4.90 = ( ( ord_less_real @ A @ B )
% 8.64/4.90 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8411_abs__less__iff,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 8.64/4.90 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 8.64/4.90 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8412_abs__less__iff,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 8.64/4.90 = ( ( ord_less_rat @ A @ B )
% 8.64/4.90 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8413_polar__Ex,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ? [R4: real,A3: real] :
% 8.64/4.90 ( ( X
% 8.64/4.90 = ( times_times_real @ R4 @ ( cos_real @ A3 ) ) )
% 8.64/4.90 & ( Y
% 8.64/4.90 = ( times_times_real @ R4 @ ( sin_real @ A3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8414_numeral__eq__Suc,axiom,
% 8.64/4.90 ( numeral_numeral_nat
% 8.64/4.90 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8415_sin__cos__le1,axiom,
% 8.64/4.90 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8416_dense__eq0__I,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ! [E2: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 8.64/4.90 => ( X = zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8417_dense__eq0__I,axiom,
% 8.64/4.90 ! [X: rat] :
% 8.64/4.90 ( ! [E2: rat] :
% 8.64/4.90 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 8.64/4.90 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 8.64/4.90 => ( X = zero_zero_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8418_abs__mult__pos,axiom,
% 8.64/4.90 ! [X: code_integer,Y: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 8.64/4.90 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 8.64/4.90 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8419_abs__mult__pos,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 8.64/4.90 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8420_abs__mult__pos,axiom,
% 8.64/4.90 ! [X: rat,Y: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 8.64/4.90 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 8.64/4.90 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8421_abs__mult__pos,axiom,
% 8.64/4.90 ! [X: int,Y: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 8.64/4.90 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 8.64/4.90 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8422_abs__eq__mult,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.64/4.90 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 8.64/4.90 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.64/4.90 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 8.64/4.90 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 8.64/4.90 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8423_abs__eq__mult,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.64/4.90 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 8.64/4.90 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.64/4.90 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 8.64/4.90 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 8.64/4.90 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8424_abs__eq__mult,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.64/4.90 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 8.64/4.90 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.64/4.90 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 8.64/4.90 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 8.64/4.90 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8425_abs__eq__mult,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.90 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 8.64/4.90 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.64/4.90 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 8.64/4.90 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 8.64/4.90 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8426_cos__one__sin__zero,axiom,
% 8.64/4.90 ! [X: complex] :
% 8.64/4.90 ( ( ( cos_complex @ X )
% 8.64/4.90 = one_one_complex )
% 8.64/4.90 => ( ( sin_complex @ X )
% 8.64/4.90 = zero_zero_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8427_cos__one__sin__zero,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( cos_real @ X )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 => ( ( sin_real @ X )
% 8.64/4.90 = zero_zero_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8428_abs__minus__le__zero,axiom,
% 8.64/4.90 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8429_abs__minus__le__zero,axiom,
% 8.64/4.90 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8430_abs__minus__le__zero,axiom,
% 8.64/4.90 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8431_abs__minus__le__zero,axiom,
% 8.64/4.90 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8432_eq__abs__iff_H,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( A
% 8.64/4.90 = ( abs_abs_real @ B ) )
% 8.64/4.90 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 8.64/4.90 & ( ( B = A )
% 8.64/4.90 | ( B
% 8.64/4.90 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8433_eq__abs__iff_H,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( A
% 8.64/4.90 = ( abs_abs_Code_integer @ B ) )
% 8.64/4.90 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 8.64/4.90 & ( ( B = A )
% 8.64/4.90 | ( B
% 8.64/4.90 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8434_eq__abs__iff_H,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( A
% 8.64/4.90 = ( abs_abs_rat @ B ) )
% 8.64/4.90 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 8.64/4.90 & ( ( B = A )
% 8.64/4.90 | ( B
% 8.64/4.90 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8435_eq__abs__iff_H,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( A
% 8.64/4.90 = ( abs_abs_int @ B ) )
% 8.64/4.90 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 8.64/4.90 & ( ( B = A )
% 8.64/4.90 | ( B
% 8.64/4.90 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8436_abs__eq__iff_H,axiom,
% 8.64/4.90 ! [A: real,B: real] :
% 8.64/4.90 ( ( ( abs_abs_real @ A )
% 8.64/4.90 = B )
% 8.64/4.90 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 8.64/4.90 & ( ( A = B )
% 8.64/4.90 | ( A
% 8.64/4.90 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8437_abs__eq__iff_H,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( ( abs_abs_Code_integer @ A )
% 8.64/4.90 = B )
% 8.64/4.90 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 8.64/4.90 & ( ( A = B )
% 8.64/4.90 | ( A
% 8.64/4.90 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8438_abs__eq__iff_H,axiom,
% 8.64/4.90 ! [A: rat,B: rat] :
% 8.64/4.90 ( ( ( abs_abs_rat @ A )
% 8.64/4.90 = B )
% 8.64/4.90 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 8.64/4.90 & ( ( A = B )
% 8.64/4.90 | ( A
% 8.64/4.90 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8439_abs__eq__iff_H,axiom,
% 8.64/4.90 ! [A: int,B: int] :
% 8.64/4.90 ( ( ( abs_abs_int @ A )
% 8.64/4.90 = B )
% 8.64/4.90 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 8.64/4.90 & ( ( A = B )
% 8.64/4.90 | ( A
% 8.64/4.90 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8440_abs__div__pos,axiom,
% 8.64/4.90 ! [Y: real,X: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.90 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 8.64/4.90 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8441_abs__div__pos,axiom,
% 8.64/4.90 ! [Y: rat,X: rat] :
% 8.64/4.90 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 8.64/4.90 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 8.64/4.90 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8442_zero__le__power__abs,axiom,
% 8.64/4.90 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8443_zero__le__power__abs,axiom,
% 8.64/4.90 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8444_zero__le__power__abs,axiom,
% 8.64/4.90 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8445_zero__le__power__abs,axiom,
% 8.64/4.90 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8446_abs__if__raw,axiom,
% 8.64/4.90 ( abs_abs_int
% 8.64/4.90 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8447_abs__if__raw,axiom,
% 8.64/4.90 ( abs_abs_real
% 8.64/4.90 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8448_abs__if__raw,axiom,
% 8.64/4.90 ( abs_abs_Code_integer
% 8.64/4.90 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8449_abs__if__raw,axiom,
% 8.64/4.90 ( abs_abs_rat
% 8.64/4.90 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8450_abs__if,axiom,
% 8.64/4.90 ( abs_abs_int
% 8.64/4.90 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8451_abs__if,axiom,
% 8.64/4.90 ( abs_abs_real
% 8.64/4.90 = ( ^ [A5: real] : ( if_real @ ( ord_less_real @ A5 @ zero_zero_real ) @ ( uminus_uminus_real @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8452_abs__if,axiom,
% 8.64/4.90 ( abs_abs_Code_integer
% 8.64/4.90 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8453_abs__if,axiom,
% 8.64/4.90 ( abs_abs_rat
% 8.64/4.90 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8454_abs__of__neg,axiom,
% 8.64/4.90 ! [A: int] :
% 8.64/4.90 ( ( ord_less_int @ A @ zero_zero_int )
% 8.64/4.90 => ( ( abs_abs_int @ A )
% 8.64/4.90 = ( uminus_uminus_int @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8455_abs__of__neg,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( ord_less_real @ A @ zero_zero_real )
% 8.64/4.90 => ( ( abs_abs_real @ A )
% 8.64/4.90 = ( uminus_uminus_real @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8456_abs__of__neg,axiom,
% 8.64/4.90 ! [A: code_integer] :
% 8.64/4.90 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 8.64/4.90 => ( ( abs_abs_Code_integer @ A )
% 8.64/4.90 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8457_abs__of__neg,axiom,
% 8.64/4.90 ! [A: rat] :
% 8.64/4.90 ( ( ord_less_rat @ A @ zero_zero_rat )
% 8.64/4.90 => ( ( abs_abs_rat @ A )
% 8.64/4.90 = ( uminus_uminus_rat @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8458_sin__add,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( sin_real @ ( plus_plus_real @ X @ Y ) )
% 8.64/4.90 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8459_abs__diff__le__iff,axiom,
% 8.64/4.90 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8460_abs__diff__le__iff,axiom,
% 8.64/4.90 ! [X: real,A: real,R3: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8461_abs__diff__le__iff,axiom,
% 8.64/4.90 ! [X: rat,A: rat,R3: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8462_abs__diff__le__iff,axiom,
% 8.64/4.90 ! [X: int,A: int,R3: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8463_abs__diff__triangle__ineq,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer,C2: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C2 @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C2 ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8464_abs__diff__triangle__ineq,axiom,
% 8.64/4.90 ! [A: real,B: real,C2: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C2 @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C2 ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8465_abs__diff__triangle__ineq,axiom,
% 8.64/4.90 ! [A: rat,B: rat,C2: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C2 @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C2 ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8466_abs__diff__triangle__ineq,axiom,
% 8.64/4.90 ! [A: int,B: int,C2: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C2 @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C2 ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8467_abs__triangle__ineq4,axiom,
% 8.64/4.90 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8468_abs__triangle__ineq4,axiom,
% 8.64/4.90 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8469_abs__triangle__ineq4,axiom,
% 8.64/4.90 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8470_abs__triangle__ineq4,axiom,
% 8.64/4.90 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8471_sin__diff,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( sin_real @ ( minus_minus_real @ X @ Y ) )
% 8.64/4.90 = ( minus_minus_real @ ( times_times_real @ ( sin_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8472_abs__diff__less__iff,axiom,
% 8.64/4.90 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 8.64/4.90 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8473_abs__diff__less__iff,axiom,
% 8.64/4.90 ! [X: real,A: real,R3: real] :
% 8.64/4.90 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_less_real @ ( minus_minus_real @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8474_abs__diff__less__iff,axiom,
% 8.64/4.90 ! [X: rat,A: rat,R3: rat] :
% 8.64/4.90 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8475_abs__diff__less__iff,axiom,
% 8.64/4.90 ! [X: int,A: int,R3: int] :
% 8.64/4.90 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 8.64/4.90 = ( ( ord_less_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 8.64/4.90 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8476_pred__numeral__def,axiom,
% 8.64/4.90 ( pred_numeral
% 8.64/4.90 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8477_lessThan__nat__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( insert_nat @ ( pred_numeral @ K2 ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8478_atMost__nat__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( insert_nat @ ( numeral_numeral_nat @ K2 ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8479_cos__add,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( cos_real @ ( plus_plus_real @ X @ Y ) )
% 8.64/4.90 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8480_cos__diff,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( cos_real @ ( minus_minus_real @ X @ Y ) )
% 8.64/4.90 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8481_abs__add__one__gt__zero,axiom,
% 8.64/4.90 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8482_abs__add__one__gt__zero,axiom,
% 8.64/4.90 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8483_abs__add__one__gt__zero,axiom,
% 8.64/4.90 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8484_abs__add__one__gt__zero,axiom,
% 8.64/4.90 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8485_sin__zero__norm__cos__one,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( sin_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X ) )
% 8.64/4.90 = one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8486_sin__zero__norm__cos__one,axiom,
% 8.64/4.90 ! [X: complex] :
% 8.64/4.90 ( ( ( sin_complex @ X )
% 8.64/4.90 = zero_zero_complex )
% 8.64/4.90 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X ) )
% 8.64/4.90 = one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8487_fact__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( times_times_rat @ ( numeral_numeral_rat @ K2 ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8488_fact__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ K2 ) @ ( semiri4449623510593786356d_enat @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8489_fact__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( times_times_complex @ ( numera6690914467698888265omplex @ K2 ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8490_fact__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( times_times_int @ ( numeral_numeral_int @ K2 ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8491_fact__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( times_times_nat @ ( numeral_numeral_nat @ K2 ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8492_fact__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.90 = ( times_times_real @ ( numeral_numeral_real @ K2 ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8493_sin__double,axiom,
% 8.64/4.90 ! [X: complex] :
% 8.64/4.90 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X ) ) @ ( cos_complex @ X ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8494_sin__double,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X ) ) @ ( cos_real @ X ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8495_abs__le__square__iff,axiom,
% 8.64/4.90 ! [X: code_integer,Y: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 8.64/4.90 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8496_abs__le__square__iff,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 8.64/4.90 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8497_abs__le__square__iff,axiom,
% 8.64/4.90 ! [X: rat,Y: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 8.64/4.90 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8498_abs__le__square__iff,axiom,
% 8.64/4.90 ! [X: int,Y: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 8.64/4.90 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8499_divmod__int__def,axiom,
% 8.64/4.90 ( unique5052692396658037445od_int
% 8.64/4.90 = ( ^ [M6: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8500_abs__sqrt__wlog,axiom,
% 8.64/4.90 ! [P2: code_integer > code_integer > $o,X: code_integer] :
% 8.64/4.90 ( ! [X3: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X3 )
% 8.64/4.90 => ( P2 @ X3 @ ( power_8256067586552552935nteger @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.90 => ( P2 @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8501_abs__sqrt__wlog,axiom,
% 8.64/4.90 ! [P2: real > real > $o,X: real] :
% 8.64/4.90 ( ! [X3: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 8.64/4.90 => ( P2 @ X3 @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.90 => ( P2 @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8502_abs__sqrt__wlog,axiom,
% 8.64/4.90 ! [P2: rat > rat > $o,X: rat] :
% 8.64/4.90 ( ! [X3: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ zero_zero_rat @ X3 )
% 8.64/4.90 => ( P2 @ X3 @ ( power_power_rat @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.90 => ( P2 @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8503_abs__sqrt__wlog,axiom,
% 8.64/4.90 ! [P2: int > int > $o,X: int] :
% 8.64/4.90 ( ! [X3: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 8.64/4.90 => ( P2 @ X3 @ ( power_power_int @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.90 => ( P2 @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8504_power2__le__iff__abs__le,axiom,
% 8.64/4.90 ! [Y: code_integer,X: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 8.64/4.90 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8505_power2__le__iff__abs__le,axiom,
% 8.64/4.90 ! [Y: real,X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.90 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8506_power2__le__iff__abs__le,axiom,
% 8.64/4.90 ! [Y: rat,X: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 8.64/4.90 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8507_power2__le__iff__abs__le,axiom,
% 8.64/4.90 ! [Y: int,X: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 8.64/4.90 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8508_abs__square__le__1,axiom,
% 8.64/4.90 ! [X: code_integer] :
% 8.64/4.90 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 8.64/4.90 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8509_abs__square__le__1,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 8.64/4.90 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8510_abs__square__le__1,axiom,
% 8.64/4.90 ! [X: rat] :
% 8.64/4.90 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 8.64/4.90 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8511_abs__square__le__1,axiom,
% 8.64/4.90 ! [X: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 8.64/4.90 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8512_divmod__def,axiom,
% 8.64/4.90 ( unique3479559517661332726nteger
% 8.64/4.90 = ( ^ [M6: num,N4: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8513_divmod__def,axiom,
% 8.64/4.90 ( unique5052692396658037445od_int
% 8.64/4.90 = ( ^ [M6: num,N4: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8514_divmod__def,axiom,
% 8.64/4.90 ( unique5055182867167087721od_nat
% 8.64/4.90 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8515_divmod_H__nat__def,axiom,
% 8.64/4.90 ( unique5055182867167087721od_nat
% 8.64/4.90 = ( ^ [M6: num,N4: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8516_power__mono__even,axiom,
% 8.64/4.90 ! [N: nat,A: code_integer,B: code_integer] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8517_power__mono__even,axiom,
% 8.64/4.90 ! [N: nat,A: real,B: real] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 8.64/4.90 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8518_power__mono__even,axiom,
% 8.64/4.90 ! [N: nat,A: rat,B: rat] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 8.64/4.90 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8519_power__mono__even,axiom,
% 8.64/4.90 ! [N: nat,A: int,B: int] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 8.64/4.90 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8520_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 8.64/4.90 ( ! [I3: complex] :
% 8.64/4.90 ( ( member_complex @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups6621422865394947399nteger @ X @ I5 )
% 8.64/4.90 = one_one_Code_integer )
% 8.64/4.90 => ( ! [I3: complex] :
% 8.64/4.90 ( ( member_complex @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_le3102999989581377725nteger
% 8.64/4.90 @ ( abs_abs_Code_integer
% 8.64/4.90 @ ( minus_8373710615458151222nteger
% 8.64/4.90 @ ( groups6621422865394947399nteger
% 8.64/4.90 @ ^ [I: complex] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8521_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 8.64/4.90 ( ! [I3: real] :
% 8.64/4.90 ( ( member_real @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups7713935264441627589nteger @ X @ I5 )
% 8.64/4.90 = one_one_Code_integer )
% 8.64/4.90 => ( ! [I3: real] :
% 8.64/4.90 ( ( member_real @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_le3102999989581377725nteger
% 8.64/4.90 @ ( abs_abs_Code_integer
% 8.64/4.90 @ ( minus_8373710615458151222nteger
% 8.64/4.90 @ ( groups7713935264441627589nteger
% 8.64/4.90 @ ^ [I: real] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8522_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 8.64/4.90 ( ! [I3: nat] :
% 8.64/4.90 ( ( member_nat @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 8.64/4.90 = one_one_Code_integer )
% 8.64/4.90 => ( ! [I3: nat] :
% 8.64/4.90 ( ( member_nat @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_le3102999989581377725nteger
% 8.64/4.90 @ ( abs_abs_Code_integer
% 8.64/4.90 @ ( minus_8373710615458151222nteger
% 8.64/4.90 @ ( groups7501900531339628137nteger
% 8.64/4.90 @ ^ [I: nat] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8523_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 8.64/4.90 ( ! [I3: int] :
% 8.64/4.90 ( ( member_int @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 8.64/4.90 = one_one_Code_integer )
% 8.64/4.90 => ( ! [I3: int] :
% 8.64/4.90 ( ( member_int @ I3 @ I5 )
% 8.64/4.90 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_le3102999989581377725nteger
% 8.64/4.90 @ ( abs_abs_Code_integer
% 8.64/4.90 @ ( minus_8373710615458151222nteger
% 8.64/4.90 @ ( groups7873554091576472773nteger
% 8.64/4.90 @ ^ [I: int] : ( times_3573771949741848930nteger @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8524_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 8.64/4.90 ( ! [I3: complex] :
% 8.64/4.90 ( ( member_complex @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups5808333547571424918x_real @ X @ I5 )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 => ( ! [I3: complex] :
% 8.64/4.90 ( ( member_complex @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_less_eq_real
% 8.64/4.90 @ ( abs_abs_real
% 8.64/4.90 @ ( minus_minus_real
% 8.64/4.90 @ ( groups5808333547571424918x_real
% 8.64/4.90 @ ^ [I: complex] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8525_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 8.64/4.90 ( ! [I3: real] :
% 8.64/4.90 ( ( member_real @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups8097168146408367636l_real @ X @ I5 )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 => ( ! [I3: real] :
% 8.64/4.90 ( ( member_real @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_less_eq_real
% 8.64/4.90 @ ( abs_abs_real
% 8.64/4.90 @ ( minus_minus_real
% 8.64/4.90 @ ( groups8097168146408367636l_real
% 8.64/4.90 @ ^ [I: real] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8526_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 8.64/4.90 ( ! [I3: int] :
% 8.64/4.90 ( ( member_int @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups8778361861064173332t_real @ X @ I5 )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 => ( ! [I3: int] :
% 8.64/4.90 ( ( member_int @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_less_eq_real
% 8.64/4.90 @ ( abs_abs_real
% 8.64/4.90 @ ( minus_minus_real
% 8.64/4.90 @ ( groups8778361861064173332t_real
% 8.64/4.90 @ ^ [I: int] : ( times_times_real @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8527_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 8.64/4.90 ( ! [I3: complex] :
% 8.64/4.90 ( ( member_complex @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups5058264527183730370ex_rat @ X @ I5 )
% 8.64/4.90 = one_one_rat )
% 8.64/4.90 => ( ! [I3: complex] :
% 8.64/4.90 ( ( member_complex @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_less_eq_rat
% 8.64/4.90 @ ( abs_abs_rat
% 8.64/4.90 @ ( minus_minus_rat
% 8.64/4.90 @ ( groups5058264527183730370ex_rat
% 8.64/4.90 @ ^ [I: complex] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8528_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 8.64/4.90 ( ! [I3: real] :
% 8.64/4.90 ( ( member_real @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups1300246762558778688al_rat @ X @ I5 )
% 8.64/4.90 = one_one_rat )
% 8.64/4.90 => ( ! [I3: real] :
% 8.64/4.90 ( ( member_real @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_less_eq_rat
% 8.64/4.90 @ ( abs_abs_rat
% 8.64/4.90 @ ( minus_minus_rat
% 8.64/4.90 @ ( groups1300246762558778688al_rat
% 8.64/4.90 @ ^ [I: real] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8529_convex__sum__bound__le,axiom,
% 8.64/4.90 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 8.64/4.90 ( ! [I3: nat] :
% 8.64/4.90 ( ( member_nat @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 8.64/4.90 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 8.64/4.90 = one_one_rat )
% 8.64/4.90 => ( ! [I3: nat] :
% 8.64/4.90 ( ( member_nat @ I3 @ I5 )
% 8.64/4.90 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 8.64/4.90 => ( ord_less_eq_rat
% 8.64/4.90 @ ( abs_abs_rat
% 8.64/4.90 @ ( minus_minus_rat
% 8.64/4.90 @ ( groups2906978787729119204at_rat
% 8.64/4.90 @ ^ [I: nat] : ( times_times_rat @ ( A @ I ) @ ( X @ I ) )
% 8.64/4.90 @ I5 )
% 8.64/4.90 @ B ) )
% 8.64/4.90 @ Delta ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8530_cos__plus__cos,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( plus_plus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8531_cos__plus__cos,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( plus_plus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8532_cos__times__cos,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 8.64/4.90 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8533_cos__times__cos,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( times_times_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 8.64/4.90 = ( divide_divide_real @ ( plus_plus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8534_cos__double__less__one,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.64/4.90 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8535_cos__double__cos,axiom,
% 8.64/4.90 ! [W2: complex] :
% 8.64/4.90 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W2 ) )
% 8.64/4.90 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8536_cos__double__cos,axiom,
% 8.64/4.90 ! [W2: real] :
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W2 ) )
% 8.64/4.90 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ ( cos_real @ W2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_real ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8537_cos__treble__cos,axiom,
% 8.64/4.90 ! [X: complex] :
% 8.64/4.90 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X ) )
% 8.64/4.90 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8538_cos__treble__cos,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X ) )
% 8.64/4.90 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8539_cos__diff__cos,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( minus_minus_complex @ ( cos_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ Z3 @ W2 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8540_cos__diff__cos,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( minus_minus_real @ ( cos_real @ W2 ) @ ( cos_real @ Z3 ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ Z3 @ W2 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8541_sin__diff__sin,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( minus_minus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8542_sin__diff__sin,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( minus_minus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8543_sin__plus__sin,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( plus_plus_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 8.64/4.90 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) @ ( cos_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ W2 @ Z3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8544_sin__plus__sin,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( plus_plus_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ ( divide_divide_real @ ( plus_plus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ ( cos_real @ ( divide_divide_real @ ( minus_minus_real @ W2 @ Z3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8545_cos__times__sin,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( times_times_complex @ ( cos_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 8.64/4.90 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8546_cos__times__sin,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( times_times_real @ ( cos_real @ W2 ) @ ( sin_real @ Z3 ) )
% 8.64/4.90 = ( divide_divide_real @ ( minus_minus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8547_sin__times__cos,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( cos_complex @ Z3 ) )
% 8.64/4.90 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) @ ( sin_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8548_sin__times__cos,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( times_times_real @ ( sin_real @ W2 ) @ ( cos_real @ Z3 ) )
% 8.64/4.90 = ( divide_divide_real @ ( plus_plus_real @ ( sin_real @ ( plus_plus_real @ W2 @ Z3 ) ) @ ( sin_real @ ( minus_minus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8549_sin__times__sin,axiom,
% 8.64/4.90 ! [W2: complex,Z3: complex] :
% 8.64/4.90 ( ( times_times_complex @ ( sin_complex @ W2 ) @ ( sin_complex @ Z3 ) )
% 8.64/4.90 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W2 @ Z3 ) ) @ ( cos_complex @ ( plus_plus_complex @ W2 @ Z3 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8550_sin__times__sin,axiom,
% 8.64/4.90 ! [W2: real,Z3: real] :
% 8.64/4.90 ( ( times_times_real @ ( sin_real @ W2 ) @ ( sin_real @ Z3 ) )
% 8.64/4.90 = ( divide_divide_real @ ( minus_minus_real @ ( cos_real @ ( minus_minus_real @ W2 @ Z3 ) ) @ ( cos_real @ ( plus_plus_real @ W2 @ Z3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8551_Maclaurin__cos__expansion,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ? [T6: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.90 & ( ( cos_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ T6 @ ( times_times_real @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8552_cos__one__2pi,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( cos_real @ X )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 = ( ? [X4: nat] :
% 8.64/4.90 ( X
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 8.64/4.90 | ? [X4: nat] :
% 8.64/4.90 ( X
% 8.64/4.90 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8553_sin__expansion__lemma,axiom,
% 8.64/4.90 ! [X: real,M2: nat] :
% 8.64/4.90 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.64/4.90 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8554_cos__zero__lemma,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ( cos_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 => ? [N3: nat] :
% 8.64/4.90 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8555_cos__zero__iff,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( cos_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( ? [N4: nat] :
% 8.64/4.90 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.90 | ? [N4: nat] :
% 8.64/4.90 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8556_cos__expansion__lemma,axiom,
% 8.64/4.90 ! [X: real,M2: nat] :
% 8.64/4.90 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M2 ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 8.64/4.90 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M2 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8557_cos__paired,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( sums_real
% 8.64/4.90 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 8.64/4.90 @ ( cos_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8558_sincos__total__2pi__le,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 => ? [T6: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.64/4.90 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( cos_real @ T6 ) )
% 8.64/4.90 & ( Y
% 8.64/4.90 = ( sin_real @ T6 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8559_sincos__total__2pi,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 => ~ ! [T6: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.64/4.90 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.90 => ( ( X
% 8.64/4.90 = ( cos_real @ T6 ) )
% 8.64/4.90 => ( Y
% 8.64/4.90 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8560_monoseq__arctan__series,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.64/4.90 => ( topolo6980174941875973593q_real
% 8.64/4.90 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8561_summable__arctan__series,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.64/4.90 => ( summable_real
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8562_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 8.64/4.90 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8563_pi__series,axiom,
% 8.64/4.90 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( suminf_real
% 8.64/4.90 @ ^ [K3: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8564_and__int_Opsimps,axiom,
% 8.64/4.90 ! [K2: int,L: int] :
% 8.64/4.90 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L ) )
% 8.64/4.90 => ( ( ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.64/4.90 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.64/4.90 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 8.64/4.90 = ( uminus_uminus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 8.64/4.90 & ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.64/4.90 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.64/4.90 => ( ( bit_se725231765392027082nd_int @ K2 @ L )
% 8.64/4.90 = ( plus_plus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 8.64/4.90 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8565_tan__npi,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8566_tan__periodic__n,axiom,
% 8.64/4.90 ! [X: real,N: num] :
% 8.64/4.90 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 8.64/4.90 = ( tan_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8567_tan__periodic__nat,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 8.64/4.90 = ( tan_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8568_tan__periodic,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.64/4.90 = ( tan_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8569_abs__zmult__eq__1,axiom,
% 8.64/4.90 ! [M2: int,N: int] :
% 8.64/4.90 ( ( ( abs_abs_int @ ( times_times_int @ M2 @ N ) )
% 8.64/4.90 = one_one_int )
% 8.64/4.90 => ( ( abs_abs_int @ M2 )
% 8.64/4.90 = one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8570_abs__div,axiom,
% 8.64/4.90 ! [Y: int,X: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ Y @ X )
% 8.64/4.90 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 8.64/4.90 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8571_summable__rabs__comparison__test,axiom,
% 8.64/4.90 ! [F2: nat > real,G2: nat > real] :
% 8.64/4.90 ( ? [N7: nat] :
% 8.64/4.90 ! [N3: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ N7 @ N3 )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ ( F2 @ N3 ) ) @ ( G2 @ N3 ) ) )
% 8.64/4.90 => ( ( summable_real @ G2 )
% 8.64/4.90 => ( summable_real
% 8.64/4.90 @ ^ [N4: nat] : ( abs_abs_real @ ( F2 @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8572_ln__mult,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.90 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 8.64/4.90 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8573_zdvd__mult__cancel1,axiom,
% 8.64/4.90 ! [M2: int,N: int] :
% 8.64/4.90 ( ( M2 != zero_zero_int )
% 8.64/4.90 => ( ( dvd_dvd_int @ ( times_times_int @ M2 @ N ) @ M2 )
% 8.64/4.90 = ( ( abs_abs_int @ N )
% 8.64/4.90 = one_one_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8574_sum__pos__lt__pair,axiom,
% 8.64/4.90 ! [F2: nat > real,K2: nat] :
% 8.64/4.90 ( ( summable_real @ F2 )
% 8.64/4.90 => ( ! [D5: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F2 @ ( plus_plus_nat @ K2 @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) ) ) @ ( F2 @ ( plus_plus_nat @ K2 @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D5 ) @ one_one_nat ) ) ) ) )
% 8.64/4.90 => ( ord_less_real @ ( groups6591440286371151544t_real @ F2 @ ( set_ord_lessThan_nat @ K2 ) ) @ ( suminf_real @ F2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8575_ln__realpow,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 8.64/4.90 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8576_summable__power__series,axiom,
% 8.64/4.90 ! [F2: nat > real,Z3: real] :
% 8.64/4.90 ( ! [I3: nat] : ( ord_less_eq_real @ ( F2 @ I3 ) @ one_one_real )
% 8.64/4.90 => ( ! [I3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F2 @ I3 ) )
% 8.64/4.90 => ( ( ord_less_eq_real @ zero_zero_real @ Z3 )
% 8.64/4.90 => ( ( ord_less_real @ Z3 @ one_one_real )
% 8.64/4.90 => ( summable_real
% 8.64/4.90 @ ^ [I: nat] : ( times_times_real @ ( F2 @ I ) @ ( power_power_real @ Z3 @ I ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8577_nat__intermed__int__val,axiom,
% 8.64/4.90 ! [M2: nat,N: nat,F2: nat > int,K2: int] :
% 8.64/4.90 ( ! [I3: nat] :
% 8.64/4.90 ( ( ( ord_less_eq_nat @ M2 @ I3 )
% 8.64/4.90 & ( ord_less_nat @ I3 @ N ) )
% 8.64/4.90 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 8.64/4.90 => ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.90 => ( ( ord_less_eq_int @ ( F2 @ M2 ) @ K2 )
% 8.64/4.90 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 8.64/4.90 => ? [I3: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ M2 @ I3 )
% 8.64/4.90 & ( ord_less_eq_nat @ I3 @ N )
% 8.64/4.90 & ( ( F2 @ I3 )
% 8.64/4.90 = K2 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8578_incr__lemma,axiom,
% 8.64/4.90 ! [D: int,Z3: int,X: int] :
% 8.64/4.90 ( ( ord_less_int @ zero_zero_int @ D )
% 8.64/4.90 => ( ord_less_int @ Z3 @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8579_decr__lemma,axiom,
% 8.64/4.90 ! [D: int,X: int,Z3: int] :
% 8.64/4.90 ( ( ord_less_int @ zero_zero_int @ D )
% 8.64/4.90 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z3 ) ) @ one_one_int ) @ D ) ) @ Z3 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8580_ln__series,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.64/4.90 => ( ( ln_ln_real @ X )
% 8.64/4.90 = ( suminf_real
% 8.64/4.90 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N4 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N4 ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8581_nat__ivt__aux,axiom,
% 8.64/4.90 ! [N: nat,F2: nat > int,K2: int] :
% 8.64/4.90 ( ! [I3: nat] :
% 8.64/4.90 ( ( ord_less_nat @ I3 @ N )
% 8.64/4.90 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( suc @ I3 ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 8.64/4.90 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K2 )
% 8.64/4.90 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 8.64/4.90 => ? [I3: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ I3 @ N )
% 8.64/4.90 & ( ( F2 @ I3 )
% 8.64/4.90 = K2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8582_nat0__intermed__int__val,axiom,
% 8.64/4.90 ! [N: nat,F2: nat > int,K2: int] :
% 8.64/4.90 ( ! [I3: nat] :
% 8.64/4.90 ( ( ord_less_nat @ I3 @ N )
% 8.64/4.90 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F2 @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F2 @ I3 ) ) ) @ one_one_int ) )
% 8.64/4.90 => ( ( ord_less_eq_int @ ( F2 @ zero_zero_nat ) @ K2 )
% 8.64/4.90 => ( ( ord_less_eq_int @ K2 @ ( F2 @ N ) )
% 8.64/4.90 => ? [I3: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ I3 @ N )
% 8.64/4.90 & ( ( F2 @ I3 )
% 8.64/4.90 = K2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8583_ln__one__minus__pos__lower__bound,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.90 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8584_abs__ln__one__plus__x__minus__x__bound,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.90 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8585_and__int_Opelims,axiom,
% 8.64/4.90 ! [X: int,Xa2: int,Y: int] :
% 8.64/4.90 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 8.64/4.90 = Y )
% 8.64/4.90 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 8.64/4.90 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.64/4.90 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.64/4.90 => ( Y
% 8.64/4.90 = ( uminus_uminus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 8.64/4.90 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 8.64/4.90 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 8.64/4.90 => ( Y
% 8.64/4.90 = ( plus_plus_int
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 8.64/4.90 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 8.64/4.90 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 8.64/4.90 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8586_arctan__series,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.64/4.90 => ( ( arctan @ X )
% 8.64/4.90 = ( suminf_real
% 8.64/4.90 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8587_Maclaurin__exp__lt,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ( X != zero_zero_real )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ? [T6: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 8.64/4.90 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.90 & ( ( exp_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8588_arctan__double,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.64/4.90 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 8.64/4.90 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8589_real__exp__bound__lemma,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.90 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8590_exp__ge__one__plus__x__over__n__power__n,axiom,
% 8.64/4.90 ! [N: nat,X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8591_exp__ge__one__minus__x__over__n__power__n,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8592_arctan__add,axiom,
% 8.64/4.90 ! [X: real,Y: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.64/4.90 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 8.64/4.90 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 8.64/4.90 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8593_Maclaurin__exp__le,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ? [T6: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.90 & ( ( exp_real @ X )
% 8.64/4.90 = ( plus_plus_real
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.90 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8594_machin__Euler,axiom,
% 8.64/4.90 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.90 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8595_machin,axiom,
% 8.64/4.90 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 8.64/4.90 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8596_tanh__real__altdef,axiom,
% 8.64/4.90 ( tanh_real
% 8.64/4.90 = ( ^ [X4: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8597_Maclaurin__sin__bound,axiom,
% 8.64/4.90 ! [X: real,N: nat] :
% 8.64/4.90 ( ord_less_eq_real
% 8.64/4.90 @ ( abs_abs_real
% 8.64/4.90 @ ( minus_minus_real @ ( sin_real @ X )
% 8.64/4.90 @ ( groups6591440286371151544t_real
% 8.64/4.90 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.90 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 8.64/4.90 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8598_divmod__BitM__2__eq,axiom,
% 8.64/4.90 ! [M2: num] :
% 8.64/4.90 ( ( unique5052692396658037445od_int @ ( bitM @ M2 ) @ ( bit0 @ one ) )
% 8.64/4.90 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M2 ) @ one_one_int ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8599_pred__numeral__simps_I2_J,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( pred_numeral @ ( bit0 @ K2 ) )
% 8.64/4.90 = ( numeral_numeral_nat @ ( bitM @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8600_sin__npi__int,axiom,
% 8.64/4.90 ! [N: int] :
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8601_tan__periodic__int,axiom,
% 8.64/4.90 ! [X: real,I2: int] :
% 8.64/4.90 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I2 ) @ pi ) ) )
% 8.64/4.90 = ( tan_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8602_sin__int__2pin,axiom,
% 8.64/4.90 ! [N: int] :
% 8.64/4.90 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8603_cos__int__2pin,axiom,
% 8.64/4.90 ! [N: int] :
% 8.64/4.90 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 8.64/4.90 = one_one_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8604_cos__npi__int,axiom,
% 8.64/4.90 ! [N: int] :
% 8.64/4.90 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 8.64/4.90 = one_one_real ) )
% 8.64/4.90 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 8.64/4.90 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8605_real__scaleR__def,axiom,
% 8.64/4.90 real_V1485227260804924795R_real = times_times_real ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8606_divide__real__def,axiom,
% 8.64/4.90 ( divide_divide_real
% 8.64/4.90 = ( ^ [X4: real,Y4: real] : ( times_times_real @ X4 @ ( inverse_inverse_real @ Y4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8607_eval__nat__numeral_I2_J,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 8.64/4.90 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8608_BitM__plus__one,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 8.64/4.90 = ( bit0 @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8609_one__plus__BitM,axiom,
% 8.64/4.90 ! [N: num] :
% 8.64/4.90 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 8.64/4.90 = ( bit0 @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8610_forall__pos__mono__1,axiom,
% 8.64/4.90 ! [P2: real > $o,E: real] :
% 8.64/4.90 ( ! [D5: real,E2: real] :
% 8.64/4.90 ( ( ord_less_real @ D5 @ E2 )
% 8.64/4.90 => ( ( P2 @ D5 )
% 8.64/4.90 => ( P2 @ E2 ) ) )
% 8.64/4.90 => ( ! [N3: nat] : ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ E )
% 8.64/4.90 => ( P2 @ E ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8611_forall__pos__mono,axiom,
% 8.64/4.90 ! [P2: real > $o,E: real] :
% 8.64/4.90 ( ! [D5: real,E2: real] :
% 8.64/4.90 ( ( ord_less_real @ D5 @ E2 )
% 8.64/4.90 => ( ( P2 @ D5 )
% 8.64/4.90 => ( P2 @ E2 ) ) )
% 8.64/4.90 => ( ! [N3: nat] :
% 8.64/4.90 ( ( N3 != zero_zero_nat )
% 8.64/4.90 => ( P2 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ E )
% 8.64/4.90 => ( P2 @ E ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8612_real__arch__inverse,axiom,
% 8.64/4.90 ! [E: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ E )
% 8.64/4.90 = ( ? [N4: nat] :
% 8.64/4.90 ( ( N4 != zero_zero_nat )
% 8.64/4.90 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 8.64/4.90 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N4 ) ) @ E ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8613_sin__zero__iff__int2,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( sin_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( ? [I: int] :
% 8.64/4.90 ( X
% 8.64/4.90 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8614_cos__one__2pi__int,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( cos_real @ X )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 = ( ? [X4: int] :
% 8.64/4.90 ( X
% 8.64/4.90 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8615_cos__zero__iff__int,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( cos_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( ? [I: int] :
% 8.64/4.90 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8616_sin__zero__iff__int,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ( sin_real @ X )
% 8.64/4.90 = zero_zero_real )
% 8.64/4.90 = ( ? [I: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I )
% 8.64/4.90 & ( X
% 8.64/4.90 = ( times_times_real @ ( ring_1_of_int_real @ I ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8617_complex__unimodular__polar,axiom,
% 8.64/4.90 ! [Z3: complex] :
% 8.64/4.90 ( ( ( real_V1022390504157884413omplex @ Z3 )
% 8.64/4.90 = one_one_real )
% 8.64/4.90 => ~ ! [T6: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.64/4.90 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.90 => ( Z3
% 8.64/4.90 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8618_arccos__cos__eq__abs__2pi,axiom,
% 8.64/4.90 ! [Theta: real] :
% 8.64/4.90 ~ ! [K: int] :
% 8.64/4.90 ( ( arccos @ ( cos_real @ Theta ) )
% 8.64/4.90 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8619_log__base__10__eq1,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 8.64/4.90 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8620_complex__scaleR,axiom,
% 8.64/4.90 ! [R3: real,A: real,B: real] :
% 8.64/4.90 ( ( real_V2046097035970521341omplex @ R3 @ ( complex2 @ A @ B ) )
% 8.64/4.90 = ( complex2 @ ( times_times_real @ R3 @ A ) @ ( times_times_real @ R3 @ B ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8621_complex__mult,axiom,
% 8.64/4.90 ! [A: real,B: real,C2: real,D: real] :
% 8.64/4.90 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C2 @ D ) )
% 8.64/4.90 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C2 ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8622_log__mult,axiom,
% 8.64/4.90 ! [A: real,X: real,Y: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.90 => ( ( A != one_one_real )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ Y )
% 8.64/4.90 => ( ( log2 @ A @ ( times_times_real @ X @ Y ) )
% 8.64/4.90 = ( plus_plus_real @ ( log2 @ A @ X ) @ ( log2 @ A @ Y ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8623_log__nat__power,axiom,
% 8.64/4.90 ! [X: real,B: real,N: nat] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( log2 @ B @ ( power_power_real @ X @ N ) )
% 8.64/4.90 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8624_log__of__power__less,axiom,
% 8.64/4.90 ! [M2: nat,B: real,N: nat] :
% 8.64/4.90 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 8.64/4.90 => ( ( ord_less_real @ one_one_real @ B )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.90 => ( ord_less_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8625_log__eq__div__ln__mult__log,axiom,
% 8.64/4.90 ! [A: real,B: real,X: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.90 => ( ( A != one_one_real )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.64/4.90 => ( ( B != one_one_real )
% 8.64/4.90 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( log2 @ A @ X )
% 8.64/4.90 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log2 @ B @ X ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8626_log__of__power__le,axiom,
% 8.64/4.90 ! [M2: nat,B: real,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M2 ) @ ( power_power_real @ B @ N ) )
% 8.64/4.90 => ( ( ord_less_real @ one_one_real @ B )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.90 => ( ord_less_eq_real @ ( log2 @ B @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8627_le__log2__of__power,axiom,
% 8.64/4.90 ! [N: nat,M2: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 )
% 8.64/4.90 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8628_divmod__step__nat__def,axiom,
% 8.64/4.90 ( unique5026877609467782581ep_nat
% 8.64/4.90 = ( ^ [L2: num] :
% 8.64/4.90 ( produc2626176000494625587at_nat
% 8.64/4.90 @ ^ [Q5: nat,R: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8629_log2__of__power__less,axiom,
% 8.64/4.90 ! [M2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.90 => ( ord_less_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8630_divmod__step__int__def,axiom,
% 8.64/4.90 ( unique5024387138958732305ep_int
% 8.64/4.90 = ( ^ [L2: num] :
% 8.64/4.90 ( produc4245557441103728435nt_int
% 8.64/4.90 @ ^ [Q5: int,R: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8631_log2__of__power__le,axiom,
% 8.64/4.90 ! [M2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ M2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.90 => ( ord_less_eq_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8632_log__base__10__eq2,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.90 => ( ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 8.64/4.90 = ( times_times_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8633_ceiling__log__nat__eq__powr__iff,axiom,
% 8.64/4.90 ! [B: nat,K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.90 => ( ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 8.64/4.90 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 8.64/4.90 & ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8634_ceiling__log__nat__eq__if,axiom,
% 8.64/4.90 ! [B: nat,N: nat,K2: nat] :
% 8.64/4.90 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 8.64/4.90 => ( ( ord_less_eq_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 8.64/4.90 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.64/4.90 => ( ( archim7802044766580827645g_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8635_ceiling__log2__div2,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( archim7802044766580827645g_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8636_divmod__nat__if,axiom,
% 8.64/4.90 ( divmod_nat
% 8.64/4.90 = ( ^ [M6: nat,N4: nat] :
% 8.64/4.90 ( if_Pro6206227464963214023at_nat
% 8.64/4.90 @ ( ( N4 = zero_zero_nat )
% 8.64/4.90 | ( ord_less_nat @ M6 @ N4 ) )
% 8.64/4.90 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 8.64/4.90 @ ( produc2626176000494625587at_nat
% 8.64/4.90 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 8.64/4.90 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N4 ) @ N4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8637_floor__log__nat__eq__powr__iff,axiom,
% 8.64/4.90 ! [B: nat,K2: nat,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 8.64/4.90 => ( ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 8.64/4.90 = ( semiri1314217659103216013at_int @ N ) )
% 8.64/4.90 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 8.64/4.90 & ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8638_divide__complex__def,axiom,
% 8.64/4.90 ( divide1717551699836669952omplex
% 8.64/4.90 = ( ^ [X4: complex,Y4: complex] : ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8639_prod__encode__def,axiom,
% 8.64/4.90 ( nat_prod_encode
% 8.64/4.90 = ( produc6842872674320459806at_nat
% 8.64/4.90 @ ^ [M6: nat,N4: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N4 ) ) @ M6 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8640_Divides_Oadjust__div__def,axiom,
% 8.64/4.90 ( adjust_div
% 8.64/4.90 = ( produc8211389475949308722nt_int
% 8.64/4.90 @ ^ [Q5: int,R: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8641_divmod__nat__def,axiom,
% 8.64/4.90 ( divmod_nat
% 8.64/4.90 = ( ^ [M6: nat,N4: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N4 ) @ ( modulo_modulo_nat @ M6 @ N4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8642_floor__log2__div2,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.90 => ( ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8643_floor__log__nat__eq__if,axiom,
% 8.64/4.90 ! [B: nat,N: nat,K2: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K2 )
% 8.64/4.90 => ( ( ord_less_nat @ K2 @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 8.64/4.90 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 8.64/4.90 => ( ( archim6058952711729229775r_real @ ( log2 @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K2 ) ) )
% 8.64/4.90 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8644_cot__periodic,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.64/4.90 = ( cot_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8645_modulo__int__unfold,axiom,
% 8.64/4.90 ! [L: int,K2: int,N: nat,M2: nat] :
% 8.64/4.90 ( ( ( ( ( sgn_sgn_int @ L )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( N = zero_zero_nat ) )
% 8.64/4.90 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.90 = ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) ) )
% 8.64/4.90 & ( ~ ( ( ( sgn_sgn_int @ L )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( N = zero_zero_nat ) )
% 8.64/4.90 => ( ( ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 = ( sgn_sgn_int @ L ) )
% 8.64/4.90 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.90 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) )
% 8.64/4.90 & ( ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 != ( sgn_sgn_int @ L ) )
% 8.64/4.90 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.90 = ( times_times_int @ ( sgn_sgn_int @ L )
% 8.64/4.90 @ ( minus_minus_int
% 8.64/4.90 @ ( semiri1314217659103216013at_int
% 8.64/4.90 @ ( times_times_nat @ N
% 8.64/4.90 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.90 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) )
% 8.64/4.90 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M2 @ N ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8646_dvd__mult__sgn__iff,axiom,
% 8.64/4.90 ! [L: int,K2: int,R3: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ L @ ( times_times_int @ K2 @ ( sgn_sgn_int @ R3 ) ) )
% 8.64/4.90 = ( ( dvd_dvd_int @ L @ K2 )
% 8.64/4.90 | ( R3 = zero_zero_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8647_dvd__sgn__mult__iff,axiom,
% 8.64/4.90 ! [L: int,R3: int,K2: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ L @ ( times_times_int @ ( sgn_sgn_int @ R3 ) @ K2 ) )
% 8.64/4.90 = ( ( dvd_dvd_int @ L @ K2 )
% 8.64/4.90 | ( R3 = zero_zero_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8648_mult__sgn__dvd__iff,axiom,
% 8.64/4.90 ! [L: int,R3: int,K2: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ ( times_times_int @ L @ ( sgn_sgn_int @ R3 ) ) @ K2 )
% 8.64/4.90 = ( ( dvd_dvd_int @ L @ K2 )
% 8.64/4.90 & ( ( R3 = zero_zero_int )
% 8.64/4.90 => ( K2 = zero_zero_int ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8649_sgn__mult__dvd__iff,axiom,
% 8.64/4.90 ! [R3: int,L: int,K2: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R3 ) @ L ) @ K2 )
% 8.64/4.90 = ( ( dvd_dvd_int @ L @ K2 )
% 8.64/4.90 & ( ( R3 = zero_zero_int )
% 8.64/4.90 => ( K2 = zero_zero_int ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8650_cot__npi,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 8.64/4.90 = zero_zero_real ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8651_int__sgnE,axiom,
% 8.64/4.90 ! [K2: int] :
% 8.64/4.90 ~ ! [N3: nat,L4: int] :
% 8.64/4.90 ( K2
% 8.64/4.90 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8652_div__eq__sgn__abs,axiom,
% 8.64/4.90 ! [K2: int,L: int] :
% 8.64/4.90 ( ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 = ( sgn_sgn_int @ L ) )
% 8.64/4.90 => ( ( divide_divide_int @ K2 @ L )
% 8.64/4.90 = ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8653_div__sgn__abs__cancel,axiom,
% 8.64/4.90 ! [V2: int,K2: int,L: int] :
% 8.64/4.90 ( ( V2 != zero_zero_int )
% 8.64/4.90 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ K2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ V2 ) @ ( abs_abs_int @ L ) ) )
% 8.64/4.90 = ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8654_div__dvd__sgn__abs,axiom,
% 8.64/4.90 ! [L: int,K2: int] :
% 8.64/4.90 ( ( dvd_dvd_int @ L @ K2 )
% 8.64/4.90 => ( ( divide_divide_int @ K2 @ L )
% 8.64/4.90 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8655_eucl__rel__int__remainderI,axiom,
% 8.64/4.90 ! [R3: int,L: int,K2: int,Q2: int] :
% 8.64/4.90 ( ( ( sgn_sgn_int @ R3 )
% 8.64/4.90 = ( sgn_sgn_int @ L ) )
% 8.64/4.90 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 8.64/4.90 => ( ( K2
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ Q2 @ L ) @ R3 ) )
% 8.64/4.90 => ( eucl_rel_int @ K2 @ L @ ( product_Pair_int_int @ Q2 @ R3 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8656_eucl__rel__int_Osimps,axiom,
% 8.64/4.90 ( eucl_rel_int
% 8.64/4.90 = ( ^ [A13: int,A24: int,A32: product_prod_int_int] :
% 8.64/4.90 ( ? [K3: int] :
% 8.64/4.90 ( ( A13 = K3 )
% 8.64/4.90 & ( A24 = zero_zero_int )
% 8.64/4.90 & ( A32
% 8.64/4.90 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 8.64/4.90 | ? [L2: int,K3: int,Q5: int] :
% 8.64/4.90 ( ( A13 = K3 )
% 8.64/4.90 & ( A24 = L2 )
% 8.64/4.90 & ( A32
% 8.64/4.90 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 8.64/4.90 & ( L2 != zero_zero_int )
% 8.64/4.90 & ( K3
% 8.64/4.90 = ( times_times_int @ Q5 @ L2 ) ) )
% 8.64/4.90 | ? [R: int,L2: int,K3: int,Q5: int] :
% 8.64/4.90 ( ( A13 = K3 )
% 8.64/4.90 & ( A24 = L2 )
% 8.64/4.90 & ( A32
% 8.64/4.90 = ( product_Pair_int_int @ Q5 @ R ) )
% 8.64/4.90 & ( ( sgn_sgn_int @ R )
% 8.64/4.90 = ( sgn_sgn_int @ L2 ) )
% 8.64/4.90 & ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 8.64/4.90 & ( K3
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8657_eucl__rel__int_Ocases,axiom,
% 8.64/4.90 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 8.64/4.90 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 8.64/4.90 => ( ( ( A23 = zero_zero_int )
% 8.64/4.90 => ( A33
% 8.64/4.90 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 8.64/4.90 => ( ! [Q3: int] :
% 8.64/4.90 ( ( A33
% 8.64/4.90 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 8.64/4.90 => ( ( A23 != zero_zero_int )
% 8.64/4.90 => ( A12
% 8.64/4.90 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 8.64/4.90 => ~ ! [R4: int,Q3: int] :
% 8.64/4.90 ( ( A33
% 8.64/4.90 = ( product_Pair_int_int @ Q3 @ R4 ) )
% 8.64/4.90 => ( ( ( sgn_sgn_int @ R4 )
% 8.64/4.90 = ( sgn_sgn_int @ A23 ) )
% 8.64/4.90 => ( ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ A23 ) )
% 8.64/4.90 => ( A12
% 8.64/4.90 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R4 ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8658_div__noneq__sgn__abs,axiom,
% 8.64/4.90 ! [L: int,K2: int] :
% 8.64/4.90 ( ( L != zero_zero_int )
% 8.64/4.90 => ( ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 != ( sgn_sgn_int @ L ) )
% 8.64/4.90 => ( ( divide_divide_int @ K2 @ L )
% 8.64/4.90 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) )
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ~ ( dvd_dvd_int @ L @ K2 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8659_divide__int__unfold,axiom,
% 8.64/4.90 ! [L: int,K2: int,N: nat,M2: nat] :
% 8.64/4.90 ( ( ( ( ( sgn_sgn_int @ L )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( N = zero_zero_nat ) )
% 8.64/4.90 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.90 = zero_zero_int ) )
% 8.64/4.90 & ( ~ ( ( ( sgn_sgn_int @ L )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 = zero_zero_int )
% 8.64/4.90 | ( N = zero_zero_nat ) )
% 8.64/4.90 => ( ( ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 = ( sgn_sgn_int @ L ) )
% 8.64/4.90 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.90 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M2 @ N ) ) ) )
% 8.64/4.90 & ( ( ( sgn_sgn_int @ K2 )
% 8.64/4.90 != ( sgn_sgn_int @ L ) )
% 8.64/4.90 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K2 ) @ ( semiri1314217659103216013at_int @ M2 ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.90 = ( uminus_uminus_int
% 8.64/4.90 @ ( semiri1314217659103216013at_int
% 8.64/4.90 @ ( plus_plus_nat @ ( divide_divide_nat @ M2 @ N )
% 8.64/4.90 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.90 @ ~ ( dvd_dvd_nat @ N @ M2 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8660_natLess__def,axiom,
% 8.64/4.90 ( bNF_Ca8459412986667044542atLess
% 8.64/4.90 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8661_modulo__int__def,axiom,
% 8.64/4.90 ( modulo_modulo_int
% 8.64/4.90 = ( ^ [K3: int,L2: int] :
% 8.64/4.90 ( if_int @ ( L2 = zero_zero_int ) @ K3
% 8.64/4.90 @ ( if_int
% 8.64/4.90 @ ( ( sgn_sgn_int @ K3 )
% 8.64/4.90 = ( sgn_sgn_int @ L2 ) )
% 8.64/4.90 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 8.64/4.90 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 8.64/4.90 @ ( minus_minus_int
% 8.64/4.90 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 8.64/4.90 @ ( zero_n2684676970156552555ol_int
% 8.64/4.90 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 8.64/4.90 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8662_num_Osize__gen_I3_J,axiom,
% 8.64/4.90 ! [X33: num] :
% 8.64/4.90 ( ( size_num @ ( bit1 @ X33 ) )
% 8.64/4.90 = ( plus_plus_nat @ ( size_num @ X33 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8663_mask__nat__positive__iff,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.64/4.90 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8664_nat__1,axiom,
% 8.64/4.90 ( ( nat2 @ one_one_int )
% 8.64/4.90 = ( suc @ zero_zero_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8665_nat__0__iff,axiom,
% 8.64/4.90 ! [I2: int] :
% 8.64/4.90 ( ( ( nat2 @ I2 )
% 8.64/4.90 = zero_zero_nat )
% 8.64/4.90 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8666_nat__le__0,axiom,
% 8.64/4.90 ! [Z3: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 8.64/4.90 => ( ( nat2 @ Z3 )
% 8.64/4.90 = zero_zero_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8667_nat__neg__numeral,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8668_nat__zminus__int,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8669_take__bit__of__Suc__0,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.64/4.90 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8670_zero__less__nat__eq,axiom,
% 8.64/4.90 ! [Z3: int] :
% 8.64/4.90 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z3 ) )
% 8.64/4.90 = ( ord_less_int @ zero_zero_int @ Z3 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8671_card__atLeastAtMost__int,axiom,
% 8.64/4.90 ! [L: int,U: int] :
% 8.64/4.90 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 8.64/4.90 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8672_nat__ceiling__le__eq,axiom,
% 8.64/4.90 ! [X: real,A: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 8.64/4.90 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8673_one__less__nat__eq,axiom,
% 8.64/4.90 ! [Z3: int] :
% 8.64/4.90 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z3 ) )
% 8.64/4.90 = ( ord_less_int @ one_one_int @ Z3 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8674_numeral__power__le__nat__cancel__iff,axiom,
% 8.64/4.90 ! [X: num,N: nat,A: int] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 8.64/4.90 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8675_nat__le__numeral__power__cancel__iff,axiom,
% 8.64/4.90 ! [A: int,X: num,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 8.64/4.90 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8676_take__bit__tightened__less__eq__nat,axiom,
% 8.64/4.90 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.90 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M2 @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8677_take__bit__nat__less__eq__self,axiom,
% 8.64/4.90 ! [N: nat,M2: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8678_take__bit__mult,axiom,
% 8.64/4.90 ! [N: nat,K2: int,L: int] :
% 8.64/4.90 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K2 ) @ ( bit_se2923211474154528505it_int @ N @ L ) ) )
% 8.64/4.90 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K2 @ L ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8679_less__eq__mask,axiom,
% 8.64/4.90 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8680_nat__zero__as__int,axiom,
% 8.64/4.90 ( zero_zero_nat
% 8.64/4.90 = ( nat2 @ zero_zero_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8681_take__bit__tightened__less__eq__int,axiom,
% 8.64/4.90 ! [M2: nat,N: nat,K2: int] :
% 8.64/4.90 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.90 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M2 @ K2 ) @ ( bit_se2923211474154528505it_int @ N @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8682_nat__mono,axiom,
% 8.64/4.90 ! [X: int,Y: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ X @ Y )
% 8.64/4.90 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8683_nat__le__iff,axiom,
% 8.64/4.90 ! [X: int,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 8.64/4.90 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8684_nat__abs__mult__distrib,axiom,
% 8.64/4.90 ! [W2: int,Z3: int] :
% 8.64/4.90 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W2 @ Z3 ) ) )
% 8.64/4.90 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W2 ) ) @ ( nat2 @ ( abs_abs_int @ Z3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8685_nat__times__as__int,axiom,
% 8.64/4.90 ( times_times_nat
% 8.64/4.90 = ( ^ [A5: nat,B4: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B4 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8686_less__mask,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.90 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8687_nat__le__eq__zle,axiom,
% 8.64/4.90 ! [W2: int,Z3: int] :
% 8.64/4.90 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 8.64/4.90 | ( ord_less_eq_int @ zero_zero_int @ Z3 ) )
% 8.64/4.90 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z3 ) )
% 8.64/4.90 = ( ord_less_eq_int @ W2 @ Z3 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8688_nat__eq__iff2,axiom,
% 8.64/4.90 ! [M2: nat,W2: int] :
% 8.64/4.90 ( ( M2
% 8.64/4.90 = ( nat2 @ W2 ) )
% 8.64/4.90 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.64/4.90 => ( W2
% 8.64/4.90 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.64/4.90 => ( M2 = zero_zero_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8689_nat__eq__iff,axiom,
% 8.64/4.90 ! [W2: int,M2: nat] :
% 8.64/4.90 ( ( ( nat2 @ W2 )
% 8.64/4.90 = M2 )
% 8.64/4.90 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.64/4.90 => ( W2
% 8.64/4.90 = ( semiri1314217659103216013at_int @ M2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 8.64/4.90 => ( M2 = zero_zero_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8690_split__nat,axiom,
% 8.64/4.90 ! [P2: nat > $o,I2: int] :
% 8.64/4.90 ( ( P2 @ ( nat2 @ I2 ) )
% 8.64/4.90 = ( ! [N4: nat] :
% 8.64/4.90 ( ( I2
% 8.64/4.90 = ( semiri1314217659103216013at_int @ N4 ) )
% 8.64/4.90 => ( P2 @ N4 ) )
% 8.64/4.90 & ( ( ord_less_int @ I2 @ zero_zero_int )
% 8.64/4.90 => ( P2 @ zero_zero_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8691_le__nat__iff,axiom,
% 8.64/4.90 ! [K2: int,N: nat] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ K2 )
% 8.64/4.90 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K2 ) )
% 8.64/4.90 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K2 ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8692_nat__mult__distrib,axiom,
% 8.64/4.90 ! [Z3: int,Z6: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 8.64/4.90 => ( ( nat2 @ ( times_times_int @ Z3 @ Z6 ) )
% 8.64/4.90 = ( times_times_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8693_Suc__as__int,axiom,
% 8.64/4.90 ( suc
% 8.64/4.90 = ( ^ [A5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ one_one_int ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8694_nat__abs__triangle__ineq,axiom,
% 8.64/4.90 ! [K2: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K2 @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8695_nat__floor__neg,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 8.64/4.90 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 8.64/4.90 = zero_zero_nat ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8696_div__abs__eq__div__nat,axiom,
% 8.64/4.90 ! [K2: int,L: int] :
% 8.64/4.90 ( ( divide_divide_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) )
% 8.64/4.90 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8697_floor__eq3,axiom,
% 8.64/4.90 ! [N: nat,X: real] :
% 8.64/4.90 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 8.64/4.90 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 8.64/4.90 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 8.64/4.90 = N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8698_le__nat__floor,axiom,
% 8.64/4.90 ! [X: nat,A: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 8.64/4.90 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8699_mod__abs__eq__div__nat,axiom,
% 8.64/4.90 ! [K2: int,L: int] :
% 8.64/4.90 ( ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) )
% 8.64/4.90 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8700_nat__2,axiom,
% 8.64/4.90 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.90 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8701_sgn__power__injE,axiom,
% 8.64/4.90 ! [A: real,N: nat,X: real,B: real] :
% 8.64/4.90 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 8.64/4.90 = X )
% 8.64/4.90 => ( ( X
% 8.64/4.90 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( A = B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8702_Suc__nat__eq__nat__zadd1,axiom,
% 8.64/4.90 ! [Z3: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 8.64/4.90 => ( ( suc @ ( nat2 @ Z3 ) )
% 8.64/4.90 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z3 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8703_nat__mult__distrib__neg,axiom,
% 8.64/4.90 ! [Z3: int,Z6: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ Z3 @ zero_zero_int )
% 8.64/4.90 => ( ( nat2 @ ( times_times_int @ Z3 @ Z6 ) )
% 8.64/4.90 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z3 ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8704_nat__abs__int__diff,axiom,
% 8.64/4.90 ! [A: nat,B: nat] :
% 8.64/4.90 ( ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.90 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 8.64/4.90 = ( minus_minus_nat @ B @ A ) ) )
% 8.64/4.90 & ( ~ ( ord_less_eq_nat @ A @ B )
% 8.64/4.90 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 8.64/4.90 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8705_floor__eq4,axiom,
% 8.64/4.90 ! [N: nat,X: real] :
% 8.64/4.90 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 8.64/4.90 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 8.64/4.90 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 8.64/4.90 = N ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8706_num_Osize__gen_I1_J,axiom,
% 8.64/4.90 ( ( size_num @ one )
% 8.64/4.90 = zero_zero_nat ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8707_diff__nat__eq__if,axiom,
% 8.64/4.90 ! [Z6: int,Z3: int] :
% 8.64/4.90 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 8.64/4.90 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) )
% 8.64/4.90 = ( nat2 @ Z3 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 8.64/4.90 => ( ( minus_minus_nat @ ( nat2 @ Z3 ) @ ( nat2 @ Z6 ) )
% 8.64/4.90 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z3 @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z3 @ Z6 ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8708_take__bit__nat__less__self__iff,axiom,
% 8.64/4.90 ! [N: nat,M2: nat] :
% 8.64/4.90 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M2 ) @ M2 )
% 8.64/4.90 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M2 ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8709_Suc__mask__eq__exp,axiom,
% 8.64/4.90 ! [N: nat] :
% 8.64/4.90 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 8.64/4.90 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8710_take__bit__Suc__minus__bit0,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 8.64/4.90 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8711_nat__dvd__iff,axiom,
% 8.64/4.90 ! [Z3: int,M2: nat] :
% 8.64/4.90 ( ( dvd_dvd_nat @ ( nat2 @ Z3 ) @ M2 )
% 8.64/4.90 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 8.64/4.90 => ( dvd_dvd_int @ Z3 @ ( semiri1314217659103216013at_int @ M2 ) ) )
% 8.64/4.90 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z3 )
% 8.64/4.90 => ( M2 = zero_zero_nat ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8712_take__bit__numeral__minus__bit0,axiom,
% 8.64/4.90 ! [L: num,K2: num] :
% 8.64/4.90 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 8.64/4.90 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8713_take__bit__int__less__eq,axiom,
% 8.64/4.90 ! [N: nat,K2: int] :
% 8.64/4.90 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K2 )
% 8.64/4.90 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.90 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K2 ) @ ( minus_minus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8714_signed__take__bit__eq__take__bit__shift,axiom,
% 8.64/4.90 ( bit_ri631733984087533419it_int
% 8.64/4.90 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8715_arctan__inverse,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( X != zero_zero_real )
% 8.64/4.90 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 8.64/4.90 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8716_num_Osize__gen_I2_J,axiom,
% 8.64/4.90 ! [X2: num] :
% 8.64/4.90 ( ( size_num @ ( bit0 @ X2 ) )
% 8.64/4.90 = ( plus_plus_nat @ ( size_num @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8717_take__bit__numeral__minus__bit1,axiom,
% 8.64/4.90 ! [L: num,K2: num] :
% 8.64/4.90 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8718_take__bit__Suc__minus__bit1,axiom,
% 8.64/4.90 ! [N: nat,K2: num] :
% 8.64/4.90 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 8.64/4.90 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8719_or__int__unfold,axiom,
% 8.64/4.90 ( bit_se1409905431419307370or_int
% 8.64/4.90 = ( ^ [K3: int,L2: int] :
% 8.64/4.90 ( if_int
% 8.64/4.90 @ ( ( K3
% 8.64/4.90 = ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.90 | ( L2
% 8.64/4.90 = ( uminus_uminus_int @ one_one_int ) ) )
% 8.64/4.90 @ ( uminus_uminus_int @ one_one_int )
% 8.64/4.90 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8720_arctan__half,axiom,
% 8.64/4.90 ( arctan
% 8.64/4.90 = ( ^ [X4: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X4 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8721_real__sqrt__mult__self,axiom,
% 8.64/4.90 ! [A: real] :
% 8.64/4.90 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 8.64/4.90 = ( abs_abs_real @ A ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8722_real__sqrt__abs2,axiom,
% 8.64/4.90 ! [X: real] :
% 8.64/4.90 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 8.64/4.90 = ( abs_abs_real @ X ) ) ).
% 8.64/4.90
% 8.64/4.90 thf(fact_8723_pred__numeral__inc,axiom,
% 8.64/4.90 ! [K2: num] :
% 8.64/4.90 ( ( pred_numeral @ ( inc @ K2 ) )
% 8.64/4.90 = ( numeral_numeral_nat @ K2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8724_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 8.64/4.91 ! [X: real,Y: real,Xa2: real,Ya: real] :
% 8.64/4.91 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.91 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8725_real__sqrt__mult,axiom,
% 8.64/4.91 ! [X: real,Y: real] :
% 8.64/4.91 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 8.64/4.91 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8726_num__induct,axiom,
% 8.64/4.91 ! [P2: num > $o,X: num] :
% 8.64/4.91 ( ( P2 @ one )
% 8.64/4.91 => ( ! [X3: num] :
% 8.64/4.91 ( ( P2 @ X3 )
% 8.64/4.91 => ( P2 @ ( inc @ X3 ) ) )
% 8.64/4.91 => ( P2 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8727_add__inc,axiom,
% 8.64/4.91 ! [X: num,Y: num] :
% 8.64/4.91 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 8.64/4.91 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8728_inc_Osimps_I1_J,axiom,
% 8.64/4.91 ( ( inc @ one )
% 8.64/4.91 = ( bit0 @ one ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8729_inc_Osimps_I2_J,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( inc @ ( bit0 @ X ) )
% 8.64/4.91 = ( bit1 @ X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8730_inc_Osimps_I3_J,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( inc @ ( bit1 @ X ) )
% 8.64/4.91 = ( bit0 @ ( inc @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8731_add__One,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( plus_plus_num @ X @ one )
% 8.64/4.91 = ( inc @ X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8732_le__real__sqrt__sumsq,axiom,
% 8.64/4.91 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8733_inc__BitM__eq,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ( ( inc @ ( bitM @ N ) )
% 8.64/4.91 = ( bit0 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8734_BitM__inc__eq,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ( ( bitM @ ( inc @ N ) )
% 8.64/4.91 = ( bit1 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8735_mult__inc,axiom,
% 8.64/4.91 ! [X: num,Y: num] :
% 8.64/4.91 ( ( times_times_num @ X @ ( inc @ Y ) )
% 8.64/4.91 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8736_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 8.64/4.91 ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8737_arith__geo__mean__sqrt,axiom,
% 8.64/4.91 ! [X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.91 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8738_or__int__rec,axiom,
% 8.64/4.91 ( bit_se1409905431419307370or_int
% 8.64/4.91 = ( ^ [K3: int,L2: int] :
% 8.64/4.91 ( plus_plus_int
% 8.64/4.91 @ ( zero_n2684676970156552555ol_int
% 8.64/4.91 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 8.64/4.91 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 8.64/4.91 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8739_signed__take__bit__eq__take__bit__minus,axiom,
% 8.64/4.91 ( bit_ri631733984087533419it_int
% 8.64/4.91 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N4 ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N4 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8740_cis__2pi,axiom,
% 8.64/4.91 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 8.64/4.91 = one_one_complex ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8741_take__bit__Suc__from__most,axiom,
% 8.64/4.91 ! [N: nat,K2: int] :
% 8.64/4.91 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K2 )
% 8.64/4.91 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8742_pi__def,axiom,
% 8.64/4.91 ( pi
% 8.64/4.91 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 8.64/4.91 @ ( the_real
% 8.64/4.91 @ ^ [X4: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 8.64/4.91 & ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 8.64/4.91 & ( ( cos_real @ X4 )
% 8.64/4.91 = zero_zero_real ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8743_or__nat__numerals_I4_J,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8744_or__nat__numerals_I2_J,axiom,
% 8.64/4.91 ! [Y: num] :
% 8.64/4.91 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8745_or__nat__numerals_I1_J,axiom,
% 8.64/4.91 ! [Y: num] :
% 8.64/4.91 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8746_or__nat__numerals_I3_J,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8747_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 8.64/4.91 ! [W2: num,N: nat] :
% 8.64/4.91 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W2 ) ) ) @ ( suc @ N ) )
% 8.64/4.91 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8748_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 8.64/4.91 ! [W2: num,N: nat] :
% 8.64/4.91 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W2 ) ) ) @ ( suc @ N ) )
% 8.64/4.91 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W2 ) @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8749_cis__mult,axiom,
% 8.64/4.91 ! [A: real,B: real] :
% 8.64/4.91 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 8.64/4.91 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8750_DeMoivre,axiom,
% 8.64/4.91 ! [A: real,N: nat] :
% 8.64/4.91 ( ( power_power_complex @ ( cis @ A ) @ N )
% 8.64/4.91 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8751_bit__concat__bit__iff,axiom,
% 8.64/4.91 ! [M2: nat,K2: int,L: int,N: nat] :
% 8.64/4.91 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M2 @ K2 @ L ) @ N )
% 8.64/4.91 = ( ( ( ord_less_nat @ N @ M2 )
% 8.64/4.91 & ( bit_se1146084159140164899it_int @ K2 @ N ) )
% 8.64/4.91 | ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.91 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8752_int__bit__bound,axiom,
% 8.64/4.91 ! [K2: int] :
% 8.64/4.91 ~ ! [N3: nat] :
% 8.64/4.91 ( ! [M3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ N3 @ M3 )
% 8.64/4.91 => ( ( bit_se1146084159140164899it_int @ K2 @ M3 )
% 8.64/4.91 = ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) )
% 8.64/4.91 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 8.64/4.91 => ( ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 8.64/4.91 = ( ~ ( bit_se1146084159140164899it_int @ K2 @ N3 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8753_set__bit__eq,axiom,
% 8.64/4.91 ( bit_se7879613467334960850it_int
% 8.64/4.91 = ( ^ [N4: nat,K3: int] :
% 8.64/4.91 ( plus_plus_int @ K3
% 8.64/4.91 @ ( times_times_int
% 8.64/4.91 @ ( zero_n2684676970156552555ol_int
% 8.64/4.91 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N4 ) )
% 8.64/4.91 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8754_unset__bit__eq,axiom,
% 8.64/4.91 ( bit_se4203085406695923979it_int
% 8.64/4.91 = ( ^ [N4: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N4 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8755_or__Suc__0__eq,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8756_Suc__0__or__eq,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.91 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8757_or__nat__rec,axiom,
% 8.64/4.91 ( bit_se1412395901928357646or_nat
% 8.64/4.91 = ( ^ [M6: nat,N4: nat] :
% 8.64/4.91 ( plus_plus_nat
% 8.64/4.91 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.91 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 8.64/4.91 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 8.64/4.91 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8758_or__nat__unfold,axiom,
% 8.64/4.91 ( bit_se1412395901928357646or_nat
% 8.64/4.91 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8759_bij__betw__roots__unity,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( bij_betw_nat_complex
% 8.64/4.91 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N )
% 8.64/4.91 @ ( collect_complex
% 8.64/4.91 @ ^ [Z4: complex] :
% 8.64/4.91 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.91 = one_one_complex ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8760_cis__multiple__2pi,axiom,
% 8.64/4.91 ! [N: real] :
% 8.64/4.91 ( ( member_real @ N @ ring_1_Ints_real )
% 8.64/4.91 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 8.64/4.91 = one_one_complex ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8761_not__bit__Suc__0__Suc,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8762_bit__Suc__0__iff,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.91 = ( N = zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8763_not__bit__Suc__0__numeral,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8764_sin__times__pi__eq__0,axiom,
% 8.64/4.91 ! [X: real] :
% 8.64/4.91 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8765_sin__integer__2pi,axiom,
% 8.64/4.91 ! [N: real] :
% 8.64/4.91 ( ( member_real @ N @ ring_1_Ints_real )
% 8.64/4.91 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 8.64/4.91 = zero_zero_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8766_cos__integer__2pi,axiom,
% 8.64/4.91 ! [N: real] :
% 8.64/4.91 ( ( member_real @ N @ ring_1_Ints_real )
% 8.64/4.91 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 8.64/4.91 = one_one_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8767_i__even__power,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.91 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8768_Suc__0__xor__eq,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.91 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.91 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.91 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8769_xor__Suc__0__eq,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.91 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.91 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8770_horner__sum__of__bool__2__less,axiom,
% 8.64/4.91 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8771_complex__i__mult__minus,axiom,
% 8.64/4.91 ! [X: complex] :
% 8.64/4.91 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 8.64/4.91 = ( uminus1482373934393186551omplex @ X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8772_divide__numeral__i,axiom,
% 8.64/4.91 ! [Z3: complex,N: num] :
% 8.64/4.91 ( ( divide1717551699836669952omplex @ Z3 @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 8.64/4.91 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z3 ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8773_divide__i,axiom,
% 8.64/4.91 ! [X: complex] :
% 8.64/4.91 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 8.64/4.91 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8774_i__squared,axiom,
% 8.64/4.91 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 8.64/4.91 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8775_xor__nat__numerals_I1_J,axiom,
% 8.64/4.91 ! [Y: num] :
% 8.64/4.91 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8776_xor__nat__numerals_I2_J,axiom,
% 8.64/4.91 ! [Y: num] :
% 8.64/4.91 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8777_xor__nat__numerals_I3_J,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8778_xor__nat__numerals_I4_J,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8779_i__times__eq__iff,axiom,
% 8.64/4.91 ! [W2: complex,Z3: complex] :
% 8.64/4.91 ( ( ( times_times_complex @ imaginary_unit @ W2 )
% 8.64/4.91 = Z3 )
% 8.64/4.91 = ( W2
% 8.64/4.91 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8780_i__mult__Complex,axiom,
% 8.64/4.91 ! [A: real,B: real] :
% 8.64/4.91 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 8.64/4.91 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8781_Complex__mult__i,axiom,
% 8.64/4.91 ! [A: real,B: real] :
% 8.64/4.91 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 8.64/4.91 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8782_xor__nat__unfold,axiom,
% 8.64/4.91 ( bit_se6528837805403552850or_nat
% 8.64/4.91 = ( ^ [M6: nat,N4: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N4 @ ( if_nat @ ( N4 = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8783_xor__nat__rec,axiom,
% 8.64/4.91 ( bit_se6528837805403552850or_nat
% 8.64/4.91 = ( ^ [M6: nat,N4: nat] :
% 8.64/4.91 ( plus_plus_nat
% 8.64/4.91 @ ( zero_n2687167440665602831ol_nat
% 8.64/4.91 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 8.64/4.91 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) )
% 8.64/4.91 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8784_Sum__Ico__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( groups3542108847815614940at_nat
% 8.64/4.91 @ ^ [X4: nat] : X4
% 8.64/4.91 @ ( set_or4665077453230672383an_nat @ M2 @ N ) )
% 8.64/4.91 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M2 @ ( minus_minus_nat @ M2 @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8785_Least__eq__0,axiom,
% 8.64/4.91 ! [P2: nat > $o] :
% 8.64/4.91 ( ( P2 @ zero_zero_nat )
% 8.64/4.91 => ( ( ord_Least_nat @ P2 )
% 8.64/4.91 = zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8786_finite__atLeastLessThan,axiom,
% 8.64/4.91 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8787_card__atLeastLessThan,axiom,
% 8.64/4.91 ! [L: nat,U: nat] :
% 8.64/4.91 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 8.64/4.91 = ( minus_minus_nat @ U @ L ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8788_atLeastLessThan__singleton,axiom,
% 8.64/4.91 ! [M2: nat] :
% 8.64/4.91 ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ M2 ) )
% 8.64/4.91 = ( insert_nat @ M2 @ bot_bot_set_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8789_all__nat__less__eq,axiom,
% 8.64/4.91 ! [N: nat,P2: nat > $o] :
% 8.64/4.91 ( ( ! [M6: nat] :
% 8.64/4.91 ( ( ord_less_nat @ M6 @ N )
% 8.64/4.91 => ( P2 @ M6 ) ) )
% 8.64/4.91 = ( ! [X4: nat] :
% 8.64/4.91 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.64/4.91 => ( P2 @ X4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8790_ex__nat__less__eq,axiom,
% 8.64/4.91 ! [N: nat,P2: nat > $o] :
% 8.64/4.91 ( ( ? [M6: nat] :
% 8.64/4.91 ( ( ord_less_nat @ M6 @ N )
% 8.64/4.91 & ( P2 @ M6 ) ) )
% 8.64/4.91 = ( ? [X4: nat] :
% 8.64/4.91 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.64/4.91 & ( P2 @ X4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8791_atLeastLessThanSuc__atLeastAtMost,axiom,
% 8.64/4.91 ! [L: nat,U: nat] :
% 8.64/4.91 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 8.64/4.91 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8792_lessThan__atLeast0,axiom,
% 8.64/4.91 ( set_ord_lessThan_nat
% 8.64/4.91 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8793_atLeastLessThan0,axiom,
% 8.64/4.91 ! [M2: nat] :
% 8.64/4.91 ( ( set_or4665077453230672383an_nat @ M2 @ zero_zero_nat )
% 8.64/4.91 = bot_bot_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8794_Least__Suc2,axiom,
% 8.64/4.91 ! [P2: nat > $o,N: nat,Q: nat > $o,M2: nat] :
% 8.64/4.91 ( ( P2 @ N )
% 8.64/4.91 => ( ( Q @ M2 )
% 8.64/4.91 => ( ~ ( P2 @ zero_zero_nat )
% 8.64/4.91 => ( ! [K: nat] :
% 8.64/4.91 ( ( P2 @ ( suc @ K ) )
% 8.64/4.91 = ( Q @ K ) )
% 8.64/4.91 => ( ( ord_Least_nat @ P2 )
% 8.64/4.91 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8795_Least__Suc,axiom,
% 8.64/4.91 ! [P2: nat > $o,N: nat] :
% 8.64/4.91 ( ( P2 @ N )
% 8.64/4.91 => ( ~ ( P2 @ zero_zero_nat )
% 8.64/4.91 => ( ( ord_Least_nat @ P2 )
% 8.64/4.91 = ( suc
% 8.64/4.91 @ ( ord_Least_nat
% 8.64/4.91 @ ^ [M6: nat] : ( P2 @ ( suc @ M6 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8796_atLeast0__lessThan__Suc,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.64/4.91 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8797_subset__eq__atLeast0__lessThan__finite,axiom,
% 8.64/4.91 ! [N6: set_nat,N: nat] :
% 8.64/4.91 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.64/4.91 => ( finite_finite_nat @ N6 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8798_subset__card__intvl__is__intvl,axiom,
% 8.64/4.91 ! [A4: set_nat,K2: nat] :
% 8.64/4.91 ( ( ord_less_eq_set_nat @ A4 @ ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) )
% 8.64/4.91 => ( A4
% 8.64/4.91 = ( set_or4665077453230672383an_nat @ K2 @ ( plus_plus_nat @ K2 @ ( finite_card_nat @ A4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8799_atLeastLessThan__add__Un,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat,K2: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.91 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 8.64/4.91 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) @ ( set_or4665077453230672383an_nat @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8800_atLeastLessThanSuc,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.91 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 8.64/4.91 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) )
% 8.64/4.91 & ( ~ ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.91 => ( ( set_or4665077453230672383an_nat @ M2 @ ( suc @ N ) )
% 8.64/4.91 = bot_bot_set_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8801_prod__Suc__Suc__fact,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 8.64/4.91 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8802_prod__Suc__fact,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.64/4.91 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8803_subset__eq__atLeast0__lessThan__card,axiom,
% 8.64/4.91 ! [N6: set_nat,N: nat] :
% 8.64/4.91 ( ( ord_less_eq_set_nat @ N6 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 8.64/4.91 => ( ord_less_eq_nat @ ( finite_card_nat @ N6 ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8804_card__sum__le__nat__sum,axiom,
% 8.64/4.91 ! [S3: set_nat] :
% 8.64/4.91 ( ord_less_eq_nat
% 8.64/4.91 @ ( groups3542108847815614940at_nat
% 8.64/4.91 @ ^ [X4: nat] : X4
% 8.64/4.91 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S3 ) ) )
% 8.64/4.91 @ ( groups3542108847815614940at_nat
% 8.64/4.91 @ ^ [X4: nat] : X4
% 8.64/4.91 @ S3 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8805_atLeastLessThan__nat__numeral,axiom,
% 8.64/4.91 ! [M2: nat,K2: num] :
% 8.64/4.91 ( ( ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K2 ) )
% 8.64/4.91 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.91 = ( insert_nat @ ( pred_numeral @ K2 ) @ ( set_or4665077453230672383an_nat @ M2 @ ( pred_numeral @ K2 ) ) ) ) )
% 8.64/4.91 & ( ~ ( ord_less_eq_nat @ M2 @ ( pred_numeral @ K2 ) )
% 8.64/4.91 => ( ( set_or4665077453230672383an_nat @ M2 @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.91 = bot_bot_set_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8806_atLeast1__lessThan__eq__remove0,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 8.64/4.91 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8807_xor__int__rec,axiom,
% 8.64/4.91 ( bit_se6526347334894502574or_int
% 8.64/4.91 = ( ^ [K3: int,L2: int] :
% 8.64/4.91 ( plus_plus_int
% 8.64/4.91 @ ( zero_n2684676970156552555ol_int
% 8.64/4.91 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 8.64/4.91 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 8.64/4.91 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8808_sum__power2,axiom,
% 8.64/4.91 ! [K2: nat] :
% 8.64/4.91 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K2 ) )
% 8.64/4.91 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) @ one_one_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8809_Chebyshev__sum__upper__nat,axiom,
% 8.64/4.91 ! [N: nat,A: nat > nat,B: nat > nat] :
% 8.64/4.91 ( ! [I3: nat,J3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ I3 @ J3 )
% 8.64/4.91 => ( ( ord_less_nat @ J3 @ N )
% 8.64/4.91 => ( ord_less_eq_nat @ ( A @ I3 ) @ ( A @ J3 ) ) ) )
% 8.64/4.91 => ( ! [I3: nat,J3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ I3 @ J3 )
% 8.64/4.91 => ( ( ord_less_nat @ J3 @ N )
% 8.64/4.91 => ( ord_less_eq_nat @ ( B @ J3 ) @ ( B @ I3 ) ) ) )
% 8.64/4.91 => ( ord_less_eq_nat
% 8.64/4.91 @ ( times_times_nat @ N
% 8.64/4.91 @ ( groups3542108847815614940at_nat
% 8.64/4.91 @ ^ [I: nat] : ( times_times_nat @ ( A @ I ) @ ( B @ I ) )
% 8.64/4.91 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 8.64/4.91 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8810_xor__int__unfold,axiom,
% 8.64/4.91 ( bit_se6526347334894502574or_int
% 8.64/4.91 = ( ^ [K3: int,L2: int] :
% 8.64/4.91 ( if_int
% 8.64/4.91 @ ( K3
% 8.64/4.91 = ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.91 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 8.64/4.91 @ ( if_int
% 8.64/4.91 @ ( L2
% 8.64/4.91 = ( uminus_uminus_int @ one_one_int ) )
% 8.64/4.91 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 8.64/4.91 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8811_exp__two__pi__i_H,axiom,
% 8.64/4.91 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 = one_one_complex ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8812_finite__atLeastLessThan__int,axiom,
% 8.64/4.91 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8813_card__atLeastLessThan__int,axiom,
% 8.64/4.91 ! [L: int,U: int] :
% 8.64/4.91 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 8.64/4.91 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8814_exp__pi__i_H,axiom,
% 8.64/4.91 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 8.64/4.91 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8815_exp__pi__i,axiom,
% 8.64/4.91 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 8.64/4.91 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8816_exp__two__pi__i,axiom,
% 8.64/4.91 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 8.64/4.91 = one_one_complex ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8817_complex__exp__exists,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ? [A3: complex,R4: real] :
% 8.64/4.91 ( Z3
% 8.64/4.91 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) @ ( exp_complex @ A3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8818_finite__atLeastZeroLessThan__int,axiom,
% 8.64/4.91 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8819_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 8.64/4.91 ! [L: int,U: int] :
% 8.64/4.91 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 8.64/4.91 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8820_Complex__mult__complex__of__real,axiom,
% 8.64/4.91 ! [X: real,Y: real,R3: real] :
% 8.64/4.91 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R3 ) )
% 8.64/4.91 = ( complex2 @ ( times_times_real @ X @ R3 ) @ ( times_times_real @ Y @ R3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8821_complex__of__real__mult__Complex,axiom,
% 8.64/4.91 ! [R3: real,X: real,Y: real] :
% 8.64/4.91 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( complex2 @ X @ Y ) )
% 8.64/4.91 = ( complex2 @ ( times_times_real @ R3 @ X ) @ ( times_times_real @ R3 @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8822_Complex__eq,axiom,
% 8.64/4.91 ( complex2
% 8.64/4.91 = ( ^ [A5: real,B4: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A5 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8823_cis__conv__exp,axiom,
% 8.64/4.91 ( cis
% 8.64/4.91 = ( ^ [B4: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8824_card__atLeastZeroLessThan__int,axiom,
% 8.64/4.91 ! [U: int] :
% 8.64/4.91 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 8.64/4.91 = ( nat2 @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8825_complex__of__real__i,axiom,
% 8.64/4.91 ! [R3: real] :
% 8.64/4.91 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ imaginary_unit )
% 8.64/4.91 = ( complex2 @ zero_zero_real @ R3 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8826_i__complex__of__real,axiom,
% 8.64/4.91 ! [R3: real] :
% 8.64/4.91 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R3 ) )
% 8.64/4.91 = ( complex2 @ zero_zero_real @ R3 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8827_complex__split__polar,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ? [R4: real,A3: real] :
% 8.64/4.91 ( Z3
% 8.64/4.91 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R4 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A3 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A3 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8828_and__not__numerals_I5_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.64/4.91 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8829_and__not__numerals_I6_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.64/4.91 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8830_and__not__numerals_I9_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.64/4.91 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8831_or__not__numerals_I6_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.64/4.91 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8832_cmod__unit__one,axiom,
% 8.64/4.91 ! [A: real] :
% 8.64/4.91 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 8.64/4.91 = one_one_real ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8833_cmod__complex__polar,axiom,
% 8.64/4.91 ! [R3: real,A: real] :
% 8.64/4.91 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R3 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 8.64/4.91 = ( abs_abs_real @ R3 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8834_or__not__numerals_I5_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.64/4.91 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8835_and__not__numerals_I8_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.64/4.91 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8836_or__not__numerals_I8_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 8.64/4.91 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8837_or__not__numerals_I9_J,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M2 ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 8.64/4.91 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M2 ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8838_not__int__rec,axiom,
% 8.64/4.91 ( bit_ri7919022796975470100ot_int
% 8.64/4.91 = ( ^ [K3: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8839_Cauchy__iff2,axiom,
% 8.64/4.91 ( topolo4055970368930404560y_real
% 8.64/4.91 = ( ^ [X7: nat > real] :
% 8.64/4.91 ! [J: nat] :
% 8.64/4.91 ? [M9: nat] :
% 8.64/4.91 ! [M6: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ M9 @ M6 )
% 8.64/4.91 => ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ M9 @ N4 )
% 8.64/4.91 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X7 @ M6 ) @ ( X7 @ N4 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8840_VEBT_Osize__gen_I1_J,axiom,
% 8.64/4.91 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 8.64/4.91 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 8.64/4.91 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8841_VEBT_Osize_I3_J,axiom,
% 8.64/4.91 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 8.64/4.91 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 8.64/4.91 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8842_divmod__step__integer__def,axiom,
% 8.64/4.91 ( unique4921790084139445826nteger
% 8.64/4.91 = ( ^ [L2: num] :
% 8.64/4.91 ( produc6916734918728496179nteger
% 8.64/4.91 @ ^ [Q5: code_integer,R: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8843_complex__div__cnj,axiom,
% 8.64/4.91 ( divide1717551699836669952omplex
% 8.64/4.91 = ( ^ [A5: complex,B4: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A5 @ ( cnj @ B4 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8844_list__decode_Opsimps_I2_J,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( accp_nat @ nat_list_decode_rel @ ( suc @ N ) )
% 8.64/4.91 => ( ( nat_list_decode @ ( suc @ N ) )
% 8.64/4.91 = ( produc2761476792215241774st_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 8.64/4.91 @ ( nat_prod_decode @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8845_complex__cnj__mult,axiom,
% 8.64/4.91 ! [X: complex,Y: complex] :
% 8.64/4.91 ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 8.64/4.91 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8846_list__decode__eq,axiom,
% 8.64/4.91 ! [X: nat,Y: nat] :
% 8.64/4.91 ( ( ( nat_list_decode @ X )
% 8.64/4.91 = ( nat_list_decode @ Y ) )
% 8.64/4.91 = ( X = Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8847_times__integer__code_I1_J,axiom,
% 8.64/4.91 ! [K2: code_integer] :
% 8.64/4.91 ( ( times_3573771949741848930nteger @ K2 @ zero_z3403309356797280102nteger )
% 8.64/4.91 = zero_z3403309356797280102nteger ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8848_times__integer__code_I2_J,axiom,
% 8.64/4.91 ! [L: code_integer] :
% 8.64/4.91 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L )
% 8.64/4.91 = zero_z3403309356797280102nteger ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8849_zero__natural_Orsp,axiom,
% 8.64/4.91 zero_zero_nat = zero_zero_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8850_list__decode_Osimps_I2_J,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( nat_list_decode @ ( suc @ N ) )
% 8.64/4.91 = ( produc2761476792215241774st_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 8.64/4.91 @ ( nat_prod_decode @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8851_complex__mod__mult__cnj,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) )
% 8.64/4.91 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8852_complex__norm__square,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.91 = ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8853_integer__of__int__code,axiom,
% 8.64/4.91 ( code_integer_of_int
% 8.64/4.91 = ( ^ [K3: int] :
% 8.64/4.91 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 8.64/4.91 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 8.64/4.91 @ ( if_Code_integer
% 8.64/4.91 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 8.64/4.91 = zero_zero_int )
% 8.64/4.91 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8854_list__decode_Opelims,axiom,
% 8.64/4.91 ! [X: nat,Y: list_nat] :
% 8.64/4.91 ( ( ( nat_list_decode @ X )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( accp_nat @ nat_list_decode_rel @ X )
% 8.64/4.91 => ( ( ( X = zero_zero_nat )
% 8.64/4.91 => ( ( Y = nil_nat )
% 8.64/4.91 => ~ ( accp_nat @ nat_list_decode_rel @ zero_zero_nat ) ) )
% 8.64/4.91 => ~ ! [N3: nat] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( suc @ N3 ) )
% 8.64/4.91 => ( ( Y
% 8.64/4.91 = ( produc2761476792215241774st_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 8.64/4.91 @ ( nat_prod_decode @ N3 ) ) )
% 8.64/4.91 => ~ ( accp_nat @ nat_list_decode_rel @ ( suc @ N3 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8855_list__decode_Oelims,axiom,
% 8.64/4.91 ! [X: nat,Y: list_nat] :
% 8.64/4.91 ( ( ( nat_list_decode @ X )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( ( X = zero_zero_nat )
% 8.64/4.91 => ( Y != nil_nat ) )
% 8.64/4.91 => ~ ! [N3: nat] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( suc @ N3 ) )
% 8.64/4.91 => ( Y
% 8.64/4.91 != ( produc2761476792215241774st_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( cons_nat @ X4 @ ( nat_list_decode @ Y4 ) )
% 8.64/4.91 @ ( nat_prod_decode @ N3 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8856_cnj__add__mult__eq__Re,axiom,
% 8.64/4.91 ! [Z3: complex,W2: complex] :
% 8.64/4.91 ( ( plus_plus_complex @ ( times_times_complex @ Z3 @ ( cnj @ W2 ) ) @ ( times_times_complex @ ( cnj @ Z3 ) @ W2 ) )
% 8.64/4.91 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z3 @ ( cnj @ W2 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8857_list__encode_Ocases,axiom,
% 8.64/4.91 ! [X: list_nat] :
% 8.64/4.91 ( ( X != nil_nat )
% 8.64/4.91 => ~ ! [X3: nat,Xs3: list_nat] :
% 8.64/4.91 ( X
% 8.64/4.91 != ( cons_nat @ X3 @ Xs3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8858_times__integer_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: int,X: int] :
% 8.64/4.91 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 8.64/4.91 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8859_scaleR__complex_Osimps_I1_J,axiom,
% 8.64/4.91 ! [R3: real,X: complex] :
% 8.64/4.91 ( ( re @ ( real_V2046097035970521341omplex @ R3 @ X ) )
% 8.64/4.91 = ( times_times_real @ R3 @ ( re @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8860_list__decode_Osimps_I1_J,axiom,
% 8.64/4.91 ( ( nat_list_decode @ zero_zero_nat )
% 8.64/4.91 = nil_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8861_Re__complex__div__eq__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 8.64/4.91 = zero_zero_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8862_complex__mod__sqrt__Re__mult__cnj,axiom,
% 8.64/4.91 ( real_V1022390504157884413omplex
% 8.64/4.91 = ( ^ [Z4: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z4 @ ( cnj @ Z4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8863_Re__complex__div__gt__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.64/4.91 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8864_Re__complex__div__lt__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.64/4.91 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8865_Re__complex__div__le__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.64/4.91 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8866_Re__complex__div__ge__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.64/4.91 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8867_list__decode_Opsimps_I1_J,axiom,
% 8.64/4.91 ( ( accp_nat @ nat_list_decode_rel @ zero_zero_nat )
% 8.64/4.91 => ( ( nat_list_decode @ zero_zero_nat )
% 8.64/4.91 = nil_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8868_cos__n__Re__cis__pow__n,axiom,
% 8.64/4.91 ! [N: nat,A: real] :
% 8.64/4.91 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 8.64/4.91 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8869_complex__add__cnj,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( plus_plus_complex @ Z3 @ ( cnj @ Z3 ) )
% 8.64/4.91 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8870_list__encode_Oelims,axiom,
% 8.64/4.91 ! [X: list_nat,Y: nat] :
% 8.64/4.91 ( ( ( nat_list_encode @ X )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( ( X = nil_nat )
% 8.64/4.91 => ( Y != zero_zero_nat ) )
% 8.64/4.91 => ~ ! [X3: nat,Xs3: list_nat] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( cons_nat @ X3 @ Xs3 ) )
% 8.64/4.91 => ( Y
% 8.64/4.91 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8871_Complex__divide,axiom,
% 8.64/4.91 ( divide1717551699836669952omplex
% 8.64/4.91 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8872_Re__Reals__divide,axiom,
% 8.64/4.91 ! [R3: complex,Z3: complex] :
% 8.64/4.91 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 8.64/4.91 => ( ( re @ ( divide1717551699836669952omplex @ R3 @ Z3 ) )
% 8.64/4.91 = ( divide_divide_real @ ( times_times_real @ ( re @ R3 ) @ ( re @ Z3 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8873_list__encode__inverse,axiom,
% 8.64/4.91 ! [X: list_nat] :
% 8.64/4.91 ( ( nat_list_decode @ ( nat_list_encode @ X ) )
% 8.64/4.91 = X ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8874_list__decode__inverse,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( nat_list_encode @ ( nat_list_decode @ N ) )
% 8.64/4.91 = N ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8875_complex__In__mult__cnj__zero,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( im @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) )
% 8.64/4.91 = zero_zero_real ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8876_Im__i__times,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( im @ ( times_times_complex @ imaginary_unit @ Z3 ) )
% 8.64/4.91 = ( re @ Z3 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8877_real__eq__imaginary__iff,axiom,
% 8.64/4.91 ! [Y: complex,X: complex] :
% 8.64/4.91 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 8.64/4.91 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 8.64/4.91 => ( ( X
% 8.64/4.91 = ( times_times_complex @ imaginary_unit @ Y ) )
% 8.64/4.91 = ( ( X = zero_zero_complex )
% 8.64/4.91 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8878_imaginary__eq__real__iff,axiom,
% 8.64/4.91 ! [Y: complex,X: complex] :
% 8.64/4.91 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 8.64/4.91 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 8.64/4.91 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 8.64/4.91 = X )
% 8.64/4.91 = ( ( X = zero_zero_complex )
% 8.64/4.91 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8879_Re__i__times,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( re @ ( times_times_complex @ imaginary_unit @ Z3 ) )
% 8.64/4.91 = ( uminus_uminus_real @ ( im @ Z3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8880_list__encode__eq,axiom,
% 8.64/4.91 ! [X: list_nat,Y: list_nat] :
% 8.64/4.91 ( ( ( nat_list_encode @ X )
% 8.64/4.91 = ( nat_list_encode @ Y ) )
% 8.64/4.91 = ( X = Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8881_scaleR__complex_Osimps_I2_J,axiom,
% 8.64/4.91 ! [R3: real,X: complex] :
% 8.64/4.91 ( ( im @ ( real_V2046097035970521341omplex @ R3 @ X ) )
% 8.64/4.91 = ( times_times_real @ R3 @ ( im @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8882_list__encode_Osimps_I1_J,axiom,
% 8.64/4.91 ( ( nat_list_encode @ nil_nat )
% 8.64/4.91 = zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8883_times__complex_Osimps_I2_J,axiom,
% 8.64/4.91 ! [X: complex,Y: complex] :
% 8.64/4.91 ( ( im @ ( times_times_complex @ X @ Y ) )
% 8.64/4.91 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8884_times__complex_Osimps_I1_J,axiom,
% 8.64/4.91 ! [X: complex,Y: complex] :
% 8.64/4.91 ( ( re @ ( times_times_complex @ X @ Y ) )
% 8.64/4.91 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8885_Im__complex__div__eq__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 8.64/4.91 = zero_zero_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8886_scaleR__complex_Ocode,axiom,
% 8.64/4.91 ( real_V2046097035970521341omplex
% 8.64/4.91 = ( ^ [R: real,X4: complex] : ( complex2 @ ( times_times_real @ R @ ( re @ X4 ) ) @ ( times_times_real @ R @ ( im @ X4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8887_Im__Reals__divide,axiom,
% 8.64/4.91 ! [R3: complex,Z3: complex] :
% 8.64/4.91 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 8.64/4.91 => ( ( im @ ( divide1717551699836669952omplex @ R3 @ Z3 ) )
% 8.64/4.91 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R3 ) ) @ ( im @ Z3 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8888_Im__complex__div__lt__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.64/4.91 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8889_Im__complex__div__gt__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.64/4.91 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8890_Im__complex__div__ge__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.64/4.91 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8891_Im__complex__div__le__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 8.64/4.91 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8892_sin__n__Im__cis__pow__n,axiom,
% 8.64/4.91 ! [N: nat,A: real] :
% 8.64/4.91 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 8.64/4.91 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8893_Re__exp,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( re @ ( exp_complex @ Z3 ) )
% 8.64/4.91 = ( times_times_real @ ( exp_real @ ( re @ Z3 ) ) @ ( cos_real @ ( im @ Z3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8894_Im__exp,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( im @ ( exp_complex @ Z3 ) )
% 8.64/4.91 = ( times_times_real @ ( exp_real @ ( re @ Z3 ) ) @ ( sin_real @ ( im @ Z3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8895_complex__eq,axiom,
% 8.64/4.91 ! [A: complex] :
% 8.64/4.91 ( A
% 8.64/4.91 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8896_times__complex_Ocode,axiom,
% 8.64/4.91 ( times_times_complex
% 8.64/4.91 = ( ^ [X4: complex,Y4: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( im @ Y4 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( im @ Y4 ) ) @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8897_complex__div__gt__0,axiom,
% 8.64/4.91 ! [A: complex,B: complex] :
% 8.64/4.91 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.64/4.91 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 8.64/4.91 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 8.64/4.91 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8898_exp__eq__polar,axiom,
% 8.64/4.91 ( exp_complex
% 8.64/4.91 = ( ^ [Z4: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z4 ) ) ) @ ( cis @ ( im @ Z4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8899_Im__power2,axiom,
% 8.64/4.91 ! [X: complex] :
% 8.64/4.91 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.91 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8900_list__encode_Osimps_I2_J,axiom,
% 8.64/4.91 ! [X: nat,Xs2: list_nat] :
% 8.64/4.91 ( ( nat_list_encode @ ( cons_nat @ X @ Xs2 ) )
% 8.64/4.91 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8901_complex__diff__cnj,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( minus_minus_complex @ Z3 @ ( cnj @ Z3 ) )
% 8.64/4.91 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z3 ) ) ) @ imaginary_unit ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8902_Re__divide,axiom,
% 8.64/4.91 ! [X: complex,Y: complex] :
% 8.64/4.91 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.64/4.91 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8903_complex__mult__cnj,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( times_times_complex @ Z3 @ ( cnj @ Z3 ) )
% 8.64/4.91 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8904_Im__divide,axiom,
% 8.64/4.91 ! [X: complex,Y: complex] :
% 8.64/4.91 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 8.64/4.91 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8905_complex__abs__le__norm,axiom,
% 8.64/4.91 ! [Z3: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z3 ) ) @ ( abs_abs_real @ ( im @ Z3 ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8906_csqrt_Ocode,axiom,
% 8.64/4.91 ( csqrt
% 8.64/4.91 = ( ^ [Z4: complex] :
% 8.64/4.91 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 8.64/4.91 @ ( times_times_real
% 8.64/4.91 @ ( if_real
% 8.64/4.91 @ ( ( im @ Z4 )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 @ one_one_real
% 8.64/4.91 @ ( sgn_sgn_real @ ( im @ Z4 ) ) )
% 8.64/4.91 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z4 ) @ ( re @ Z4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8907_csqrt_Osimps_I2_J,axiom,
% 8.64/4.91 ! [Z3: complex] :
% 8.64/4.91 ( ( im @ ( csqrt @ Z3 ) )
% 8.64/4.91 = ( times_times_real
% 8.64/4.91 @ ( if_real
% 8.64/4.91 @ ( ( im @ Z3 )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 @ one_one_real
% 8.64/4.91 @ ( sgn_sgn_real @ ( im @ Z3 ) ) )
% 8.64/4.91 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8908_csqrt__of__real__nonpos,axiom,
% 8.64/4.91 ! [X: complex] :
% 8.64/4.91 ( ( ( im @ X )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 8.64/4.91 => ( ( csqrt @ X )
% 8.64/4.91 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8909_csqrt__minus,axiom,
% 8.64/4.91 ! [X: complex] :
% 8.64/4.91 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 8.64/4.91 | ( ( ( im @ X )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 8.64/4.91 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 8.64/4.91 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8910_bezw__0,axiom,
% 8.64/4.91 ! [X: nat] :
% 8.64/4.91 ( ( bezw @ X @ zero_zero_nat )
% 8.64/4.91 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8911_push__bit__of__Suc__0,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8912_nat_Odisc__eq__case_I1_J,axiom,
% 8.64/4.91 ! [Nat: nat] :
% 8.64/4.91 ( ( Nat = zero_zero_nat )
% 8.64/4.91 = ( case_nat_o @ $true
% 8.64/4.91 @ ^ [Uu3: nat] : $false
% 8.64/4.91 @ Nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8913_nat_Odisc__eq__case_I2_J,axiom,
% 8.64/4.91 ! [Nat: nat] :
% 8.64/4.91 ( ( Nat != zero_zero_nat )
% 8.64/4.91 = ( case_nat_o @ $false
% 8.64/4.91 @ ^ [Uu3: nat] : $true
% 8.64/4.91 @ Nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8914_bit__push__bit__iff__int,axiom,
% 8.64/4.91 ! [M2: nat,K2: int,N: nat] :
% 8.64/4.91 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M2 @ K2 ) @ N )
% 8.64/4.91 = ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.91 & ( bit_se1146084159140164899it_int @ K2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8915_bit__push__bit__iff__nat,axiom,
% 8.64/4.91 ! [M2: nat,Q2: nat,N: nat] :
% 8.64/4.91 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M2 @ Q2 ) @ N )
% 8.64/4.91 = ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.91 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8916_less__eq__nat_Osimps_I2_J,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N )
% 8.64/4.91 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M2 ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8917_max__Suc2,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_max_nat @ M2 @ ( suc @ N ) )
% 8.64/4.91 = ( case_nat_nat @ ( suc @ N )
% 8.64/4.91 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ M7 @ N ) )
% 8.64/4.91 @ M2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8918_max__Suc1,axiom,
% 8.64/4.91 ! [N: nat,M2: nat] :
% 8.64/4.91 ( ( ord_max_nat @ ( suc @ N ) @ M2 )
% 8.64/4.91 = ( case_nat_nat @ ( suc @ N )
% 8.64/4.91 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ N @ M7 ) )
% 8.64/4.91 @ M2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8919_diff__Suc,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( minus_minus_nat @ M2 @ ( suc @ N ) )
% 8.64/4.91 = ( case_nat_nat @ zero_zero_nat
% 8.64/4.91 @ ^ [K3: nat] : K3
% 8.64/4.91 @ ( minus_minus_nat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8920_push__bit__nat__def,axiom,
% 8.64/4.91 ( bit_se547839408752420682it_nat
% 8.64/4.91 = ( ^ [N4: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8921_push__bit__int__def,axiom,
% 8.64/4.91 ( bit_se545348938243370406it_int
% 8.64/4.91 = ( ^ [N4: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8922_pred__def,axiom,
% 8.64/4.91 ( pred
% 8.64/4.91 = ( case_nat_nat @ zero_zero_nat
% 8.64/4.91 @ ^ [X24: nat] : X24 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8923_Suc__0__mod__numeral,axiom,
% 8.64/4.91 ! [K2: num] :
% 8.64/4.91 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.91 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8924_Suc__0__div__numeral,axiom,
% 8.64/4.91 ! [K2: num] :
% 8.64/4.91 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.91 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8925_nat__of__integer__code,axiom,
% 8.64/4.91 ( code_nat_of_integer
% 8.64/4.91 = ( ^ [K3: code_integer] :
% 8.64/4.91 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 8.64/4.91 @ ( produc1555791787009142072er_nat
% 8.64/4.91 @ ^ [L2: code_integer,J: code_integer] : ( if_nat @ ( J = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 8.64/4.91 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8926_drop__bit__of__Suc__0,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8927_drop__bit__Suc__minus__bit0,axiom,
% 8.64/4.91 ! [N: nat,K2: num] :
% 8.64/4.91 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K2 ) ) ) )
% 8.64/4.91 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8928_fst__divmod__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( product_fst_nat_nat @ ( divmod_nat @ M2 @ N ) )
% 8.64/4.91 = ( divide_divide_nat @ M2 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8929_nat__of__integer__non__positive,axiom,
% 8.64/4.91 ! [K2: code_integer] :
% 8.64/4.91 ( ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger )
% 8.64/4.91 => ( ( code_nat_of_integer @ K2 )
% 8.64/4.91 = zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8930_snd__divmod__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( product_snd_nat_nat @ ( divmod_nat @ M2 @ N ) )
% 8.64/4.91 = ( modulo_modulo_nat @ M2 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8931_drop__bit__Suc__minus__bit1,axiom,
% 8.64/4.91 ! [N: nat,K2: num] :
% 8.64/4.91 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K2 ) ) ) )
% 8.64/4.91 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8932_nat__of__integer__code__post_I1_J,axiom,
% 8.64/4.91 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 8.64/4.91 = zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8933_int__of__integer__code,axiom,
% 8.64/4.91 ( code_int_of_integer
% 8.64/4.91 = ( ^ [K3: code_integer] :
% 8.64/4.91 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 8.64/4.91 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 8.64/4.91 @ ( produc1553301316500091796er_int
% 8.64/4.91 @ ^ [L2: code_integer,J: code_integer] : ( if_int @ ( J = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 8.64/4.91 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8934_times__integer_Orep__eq,axiom,
% 8.64/4.91 ! [X: code_integer,Xa2: code_integer] :
% 8.64/4.91 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 8.64/4.91 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8935_bezw__non__0,axiom,
% 8.64/4.91 ! [Y: nat,X: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 8.64/4.91 => ( ( bezw @ X @ Y )
% 8.64/4.91 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8936_bezw_Oelims,axiom,
% 8.64/4.91 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 8.64/4.91 ( ( ( bezw @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 8.64/4.91 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8937_bezw_Osimps,axiom,
% 8.64/4.91 ( bezw
% 8.64/4.91 = ( ^ [X4: nat,Y4: nat] : ( if_Pro3027730157355071871nt_int @ ( Y4 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y4 ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8938_one__mod__minus__numeral,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.91 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8939_minus__one__mod__numeral,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 8.64/4.91 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8940_numeral__mod__minus__numeral,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 8.64/4.91 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8941_minus__numeral__mod__numeral,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M2 ) ) @ ( numeral_numeral_int @ N ) )
% 8.64/4.91 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M2 @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8942_Divides_Oadjust__mod__def,axiom,
% 8.64/4.91 ( adjust_mod
% 8.64/4.91 = ( ^ [L2: int,R: int] : ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8943_bezw_Opelims,axiom,
% 8.64/4.91 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 8.64/4.91 ( ( ( bezw @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 8.64/4.91 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 8.64/4.91 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 8.64/4.91 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8944_card__greaterThanLessThan__int,axiom,
% 8.64/4.91 ! [L: int,U: int] :
% 8.64/4.91 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 8.64/4.91 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8945_finite__greaterThanLessThan__int,axiom,
% 8.64/4.91 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8946_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 8.64/4.91 ! [L: int,U: int] :
% 8.64/4.91 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 8.64/4.91 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8947_prod__decode__aux_Opelims,axiom,
% 8.64/4.91 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 8.64/4.91 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 8.64/4.91 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 8.64/4.91 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 8.64/4.91 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8948_finite__greaterThanLessThan,axiom,
% 8.64/4.91 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8949_Suc__funpow,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( compow_nat_nat @ N @ suc )
% 8.64/4.91 = ( plus_plus_nat @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8950_card__greaterThanLessThan,axiom,
% 8.64/4.91 ! [L: nat,U: nat] :
% 8.64/4.91 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 8.64/4.91 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8951_atLeastSucLessThan__greaterThanLessThan,axiom,
% 8.64/4.91 ! [L: nat,U: nat] :
% 8.64/4.91 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 8.64/4.91 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8952_sub__BitM__One__eq,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 8.64/4.91 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8953_bij__betw__nth__root__unity,axiom,
% 8.64/4.91 ! [C2: complex,N: nat] :
% 8.64/4.91 ( ( C2 != zero_zero_complex )
% 8.64/4.91 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C2 ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C2 ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 8.64/4.91 @ ( collect_complex
% 8.64/4.91 @ ^ [Z4: complex] :
% 8.64/4.91 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.91 = one_one_complex ) )
% 8.64/4.91 @ ( collect_complex
% 8.64/4.91 @ ^ [Z4: complex] :
% 8.64/4.91 ( ( power_power_complex @ Z4 @ N )
% 8.64/4.91 = C2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8954_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 8.64/4.91 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8955_real__root__Suc__0,axiom,
% 8.64/4.91 ! [X: real] :
% 8.64/4.91 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 8.64/4.91 = X ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8956_real__root__eq__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( root @ N @ X )
% 8.64/4.91 = ( root @ N @ Y ) )
% 8.64/4.91 = ( X = Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8957_root__0,axiom,
% 8.64/4.91 ! [X: real] :
% 8.64/4.91 ( ( root @ zero_zero_nat @ X )
% 8.64/4.91 = zero_zero_real ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8958_real__root__eq__0__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( root @ N @ X )
% 8.64/4.91 = zero_zero_real )
% 8.64/4.91 = ( X = zero_zero_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8959_real__root__less__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 8.64/4.91 = ( ord_less_real @ X @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8960_real__root__le__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 8.64/4.91 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8961_real__root__one,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( root @ N @ one_one_real )
% 8.64/4.91 = one_one_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8962_real__root__eq__1__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( root @ N @ X )
% 8.64/4.91 = one_one_real )
% 8.64/4.91 = ( X = one_one_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8963_real__root__gt__0__iff,axiom,
% 8.64/4.91 ! [N: nat,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 8.64/4.91 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8964_real__root__lt__0__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 8.64/4.91 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8965_real__root__ge__0__iff,axiom,
% 8.64/4.91 ! [N: nat,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 8.64/4.91 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8966_real__root__le__0__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 8.64/4.91 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8967_real__root__gt__1__iff,axiom,
% 8.64/4.91 ! [N: nat,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 8.64/4.91 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8968_real__root__lt__1__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 8.64/4.91 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8969_real__root__ge__1__iff,axiom,
% 8.64/4.91 ! [N: nat,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 8.64/4.91 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8970_real__root__le__1__iff,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 8.64/4.91 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8971_real__root__pow__pos2,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 8.64/4.91 = X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8972_real__root__mult__exp,axiom,
% 8.64/4.91 ! [M2: nat,N: nat,X: real] :
% 8.64/4.91 ( ( root @ ( times_times_nat @ M2 @ N ) @ X )
% 8.64/4.91 = ( root @ M2 @ ( root @ N @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8973_real__root__mult,axiom,
% 8.64/4.91 ! [N: nat,X: real,Y: real] :
% 8.64/4.91 ( ( root @ N @ ( times_times_real @ X @ Y ) )
% 8.64/4.91 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8974_real__root__less__mono,axiom,
% 8.64/4.91 ! [N: nat,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ X @ Y )
% 8.64/4.91 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8975_real__root__le__mono,axiom,
% 8.64/4.91 ! [N: nat,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ X @ Y )
% 8.64/4.91 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8976_real__root__power,axiom,
% 8.64/4.91 ! [N: nat,X: real,K2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( root @ N @ ( power_power_real @ X @ K2 ) )
% 8.64/4.91 = ( power_power_real @ ( root @ N @ X ) @ K2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8977_real__root__abs,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 8.64/4.91 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8978_sgn__root,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 8.64/4.91 = ( sgn_sgn_real @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8979_real__root__gt__zero,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8980_real__root__strict__decreasing,axiom,
% 8.64/4.91 ! [N: nat,N6: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_nat @ N @ N6 )
% 8.64/4.91 => ( ( ord_less_real @ one_one_real @ X )
% 8.64/4.91 => ( ord_less_real @ ( root @ N6 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8981_root__abs__power,axiom,
% 8.64/4.91 ! [N: nat,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 8.64/4.91 = ( abs_abs_real @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8982_real__root__pos__pos,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8983_real__root__strict__increasing,axiom,
% 8.64/4.91 ! [N: nat,N6: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_nat @ N @ N6 )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( ord_less_real @ X @ one_one_real )
% 8.64/4.91 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8984_real__root__decreasing,axiom,
% 8.64/4.91 ! [N: nat,N6: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_nat @ N @ N6 )
% 8.64/4.91 => ( ( ord_less_eq_real @ one_one_real @ X )
% 8.64/4.91 => ( ord_less_eq_real @ ( root @ N6 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8985_real__root__pow__pos,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 8.64/4.91 = X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8986_real__root__pos__unique,axiom,
% 8.64/4.91 ! [N: nat,Y: real,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.91 => ( ( ( power_power_real @ Y @ N )
% 8.64/4.91 = X )
% 8.64/4.91 => ( ( root @ N @ X )
% 8.64/4.91 = Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8987_real__root__power__cancel,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 8.64/4.91 = X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8988_real__root__increasing,axiom,
% 8.64/4.91 ! [N: nat,N6: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_eq_nat @ N @ N6 )
% 8.64/4.91 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( ord_less_eq_real @ X @ one_one_real )
% 8.64/4.91 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N6 @ X ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8989_sgn__power__root,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 8.64/4.91 = X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8990_root__sgn__power,axiom,
% 8.64/4.91 ! [N: nat,Y: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 8.64/4.91 = Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8991_ln__root,axiom,
% 8.64/4.91 ! [N: nat,B: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.64/4.91 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 8.64/4.91 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8992_log__root,axiom,
% 8.64/4.91 ! [N: nat,A: real,B: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.91 => ( ( log2 @ B @ ( root @ N @ A ) )
% 8.64/4.91 = ( divide_divide_real @ ( log2 @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8993_log__base__root,axiom,
% 8.64/4.91 ! [N: nat,B: real,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ B )
% 8.64/4.91 => ( ( log2 @ ( root @ N @ B ) @ X )
% 8.64/4.91 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log2 @ B @ X ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8994_split__root,axiom,
% 8.64/4.91 ! [P2: real > $o,N: nat,X: real] :
% 8.64/4.91 ( ( P2 @ ( root @ N @ X ) )
% 8.64/4.91 = ( ( ( N = zero_zero_nat )
% 8.64/4.91 => ( P2 @ zero_zero_real ) )
% 8.64/4.91 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ! [Y4: real] :
% 8.64/4.91 ( ( ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 8.64/4.91 = X )
% 8.64/4.91 => ( P2 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8995_root__powr__inverse,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( root @ N @ X )
% 8.64/4.91 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8996_powr__powr,axiom,
% 8.64/4.91 ! [X: real,A: real,B: real] :
% 8.64/4.91 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 8.64/4.91 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8997_powr__mult,axiom,
% 8.64/4.91 ! [X: real,Y: real,A: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 8.64/4.91 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 8.64/4.91 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8998_divide__powr__uminus,axiom,
% 8.64/4.91 ! [A: real,B: real,C2: real] :
% 8.64/4.91 ( ( divide_divide_real @ A @ ( powr_real @ B @ C2 ) )
% 8.64/4.91 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_8999_ln__powr,axiom,
% 8.64/4.91 ! [X: real,Y: real] :
% 8.64/4.91 ( ( X != zero_zero_real )
% 8.64/4.91 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 8.64/4.91 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9000_log__powr,axiom,
% 8.64/4.91 ! [X: real,B: real,Y: real] :
% 8.64/4.91 ( ( X != zero_zero_real )
% 8.64/4.91 => ( ( log2 @ B @ ( powr_real @ X @ Y ) )
% 8.64/4.91 = ( times_times_real @ Y @ ( log2 @ B @ X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9001_powr__mult__base,axiom,
% 8.64/4.91 ! [X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 8.64/4.91 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9002_ln__powr__bound2,axiom,
% 8.64/4.91 ! [X: real,A: real] :
% 8.64/4.91 ( ( ord_less_real @ one_one_real @ X )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ A )
% 8.64/4.91 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9003_log__add__eq__powr,axiom,
% 8.64/4.91 ! [B: real,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ B )
% 8.64/4.91 => ( ( B != one_one_real )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( plus_plus_real @ ( log2 @ B @ X ) @ Y )
% 8.64/4.91 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9004_add__log__eq__powr,axiom,
% 8.64/4.91 ! [B: real,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ B )
% 8.64/4.91 => ( ( B != one_one_real )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( plus_plus_real @ Y @ ( log2 @ B @ X ) )
% 8.64/4.91 = ( log2 @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9005_log__minus__eq__powr,axiom,
% 8.64/4.91 ! [B: real,X: real,Y: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ B )
% 8.64/4.91 => ( ( B != one_one_real )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( ( minus_minus_real @ ( log2 @ B @ X ) @ Y )
% 8.64/4.91 = ( log2 @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9006_times__int_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.64/4.91 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.64/4.91 = ( abs_Integ
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) )
% 8.64/4.91 @ Xa2
% 8.64/4.91 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9007_num__of__nat_Osimps_I2_J,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( num_of_nat @ ( suc @ N ) )
% 8.64/4.91 = ( inc @ ( num_of_nat @ N ) ) ) )
% 8.64/4.91 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( num_of_nat @ ( suc @ N ) )
% 8.64/4.91 = one ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9008_num__of__nat__numeral__eq,axiom,
% 8.64/4.91 ! [Q2: num] :
% 8.64/4.91 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 8.64/4.91 = Q2 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9009_eq__Abs__Integ,axiom,
% 8.64/4.91 ! [Z3: int] :
% 8.64/4.91 ~ ! [X3: nat,Y3: nat] :
% 8.64/4.91 ( Z3
% 8.64/4.91 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9010_num__of__nat_Osimps_I1_J,axiom,
% 8.64/4.91 ( ( num_of_nat @ zero_zero_nat )
% 8.64/4.91 = one ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9011_zero__int__def,axiom,
% 8.64/4.91 ( zero_zero_int
% 8.64/4.91 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9012_int__def,axiom,
% 8.64/4.91 ( semiri1314217659103216013at_int
% 8.64/4.91 = ( ^ [N4: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N4 @ zero_zero_nat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9013_numeral__num__of__nat,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 8.64/4.91 = N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9014_num__of__nat__One,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 8.64/4.91 => ( ( num_of_nat @ N )
% 8.64/4.91 = one ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9015_uminus__int_Oabs__eq,axiom,
% 8.64/4.91 ! [X: product_prod_nat_nat] :
% 8.64/4.91 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 8.64/4.91 = ( abs_Integ
% 8.64/4.91 @ ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 )
% 8.64/4.91 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9016_one__int__def,axiom,
% 8.64/4.91 ( one_one_int
% 8.64/4.91 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9017_num__of__nat__double,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 8.64/4.91 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9018_num__of__nat__plus__distrib,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.91 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( num_of_nat @ ( plus_plus_nat @ M2 @ N ) )
% 8.64/4.91 = ( plus_plus_num @ ( num_of_nat @ M2 ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9019_less__eq__int_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.64/4.91 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.64/4.91 = ( produc8739625826339149834_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 8.64/4.91 @ Xa2
% 8.64/4.91 @ X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9020_plus__int_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.64/4.91 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.64/4.91 = ( abs_Integ
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) )
% 8.64/4.91 @ Xa2
% 8.64/4.91 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9021_minus__int_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 8.64/4.91 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 8.64/4.91 = ( abs_Integ
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) )
% 8.64/4.91 @ Xa2
% 8.64/4.91 @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9022_sorted__list__of__set__atMost__Suc,axiom,
% 8.64/4.91 ! [K2: nat] :
% 8.64/4.91 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K2 ) ) )
% 8.64/4.91 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K2 ) ) @ ( cons_nat @ ( suc @ K2 ) @ nil_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9023_sorted__list__of__set__lessThan__Suc,axiom,
% 8.64/4.91 ! [K2: nat] :
% 8.64/4.91 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K2 ) ) )
% 8.64/4.91 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K2 ) ) @ ( cons_nat @ K2 @ nil_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9024_sorted__list__of__set__greaterThanLessThan,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ ( suc @ I2 ) @ J2 )
% 8.64/4.91 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) )
% 8.64/4.91 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9025_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 8.64/4.91 ! [N: nat,J2: nat,I2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ ( suc @ I2 ) ) )
% 8.64/4.91 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J2 ) ) @ N )
% 8.64/4.91 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9026_less__eq__int_Orep__eq,axiom,
% 8.64/4.91 ( ord_less_eq_int
% 8.64/4.91 = ( ^ [X4: int,Xa3: int] :
% 8.64/4.91 ( produc8739625826339149834_nat_o
% 8.64/4.91 @ ^ [Y4: nat,Z4: nat] :
% 8.64/4.91 ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V3 ) @ ( plus_plus_nat @ U2 @ Z4 ) ) )
% 8.64/4.91 @ ( rep_Integ @ X4 )
% 8.64/4.91 @ ( rep_Integ @ Xa3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9027_image__minus__const__atLeastLessThan__nat,axiom,
% 8.64/4.91 ! [C2: nat,Y: nat,X: nat] :
% 8.64/4.91 ( ( ( ord_less_nat @ C2 @ Y )
% 8.64/4.91 => ( ( image_nat_nat
% 8.64/4.91 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 8.64/4.91 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.64/4.91 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C2 ) @ ( minus_minus_nat @ Y @ C2 ) ) ) )
% 8.64/4.91 & ( ~ ( ord_less_nat @ C2 @ Y )
% 8.64/4.91 => ( ( ( ord_less_nat @ X @ Y )
% 8.64/4.91 => ( ( image_nat_nat
% 8.64/4.91 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 8.64/4.91 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.64/4.91 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 8.64/4.91 & ( ~ ( ord_less_nat @ X @ Y )
% 8.64/4.91 => ( ( image_nat_nat
% 8.64/4.91 @ ^ [I: nat] : ( minus_minus_nat @ I @ C2 )
% 8.64/4.91 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 8.64/4.91 = bot_bot_set_nat ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9028_bij__betw__Suc,axiom,
% 8.64/4.91 ! [M5: set_nat,N6: set_nat] :
% 8.64/4.91 ( ( bij_betw_nat_nat @ suc @ M5 @ N6 )
% 8.64/4.91 = ( ( image_nat_nat @ suc @ M5 )
% 8.64/4.91 = N6 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9029_image__Suc__atLeastAtMost,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J2 ) )
% 8.64/4.91 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9030_image__Suc__atLeastLessThan,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J2 ) )
% 8.64/4.91 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9031_zero__notin__Suc__image,axiom,
% 8.64/4.91 ! [A4: set_nat] :
% 8.64/4.91 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A4 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9032_image__Suc__lessThan,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9033_image__Suc__atMost,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 8.64/4.91 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9034_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.64/4.91 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9035_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 8.64/4.91 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9036_lessThan__Suc__eq__insert__0,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 8.64/4.91 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9037_atMost__Suc__eq__insert__0,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 8.64/4.91 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9038_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 8.64/4.91 ! [N: nat,J2: nat,I2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J2 @ I2 ) )
% 8.64/4.91 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) ) @ N )
% 8.64/4.91 = ( suc @ ( plus_plus_nat @ I2 @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9039_uminus__int__def,axiom,
% 8.64/4.91 ( uminus_uminus_int
% 8.64/4.91 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 8.64/4.91 @ ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9040_rat__inverse__code,axiom,
% 8.64/4.91 ! [P: rat] :
% 8.64/4.91 ( ( quotient_of @ ( inverse_inverse_rat @ P ) )
% 8.64/4.91 = ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [A5: int,B4: int] : ( if_Pro3027730157355071871nt_int @ ( A5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A5 ) @ B4 ) @ ( abs_abs_int @ A5 ) ) )
% 8.64/4.91 @ ( quotient_of @ P ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9041_finite__greaterThanAtMost,axiom,
% 8.64/4.91 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9042_card__greaterThanAtMost,axiom,
% 8.64/4.91 ! [L: nat,U: nat] :
% 8.64/4.91 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 8.64/4.91 = ( minus_minus_nat @ U @ L ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9043_divide__rat__def,axiom,
% 8.64/4.91 ( divide_divide_rat
% 8.64/4.91 = ( ^ [Q5: rat,R: rat] : ( times_times_rat @ Q5 @ ( inverse_inverse_rat @ R ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9044_rat__less__eq__code,axiom,
% 8.64/4.91 ( ord_less_eq_rat
% 8.64/4.91 = ( ^ [P5: rat,Q5: rat] :
% 8.64/4.91 ( produc4947309494688390418_int_o
% 8.64/4.91 @ ^ [A5: int,C3: int] :
% 8.64/4.91 ( produc4947309494688390418_int_o
% 8.64/4.91 @ ^ [B4: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 8.64/4.91 @ ( quotient_of @ Q5 ) )
% 8.64/4.91 @ ( quotient_of @ P5 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9045_rat__less__code,axiom,
% 8.64/4.91 ( ord_less_rat
% 8.64/4.91 = ( ^ [P5: rat,Q5: rat] :
% 8.64/4.91 ( produc4947309494688390418_int_o
% 8.64/4.91 @ ^ [A5: int,C3: int] :
% 8.64/4.91 ( produc4947309494688390418_int_o
% 8.64/4.91 @ ^ [B4: int,D2: int] : ( ord_less_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) )
% 8.64/4.91 @ ( quotient_of @ Q5 ) )
% 8.64/4.91 @ ( quotient_of @ P5 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9046_atLeastSucAtMost__greaterThanAtMost,axiom,
% 8.64/4.91 ! [L: nat,U: nat] :
% 8.64/4.91 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 8.64/4.91 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9047_image__int__atLeastAtMost,axiom,
% 8.64/4.91 ! [A: nat,B: nat] :
% 8.64/4.91 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 8.64/4.91 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9048_image__int__atLeastLessThan,axiom,
% 8.64/4.91 ! [A: nat,B: nat] :
% 8.64/4.91 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 8.64/4.91 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9049_sorted__list__of__set__greaterThanAtMost,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J2 )
% 8.64/4.91 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J2 ) )
% 8.64/4.91 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9050_image__add__int__atLeastLessThan,axiom,
% 8.64/4.91 ! [L: int,U: int] :
% 8.64/4.91 ( ( image_int_int
% 8.64/4.91 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 8.64/4.91 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 8.64/4.91 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9051_image__atLeastZeroLessThan__int,axiom,
% 8.64/4.91 ! [U: int] :
% 8.64/4.91 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 8.64/4.91 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 8.64/4.91 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9052_times__int__def,axiom,
% 8.64/4.91 ( times_times_int
% 8.64/4.91 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9053_minus__int__def,axiom,
% 8.64/4.91 ( minus_minus_int
% 8.64/4.91 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9054_plus__int__def,axiom,
% 8.64/4.91 ( plus_plus_int
% 8.64/4.91 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9055_rat__minus__code,axiom,
% 8.64/4.91 ! [P: rat,Q2: rat] :
% 8.64/4.91 ( ( quotient_of @ ( minus_minus_rat @ P @ Q2 ) )
% 8.64/4.91 = ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [A5: int,C3: int] :
% 8.64/4.91 ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 8.64/4.91 @ ( quotient_of @ Q2 ) )
% 8.64/4.91 @ ( quotient_of @ P ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9056_finite__greaterThanAtMost__int,axiom,
% 8.64/4.91 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9057_card__greaterThanAtMost__int,axiom,
% 8.64/4.91 ! [L: int,U: int] :
% 8.64/4.91 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 8.64/4.91 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9058_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 8.64/4.91 ! [L: int,U: int] :
% 8.64/4.91 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 8.64/4.91 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9059_normalize__crossproduct,axiom,
% 8.64/4.91 ! [Q2: int,S2: int,P: int,R3: int] :
% 8.64/4.91 ( ( Q2 != zero_zero_int )
% 8.64/4.91 => ( ( S2 != zero_zero_int )
% 8.64/4.91 => ( ( ( normalize @ ( product_Pair_int_int @ P @ Q2 ) )
% 8.64/4.91 = ( normalize @ ( product_Pair_int_int @ R3 @ S2 ) ) )
% 8.64/4.91 => ( ( times_times_int @ P @ S2 )
% 8.64/4.91 = ( times_times_int @ R3 @ Q2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9060_rat__times__code,axiom,
% 8.64/4.91 ! [P: rat,Q2: rat] :
% 8.64/4.91 ( ( quotient_of @ ( times_times_rat @ P @ Q2 ) )
% 8.64/4.91 = ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [A5: int,C3: int] :
% 8.64/4.91 ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B4 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 8.64/4.91 @ ( quotient_of @ Q2 ) )
% 8.64/4.91 @ ( quotient_of @ P ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9061_rat__divide__code,axiom,
% 8.64/4.91 ! [P: rat,Q2: rat] :
% 8.64/4.91 ( ( quotient_of @ ( divide_divide_rat @ P @ Q2 ) )
% 8.64/4.91 = ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [A5: int,C3: int] :
% 8.64/4.91 ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ C3 @ B4 ) ) )
% 8.64/4.91 @ ( quotient_of @ Q2 ) )
% 8.64/4.91 @ ( quotient_of @ P ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9062_rat__plus__code,axiom,
% 8.64/4.91 ! [P: rat,Q2: rat] :
% 8.64/4.91 ( ( quotient_of @ ( plus_plus_rat @ P @ Q2 ) )
% 8.64/4.91 = ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [A5: int,C3: int] :
% 8.64/4.91 ( produc4245557441103728435nt_int
% 8.64/4.91 @ ^ [B4: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D2 ) @ ( times_times_int @ B4 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 8.64/4.91 @ ( quotient_of @ Q2 ) )
% 8.64/4.91 @ ( quotient_of @ P ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9063_list__encode_Opelims,axiom,
% 8.64/4.91 ! [X: list_nat,Y: nat] :
% 8.64/4.91 ( ( ( nat_list_encode @ X )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 8.64/4.91 => ( ( ( X = nil_nat )
% 8.64/4.91 => ( ( Y = zero_zero_nat )
% 8.64/4.91 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 8.64/4.91 => ~ ! [X3: nat,Xs3: list_nat] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( cons_nat @ X3 @ Xs3 ) )
% 8.64/4.91 => ( ( Y
% 8.64/4.91 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X3 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 8.64/4.91 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X3 @ Xs3 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9064_upt__rec__numeral,axiom,
% 8.64/4.91 ! [M2: num,N: num] :
% 8.64/4.91 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.64/4.91 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.64/4.91 = ( cons_nat @ ( numeral_numeral_nat @ M2 ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M2 ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 8.64/4.91 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.64/4.91 => ( ( upt @ ( numeral_numeral_nat @ M2 ) @ ( numeral_numeral_nat @ N ) )
% 8.64/4.91 = nil_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9065_tl__upt,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( tl_nat @ ( upt @ M2 @ N ) )
% 8.64/4.91 = ( upt @ ( suc @ M2 ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9066_length__upt,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( size_size_list_nat @ ( upt @ I2 @ J2 ) )
% 8.64/4.91 = ( minus_minus_nat @ J2 @ I2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9067_take__upt,axiom,
% 8.64/4.91 ! [I2: nat,M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M2 ) @ N )
% 8.64/4.91 => ( ( take_nat @ M2 @ ( upt @ I2 @ N ) )
% 8.64/4.91 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9068_upt__conv__Nil,axiom,
% 8.64/4.91 ! [J2: nat,I2: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ J2 @ I2 )
% 8.64/4.91 => ( ( upt @ I2 @ J2 )
% 8.64/4.91 = nil_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9069_upt__eq__Nil__conv,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( ( upt @ I2 @ J2 )
% 8.64/4.91 = nil_nat )
% 8.64/4.91 = ( ( J2 = zero_zero_nat )
% 8.64/4.91 | ( ord_less_eq_nat @ J2 @ I2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9070_atLeastAtMost__upt,axiom,
% 8.64/4.91 ( set_or1269000886237332187st_nat
% 8.64/4.91 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ N4 @ ( suc @ M6 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9071_atLeast__upt,axiom,
% 8.64/4.91 ( set_ord_lessThan_nat
% 8.64/4.91 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9072_upt__conv__Cons__Cons,axiom,
% 8.64/4.91 ! [M2: nat,N: nat,Ns: list_nat,Q2: nat] :
% 8.64/4.91 ( ( ( cons_nat @ M2 @ ( cons_nat @ N @ Ns ) )
% 8.64/4.91 = ( upt @ M2 @ Q2 ) )
% 8.64/4.91 = ( ( cons_nat @ N @ Ns )
% 8.64/4.91 = ( upt @ ( suc @ M2 ) @ Q2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9073_upt__0,axiom,
% 8.64/4.91 ! [I2: nat] :
% 8.64/4.91 ( ( upt @ I2 @ zero_zero_nat )
% 8.64/4.91 = nil_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9074_greaterThanAtMost__upt,axiom,
% 8.64/4.91 ( set_or6659071591806873216st_nat
% 8.64/4.91 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ ( suc @ M6 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9075_greaterThanLessThan__upt,axiom,
% 8.64/4.91 ( set_or5834768355832116004an_nat
% 8.64/4.91 = ( ^ [N4: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N4 ) @ M6 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9076_atMost__upto,axiom,
% 8.64/4.91 ( set_ord_atMost_nat
% 8.64/4.91 = ( ^ [N4: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9077_upt__conv__Cons,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I2 @ J2 )
% 8.64/4.91 => ( ( upt @ I2 @ J2 )
% 8.64/4.91 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9078_upt__add__eq__append,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat,K2: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.91 => ( ( upt @ I2 @ ( plus_plus_nat @ J2 @ K2 ) )
% 8.64/4.91 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( upt @ J2 @ ( plus_plus_nat @ J2 @ K2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9079_upt__rec,axiom,
% 8.64/4.91 ( upt
% 8.64/4.91 = ( ^ [I: nat,J: nat] : ( if_list_nat @ ( ord_less_nat @ I @ J ) @ ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) @ nil_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9080_upt__Suc,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.91 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 8.64/4.91 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) )
% 8.64/4.91 & ( ~ ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.91 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 8.64/4.91 = nil_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9081_upt__Suc__append,axiom,
% 8.64/4.91 ! [I2: nat,J2: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ I2 @ J2 )
% 8.64/4.91 => ( ( upt @ I2 @ ( suc @ J2 ) )
% 8.64/4.91 = ( append_nat @ ( upt @ I2 @ J2 ) @ ( cons_nat @ J2 @ nil_nat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9082_mono__Suc,axiom,
% 8.64/4.91 order_mono_nat_nat @ suc ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9083_mono__times__nat,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9084_mono__ge2__power__minus__self,axiom,
% 8.64/4.91 ! [K2: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 )
% 8.64/4.91 => ( order_mono_nat_nat
% 8.64/4.91 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K2 @ M6 ) @ M6 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9085_sum__list__upt,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.91 => ( ( groups4561878855575611511st_nat @ ( upt @ M2 @ N ) )
% 8.64/4.91 = ( groups3542108847815614940at_nat
% 8.64/4.91 @ ^ [X4: nat] : X4
% 8.64/4.91 @ ( set_or4665077453230672383an_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9086_map__Suc__upt,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( map_nat_nat @ suc @ ( upt @ M2 @ N ) )
% 8.64/4.91 = ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9087_map__add__upt,axiom,
% 8.64/4.91 ! [N: nat,M2: nat] :
% 8.64/4.91 ( ( map_nat_nat
% 8.64/4.91 @ ^ [I: nat] : ( plus_plus_nat @ I @ N )
% 8.64/4.91 @ ( upt @ zero_zero_nat @ M2 ) )
% 8.64/4.91 = ( upt @ N @ ( plus_plus_nat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9088_map__decr__upt,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( map_nat_nat
% 8.64/4.91 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 @ ( upt @ ( suc @ M2 ) @ ( suc @ N ) ) )
% 8.64/4.91 = ( upt @ M2 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9089_card__length__sum__list__rec,axiom,
% 8.64/4.91 ! [M2: nat,N6: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ one_one_nat @ M2 )
% 8.64/4.91 => ( ( finite_card_list_nat
% 8.64/4.91 @ ( collect_list_nat
% 8.64/4.91 @ ^ [L2: list_nat] :
% 8.64/4.91 ( ( ( size_size_list_nat @ L2 )
% 8.64/4.91 = M2 )
% 8.64/4.91 & ( ( groups4561878855575611511st_nat @ L2 )
% 8.64/4.91 = N6 ) ) ) )
% 8.64/4.91 = ( plus_plus_nat
% 8.64/4.91 @ ( finite_card_list_nat
% 8.64/4.91 @ ( collect_list_nat
% 8.64/4.91 @ ^ [L2: list_nat] :
% 8.64/4.91 ( ( ( size_size_list_nat @ L2 )
% 8.64/4.91 = ( minus_minus_nat @ M2 @ one_one_nat ) )
% 8.64/4.91 & ( ( groups4561878855575611511st_nat @ L2 )
% 8.64/4.91 = N6 ) ) ) )
% 8.64/4.91 @ ( finite_card_list_nat
% 8.64/4.91 @ ( collect_list_nat
% 8.64/4.91 @ ^ [L2: list_nat] :
% 8.64/4.91 ( ( ( size_size_list_nat @ L2 )
% 8.64/4.91 = M2 )
% 8.64/4.91 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 8.64/4.91 = N6 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9090_card__length__sum__list,axiom,
% 8.64/4.91 ! [M2: nat,N6: nat] :
% 8.64/4.91 ( ( finite_card_list_nat
% 8.64/4.91 @ ( collect_list_nat
% 8.64/4.91 @ ^ [L2: list_nat] :
% 8.64/4.91 ( ( ( size_size_list_nat @ L2 )
% 8.64/4.91 = M2 )
% 8.64/4.91 & ( ( groups4561878855575611511st_nat @ L2 )
% 8.64/4.91 = N6 ) ) ) )
% 8.64/4.91 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N6 @ M2 ) @ one_one_nat ) @ N6 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9091_range__mod,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( image_nat_nat
% 8.64/4.91 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N )
% 8.64/4.91 @ top_top_set_nat )
% 8.64/4.91 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9092_UNIV__nat__eq,axiom,
% 8.64/4.91 ( top_top_set_nat
% 8.64/4.91 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9093_range__mult,axiom,
% 8.64/4.91 ! [A: real] :
% 8.64/4.91 ( ( ( A = zero_zero_real )
% 8.64/4.91 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 8.64/4.91 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 8.64/4.91 & ( ( A != zero_zero_real )
% 8.64/4.91 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 8.64/4.91 = top_top_set_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9094_sorted__upt,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M2 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9095_surj__prod__decode,axiom,
% 8.64/4.91 ( ( image_5846123807819985514at_nat @ nat_prod_decode @ top_top_set_nat )
% 8.64/4.91 = top_to4669805908274784177at_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9096_bij__prod__decode,axiom,
% 8.64/4.91 bij_be8693218025023041337at_nat @ nat_prod_decode @ top_top_set_nat @ top_to4669805908274784177at_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9097_surj__list__decode,axiom,
% 8.64/4.91 ( ( image_nat_list_nat @ nat_list_decode @ top_top_set_nat )
% 8.64/4.91 = top_top_set_list_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9098_bij__list__decode,axiom,
% 8.64/4.91 bij_be6293887246118711976st_nat @ nat_list_decode @ top_top_set_nat @ top_top_set_list_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9099_surj__list__encode,axiom,
% 8.64/4.91 ( ( image_list_nat_nat @ nat_list_encode @ top_top_set_list_nat )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9100_bij__list__encode,axiom,
% 8.64/4.91 bij_be8532844293280997160at_nat @ nat_list_encode @ top_top_set_list_nat @ top_top_set_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9101_surj__prod__encode,axiom,
% 8.64/4.91 ( ( image_2486076414777270412at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9102_bij__prod__encode,axiom,
% 8.64/4.91 bij_be5333170631980326235at_nat @ nat_prod_encode @ top_to4669805908274784177at_nat @ top_top_set_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9103_sorted__wrt__less__idx,axiom,
% 8.64/4.91 ! [Ns: list_nat,I2: nat] :
% 8.64/4.91 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 8.64/4.91 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 8.64/4.91 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9104_root__def,axiom,
% 8.64/4.91 ( root
% 8.64/4.91 = ( ^ [N4: nat,X4: real] :
% 8.64/4.91 ( if_real @ ( N4 = zero_zero_nat ) @ zero_zero_real
% 8.64/4.91 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 8.64/4.91 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N4 ) )
% 8.64/4.91 @ X4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9105_DERIV__even__real__root,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.91 => ( ( ord_less_real @ X @ zero_zero_real )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9106_DERIV__real__root__generic,axiom,
% 8.64/4.91 ! [N: nat,X: real,D3: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( X != zero_zero_real )
% 8.64/4.91 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( D3
% 8.64/4.91 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 8.64/4.91 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.91 => ( ( ord_less_real @ X @ zero_zero_real )
% 8.64/4.91 => ( D3
% 8.64/4.91 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 8.64/4.91 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.91 => ( D3
% 8.64/4.91 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9107_DERIV__arctan__series,axiom,
% 8.64/4.91 ! [X: real] :
% 8.64/4.91 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X9: real] :
% 8.64/4.91 ( suminf_real
% 8.64/4.91 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9108_DERIV__fun__pow,axiom,
% 8.64/4.91 ! [G2: real > real,M2: real,X: real,N: nat] :
% 8.64/4.91 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X4: real] : ( power_power_real @ ( G2 @ X4 ) @ N )
% 8.64/4.91 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G2 @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M2 )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9109_has__real__derivative__powr,axiom,
% 8.64/4.91 ! [Z3: real,R3: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ Z3 )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [Z4: real] : ( powr_real @ Z4 @ R3 )
% 8.64/4.91 @ ( times_times_real @ R3 @ ( powr_real @ Z3 @ ( minus_minus_real @ R3 @ one_one_real ) ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ Z3 @ top_top_set_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9110_DERIV__series_H,axiom,
% 8.64/4.91 ! [F2: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 8.64/4.91 ( ! [N3: nat] :
% 8.64/4.91 ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X4: real] : ( F2 @ X4 @ N3 )
% 8.64/4.91 @ ( F5 @ X0 @ N3 )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 8.64/4.91 => ( ! [X3: real] :
% 8.64/4.91 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.64/4.91 => ( summable_real @ ( F2 @ X3 ) ) )
% 8.64/4.91 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.64/4.91 => ( ( summable_real @ ( F5 @ X0 ) )
% 8.64/4.91 => ( ( summable_real @ L5 )
% 8.64/4.91 => ( ! [N3: nat,X3: real,Y3: real] :
% 8.64/4.91 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.64/4.91 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 8.64/4.91 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F2 @ X3 @ N3 ) @ ( F2 @ Y3 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X4: real] : ( suminf_real @ ( F2 @ X4 ) )
% 8.64/4.91 @ ( suminf_real @ ( F5 @ X0 ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9111_DERIV__log,axiom,
% 8.64/4.91 ! [X: real,B: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( log2 @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9112_DERIV__fun__powr,axiom,
% 8.64/4.91 ! [G2: real > real,M2: real,X: real,R3: real] :
% 8.64/4.91 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ ( G2 @ X ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X4: real] : ( powr_real @ ( G2 @ X4 ) @ R3 )
% 8.64/4.91 @ ( times_times_real @ ( times_times_real @ R3 @ ( powr_real @ ( G2 @ X ) @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M2 )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9113_DERIV__powr,axiom,
% 8.64/4.91 ! [G2: real > real,M2: real,X: real,F2: real > real,R3: real] :
% 8.64/4.91 ( ( has_fi5821293074295781190e_real @ G2 @ M2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ ( G2 @ X ) )
% 8.64/4.91 => ( ( has_fi5821293074295781190e_real @ F2 @ R3 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X4: real] : ( powr_real @ ( G2 @ X4 ) @ ( F2 @ X4 ) )
% 8.64/4.91 @ ( times_times_real @ ( powr_real @ ( G2 @ X ) @ ( F2 @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R3 @ ( ln_ln_real @ ( G2 @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M2 @ ( F2 @ X ) ) @ ( G2 @ X ) ) ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9114_DERIV__power__series_H,axiom,
% 8.64/4.91 ! [R2: real,F2: nat > real,X0: real] :
% 8.64/4.91 ( ! [X3: real] :
% 8.64/4.91 ( ( member_real @ X3 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 8.64/4.91 => ( summable_real
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F2 @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X3 @ N4 ) ) ) )
% 8.64/4.91 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R2 ) @ R2 ) )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ R2 )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X4: real] :
% 8.64/4.91 ( suminf_real
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_real @ ( F2 @ N4 ) @ ( power_power_real @ X4 @ ( suc @ N4 ) ) ) )
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_real @ ( times_times_real @ ( F2 @ N4 ) @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) @ ( power_power_real @ X0 @ N4 ) ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9115_DERIV__real__root,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ X )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9116_Maclaurin__all__le,axiom,
% 8.64/4.91 ! [Diff: nat > real > real,F2: real > real,X: real,N: nat] :
% 8.64/4.91 ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.91 & ( ( F2 @ X )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9117_Maclaurin__all__le__objl,axiom,
% 8.64/4.91 ! [Diff: nat > real > real,F2: real > real,X: real,N: nat] :
% 8.64/4.91 ( ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 & ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.91 & ( ( F2 @ X )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9118_DERIV__odd__real__root,axiom,
% 8.64/4.91 ! [N: nat,X: real] :
% 8.64/4.91 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.91 => ( ( X != zero_zero_real )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9119_Maclaurin__minus,axiom,
% 8.64/4.91 ! [H: real,N: nat,Diff: nat > real > real,F2: real > real] :
% 8.64/4.91 ( ( ord_less_real @ H @ zero_zero_real )
% 8.64/4.91 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ H @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_real @ H @ T6 )
% 8.64/4.91 & ( ord_less_real @ T6 @ zero_zero_real )
% 8.64/4.91 & ( ( F2 @ H )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9120_Maclaurin2,axiom,
% 8.64/4.91 ! [H: real,Diff: nat > real > real,F2: real > real,N: nat] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ H )
% 8.64/4.91 => ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ H ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ H )
% 8.64/4.91 & ( ( F2 @ H )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9121_Maclaurin,axiom,
% 8.64/4.91 ! [H: real,N: nat,Diff: nat > real > real,F2: real > real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ H )
% 8.64/4.91 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ H ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ T6 )
% 8.64/4.91 & ( ord_less_real @ T6 @ H )
% 8.64/4.91 & ( ( F2 @ H )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H @ N ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9122_Maclaurin__all__lt,axiom,
% 8.64/4.91 ! [Diff: nat > real > real,F2: real > real,N: nat,X: real] :
% 8.64/4.91 ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( X != zero_zero_real )
% 8.64/4.91 => ( ! [M: nat,X3: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 8.64/4.91 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.91 & ( ( F2 @ X )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9123_Maclaurin__bi__le,axiom,
% 8.64/4.91 ! [Diff: nat > real > real,F2: real > real,N: nat,X: real] :
% 8.64/4.91 ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 8.64/4.91 & ( ( F2 @ X )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9124_Taylor__down,axiom,
% 8.64/4.91 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ A @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ B ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ( ( ord_less_real @ A @ C2 )
% 8.64/4.91 => ( ( ord_less_eq_real @ C2 @ B )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_real @ A @ T6 )
% 8.64/4.91 & ( ord_less_real @ T6 @ C2 )
% 8.64/4.91 & ( ( F2 @ A )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9125_Taylor__up,axiom,
% 8.64/4.91 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ A @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ B ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ( ( ord_less_eq_real @ A @ C2 )
% 8.64/4.91 => ( ( ord_less_real @ C2 @ B )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ord_less_real @ C2 @ T6 )
% 8.64/4.91 & ( ord_less_real @ T6 @ B )
% 8.64/4.91 & ( ( F2 @ B )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9126_Taylor,axiom,
% 8.64/4.91 ! [N: nat,Diff: nat > real > real,F2: real > real,A: real,B: real,C2: real,X: real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( ( Diff @ zero_zero_nat )
% 8.64/4.91 = F2 )
% 8.64/4.91 => ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ A @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ B ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ( ( ord_less_eq_real @ A @ C2 )
% 8.64/4.91 => ( ( ord_less_eq_real @ C2 @ B )
% 8.64/4.91 => ( ( ord_less_eq_real @ A @ X )
% 8.64/4.91 => ( ( ord_less_eq_real @ X @ B )
% 8.64/4.91 => ( ( X != C2 )
% 8.64/4.91 => ? [T6: real] :
% 8.64/4.91 ( ( ( ord_less_real @ X @ C2 )
% 8.64/4.91 => ( ( ord_less_real @ X @ T6 )
% 8.64/4.91 & ( ord_less_real @ T6 @ C2 ) ) )
% 8.64/4.91 & ( ~ ( ord_less_real @ X @ C2 )
% 8.64/4.91 => ( ( ord_less_real @ C2 @ T6 )
% 8.64/4.91 & ( ord_less_real @ T6 @ X ) ) )
% 8.64/4.91 & ( ( F2 @ X )
% 8.64/4.91 = ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C2 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ M6 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ N ) )
% 8.64/4.91 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C2 ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9127_Maclaurin__lemma2,axiom,
% 8.64/4.91 ! [N: nat,H: real,Diff: nat > real > real,K2: nat,B5: real] :
% 8.64/4.91 ( ! [M: nat,T6: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M @ N )
% 8.64/4.91 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 8.64/4.91 & ( ord_less_eq_real @ T6 @ H ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ ( Diff @ M ) @ ( Diff @ ( suc @ M ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 8.64/4.91 => ( ( N
% 8.64/4.91 = ( suc @ K2 ) )
% 8.64/4.91 => ! [M3: nat,T7: real] :
% 8.64/4.91 ( ( ( ord_less_nat @ M3 @ N )
% 8.64/4.91 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 8.64/4.91 & ( ord_less_eq_real @ T7 @ H ) )
% 8.64/4.91 => ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [U2: real] :
% 8.64/4.91 ( minus_minus_real @ ( Diff @ M3 @ U2 )
% 8.64/4.91 @ ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M3 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M3 ) ) )
% 8.64/4.91 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M3 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M3 ) ) ) ) ) )
% 8.64/4.91 @ ( minus_minus_real @ ( Diff @ ( suc @ M3 ) @ T7 )
% 8.64/4.91 @ ( plus_plus_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M3 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T7 @ P5 ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) )
% 8.64/4.91 @ ( times_times_real @ B5 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M3 ) ) ) ) ) ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9128_DERIV__pow,axiom,
% 8.64/4.91 ! [N: nat,X: real,S2: set_real] :
% 8.64/4.91 ( has_fi5821293074295781190e_real
% 8.64/4.91 @ ^ [X4: real] : ( power_power_real @ X4 @ N )
% 8.64/4.91 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ X @ S2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9129_DERIV__const__ratio__const,axiom,
% 8.64/4.91 ! [A: real,B: real,F2: real > real,K2: real] :
% 8.64/4.91 ( ( A != B )
% 8.64/4.91 => ( ! [X3: real] : ( has_fi5821293074295781190e_real @ F2 @ K2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 8.64/4.91 => ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 8.64/4.91 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9130_MVT2,axiom,
% 8.64/4.91 ! [A: real,B: real,F2: real > real,F5: real > real] :
% 8.64/4.91 ( ( ord_less_real @ A @ B )
% 8.64/4.91 => ( ! [X3: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ A @ X3 )
% 8.64/4.91 => ( ( ord_less_eq_real @ X3 @ B )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ F2 @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.64/4.91 => ? [Z: real] :
% 8.64/4.91 ( ( ord_less_real @ A @ Z )
% 8.64/4.91 & ( ord_less_real @ Z @ B )
% 8.64/4.91 & ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 8.64/4.91 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9131_GMVT_H,axiom,
% 8.64/4.91 ! [A: real,B: real,F2: real > real,G2: real > real,G3: real > real,F5: real > real] :
% 8.64/4.91 ( ( ord_less_real @ A @ B )
% 8.64/4.91 => ( ! [Z: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ A @ Z )
% 8.64/4.91 => ( ( ord_less_eq_real @ Z @ B )
% 8.64/4.91 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ F2 ) ) )
% 8.64/4.91 => ( ! [Z: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ A @ Z )
% 8.64/4.91 => ( ( ord_less_eq_real @ Z @ B )
% 8.64/4.91 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) @ G2 ) ) )
% 8.64/4.91 => ( ! [Z: real] :
% 8.64/4.91 ( ( ord_less_real @ A @ Z )
% 8.64/4.91 => ( ( ord_less_real @ Z @ B )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ G2 @ ( G3 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 8.64/4.91 => ( ! [Z: real] :
% 8.64/4.91 ( ( ord_less_real @ A @ Z )
% 8.64/4.91 => ( ( ord_less_real @ Z @ B )
% 8.64/4.91 => ( has_fi5821293074295781190e_real @ F2 @ ( F5 @ Z ) @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) )
% 8.64/4.91 => ? [C: real] :
% 8.64/4.91 ( ( ord_less_real @ A @ C )
% 8.64/4.91 & ( ord_less_real @ C @ B )
% 8.64/4.91 & ( ( times_times_real @ ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) ) @ ( G3 @ C ) )
% 8.64/4.91 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ ( F5 @ C ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9132_summable__Leibniz_I3_J,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ( topolo6980174941875973593q_real @ A )
% 8.64/4.91 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 8.64/4.91 => ! [N8: nat] :
% 8.64/4.91 ( member_real
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 8.64/4.91 @ ( set_or1222579329274155063t_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) )
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9133_summable__Leibniz_I2_J,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ( topolo6980174941875973593q_real @ A )
% 8.64/4.91 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 8.64/4.91 => ! [N8: nat] :
% 8.64/4.91 ( member_real
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 8.64/4.91 @ ( set_or1222579329274155063t_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9134_summable__Leibniz_H_I4_J,axiom,
% 8.64/4.91 ! [A: nat > real,N: nat] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.64/4.91 => ( ord_less_eq_real
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) )
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9135_mult__nat__left__at__top,axiom,
% 8.64/4.91 ! [C2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.64/4.91 => ( filterlim_nat_nat @ ( times_times_nat @ C2 ) @ at_top_nat @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9136_mult__nat__right__at__top,axiom,
% 8.64/4.91 ! [C2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ C2 )
% 8.64/4.91 => ( filterlim_nat_nat
% 8.64/4.91 @ ^ [X4: nat] : ( times_times_nat @ X4 @ C2 )
% 8.64/4.91 @ at_top_nat
% 8.64/4.91 @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9137_nested__sequence__unique,axiom,
% 8.64/4.91 ! [F2: nat > real,G2: nat > real] :
% 8.64/4.91 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G2 @ ( suc @ N3 ) ) @ ( G2 @ N3 ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( G2 @ N3 ) )
% 8.64/4.91 => ( ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( minus_minus_real @ ( F2 @ N4 ) @ ( G2 @ N4 ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.64/4.91 @ at_top_nat )
% 8.64/4.91 => ? [L4: real] :
% 8.64/4.91 ( ! [N8: nat] : ( ord_less_eq_real @ ( F2 @ N8 ) @ L4 )
% 8.64/4.91 & ( filterlim_nat_real @ F2 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 8.64/4.91 & ! [N8: nat] : ( ord_less_eq_real @ L4 @ ( G2 @ N8 ) )
% 8.64/4.91 & ( filterlim_nat_real @ G2 @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9138_LIMSEQ__inverse__zero,axiom,
% 8.64/4.91 ! [X8: nat > real] :
% 8.64/4.91 ( ! [R4: real] :
% 8.64/4.91 ? [N7: nat] :
% 8.64/4.91 ! [N3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ N7 @ N3 )
% 8.64/4.91 => ( ord_less_real @ R4 @ ( X8 @ N3 ) ) )
% 8.64/4.91 => ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( inverse_inverse_real @ ( X8 @ N4 ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.64/4.91 @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9139_LIMSEQ__inverse__real__of__nat,axiom,
% 8.64/4.91 ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.64/4.91 @ at_top_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9140_LIMSEQ__inverse__real__of__nat__add,axiom,
% 8.64/4.91 ! [R3: real] :
% 8.64/4.91 ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( plus_plus_real @ R3 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ R3 )
% 8.64/4.91 @ at_top_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9141_increasing__LIMSEQ,axiom,
% 8.64/4.91 ! [F2: nat > real,L: real] :
% 8.64/4.91 ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ ( suc @ N3 ) ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F2 @ N3 ) @ L )
% 8.64/4.91 => ( ! [E2: real] :
% 8.64/4.91 ( ( ord_less_real @ zero_zero_real @ E2 )
% 8.64/4.91 => ? [N8: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F2 @ N8 ) @ E2 ) ) )
% 8.64/4.91 => ( filterlim_nat_real @ F2 @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9142_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 8.64/4.91 ! [R3: real] :
% 8.64/4.91 ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( plus_plus_real @ R3 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ R3 )
% 8.64/4.91 @ at_top_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9143_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 8.64/4.91 ! [R3: real] :
% 8.64/4.91 ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_real @ R3 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N4 ) ) ) ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ R3 )
% 8.64/4.91 @ at_top_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9144_summable__Leibniz_I1_J,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ( topolo6980174941875973593q_real @ A )
% 8.64/4.91 => ( summable_real
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9145_summable,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.64/4.91 => ( summable_real
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N4 ) @ ( A @ N4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9146_cos__diff__limit__1,axiom,
% 8.64/4.91 ! [Theta: nat > real,Theta2: real] :
% 8.64/4.91 ( ( filterlim_nat_real
% 8.64/4.91 @ ^ [J: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J ) @ Theta2 ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.64/4.91 @ at_top_nat )
% 8.64/4.91 => ~ ! [K: nat > int] :
% 8.64/4.91 ~ ( filterlim_nat_real
% 8.64/4.91 @ ^ [J: nat] : ( minus_minus_real @ ( Theta @ J ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K @ J ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ Theta2 )
% 8.64/4.91 @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9147_cos__limit__1,axiom,
% 8.64/4.91 ! [Theta: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real
% 8.64/4.91 @ ^ [J: nat] : ( cos_real @ ( Theta @ J ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ one_one_real )
% 8.64/4.91 @ at_top_nat )
% 8.64/4.91 => ? [K: nat > int] :
% 8.64/4.91 ( filterlim_nat_real
% 8.64/4.91 @ ^ [J: nat] : ( minus_minus_real @ ( Theta @ J ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K @ J ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.64/4.91 @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9148_summable__Leibniz_I4_J,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ( topolo6980174941875973593q_real @ A )
% 8.64/4.91 => ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] :
% 8.64/4.91 ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 8.64/4.91 @ at_top_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9149_zeroseq__arctan__series,axiom,
% 8.64/4.91 ! [X: real] :
% 8.64/4.91 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 8.64/4.91 => ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 8.64/4.91 @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9150_summable__Leibniz_H_I2_J,axiom,
% 8.64/4.91 ! [A: nat > real,N: nat] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.64/4.91 => ( ord_less_eq_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9151_summable__Leibniz_H_I3_J,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.64/4.91 => ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] :
% 8.64/4.91 ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 8.64/4.91 @ at_top_nat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9152_sums__alternating__upper__lower,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.64/4.91 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ? [L4: real] :
% 8.64/4.91 ( ! [N8: nat] :
% 8.64/4.91 ( ord_less_eq_real
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) ) )
% 8.64/4.91 @ L4 )
% 8.64/4.91 & ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] :
% 8.64/4.91 ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ L4 )
% 8.64/4.91 @ at_top_nat )
% 8.64/4.91 & ! [N8: nat] :
% 8.64/4.91 ( ord_less_eq_real @ L4
% 8.64/4.91 @ ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N8 ) @ one_one_nat ) ) ) )
% 8.64/4.91 & ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] :
% 8.64/4.91 ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ L4 )
% 8.64/4.91 @ at_top_nat ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9153_summable__Leibniz_I5_J,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ( topolo6980174941875973593q_real @ A )
% 8.64/4.91 => ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] :
% 8.64/4.91 ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 8.64/4.91 @ at_top_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9154_summable__Leibniz_H_I5_J,axiom,
% 8.64/4.91 ! [A: nat > real] :
% 8.64/4.91 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 8.64/4.91 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 8.64/4.91 => ( filterlim_nat_real
% 8.64/4.91 @ ^ [N4: nat] :
% 8.64/4.91 ( groups6591440286371151544t_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) )
% 8.64/4.91 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ one_one_nat ) ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real
% 8.64/4.91 @ ( suminf_real
% 8.64/4.91 @ ^ [I: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I ) @ ( A @ I ) ) ) )
% 8.64/4.91 @ at_top_nat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9155_real__bounded__linear,axiom,
% 8.64/4.91 ( real_V5970128139526366754l_real
% 8.64/4.91 = ( ^ [F4: real > real] :
% 8.64/4.91 ? [C3: real] :
% 8.64/4.91 ( F4
% 8.64/4.91 = ( ^ [X4: real] : ( times_times_real @ X4 @ C3 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9156_filterlim__Suc,axiom,
% 8.64/4.91 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9157_tendsto__exp__limit__at__right,axiom,
% 8.64/4.91 ! [X: real] :
% 8.64/4.91 ( filterlim_real_real
% 8.64/4.91 @ ^ [Y4: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y4 ) ) @ ( divide_divide_real @ one_one_real @ Y4 ) )
% 8.64/4.91 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 8.64/4.91 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9158_GMVT,axiom,
% 8.64/4.91 ! [A: real,B: real,F2: real > real,G2: real > real] :
% 8.64/4.91 ( ( ord_less_real @ A @ B )
% 8.64/4.91 => ( ! [X3: real] :
% 8.64/4.91 ( ( ( ord_less_eq_real @ A @ X3 )
% 8.64/4.91 & ( ord_less_eq_real @ X3 @ B ) )
% 8.64/4.91 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ F2 ) )
% 8.64/4.91 => ( ! [X3: real] :
% 8.64/4.91 ( ( ( ord_less_real @ A @ X3 )
% 8.64/4.91 & ( ord_less_real @ X3 @ B ) )
% 8.64/4.91 => ( differ6690327859849518006l_real @ F2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.64/4.91 => ( ! [X3: real] :
% 8.64/4.91 ( ( ( ord_less_eq_real @ A @ X3 )
% 8.64/4.91 & ( ord_less_eq_real @ X3 @ B ) )
% 8.64/4.91 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) @ G2 ) )
% 8.64/4.91 => ( ! [X3: real] :
% 8.64/4.91 ( ( ( ord_less_real @ A @ X3 )
% 8.64/4.91 & ( ord_less_real @ X3 @ B ) )
% 8.64/4.91 => ( differ6690327859849518006l_real @ G2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) )
% 8.64/4.91 => ? [G_c: real,F_c: real,C: real] :
% 8.64/4.91 ( ( has_fi5821293074295781190e_real @ G2 @ G_c @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.64/4.91 & ( has_fi5821293074295781190e_real @ F2 @ F_c @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 8.64/4.91 & ( ord_less_real @ A @ C )
% 8.64/4.91 & ( ord_less_real @ C @ B )
% 8.64/4.91 & ( ( times_times_real @ ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) ) @ G_c )
% 8.64/4.91 = ( times_times_real @ ( minus_minus_real @ ( G2 @ B ) @ ( G2 @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9159_eventually__sequentially__Suc,axiom,
% 8.64/4.91 ! [P2: nat > $o] :
% 8.64/4.91 ( ( eventually_nat
% 8.64/4.91 @ ^ [I: nat] : ( P2 @ ( suc @ I ) )
% 8.64/4.91 @ at_top_nat )
% 8.64/4.91 = ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9160_eventually__sequentially,axiom,
% 8.64/4.91 ! [P2: nat > $o] :
% 8.64/4.91 ( ( eventually_nat @ P2 @ at_top_nat )
% 8.64/4.91 = ( ? [N5: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ N5 @ N4 )
% 8.64/4.91 => ( P2 @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9161_eventually__sequentiallyI,axiom,
% 8.64/4.91 ! [C2: nat,P2: nat > $o] :
% 8.64/4.91 ( ! [X3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ C2 @ X3 )
% 8.64/4.91 => ( P2 @ X3 ) )
% 8.64/4.91 => ( eventually_nat @ P2 @ at_top_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9162_le__sequentially,axiom,
% 8.64/4.91 ! [F3: filter_nat] :
% 8.64/4.91 ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 8.64/4.91 = ( ! [N5: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N5 ) @ F3 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9163_atLeast__0,axiom,
% 8.64/4.91 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9164_atLeast__Suc__greaterThan,axiom,
% 8.64/4.91 ! [K2: nat] :
% 8.64/4.91 ( ( set_ord_atLeast_nat @ ( suc @ K2 ) )
% 8.64/4.91 = ( set_or1210151606488870762an_nat @ K2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9165_greaterThan__0,axiom,
% 8.64/4.91 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 8.64/4.91 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9166_greaterThan__Suc,axiom,
% 8.64/4.91 ! [K2: nat] :
% 8.64/4.91 ( ( set_or1210151606488870762an_nat @ ( suc @ K2 ) )
% 8.64/4.91 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K2 ) @ ( insert_nat @ ( suc @ K2 ) @ bot_bot_set_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9167_atLeast__Suc,axiom,
% 8.64/4.91 ! [K2: nat] :
% 8.64/4.91 ( ( set_ord_atLeast_nat @ ( suc @ K2 ) )
% 8.64/4.91 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K2 ) @ ( insert_nat @ K2 @ bot_bot_set_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9168_filterlim__pow__at__bot__even,axiom,
% 8.64/4.91 ! [N: nat,F2: real > real,F3: filter_real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( filterlim_real_real @ F2 @ at_bot_real @ F3 )
% 8.64/4.91 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.91 => ( filterlim_real_real
% 8.64/4.91 @ ^ [X4: real] : ( power_power_real @ ( F2 @ X4 ) @ N )
% 8.64/4.91 @ at_top_real
% 8.64/4.91 @ F3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9169_GreatestI__ex__nat,axiom,
% 8.64/4.91 ! [P2: nat > $o,B: nat] :
% 8.64/4.91 ( ? [X_1: nat] : ( P2 @ X_1 )
% 8.64/4.91 => ( ! [Y3: nat] :
% 8.64/4.91 ( ( P2 @ Y3 )
% 8.64/4.91 => ( ord_less_eq_nat @ Y3 @ B ) )
% 8.64/4.91 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9170_Greatest__le__nat,axiom,
% 8.64/4.91 ! [P2: nat > $o,K2: nat,B: nat] :
% 8.64/4.91 ( ( P2 @ K2 )
% 8.64/4.91 => ( ! [Y3: nat] :
% 8.64/4.91 ( ( P2 @ Y3 )
% 8.64/4.91 => ( ord_less_eq_nat @ Y3 @ B ) )
% 8.64/4.91 => ( ord_less_eq_nat @ K2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9171_GreatestI__nat,axiom,
% 8.64/4.91 ! [P2: nat > $o,K2: nat,B: nat] :
% 8.64/4.91 ( ( P2 @ K2 )
% 8.64/4.91 => ( ! [Y3: nat] :
% 8.64/4.91 ( ( P2 @ Y3 )
% 8.64/4.91 => ( ord_less_eq_nat @ Y3 @ B ) )
% 8.64/4.91 => ( P2 @ ( order_Greatest_nat @ P2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9172_filterlim__pow__at__bot__odd,axiom,
% 8.64/4.91 ! [N: nat,F2: real > real,F3: filter_real] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( filterlim_real_real @ F2 @ at_bot_real @ F3 )
% 8.64/4.91 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 8.64/4.91 => ( filterlim_real_real
% 8.64/4.91 @ ^ [X4: real] : ( power_power_real @ ( F2 @ X4 ) @ N )
% 8.64/4.91 @ at_bot_real
% 8.64/4.91 @ F3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9173_MVT,axiom,
% 8.64/4.91 ! [A: real,B: real,F2: real > real] :
% 8.64/4.91 ( ( ord_less_real @ A @ B )
% 8.64/4.91 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F2 )
% 8.64/4.91 => ( ! [X3: real] :
% 8.64/4.91 ( ( ord_less_real @ A @ X3 )
% 8.64/4.91 => ( ( ord_less_real @ X3 @ B )
% 8.64/4.91 => ( differ6690327859849518006l_real @ F2 @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) ) ) )
% 8.64/4.91 => ? [L4: real,Z: real] :
% 8.64/4.91 ( ( ord_less_real @ A @ Z )
% 8.64/4.91 & ( ord_less_real @ Z @ B )
% 8.64/4.91 & ( has_fi5821293074295781190e_real @ F2 @ L4 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) )
% 8.64/4.91 & ( ( minus_minus_real @ ( F2 @ B ) @ ( F2 @ A ) )
% 8.64/4.91 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9174_inj__sgn__power,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( inj_on_real_real
% 8.64/4.91 @ ^ [Y4: real] : ( times_times_real @ ( sgn_sgn_real @ Y4 ) @ ( power_power_real @ ( abs_abs_real @ Y4 ) @ N ) )
% 8.64/4.91 @ top_top_set_real ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9175_UN__lessThan__UNIV,axiom,
% 8.64/4.91 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9176_UN__atMost__UNIV,axiom,
% 8.64/4.91 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9177_UN__atLeast__UNIV,axiom,
% 8.64/4.91 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9178_Sup__nat__empty,axiom,
% 8.64/4.91 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 8.64/4.91 = zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9179_inj__list__encode,axiom,
% 8.64/4.91 ! [A4: set_list_nat] : ( inj_on_list_nat_nat @ nat_list_encode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9180_inj__list__decode,axiom,
% 8.64/4.91 ! [A4: set_nat] : ( inj_on_nat_list_nat @ nat_list_decode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9181_inj__prod__encode,axiom,
% 8.64/4.91 ! [A4: set_Pr1261947904930325089at_nat] : ( inj_on2178005380612969504at_nat @ nat_prod_encode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9182_inj__Suc,axiom,
% 8.64/4.91 ! [N6: set_nat] : ( inj_on_nat_nat @ suc @ N6 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9183_inj__prod__decode,axiom,
% 8.64/4.91 ! [A4: set_nat] : ( inj_on5538052773655684606at_nat @ nat_prod_decode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9184_inj__on__diff__nat,axiom,
% 8.64/4.91 ! [N6: set_nat,K2: nat] :
% 8.64/4.91 ( ! [N3: nat] :
% 8.64/4.91 ( ( member_nat @ N3 @ N6 )
% 8.64/4.91 => ( ord_less_eq_nat @ K2 @ N3 ) )
% 8.64/4.91 => ( inj_on_nat_nat
% 8.64/4.91 @ ^ [N4: nat] : ( minus_minus_nat @ N4 @ K2 )
% 8.64/4.91 @ N6 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9185_inj__on__set__encode,axiom,
% 8.64/4.91 inj_on_set_nat_nat @ nat_set_encode @ ( collect_set_nat @ finite_finite_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9186_INT__greaterThan__UNIV,axiom,
% 8.64/4.91 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 8.64/4.91 = bot_bot_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9187_Gcd__eq__Max,axiom,
% 8.64/4.91 ! [M5: set_nat] :
% 8.64/4.91 ( ( finite_finite_nat @ M5 )
% 8.64/4.91 => ( ( M5 != bot_bot_set_nat )
% 8.64/4.91 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 8.64/4.91 => ( ( gcd_Gcd_nat @ M5 )
% 8.64/4.91 = ( lattic8265883725875713057ax_nat
% 8.64/4.91 @ ( comple7806235888213564991et_nat
% 8.64/4.91 @ ( image_nat_set_nat
% 8.64/4.91 @ ^ [M6: nat] :
% 8.64/4.91 ( collect_nat
% 8.64/4.91 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M6 ) )
% 8.64/4.91 @ M5 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9188_Max__divisors__self__nat,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( N != zero_zero_nat )
% 8.64/4.91 => ( ( lattic8265883725875713057ax_nat
% 8.64/4.91 @ ( collect_nat
% 8.64/4.91 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N ) ) )
% 8.64/4.91 = N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9189_Sup__nat__def,axiom,
% 8.64/4.91 ( complete_Sup_Sup_nat
% 8.64/4.91 = ( ^ [X7: set_nat] : ( if_nat @ ( X7 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X7 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9190_card__le__Suc__Max,axiom,
% 8.64/4.91 ! [S3: set_nat] :
% 8.64/4.91 ( ( finite_finite_nat @ S3 )
% 8.64/4.91 => ( ord_less_eq_nat @ ( finite_card_nat @ S3 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9191_divide__nat__def,axiom,
% 8.64/4.91 ( divide_divide_nat
% 8.64/4.91 = ( ^ [M6: nat,N4: nat] :
% 8.64/4.91 ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat
% 8.64/4.91 @ ( lattic8265883725875713057ax_nat
% 8.64/4.91 @ ( collect_nat
% 8.64/4.91 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N4 ) @ M6 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9192_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.91 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.64/4.91 ( X
% 8.64/4.91 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( Xa2 != one_one_nat ) ) )
% 8.64/4.91 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( ~ ( ( Deg2 = Xa2 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 & ( case_o184042715313410164at_nat
% 8.64/4.91 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [Mi3: nat,Ma3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.91 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 & ! [I: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 8.64/4.91 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 8.64/4.91 & ( ( Mi3 = Ma3 )
% 8.64/4.91 => ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 & ( ( Mi3 != Ma3 )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 8.64/4.91 & ! [X4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 8.64/4.91 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 8.64/4.91 @ Mima ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9193_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.91 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.64/4.91 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.64/4.91 ( X
% 8.64/4.91 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.91 => ( Xa2 != one_one_nat ) )
% 8.64/4.91 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ~ ( ( Deg2 = Xa2 )
% 8.64/4.91 & ! [X5: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 & ( case_o184042715313410164at_nat
% 8.64/4.91 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [Mi3: nat,Ma3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.91 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 & ! [I: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 8.64/4.91 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 8.64/4.91 & ( ( Mi3 = Ma3 )
% 8.64/4.91 => ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 & ( ( Mi3 != Ma3 )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 8.64/4.91 & ! [X4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 8.64/4.91 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 8.64/4.91 @ Mima ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9194_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.91 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.64/4.91 => ( ( ? [Uu2: $o,Uv2: $o] :
% 8.64/4.91 ( X
% 8.64/4.91 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.91 => ( Xa2 = one_one_nat ) )
% 8.64/4.91 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ( ( Deg2 = Xa2 )
% 8.64/4.91 & ! [X3: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 & ( case_o184042715313410164at_nat
% 8.64/4.91 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [Mi3: nat,Ma3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.91 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 & ! [I: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 8.64/4.91 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 8.64/4.91 & ( ( Mi3 = Ma3 )
% 8.64/4.91 => ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 & ( ( Mi3 != Ma3 )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 8.64/4.91 & ! [X4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 8.64/4.91 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 8.64/4.91 @ Mima ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9195_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 8.64/4.91 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg3: nat] :
% 8.64/4.91 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg3 )
% 8.64/4.91 = ( ( Deg = Deg3 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.91 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 & ( case_o184042715313410164at_nat
% 8.64/4.91 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X7 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [Mi3: nat,Ma3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.91 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.64/4.91 & ! [I: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I ) @ X7 ) )
% 8.64/4.91 = ( vEBT_V8194947554948674370ptions @ Summary @ I ) ) )
% 8.64/4.91 & ( ( Mi3 = Ma3 )
% 8.64/4.91 => ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 & ( ( Mi3 != Ma3 )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 8.64/4.91 & ! [X4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X4 )
% 8.64/4.91 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 8.64/4.91 @ Mima2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9196_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.91 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.64/4.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.91 => ( ! [Uu2: $o,Uv2: $o] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 8.64/4.91 => ( Xa2 = one_one_nat ) ) )
% 8.64/4.91 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 8.64/4.91 => ( ( Deg2 = Xa2 )
% 8.64/4.91 & ! [X3: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 & ( case_o184042715313410164at_nat
% 8.64/4.91 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [Mi3: nat,Ma3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.91 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 & ! [I: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 8.64/4.91 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 8.64/4.91 & ( ( Mi3 = Ma3 )
% 8.64/4.91 => ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 & ( ( Mi3 != Ma3 )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 8.64/4.91 & ! [X4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 8.64/4.91 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 8.64/4.91 @ Mima ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9197_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: nat] :
% 8.64/4.91 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.64/4.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.91 => ( ! [Uu2: $o,Uv2: $o] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 8.64/4.91 => ( Xa2 != one_one_nat ) ) )
% 8.64/4.91 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) )
% 8.64/4.91 => ~ ( ( Deg2 = Xa2 )
% 8.64/4.91 & ! [X5: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 & ( case_o184042715313410164at_nat
% 8.64/4.91 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [Mi3: nat,Ma3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.91 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 & ! [I: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 8.64/4.91 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 8.64/4.91 & ( ( Mi3 = Ma3 )
% 8.64/4.91 => ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 & ( ( Mi3 != Ma3 )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 8.64/4.91 & ! [X4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 8.64/4.91 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 8.64/4.91 @ Mima ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9198_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 8.64/4.91 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 8.64/4.91 => ( ! [Uu2: $o,Uv2: $o] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 8.64/4.91 => ( ( Y
% 8.64/4.91 = ( Xa2 = one_one_nat ) )
% 8.64/4.91 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 8.64/4.91 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ( ( Y
% 8.64/4.91 = ( ( Deg2 = Xa2 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 8.64/4.91 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 & ( case_o184042715313410164at_nat
% 8.64/4.91 @ ( ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X7 )
% 8.64/4.91 & ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [Mi3: nat,Ma3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 8.64/4.91 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 & ! [I: nat] :
% 8.64/4.91 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 => ( ( ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I ) @ X7 ) )
% 8.64/4.91 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I ) ) )
% 8.64/4.91 & ( ( Mi3 = Ma3 )
% 8.64/4.91 => ! [X4: vEBT_VEBT] :
% 8.64/4.91 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 8.64/4.91 => ~ ? [X7: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X7 ) ) )
% 8.64/4.91 & ( ( Mi3 != Ma3 )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ Ma3 )
% 8.64/4.91 & ! [X4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 8.64/4.91 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList @ X4 )
% 8.64/4.91 => ( ( ord_less_nat @ Mi3 @ X4 )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Ma3 ) ) ) ) ) ) ) )
% 8.64/4.91 @ Mima ) ) )
% 8.64/4.91 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9199_min__Suc__Suc,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_min_nat @ ( suc @ M2 ) @ ( suc @ N ) )
% 8.64/4.91 = ( suc @ ( ord_min_nat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9200_min__0L,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_min_nat @ zero_zero_nat @ N )
% 8.64/4.91 = zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9201_min__0R,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_min_nat @ N @ zero_zero_nat )
% 8.64/4.91 = zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9202_take__bit__num__simps_I1_J,axiom,
% 8.64/4.91 ! [M2: num] :
% 8.64/4.91 ( ( bit_take_bit_num @ zero_zero_nat @ M2 )
% 8.64/4.91 = none_num ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9203_take__bit__num__simps_I2_J,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 8.64/4.91 = ( some_num @ one ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9204_take__bit__num__simps_I3_J,axiom,
% 8.64/4.91 ! [N: nat,M2: num] :
% 8.64/4.91 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M2 ) )
% 8.64/4.91 = ( case_o6005452278849405969um_num @ none_num
% 8.64/4.91 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 8.64/4.91 @ ( bit_take_bit_num @ N @ M2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9205_min__numeral__Suc,axiom,
% 8.64/4.91 ! [K2: num,N: nat] :
% 8.64/4.91 ( ( ord_min_nat @ ( numeral_numeral_nat @ K2 ) @ ( suc @ N ) )
% 8.64/4.91 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K2 ) @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9206_min__Suc__numeral,axiom,
% 8.64/4.91 ! [N: nat,K2: num] :
% 8.64/4.91 ( ( ord_min_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K2 ) )
% 8.64/4.91 = ( suc @ ( ord_min_nat @ N @ ( pred_numeral @ K2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9207_take__bit__num__simps_I4_J,axiom,
% 8.64/4.91 ! [N: nat,M2: num] :
% 8.64/4.91 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M2 ) )
% 8.64/4.91 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M2 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9208_min__diff,axiom,
% 8.64/4.91 ! [M2: nat,I2: nat,N: nat] :
% 8.64/4.91 ( ( ord_min_nat @ ( minus_minus_nat @ M2 @ I2 ) @ ( minus_minus_nat @ N @ I2 ) )
% 8.64/4.91 = ( minus_minus_nat @ ( ord_min_nat @ M2 @ N ) @ I2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9209_nat__mult__min__left,axiom,
% 8.64/4.91 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.91 ( ( times_times_nat @ ( ord_min_nat @ M2 @ N ) @ Q2 )
% 8.64/4.91 = ( ord_min_nat @ ( times_times_nat @ M2 @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9210_nat__mult__min__right,axiom,
% 8.64/4.91 ! [M2: nat,N: nat,Q2: nat] :
% 8.64/4.91 ( ( times_times_nat @ M2 @ ( ord_min_nat @ N @ Q2 ) )
% 8.64/4.91 = ( ord_min_nat @ ( times_times_nat @ M2 @ N ) @ ( times_times_nat @ M2 @ Q2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9211_inf__nat__def,axiom,
% 8.64/4.91 inf_inf_nat = ord_min_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9212_min__Suc1,axiom,
% 8.64/4.91 ! [N: nat,M2: nat] :
% 8.64/4.91 ( ( ord_min_nat @ ( suc @ N ) @ M2 )
% 8.64/4.91 = ( case_nat_nat @ zero_zero_nat
% 8.64/4.91 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ N @ M7 ) )
% 8.64/4.91 @ M2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9213_min__Suc2,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_min_nat @ M2 @ ( suc @ N ) )
% 8.64/4.91 = ( case_nat_nat @ zero_zero_nat
% 8.64/4.91 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ M7 @ N ) )
% 8.64/4.91 @ M2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9214_take__bit__num__def,axiom,
% 8.64/4.91 ( bit_take_bit_num
% 8.64/4.91 = ( ^ [N4: nat,M6: num] :
% 8.64/4.91 ( if_option_num
% 8.64/4.91 @ ( ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M6 ) )
% 8.64/4.91 = zero_zero_nat )
% 8.64/4.91 @ none_num
% 8.64/4.91 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N4 @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9215_pred__nat__def,axiom,
% 8.64/4.91 ( pred_nat
% 8.64/4.91 = ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [M6: nat,N4: nat] :
% 8.64/4.91 ( N4
% 8.64/4.91 = ( suc @ M6 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9216_Rats__eq__int__div__nat,axiom,
% 8.64/4.91 ( field_5140801741446780682s_real
% 8.64/4.91 = ( collect_real
% 8.64/4.91 @ ^ [Uu3: real] :
% 8.64/4.91 ? [I: int,N4: nat] :
% 8.64/4.91 ( ( Uu3
% 8.64/4.91 = ( divide_divide_real @ ( ring_1_of_int_real @ I ) @ ( semiri5074537144036343181t_real @ N4 ) ) )
% 8.64/4.91 & ( N4 != zero_zero_nat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9217_card_Ocomp__fun__commute__on,axiom,
% 8.64/4.91 ( ( comp_nat_nat_nat @ suc @ suc )
% 8.64/4.91 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9218_divmod__integer__eq__cases,axiom,
% 8.64/4.91 ( code_divmod_integer
% 8.64/4.91 = ( ^ [K3: code_integer,L2: code_integer] :
% 8.64/4.91 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 8.64/4.91 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 8.64/4.91 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 8.64/4.91 @ ( if_Pro6119634080678213985nteger
% 8.64/4.91 @ ( ( sgn_sgn_Code_integer @ K3 )
% 8.64/4.91 = ( sgn_sgn_Code_integer @ L2 ) )
% 8.64/4.91 @ ( code_divmod_abs @ K3 @ L2 )
% 8.64/4.91 @ ( produc6916734918728496179nteger
% 8.64/4.91 @ ^ [R: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 8.64/4.91 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9219_less__eq,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 8.64/4.91 = ( ord_less_nat @ M2 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9220_pred__nat__trancl__eq__le,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M2 @ N ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 8.64/4.91 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9221_bezw__aux,axiom,
% 8.64/4.91 ! [X: nat,Y: nat] :
% 8.64/4.91 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 8.64/4.91 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9222_gcd__0__left__nat,axiom,
% 8.64/4.91 ! [X: nat] :
% 8.64/4.91 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 8.64/4.91 = X ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9223_gcd__0__nat,axiom,
% 8.64/4.91 ! [X: nat] :
% 8.64/4.91 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 8.64/4.91 = X ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9224_gcd__nat_Oright__neutral,axiom,
% 8.64/4.91 ! [A: nat] :
% 8.64/4.91 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 8.64/4.91 = A ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9225_gcd__nat_Oneutr__eq__iff,axiom,
% 8.64/4.91 ! [A: nat,B: nat] :
% 8.64/4.91 ( ( zero_zero_nat
% 8.64/4.91 = ( gcd_gcd_nat @ A @ B ) )
% 8.64/4.91 = ( ( A = zero_zero_nat )
% 8.64/4.91 & ( B = zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9226_gcd__nat_Oleft__neutral,axiom,
% 8.64/4.91 ! [A: nat] :
% 8.64/4.91 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 8.64/4.91 = A ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9227_gcd__nat_Oeq__neutr__iff,axiom,
% 8.64/4.91 ! [A: nat,B: nat] :
% 8.64/4.91 ( ( ( gcd_gcd_nat @ A @ B )
% 8.64/4.91 = zero_zero_nat )
% 8.64/4.91 = ( ( A = zero_zero_nat )
% 8.64/4.91 & ( B = zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9228_gcd__Suc__0,axiom,
% 8.64/4.91 ! [M2: nat] :
% 8.64/4.91 ( ( gcd_gcd_nat @ M2 @ ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( suc @ zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9229_gcd__pos__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M2 @ N ) )
% 8.64/4.91 = ( ( M2 != zero_zero_nat )
% 8.64/4.91 | ( N != zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9230_gcd__diff2__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ M2 @ N )
% 8.64/4.91 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M2 ) @ N )
% 8.64/4.91 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9231_gcd__diff1__nat,axiom,
% 8.64/4.91 ! [N: nat,M2: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ N @ M2 )
% 8.64/4.91 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M2 @ N ) @ N )
% 8.64/4.91 = ( gcd_gcd_nat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9232_gcd__le1__nat,axiom,
% 8.64/4.91 ! [A: nat,B: nat] :
% 8.64/4.91 ( ( A != zero_zero_nat )
% 8.64/4.91 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9233_gcd__le2__nat,axiom,
% 8.64/4.91 ! [B: nat,A: nat] :
% 8.64/4.91 ( ( B != zero_zero_nat )
% 8.64/4.91 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9234_gcd__mult__distrib__nat,axiom,
% 8.64/4.91 ! [K2: nat,M2: nat,N: nat] :
% 8.64/4.91 ( ( times_times_nat @ K2 @ ( gcd_gcd_nat @ M2 @ N ) )
% 8.64/4.91 = ( gcd_gcd_nat @ ( times_times_nat @ K2 @ M2 ) @ ( times_times_nat @ K2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9235_gcd__non__0__nat,axiom,
% 8.64/4.91 ! [Y: nat,X: nat] :
% 8.64/4.91 ( ( Y != zero_zero_nat )
% 8.64/4.91 => ( ( gcd_gcd_nat @ X @ Y )
% 8.64/4.91 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9236_gcd__nat_Osimps,axiom,
% 8.64/4.91 ( gcd_gcd_nat
% 8.64/4.91 = ( ^ [X4: nat,Y4: nat] : ( if_nat @ ( Y4 = zero_zero_nat ) @ X4 @ ( gcd_gcd_nat @ Y4 @ ( modulo_modulo_nat @ X4 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9237_gcd__nat_Oelims,axiom,
% 8.64/4.91 ! [X: nat,Xa2: nat,Y: nat] :
% 8.64/4.91 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.91 => ( Y = X ) )
% 8.64/4.91 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9238_bezout__nat,axiom,
% 8.64/4.91 ! [A: nat,B: nat] :
% 8.64/4.91 ( ( A != zero_zero_nat )
% 8.64/4.91 => ? [X3: nat,Y3: nat] :
% 8.64/4.91 ( ( times_times_nat @ A @ X3 )
% 8.64/4.91 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9239_bezout__gcd__nat_H,axiom,
% 8.64/4.91 ! [B: nat,A: nat] :
% 8.64/4.91 ? [X3: nat,Y3: nat] :
% 8.64/4.91 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 8.64/4.91 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 8.64/4.91 = ( gcd_gcd_nat @ A @ B ) ) )
% 8.64/4.91 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 8.64/4.91 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 8.64/4.91 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9240_Field__natLeq__on,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( field_nat
% 8.64/4.91 @ ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ N )
% 8.64/4.91 & ( ord_less_nat @ Y4 @ N )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 8.64/4.91 = ( collect_nat
% 8.64/4.91 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9241_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 8.64/4.91 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 8.64/4.91 @ ^ [M6: nat,N4: nat] :
% 8.64/4.91 ( ( dvd_dvd_nat @ M6 @ N4 )
% 8.64/4.91 & ( M6 != N4 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9242_gcd__is__Max__divisors__nat,axiom,
% 8.64/4.91 ! [N: nat,M2: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ( gcd_gcd_nat @ M2 @ N )
% 8.64/4.91 = ( lattic8265883725875713057ax_nat
% 8.64/4.91 @ ( collect_nat
% 8.64/4.91 @ ^ [D2: nat] :
% 8.64/4.91 ( ( dvd_dvd_nat @ D2 @ M2 )
% 8.64/4.91 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9243_gcd__nat_Opelims,axiom,
% 8.64/4.91 ! [X: nat,Xa2: nat,Y: nat] :
% 8.64/4.91 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 8.64/4.91 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 8.64/4.91 => ( Y = X ) )
% 8.64/4.91 & ( ( Xa2 != zero_zero_nat )
% 8.64/4.91 => ( Y
% 8.64/4.91 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 8.64/4.91 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9244_gcd__mult__distrib__int,axiom,
% 8.64/4.91 ! [K2: int,M2: int,N: int] :
% 8.64/4.91 ( ( times_times_int @ ( abs_abs_int @ K2 ) @ ( gcd_gcd_int @ M2 @ N ) )
% 8.64/4.91 = ( gcd_gcd_int @ ( times_times_int @ K2 @ M2 ) @ ( times_times_int @ K2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9245_bezout__int,axiom,
% 8.64/4.91 ! [X: int,Y: int] :
% 8.64/4.91 ? [U3: int,V: int] :
% 8.64/4.91 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V @ Y ) )
% 8.64/4.91 = ( gcd_gcd_int @ X @ Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9246_strict__mono__imp__increasing,axiom,
% 8.64/4.91 ! [F2: nat > nat,N: nat] :
% 8.64/4.91 ( ( order_5726023648592871131at_nat @ F2 )
% 8.64/4.91 => ( ord_less_eq_nat @ N @ ( F2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9247_DeMoivre2,axiom,
% 8.64/4.91 ! [R3: real,A: real,N: nat] :
% 8.64/4.91 ( ( power_power_complex @ ( rcis @ R3 @ A ) @ N )
% 8.64/4.91 = ( rcis @ ( power_power_real @ R3 @ N ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9248_Re__rcis,axiom,
% 8.64/4.91 ! [R3: real,A: real] :
% 8.64/4.91 ( ( re @ ( rcis @ R3 @ A ) )
% 8.64/4.91 = ( times_times_real @ R3 @ ( cos_real @ A ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9249_Im__rcis,axiom,
% 8.64/4.91 ! [R3: real,A: real] :
% 8.64/4.91 ( ( im @ ( rcis @ R3 @ A ) )
% 8.64/4.91 = ( times_times_real @ R3 @ ( sin_real @ A ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9250_rcis__mult,axiom,
% 8.64/4.91 ! [R1: real,A: real,R22: real,B: real] :
% 8.64/4.91 ( ( times_times_complex @ ( rcis @ R1 @ A ) @ ( rcis @ R22 @ B ) )
% 8.64/4.91 = ( rcis @ ( times_times_real @ R1 @ R22 ) @ ( plus_plus_real @ A @ B ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9251_rcis__def,axiom,
% 8.64/4.91 ( rcis
% 8.64/4.91 = ( ^ [R: real,A5: real] : ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( cis @ A5 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9252_eventually__prod__sequentially,axiom,
% 8.64/4.91 ! [P2: product_prod_nat_nat > $o] :
% 8.64/4.91 ( ( eventu1038000079068216329at_nat @ P2 @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 8.64/4.91 = ( ? [N5: nat] :
% 8.64/4.91 ! [M6: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ N5 @ M6 )
% 8.64/4.91 => ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ N5 @ N4 )
% 8.64/4.91 => ( P2 @ ( product_Pair_nat_nat @ N4 @ M6 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9253_sqr_Osimps_I3_J,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ( ( sqr @ ( bit1 @ N ) )
% 8.64/4.91 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9254_sqr_Osimps_I2_J,axiom,
% 8.64/4.91 ! [N: num] :
% 8.64/4.91 ( ( sqr @ ( bit0 @ N ) )
% 8.64/4.91 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9255_sqr_Osimps_I1_J,axiom,
% 8.64/4.91 ( ( sqr @ one )
% 8.64/4.91 = one ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9256_sqr__conv__mult,axiom,
% 8.64/4.91 ( sqr
% 8.64/4.91 = ( ^ [X4: num] : ( times_times_num @ X4 @ X4 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9257_pow_Osimps_I3_J,axiom,
% 8.64/4.91 ! [X: num,Y: num] :
% 8.64/4.91 ( ( pow @ X @ ( bit1 @ Y ) )
% 8.64/4.91 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9258_pow_Osimps_I1_J,axiom,
% 8.64/4.91 ! [X: num] :
% 8.64/4.91 ( ( pow @ X @ one )
% 8.64/4.91 = X ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9259_pow_Osimps_I2_J,axiom,
% 8.64/4.91 ! [X: num,Y: num] :
% 8.64/4.91 ( ( pow @ X @ ( bit0 @ Y ) )
% 8.64/4.91 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9260_natLeq__on__wo__rel,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( bNF_We3818239936649020644el_nat
% 8.64/4.91 @ ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ N )
% 8.64/4.91 & ( ord_less_nat @ Y4 @ N )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9261_pairs__le__eq__Sigma,axiom,
% 8.64/4.91 ! [M2: nat] :
% 8.64/4.91 ( ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [I: nat,J: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I @ J ) @ M2 ) ) )
% 8.64/4.91 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M2 )
% 8.64/4.91 @ ^ [R: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M2 @ R ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9262_finite__vimage__Suc__iff,axiom,
% 8.64/4.91 ! [F3: set_nat] :
% 8.64/4.91 ( ( finite_finite_nat @ ( vimage_nat_nat @ suc @ F3 ) )
% 8.64/4.91 = ( finite_finite_nat @ F3 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9263_coprime__Suc__0__right,axiom,
% 8.64/4.91 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9264_coprime__Suc__0__left,axiom,
% 8.64/4.91 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ zero_zero_nat ) @ N ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9265_coprime__Suc__left__nat,axiom,
% 8.64/4.91 ! [N: nat] : ( algebr934650988132801477me_nat @ ( suc @ N ) @ N ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9266_coprime__Suc__right__nat,axiom,
% 8.64/4.91 ! [N: nat] : ( algebr934650988132801477me_nat @ N @ ( suc @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9267_coprime__crossproduct__nat,axiom,
% 8.64/4.91 ! [A: nat,D: nat,B: nat,C2: nat] :
% 8.64/4.91 ( ( algebr934650988132801477me_nat @ A @ D )
% 8.64/4.91 => ( ( algebr934650988132801477me_nat @ B @ C2 )
% 8.64/4.91 => ( ( ( times_times_nat @ A @ C2 )
% 8.64/4.91 = ( times_times_nat @ B @ D ) )
% 8.64/4.91 = ( ( A = B )
% 8.64/4.91 & ( C2 = D ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9268_vimage__Suc__insert__Suc,axiom,
% 8.64/4.91 ! [N: nat,A4: set_nat] :
% 8.64/4.91 ( ( vimage_nat_nat @ suc @ ( insert_nat @ ( suc @ N ) @ A4 ) )
% 8.64/4.91 = ( insert_nat @ N @ ( vimage_nat_nat @ suc @ A4 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9269_vimage__Suc__insert__0,axiom,
% 8.64/4.91 ! [A4: set_nat] :
% 8.64/4.91 ( ( vimage_nat_nat @ suc @ ( insert_nat @ zero_zero_nat @ A4 ) )
% 8.64/4.91 = ( vimage_nat_nat @ suc @ A4 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9270_coprime__diff__one__left__nat,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9271_coprime__diff__one__right__nat,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( algebr934650988132801477me_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9272_Rats__abs__nat__div__natE,axiom,
% 8.64/4.91 ! [X: real] :
% 8.64/4.91 ( ( member_real @ X @ field_5140801741446780682s_real )
% 8.64/4.91 => ~ ! [M: nat,N3: nat] :
% 8.64/4.91 ( ( N3 != zero_zero_nat )
% 8.64/4.91 => ( ( ( abs_abs_real @ X )
% 8.64/4.91 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N3 ) ) )
% 8.64/4.91 => ~ ( algebr934650988132801477me_nat @ M @ N3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9273_set__decode__div__2,axiom,
% 8.64/4.91 ! [X: nat] :
% 8.64/4.91 ( ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 8.64/4.91 = ( vimage_nat_nat @ suc @ ( nat_set_decode @ X ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9274_set__encode__vimage__Suc,axiom,
% 8.64/4.91 ! [A4: set_nat] :
% 8.64/4.91 ( ( nat_set_encode @ ( vimage_nat_nat @ suc @ A4 ) )
% 8.64/4.91 = ( divide_divide_nat @ ( nat_set_encode @ A4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9275_Restr__natLeq,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 8.64/4.91 @ ( produc457027306803732586at_nat
% 8.64/4.91 @ ( collect_nat
% 8.64/4.91 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) )
% 8.64/4.91 @ ^ [Uu3: nat] :
% 8.64/4.91 ( collect_nat
% 8.64/4.91 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) )
% 8.64/4.91 = ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ N )
% 8.64/4.91 & ( ord_less_nat @ Y4 @ N )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9276_of__nat__eq__id,axiom,
% 8.64/4.91 semiri1316708129612266289at_nat = id_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9277_coprime__crossproduct__int,axiom,
% 8.64/4.91 ! [A: int,D: int,B: int,C2: int] :
% 8.64/4.91 ( ( algebr932160517623751201me_int @ A @ D )
% 8.64/4.91 => ( ( algebr932160517623751201me_int @ B @ C2 )
% 8.64/4.91 => ( ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ C2 ) )
% 8.64/4.91 = ( times_times_int @ ( abs_abs_int @ B ) @ ( abs_abs_int @ D ) ) )
% 8.64/4.91 = ( ( ( abs_abs_int @ A )
% 8.64/4.91 = ( abs_abs_int @ B ) )
% 8.64/4.91 & ( ( abs_abs_int @ C2 )
% 8.64/4.91 = ( abs_abs_int @ D ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9278_natLeq__Linear__order,axiom,
% 8.64/4.91 order_4473980167227706203on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9279_natLeq__Total,axiom,
% 8.64/4.91 total_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9280_natLeq__Refl,axiom,
% 8.64/4.91 refl_on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9281_natLeq__natLess__Id,axiom,
% 8.64/4.91 ( bNF_Ca8459412986667044542atLess
% 8.64/4.91 = ( minus_1356011639430497352at_nat @ bNF_Ca8665028551170535155natLeq @ id_nat2 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9282_Field__natLeq,axiom,
% 8.64/4.91 ( ( field_nat @ bNF_Ca8665028551170535155natLeq )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9283_natLeq__def,axiom,
% 8.64/4.91 ( bNF_Ca8665028551170535155natLeq
% 8.64/4.91 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9284_Restr__natLeq2,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 8.64/4.91 @ ( produc457027306803732586at_nat @ ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 8.64/4.91 @ ^ [Uu3: nat] : ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N ) ) )
% 8.64/4.91 = ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ N )
% 8.64/4.91 & ( ord_less_nat @ Y4 @ N )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9285_natLeq__underS__less,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N )
% 8.64/4.91 = ( collect_nat
% 8.64/4.91 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9286_pair__lessI2,axiom,
% 8.64/4.91 ! [A: nat,B: nat,S2: nat,T: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.91 => ( ( ord_less_nat @ S2 @ T )
% 8.64/4.91 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9287_pair__less__iff1,axiom,
% 8.64/4.91 ! [X: nat,Y: nat,Z3: nat] :
% 8.64/4.91 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z3 ) ) @ fun_pair_less )
% 8.64/4.91 = ( ord_less_nat @ Y @ Z3 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9288_pair__lessI1,axiom,
% 8.64/4.91 ! [A: nat,B: nat,S2: nat,T: nat] :
% 8.64/4.91 ( ( ord_less_nat @ A @ B )
% 8.64/4.91 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_less ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9289_pair__leqI2,axiom,
% 8.64/4.91 ! [A: nat,B: nat,S2: nat,T: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ A @ B )
% 8.64/4.91 => ( ( ord_less_eq_nat @ S2 @ T )
% 8.64/4.91 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9290_pair__leqI1,axiom,
% 8.64/4.91 ! [A: nat,B: nat,S2: nat,T: nat] :
% 8.64/4.91 ( ( ord_less_nat @ A @ B )
% 8.64/4.91 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T ) ) @ fun_pair_leq ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9291_length__upto,axiom,
% 8.64/4.91 ! [I2: int,J2: int] :
% 8.64/4.91 ( ( size_size_list_int @ ( upto @ I2 @ J2 ) )
% 8.64/4.91 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J2 @ I2 ) @ one_one_int ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9292_gcd__nat_Oordering__top__axioms,axiom,
% 8.64/4.91 ( ordering_top_nat @ dvd_dvd_nat
% 8.64/4.91 @ ^ [M6: nat,N4: nat] :
% 8.64/4.91 ( ( dvd_dvd_nat @ M6 @ N4 )
% 8.64/4.91 & ( M6 != N4 ) )
% 8.64/4.91 @ zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9293_bot__nat__0_Oordering__top__axioms,axiom,
% 8.64/4.91 ( ordering_top_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 8.64/4.91 @ zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9294_ratrel__iff,axiom,
% 8.64/4.91 ( ratrel
% 8.64/4.91 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 8.64/4.91 ( ( ( product_snd_int_int @ X4 )
% 8.64/4.91 != zero_zero_int )
% 8.64/4.91 & ( ( product_snd_int_int @ Y4 )
% 8.64/4.91 != zero_zero_int )
% 8.64/4.91 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 8.64/4.91 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9295_ratrel__def,axiom,
% 8.64/4.91 ( ratrel
% 8.64/4.91 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 8.64/4.91 ( ( ( product_snd_int_int @ X4 )
% 8.64/4.91 != zero_zero_int )
% 8.64/4.91 & ( ( product_snd_int_int @ Y4 )
% 8.64/4.91 != zero_zero_int )
% 8.64/4.91 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 8.64/4.91 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9296_plus__rat_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 8.64/4.91 ( ( ratrel @ Xa2 @ Xa2 )
% 8.64/4.91 => ( ( ratrel @ X @ X )
% 8.64/4.91 => ( ( plus_plus_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 8.64/4.91 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9297_times__rat_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: product_prod_int_int,X: product_prod_int_int] :
% 8.64/4.91 ( ( ratrel @ Xa2 @ Xa2 )
% 8.64/4.91 => ( ( ratrel @ X @ X )
% 8.64/4.91 => ( ( times_times_rat @ ( abs_Rat @ Xa2 ) @ ( abs_Rat @ X ) )
% 8.64/4.91 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa2 ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa2 ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9298_Rat_Opositive_Oabs__eq,axiom,
% 8.64/4.91 ! [X: product_prod_int_int] :
% 8.64/4.91 ( ( ratrel @ X @ X )
% 8.64/4.91 => ( ( positive @ ( abs_Rat @ X ) )
% 8.64/4.91 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9299_Rat_Opositive__mult,axiom,
% 8.64/4.91 ! [X: rat,Y: rat] :
% 8.64/4.91 ( ( positive @ X )
% 8.64/4.91 => ( ( positive @ Y )
% 8.64/4.91 => ( positive @ ( times_times_rat @ X @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9300_Rat_Opositive_Orep__eq,axiom,
% 8.64/4.91 ( positive
% 8.64/4.91 = ( ^ [X4: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X4 ) ) @ ( product_snd_int_int @ ( rep_Rat @ X4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9301_Rat_Opositive_Orsp,axiom,
% 8.64/4.91 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 8.64/4.91 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 8.64/4.91 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9302_Rat_Opositive__def,axiom,
% 8.64/4.91 ( positive
% 8.64/4.91 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 8.64/4.91 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9303_less__eq__natural_Orsp,axiom,
% 8.64/4.91 ( bNF_re578469030762574527_nat_o
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 8.64/4.91 @ ( bNF_re4705727531993890431at_o_o
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 8.64/4.91 @ ord_less_eq_nat
% 8.64/4.91 @ ord_less_eq_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9304_Suc_Orsp,axiom,
% 8.64/4.91 ( bNF_re5653821019739307937at_nat
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 8.64/4.91 @ suc
% 8.64/4.91 @ suc ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9305_times__integer_Orsp,axiom,
% 8.64/4.91 ( bNF_re711492959462206631nt_int
% 8.64/4.91 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 8.64/4.91 @ ( bNF_re4712519889275205905nt_int
% 8.64/4.91 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [Y5: int,Z2: int] : ( Y5 = Z2 ) )
% 8.64/4.91 @ times_times_int
% 8.64/4.91 @ times_times_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9306_times__natural_Orsp,axiom,
% 8.64/4.91 ( bNF_re1345281282404953727at_nat
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 8.64/4.91 @ ( bNF_re5653821019739307937at_nat
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 ) )
% 8.64/4.91 @ times_times_nat
% 8.64/4.91 @ times_times_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9307_times__rat_Orsp,axiom,
% 8.64/4.91 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9308_plus__rat_Orsp,axiom,
% 8.64/4.91 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9309_plus__rat_Otransfer,axiom,
% 8.64/4.91 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.64/4.91 @ plus_plus_rat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9310_Rat_Opositive_Otransfer,axiom,
% 8.64/4.91 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 8.64/4.91 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 8.64/4.91 @ positive ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9311_times__rat_Otransfer,axiom,
% 8.64/4.91 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) )
% 8.64/4.91 @ times_times_rat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9312_times__int_Otransfer,axiom,
% 8.64/4.91 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 8.64/4.91 @ times_times_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9313_minus__int_Otransfer,axiom,
% 8.64/4.91 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 8.64/4.91 @ minus_minus_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9314_zero__int_Otransfer,axiom,
% 8.64/4.91 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9315_int__transfer,axiom,
% 8.64/4.91 ( bNF_re6830278522597306478at_int
% 8.64/4.91 @ ^ [Y5: nat,Z2: nat] : ( Y5 = Z2 )
% 8.64/4.91 @ pcr_int
% 8.64/4.91 @ ^ [N4: nat] : ( product_Pair_nat_nat @ N4 @ zero_zero_nat )
% 8.64/4.91 @ semiri1314217659103216013at_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9316_uminus__int_Otransfer,axiom,
% 8.64/4.91 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 8.64/4.91 @ ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 8.64/4.91 @ uminus_uminus_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9317_one__int_Otransfer,axiom,
% 8.64/4.91 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9318_less__eq__int_Otransfer,axiom,
% 8.64/4.91 ( bNF_re717283939379294677_int_o @ pcr_int
% 8.64/4.91 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 8.64/4.91 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 8.64/4.91 @ ( produc8739625826339149834_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 8.64/4.91 @ ord_less_eq_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9319_plus__int_Otransfer,axiom,
% 8.64/4.91 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 8.64/4.91 @ plus_plus_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9320_times__int_Orsp,axiom,
% 8.64/4.91 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V3 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9321_minus__int_Orsp,axiom,
% 8.64/4.91 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9322_intrel__iff,axiom,
% 8.64/4.91 ! [X: nat,Y: nat,U: nat,V2: nat] :
% 8.64/4.91 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V2 ) )
% 8.64/4.91 = ( ( plus_plus_nat @ X @ V2 )
% 8.64/4.91 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9323_zero__int_Orsp,axiom,
% 8.64/4.91 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9324_uminus__int_Orsp,axiom,
% 8.64/4.91 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 8.64/4.91 @ ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 8.64/4.91 @ ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9325_one__int_Orsp,axiom,
% 8.64/4.91 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9326_less__eq__int_Orsp,axiom,
% 8.64/4.91 ( bNF_re4202695980764964119_nat_o @ intrel
% 8.64/4.91 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 8.64/4.91 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 ) )
% 8.64/4.91 @ ( produc8739625826339149834_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 8.64/4.91 @ ( produc8739625826339149834_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9327_plus__int_Orsp,axiom,
% 8.64/4.91 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) )
% 8.64/4.91 @ ( produc27273713700761075at_nat
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc2626176000494625587at_nat
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V3 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9328_less__eq__enat__def,axiom,
% 8.64/4.91 ( ord_le2932123472753598470d_enat
% 8.64/4.91 = ( ^ [M6: extended_enat] :
% 8.64/4.91 ( extended_case_enat_o
% 8.64/4.91 @ ^ [N1: nat] :
% 8.64/4.91 ( extended_case_enat_o
% 8.64/4.91 @ ^ [M1: nat] : ( ord_less_eq_nat @ M1 @ N1 )
% 8.64/4.91 @ $false
% 8.64/4.91 @ M6 )
% 8.64/4.91 @ $true ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9329_natLeq__Well__order,axiom,
% 8.64/4.91 order_2888998067076097458on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9330_natLeq__on__well__order__on,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( order_2888998067076097458on_nat
% 8.64/4.91 @ ( collect_nat
% 8.64/4.91 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N ) )
% 8.64/4.91 @ ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ N )
% 8.64/4.91 & ( ord_less_nat @ Y4 @ N )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9331_natLeq__on__Well__order,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( order_2888998067076097458on_nat
% 8.64/4.91 @ ( field_nat
% 8.64/4.91 @ ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ N )
% 8.64/4.91 & ( ord_less_nat @ Y4 @ N )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 8.64/4.91 @ ( collec3392354462482085612at_nat
% 8.64/4.91 @ ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( ( ord_less_nat @ X4 @ N )
% 8.64/4.91 & ( ord_less_nat @ Y4 @ N )
% 8.64/4.91 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9332_inj__on__char__of__nat,axiom,
% 8.64/4.91 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9333_UNIV__char__of__nat,axiom,
% 8.64/4.91 ( top_top_set_char
% 8.64/4.91 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9334_range__nat__of__char,axiom,
% 8.64/4.91 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 8.64/4.91 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9335_plus__rat__def,axiom,
% 8.64/4.91 ( plus_plus_rat
% 8.64/4.91 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) @ ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9336_diff__rat,axiom,
% 8.64/4.91 ! [B: int,D: int,A: int,C2: int] :
% 8.64/4.91 ( ( B != zero_zero_int )
% 8.64/4.91 => ( ( D != zero_zero_int )
% 8.64/4.91 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 8.64/4.91 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C2 @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9337_sgn__rat,axiom,
% 8.64/4.91 ! [A: int,B: int] :
% 8.64/4.91 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 8.64/4.91 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9338_mult__rat,axiom,
% 8.64/4.91 ! [A: int,B: int,C2: int,D: int] :
% 8.64/4.91 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 8.64/4.91 = ( fract @ ( times_times_int @ A @ C2 ) @ ( times_times_int @ B @ D ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9339_divide__rat,axiom,
% 8.64/4.91 ! [A: int,B: int,C2: int,D: int] :
% 8.64/4.91 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 8.64/4.91 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9340_less__rat,axiom,
% 8.64/4.91 ! [B: int,D: int,A: int,C2: int] :
% 8.64/4.91 ( ( B != zero_zero_int )
% 8.64/4.91 => ( ( D != zero_zero_int )
% 8.64/4.91 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 8.64/4.91 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9341_add__rat,axiom,
% 8.64/4.91 ! [B: int,D: int,A: int,C2: int] :
% 8.64/4.91 ( ( B != zero_zero_int )
% 8.64/4.91 => ( ( D != zero_zero_int )
% 8.64/4.91 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 8.64/4.91 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C2 @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9342_le__rat,axiom,
% 8.64/4.91 ! [B: int,D: int,A: int,C2: int] :
% 8.64/4.91 ( ( B != zero_zero_int )
% 8.64/4.91 => ( ( D != zero_zero_int )
% 8.64/4.91 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C2 @ D ) )
% 8.64/4.91 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C2 @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9343_mult__rat__cancel,axiom,
% 8.64/4.91 ! [C2: int,A: int,B: int] :
% 8.64/4.91 ( ( C2 != zero_zero_int )
% 8.64/4.91 => ( ( fract @ ( times_times_int @ C2 @ A ) @ ( times_times_int @ C2 @ B ) )
% 8.64/4.91 = ( fract @ A @ B ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9344_eq__rat_I1_J,axiom,
% 8.64/4.91 ! [B: int,D: int,A: int,C2: int] :
% 8.64/4.91 ( ( B != zero_zero_int )
% 8.64/4.91 => ( ( D != zero_zero_int )
% 8.64/4.91 => ( ( ( fract @ A @ B )
% 8.64/4.91 = ( fract @ C2 @ D ) )
% 8.64/4.91 = ( ( times_times_int @ A @ D )
% 8.64/4.91 = ( times_times_int @ C2 @ B ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9345_positive__rat,axiom,
% 8.64/4.91 ! [A: int,B: int] :
% 8.64/4.91 ( ( positive @ ( fract @ A @ B ) )
% 8.64/4.91 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9346_times__rat__def,axiom,
% 8.64/4.91 ( times_times_rat
% 8.64/4.91 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 8.64/4.91 @ ^ [X4: product_prod_int_int,Y4: product_prod_int_int] : ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_fst_int_int @ Y4 ) ) @ ( times_times_int @ ( product_snd_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9347_integer__of__char__code,axiom,
% 8.64/4.91 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 8.64/4.91 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 8.64/4.91 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9348_char_Osize_I2_J,axiom,
% 8.64/4.91 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 8.64/4.91 ( ( size_size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 8.64/4.91 = zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9349_char_Osize__gen,axiom,
% 8.64/4.91 ! [X1: $o,X2: $o,X33: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 8.64/4.91 ( ( size_char @ ( char2 @ X1 @ X2 @ X33 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 8.64/4.91 = zero_zero_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9350_numeral__le__enat__iff,axiom,
% 8.64/4.91 ! [M2: num,N: nat] :
% 8.64/4.91 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M2 ) @ ( extended_enat2 @ N ) )
% 8.64/4.91 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M2 ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9351_idiff__enat__0__right,axiom,
% 8.64/4.91 ! [N: extended_enat] :
% 8.64/4.91 ( ( minus_3235023915231533773d_enat @ N @ ( extended_enat2 @ zero_zero_nat ) )
% 8.64/4.91 = N ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9352_idiff__enat__0,axiom,
% 8.64/4.91 ! [N: extended_enat] :
% 8.64/4.91 ( ( minus_3235023915231533773d_enat @ ( extended_enat2 @ zero_zero_nat ) @ N )
% 8.64/4.91 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9353_times__enat__simps_I1_J,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 8.64/4.91 = ( extended_enat2 @ ( times_times_nat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9354_enat__ord__simps_I1_J,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ M2 ) @ ( extended_enat2 @ N ) )
% 8.64/4.91 = ( ord_less_eq_nat @ M2 @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9355_Suc__ile__eq,axiom,
% 8.64/4.91 ! [M2: nat,N: extended_enat] :
% 8.64/4.91 ( ( ord_le2932123472753598470d_enat @ ( extended_enat2 @ ( suc @ M2 ) ) @ N )
% 8.64/4.91 = ( ord_le72135733267957522d_enat @ ( extended_enat2 @ M2 ) @ N ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9356_enat__0__iff_I2_J,axiom,
% 8.64/4.91 ! [X: nat] :
% 8.64/4.91 ( ( zero_z5237406670263579293d_enat
% 8.64/4.91 = ( extended_enat2 @ X ) )
% 8.64/4.91 = ( X = zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9357_enat__0__iff_I1_J,axiom,
% 8.64/4.91 ! [X: nat] :
% 8.64/4.91 ( ( ( extended_enat2 @ X )
% 8.64/4.91 = zero_z5237406670263579293d_enat )
% 8.64/4.91 = ( X = zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9358_zero__enat__def,axiom,
% 8.64/4.91 ( zero_z5237406670263579293d_enat
% 8.64/4.91 = ( extended_enat2 @ zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9359_iadd__le__enat__iff,axiom,
% 8.64/4.91 ! [X: extended_enat,Y: extended_enat,N: nat] :
% 8.64/4.91 ( ( ord_le2932123472753598470d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ ( extended_enat2 @ N ) )
% 8.64/4.91 = ( ? [Y8: nat,X9: nat] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( extended_enat2 @ X9 ) )
% 8.64/4.91 & ( Y
% 8.64/4.91 = ( extended_enat2 @ Y8 ) )
% 8.64/4.91 & ( ord_less_eq_nat @ ( plus_plus_nat @ X9 @ Y8 ) @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9360_elimnum,axiom,
% 8.64/4.91 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.64/4.91 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 8.64/4.91 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 8.64/4.91 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9361_VEBT__internal_Oelim__dead_Osimps_I3_J,axiom,
% 8.64/4.91 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,L: nat] :
% 8.64/4.91 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ ( extended_enat2 @ L ) )
% 8.64/4.91 = ( vEBT_Node @ Info2 @ Deg
% 8.64/4.91 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 @ ( map_VE8901447254227204932T_VEBT
% 8.64/4.91 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 @ TreeList2 ) )
% 8.64/4.91 @ ( vEBT_VEBT_elim_dead @ Summary @ ( extended_enat2 @ ( divide_divide_nat @ L @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9362_enat__0__less__mult__iff,axiom,
% 8.64/4.91 ! [M2: extended_enat,N: extended_enat] :
% 8.64/4.91 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M2 @ N ) )
% 8.64/4.91 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M2 )
% 8.64/4.91 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9363_imult__is__0,axiom,
% 8.64/4.91 ! [M2: extended_enat,N: extended_enat] :
% 8.64/4.91 ( ( ( times_7803423173614009249d_enat @ M2 @ N )
% 8.64/4.91 = zero_z5237406670263579293d_enat )
% 8.64/4.91 = ( ( M2 = zero_z5237406670263579293d_enat )
% 8.64/4.91 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9364_VEBT__internal_Oelim__dead_Osimps_I1_J,axiom,
% 8.64/4.91 ! [A: $o,B: $o,Uu: extended_enat] :
% 8.64/4.91 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Leaf @ A @ B ) @ Uu )
% 8.64/4.91 = ( vEBT_Leaf @ A @ B ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9365_VEBT__internal_Oelim__dead_Oelims,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 8.64/4.91 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ! [A3: $o,B3: $o] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.91 => ( Y
% 8.64/4.91 != ( vEBT_Leaf @ A3 @ B3 ) ) )
% 8.64/4.91 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ( ( Xa2 = extend5688581933313929465d_enat )
% 8.64/4.91 => ( Y
% 8.64/4.91 != ( vEBT_Node @ Info @ Deg2
% 8.64/4.91 @ ( map_VE8901447254227204932T_VEBT
% 8.64/4.91 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 @ TreeList )
% 8.64/4.91 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) ) ) )
% 8.64/4.91 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ! [L4: nat] :
% 8.64/4.91 ( ( Xa2
% 8.64/4.91 = ( extended_enat2 @ L4 ) )
% 8.64/4.91 => ( Y
% 8.64/4.91 != ( vEBT_Node @ Info @ Deg2
% 8.64/4.91 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 @ ( map_VE8901447254227204932T_VEBT
% 8.64/4.91 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 @ TreeList ) )
% 8.64/4.91 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9366_VEBT__internal_Oelim__dead_Osimps_I2_J,axiom,
% 8.64/4.91 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 8.64/4.91 ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 8.64/4.91 = ( vEBT_Node @ Info2 @ Deg
% 8.64/4.91 @ ( map_VE8901447254227204932T_VEBT
% 8.64/4.91 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 @ TreeList2 )
% 8.64/4.91 @ ( vEBT_VEBT_elim_dead @ Summary @ extend5688581933313929465d_enat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9367_elimcomplete,axiom,
% 8.64/4.91 ! [Info2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 8.64/4.91 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ N )
% 8.64/4.91 => ( ( vEBT_VEBT_elim_dead @ ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) @ extend5688581933313929465d_enat )
% 8.64/4.91 = ( vEBT_Node @ Info2 @ Deg @ TreeList2 @ Summary ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9368_times__enat__simps_I2_J,axiom,
% 8.64/4.91 ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ extend5688581933313929465d_enat )
% 8.64/4.91 = extend5688581933313929465d_enat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9369_times__enat__simps_I3_J,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( ( N = zero_zero_nat )
% 8.64/4.91 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 8.64/4.91 = zero_z5237406670263579293d_enat ) )
% 8.64/4.91 & ( ( N != zero_zero_nat )
% 8.64/4.91 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ ( extended_enat2 @ N ) )
% 8.64/4.91 = extend5688581933313929465d_enat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9370_times__enat__simps_I4_J,axiom,
% 8.64/4.91 ! [M2: nat] :
% 8.64/4.91 ( ( ( M2 = zero_zero_nat )
% 8.64/4.91 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 8.64/4.91 = zero_z5237406670263579293d_enat ) )
% 8.64/4.91 & ( ( M2 != zero_zero_nat )
% 8.64/4.91 => ( ( times_7803423173614009249d_enat @ ( extended_enat2 @ M2 ) @ extend5688581933313929465d_enat )
% 8.64/4.91 = extend5688581933313929465d_enat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9371_imult__is__infinity,axiom,
% 8.64/4.91 ! [A: extended_enat,B: extended_enat] :
% 8.64/4.91 ( ( ( times_7803423173614009249d_enat @ A @ B )
% 8.64/4.91 = extend5688581933313929465d_enat )
% 8.64/4.91 = ( ( ( A = extend5688581933313929465d_enat )
% 8.64/4.91 & ( B != zero_z5237406670263579293d_enat ) )
% 8.64/4.91 | ( ( B = extend5688581933313929465d_enat )
% 8.64/4.91 & ( A != zero_z5237406670263579293d_enat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9372_VEBT__internal_Oelim__dead_Ocases,axiom,
% 8.64/4.91 ! [X: produc7272778201969148633d_enat] :
% 8.64/4.91 ( ! [A3: $o,B3: $o,Uu2: extended_enat] :
% 8.64/4.91 ( X
% 8.64/4.91 != ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B3 ) @ Uu2 ) )
% 8.64/4.91 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( X
% 8.64/4.91 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ extend5688581933313929465d_enat ) )
% 8.64/4.91 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT,L4: nat] :
% 8.64/4.91 ( X
% 8.64/4.91 != ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9373_imult__infinity,axiom,
% 8.64/4.91 ! [N: extended_enat] :
% 8.64/4.91 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 8.64/4.91 => ( ( times_7803423173614009249d_enat @ extend5688581933313929465d_enat @ N )
% 8.64/4.91 = extend5688581933313929465d_enat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9374_imult__infinity__right,axiom,
% 8.64/4.91 ! [N: extended_enat] :
% 8.64/4.91 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 8.64/4.91 => ( ( times_7803423173614009249d_enat @ N @ extend5688581933313929465d_enat )
% 8.64/4.91 = extend5688581933313929465d_enat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9375_times__enat__def,axiom,
% 8.64/4.91 ( times_7803423173614009249d_enat
% 8.64/4.91 = ( ^ [M6: extended_enat,N4: extended_enat] :
% 8.64/4.91 ( extend3600170679010898289d_enat
% 8.64/4.91 @ ^ [O: nat] :
% 8.64/4.91 ( extend3600170679010898289d_enat
% 8.64/4.91 @ ^ [P5: nat] : ( extended_enat2 @ ( times_times_nat @ O @ P5 ) )
% 8.64/4.91 @ ( if_Extended_enat @ ( O = zero_zero_nat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 8.64/4.91 @ N4 )
% 8.64/4.91 @ ( if_Extended_enat @ ( N4 = zero_z5237406670263579293d_enat ) @ zero_z5237406670263579293d_enat @ extend5688581933313929465d_enat )
% 8.64/4.91 @ M6 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9376_VEBT__internal_Oelim__dead_Opelims,axiom,
% 8.64/4.91 ! [X: vEBT_VEBT,Xa2: extended_enat,Y: vEBT_VEBT] :
% 8.64/4.91 ( ( ( vEBT_VEBT_elim_dead @ X @ Xa2 )
% 8.64/4.91 = Y )
% 8.64/4.91 => ( ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ X @ Xa2 ) )
% 8.64/4.91 => ( ! [A3: $o,B3: $o] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.91 => ( ( Y
% 8.64/4.91 = ( vEBT_Leaf @ A3 @ B3 ) )
% 8.64/4.91 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Leaf @ A3 @ B3 ) @ Xa2 ) ) ) )
% 8.64/4.91 => ( ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ( ( Xa2 = extend5688581933313929465d_enat )
% 8.64/4.91 => ( ( Y
% 8.64/4.91 = ( vEBT_Node @ Info @ Deg2
% 8.64/4.91 @ ( map_VE8901447254227204932T_VEBT
% 8.64/4.91 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 @ TreeList )
% 8.64/4.91 @ ( vEBT_VEBT_elim_dead @ Summary2 @ extend5688581933313929465d_enat ) ) )
% 8.64/4.91 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ extend5688581933313929465d_enat ) ) ) ) )
% 8.64/4.91 => ~ ! [Info: option4927543243414619207at_nat,Deg2: nat,TreeList: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 8.64/4.91 ( ( X
% 8.64/4.91 = ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) )
% 8.64/4.91 => ! [L4: nat] :
% 8.64/4.91 ( ( Xa2
% 8.64/4.91 = ( extended_enat2 @ L4 ) )
% 8.64/4.91 => ( ( Y
% 8.64/4.91 = ( vEBT_Node @ Info @ Deg2
% 8.64/4.91 @ ( take_VEBT_VEBT @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 8.64/4.91 @ ( map_VE8901447254227204932T_VEBT
% 8.64/4.91 @ ^ [T2: vEBT_VEBT] : ( vEBT_VEBT_elim_dead @ T2 @ ( extended_enat2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 8.64/4.91 @ TreeList ) )
% 8.64/4.91 @ ( vEBT_VEBT_elim_dead @ Summary2 @ ( extended_enat2 @ ( divide_divide_nat @ L4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 8.64/4.91 => ~ ( accp_P6183159247885693666d_enat @ vEBT_V312737461966249ad_rel @ ( produc581526299967858633d_enat @ ( vEBT_Node @ Info @ Deg2 @ TreeList @ Summary2 ) @ ( extended_enat2 @ L4 ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9377_eSuc__def,axiom,
% 8.64/4.91 ( extended_eSuc
% 8.64/4.91 = ( extend3600170679010898289d_enat
% 8.64/4.91 @ ^ [N4: nat] : ( extended_enat2 @ ( suc @ N4 ) )
% 8.64/4.91 @ extend5688581933313929465d_enat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9378_binomial__def,axiom,
% 8.64/4.91 ( binomial
% 8.64/4.91 = ( ^ [N4: nat,K3: nat] :
% 8.64/4.91 ( finite_card_set_nat
% 8.64/4.91 @ ( collect_set_nat
% 8.64/4.91 @ ^ [K7: set_nat] :
% 8.64/4.91 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N4 ) ) )
% 8.64/4.91 & ( ( finite_card_nat @ K7 )
% 8.64/4.91 = K3 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9379_enat__eSuc__iff,axiom,
% 8.64/4.91 ! [Y: nat,X: extended_enat] :
% 8.64/4.91 ( ( ( extended_enat2 @ Y )
% 8.64/4.91 = ( extended_eSuc @ X ) )
% 8.64/4.91 = ( ? [N4: nat] :
% 8.64/4.91 ( ( Y
% 8.64/4.91 = ( suc @ N4 ) )
% 8.64/4.91 & ( ( extended_enat2 @ N4 )
% 8.64/4.91 = X ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9380_eSuc__enat__iff,axiom,
% 8.64/4.91 ! [X: extended_enat,Y: nat] :
% 8.64/4.91 ( ( ( extended_eSuc @ X )
% 8.64/4.91 = ( extended_enat2 @ Y ) )
% 8.64/4.91 = ( ? [N4: nat] :
% 8.64/4.91 ( ( Y
% 8.64/4.91 = ( suc @ N4 ) )
% 8.64/4.91 & ( X
% 8.64/4.91 = ( extended_enat2 @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9381_eSuc__enat,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( extended_eSuc @ ( extended_enat2 @ N ) )
% 8.64/4.91 = ( extended_enat2 @ ( suc @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9382_mult__eSuc__right,axiom,
% 8.64/4.91 ! [M2: extended_enat,N: extended_enat] :
% 8.64/4.91 ( ( times_7803423173614009249d_enat @ M2 @ ( extended_eSuc @ N ) )
% 8.64/4.91 = ( plus_p3455044024723400733d_enat @ M2 @ ( times_7803423173614009249d_enat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9383_mult__eSuc,axiom,
% 8.64/4.91 ! [M2: extended_enat,N: extended_enat] :
% 8.64/4.91 ( ( times_7803423173614009249d_enat @ ( extended_eSuc @ M2 ) @ N )
% 8.64/4.91 = ( plus_p3455044024723400733d_enat @ N @ ( times_7803423173614009249d_enat @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9384_less__than__iff,axiom,
% 8.64/4.91 ! [X: nat,Y: nat] :
% 8.64/4.91 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 8.64/4.91 = ( ord_less_nat @ X @ Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9385_Real_Opositive_Orsp,axiom,
% 8.64/4.91 ( bNF_re728719798268516973at_o_o @ realrel
% 8.64/4.91 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [X7: nat > rat] :
% 8.64/4.91 ? [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 & ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 8.64/4.91 @ ^ [X7: nat > rat] :
% 8.64/4.91 ? [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 & ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9386_Gcd__nat__set__eq__fold,axiom,
% 8.64/4.91 ! [Xs2: list_nat] :
% 8.64/4.91 ( ( gcd_Gcd_nat @ ( set_nat2 @ Xs2 ) )
% 8.64/4.91 = ( fold_nat_nat @ gcd_gcd_nat @ Xs2 @ zero_zero_nat ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9387_times__real_Orsp,axiom,
% 8.64/4.91 ( bNF_re1962705104956426057at_rat @ realrel @ ( bNF_re895249473297799549at_rat @ realrel @ realrel )
% 8.64/4.91 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) )
% 8.64/4.91 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9388_Real_Opositive_Otransfer,axiom,
% 8.64/4.91 ( bNF_re4297313714947099218al_o_o @ pcr_real
% 8.64/4.91 @ ^ [Y5: $o,Z2: $o] : ( Y5 = Z2 )
% 8.64/4.91 @ ^ [X7: nat > rat] :
% 8.64/4.91 ? [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 & ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) )
% 8.64/4.91 @ positive2 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9389_Real_Opositive__mult,axiom,
% 8.64/4.91 ! [X: real,Y: real] :
% 8.64/4.91 ( ( positive2 @ X )
% 8.64/4.91 => ( ( positive2 @ Y )
% 8.64/4.91 => ( positive2 @ ( times_times_real @ X @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9390_times__real_Otransfer,axiom,
% 8.64/4.91 ( bNF_re4695409256820837752l_real @ pcr_real @ ( bNF_re3023117138289059399t_real @ pcr_real @ pcr_real )
% 8.64/4.91 @ ^ [X7: nat > rat,Y9: nat > rat,N4: nat] : ( times_times_rat @ ( X7 @ N4 ) @ ( Y9 @ N4 ) )
% 8.64/4.91 @ times_times_real ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9391_Real_Opositive_Orep__eq,axiom,
% 8.64/4.91 ( positive2
% 8.64/4.91 = ( ^ [X4: real] :
% 8.64/4.91 ? [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 & ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ R @ ( rep_real @ X4 @ N4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9392_Real_Opositive__def,axiom,
% 8.64/4.91 ( positive2
% 8.64/4.91 = ( map_fu1856342031159181835at_o_o @ rep_real @ id_o
% 8.64/4.91 @ ^ [X7: nat > rat] :
% 8.64/4.91 ? [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 & ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ R @ ( X7 @ N4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9393_Real_Opositive_Oabs__eq,axiom,
% 8.64/4.91 ! [X: nat > rat] :
% 8.64/4.91 ( ( realrel @ X @ X )
% 8.64/4.91 => ( ( positive2 @ ( real2 @ X ) )
% 8.64/4.91 = ( ? [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 & ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ R @ ( X @ N4 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9394_times__real_Oabs__eq,axiom,
% 8.64/4.91 ! [Xa2: nat > rat,X: nat > rat] :
% 8.64/4.91 ( ( realrel @ Xa2 @ Xa2 )
% 8.64/4.91 => ( ( realrel @ X @ X )
% 8.64/4.91 => ( ( times_times_real @ ( real2 @ Xa2 ) @ ( real2 @ X ) )
% 8.64/4.91 = ( real2
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_rat @ ( Xa2 @ N4 ) @ ( X @ N4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9395_le__Real,axiom,
% 8.64/4.91 ! [X8: nat > rat,Y7: nat > rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ( cauchy @ Y7 )
% 8.64/4.91 => ( ( ord_less_eq_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 8.64/4.91 = ( ! [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 => ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ ( plus_plus_rat @ ( Y7 @ N4 ) @ R ) ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9396_not__positive__Real,axiom,
% 8.64/4.91 ! [X8: nat > rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ( ~ ( positive2 @ ( real2 @ X8 ) ) )
% 8.64/4.91 = ( ! [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 => ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_eq_rat @ ( X8 @ N4 ) @ R ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9397_cauchy__mult,axiom,
% 8.64/4.91 ! [X8: nat > rat,Y7: nat > rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ( cauchy @ Y7 )
% 8.64/4.91 => ( cauchy
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9398_mult__Real,axiom,
% 8.64/4.91 ! [X8: nat > rat,Y7: nat > rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ( cauchy @ Y7 )
% 8.64/4.91 => ( ( times_times_real @ ( real2 @ X8 ) @ ( real2 @ Y7 ) )
% 8.64/4.91 = ( real2
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9399_cauchyD,axiom,
% 8.64/4.91 ! [X8: nat > rat,R3: rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 8.64/4.91 => ? [K: nat] :
% 8.64/4.91 ! [M3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K @ M3 )
% 8.64/4.91 => ! [N8: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K @ N8 )
% 8.64/4.91 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M3 ) @ ( X8 @ N8 ) ) ) @ R3 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9400_cauchyI,axiom,
% 8.64/4.91 ! [X8: nat > rat] :
% 8.64/4.91 ( ! [R4: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 8.64/4.91 => ? [K4: nat] :
% 8.64/4.91 ! [M: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K4 @ M )
% 8.64/4.91 => ! [N3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K4 @ N3 )
% 8.64/4.91 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X8 @ M ) @ ( X8 @ N3 ) ) ) @ R4 ) ) ) )
% 8.64/4.91 => ( cauchy @ X8 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9401_cauchy__def,axiom,
% 8.64/4.91 ( cauchy
% 8.64/4.91 = ( ^ [X7: nat > rat] :
% 8.64/4.91 ! [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 => ? [K3: nat] :
% 8.64/4.91 ! [M6: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ M6 )
% 8.64/4.91 => ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( X7 @ M6 ) @ ( X7 @ N4 ) ) ) @ R ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9402_positive__Real,axiom,
% 8.64/4.91 ! [X8: nat > rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ( positive2 @ ( real2 @ X8 ) )
% 8.64/4.91 = ( ? [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 & ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ R @ ( X8 @ N4 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9403_cauchy__not__vanishes__cases,axiom,
% 8.64/4.91 ! [X8: nat > rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ~ ( vanishes @ X8 )
% 8.64/4.91 => ? [B3: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 8.64/4.91 & ? [K: nat] :
% 8.64/4.91 ( ! [N8: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K @ N8 )
% 8.64/4.91 => ( ord_less_rat @ B3 @ ( uminus_uminus_rat @ ( X8 @ N8 ) ) ) )
% 8.64/4.91 | ! [N8: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K @ N8 )
% 8.64/4.91 => ( ord_less_rat @ B3 @ ( X8 @ N8 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9404_cauchy__not__vanishes,axiom,
% 8.64/4.91 ! [X8: nat > rat] :
% 8.64/4.91 ( ( cauchy @ X8 )
% 8.64/4.91 => ( ~ ( vanishes @ X8 )
% 8.64/4.91 => ? [B3: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ B3 )
% 8.64/4.91 & ? [K: nat] :
% 8.64/4.91 ! [N8: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K @ N8 )
% 8.64/4.91 => ( ord_less_rat @ B3 @ ( abs_abs_rat @ ( X8 @ N8 ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9405_vanishesD,axiom,
% 8.64/4.91 ! [X8: nat > rat,R3: rat] :
% 8.64/4.91 ( ( vanishes @ X8 )
% 8.64/4.91 => ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 8.64/4.91 => ? [K: nat] :
% 8.64/4.91 ! [N8: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K @ N8 )
% 8.64/4.91 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N8 ) ) @ R3 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9406_vanishesI,axiom,
% 8.64/4.91 ! [X8: nat > rat] :
% 8.64/4.91 ( ! [R4: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R4 )
% 8.64/4.91 => ? [K4: nat] :
% 8.64/4.91 ! [N3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K4 @ N3 )
% 8.64/4.91 => ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ R4 ) ) )
% 8.64/4.91 => ( vanishes @ X8 ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9407_vanishes__def,axiom,
% 8.64/4.91 ( vanishes
% 8.64/4.91 = ( ^ [X7: nat > rat] :
% 8.64/4.91 ! [R: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ R )
% 8.64/4.91 => ? [K3: nat] :
% 8.64/4.91 ! [N4: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ K3 @ N4 )
% 8.64/4.91 => ( ord_less_rat @ ( abs_abs_rat @ ( X7 @ N4 ) ) @ R ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9408_vanishes__mult__bounded,axiom,
% 8.64/4.91 ! [X8: nat > rat,Y7: nat > rat] :
% 8.64/4.91 ( ? [A6: rat] :
% 8.64/4.91 ( ( ord_less_rat @ zero_zero_rat @ A6 )
% 8.64/4.91 & ! [N3: nat] : ( ord_less_rat @ ( abs_abs_rat @ ( X8 @ N3 ) ) @ A6 ) )
% 8.64/4.91 => ( ( vanishes @ Y7 )
% 8.64/4.91 => ( vanishes
% 8.64/4.91 @ ^ [N4: nat] : ( times_times_rat @ ( X8 @ N4 ) @ ( Y7 @ N4 ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9409_surj__int__decode,axiom,
% 8.64/4.91 ( ( image_nat_int @ nat_int_decode @ top_top_set_nat )
% 8.64/4.91 = top_top_set_int ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9410_bij__int__decode,axiom,
% 8.64/4.91 bij_betw_nat_int @ nat_int_decode @ top_top_set_nat @ top_top_set_int ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9411_inj__int__decode,axiom,
% 8.64/4.91 ! [A4: set_nat] : ( inj_on_nat_int @ nat_int_decode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9412_int__decode__eq,axiom,
% 8.64/4.91 ! [X: nat,Y: nat] :
% 8.64/4.91 ( ( ( nat_int_decode @ X )
% 8.64/4.91 = ( nat_int_decode @ Y ) )
% 8.64/4.91 = ( X = Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9413_nat__to__rat__surj__def,axiom,
% 8.64/4.91 ( nat_to_rat_surj
% 8.64/4.91 = ( ^ [N4: nat] :
% 8.64/4.91 ( produc6207742614233964070at_rat
% 8.64/4.91 @ ^ [A5: nat,B4: nat] : ( fract @ ( nat_int_decode @ A5 ) @ ( nat_int_decode @ B4 ) )
% 8.64/4.91 @ ( nat_prod_decode @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9414_bij__int__encode,axiom,
% 8.64/4.91 bij_betw_int_nat @ nat_int_encode @ top_top_set_int @ top_top_set_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9415_int__encode__inverse,axiom,
% 8.64/4.91 ! [X: int] :
% 8.64/4.91 ( ( nat_int_decode @ ( nat_int_encode @ X ) )
% 8.64/4.91 = X ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9416_int__decode__inverse,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( nat_int_encode @ ( nat_int_decode @ N ) )
% 8.64/4.91 = N ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9417_inj__int__encode,axiom,
% 8.64/4.91 ! [A4: set_int] : ( inj_on_int_nat @ nat_int_encode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9418_int__encode__eq,axiom,
% 8.64/4.91 ! [X: int,Y: int] :
% 8.64/4.91 ( ( ( nat_int_encode @ X )
% 8.64/4.91 = ( nat_int_encode @ Y ) )
% 8.64/4.91 = ( X = Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9419_surj__int__encode,axiom,
% 8.64/4.91 ( ( image_int_nat @ nat_int_encode @ top_top_set_int )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9420_linear__scale__real,axiom,
% 8.64/4.91 ! [F2: real > real,R3: real,B: real] :
% 8.64/4.91 ( ( real_V4572627801940501177l_real @ F2 )
% 8.64/4.91 => ( ( F2 @ ( times_times_real @ R3 @ B ) )
% 8.64/4.91 = ( times_times_real @ R3 @ ( F2 @ B ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9421_real__linearD,axiom,
% 8.64/4.91 ! [F2: real > real] :
% 8.64/4.91 ( ( real_V4572627801940501177l_real @ F2 )
% 8.64/4.91 => ~ ! [C: real] :
% 8.64/4.91 ( F2
% 8.64/4.91 != ( times_times_real @ C ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9422_natLeq__Partial__order,axiom,
% 8.64/4.91 order_5251275573222108571on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9423_natLeq__Preorder,axiom,
% 8.64/4.91 order_4861654808422542329on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9424_less__eq__int__def,axiom,
% 8.64/4.91 ( ord_less_eq_int
% 8.64/4.91 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 8.64/4.91 @ ( produc8739625826339149834_nat_o
% 8.64/4.91 @ ^ [X4: nat,Y4: nat] :
% 8.64/4.91 ( produc6081775807080527818_nat_o
% 8.64/4.91 @ ^ [U2: nat,V3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V3 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9425_int__encode__def,axiom,
% 8.64/4.91 ( nat_int_encode
% 8.64/4.91 = ( ^ [I: int] : ( nat_sum_encode @ ( if_Sum_sum_nat_nat @ ( ord_less_eq_int @ zero_zero_int @ I ) @ ( sum_Inl_nat_nat @ ( nat2 @ I ) ) @ ( sum_Inr_nat_nat @ ( nat2 @ ( minus_minus_int @ ( uminus_uminus_int @ I ) @ one_one_int ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9426_surj__sum__encode,axiom,
% 8.64/4.91 ( ( image_1320371278474632150at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat )
% 8.64/4.91 = top_top_set_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9427_inj__sum__encode,axiom,
% 8.64/4.91 ! [A4: set_Sum_sum_nat_nat] : ( inj_on6343450744447823682at_nat @ nat_sum_encode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9428_sum__encode__eq,axiom,
% 8.64/4.91 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 8.64/4.91 ( ( ( nat_sum_encode @ X )
% 8.64/4.91 = ( nat_sum_encode @ Y ) )
% 8.64/4.91 = ( X = Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9429_bij__sum__encode,axiom,
% 8.64/4.91 bij_be5432664580149595207at_nat @ nat_sum_encode @ top_to6661820994512907621at_nat @ top_top_set_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9430_le__sum__encode__Inl,axiom,
% 8.64/4.91 ! [X: nat,Y: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ X @ Y )
% 8.64/4.91 => ( ord_less_eq_nat @ X @ ( nat_sum_encode @ ( sum_Inl_nat_nat @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9431_le__sum__encode__Inr,axiom,
% 8.64/4.91 ! [X: nat,Y: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ X @ Y )
% 8.64/4.91 => ( ord_less_eq_nat @ X @ ( nat_sum_encode @ ( sum_Inr_nat_nat @ Y ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9432_sum__decode__def,axiom,
% 8.64/4.91 ( nat_sum_decode
% 8.64/4.91 = ( ^ [N4: nat] : ( if_Sum_sum_nat_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N4 ) @ ( sum_Inl_nat_nat @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( sum_Inr_nat_nat @ ( divide_divide_nat @ N4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9433_sum__encode__inverse,axiom,
% 8.64/4.91 ! [X: sum_sum_nat_nat] :
% 8.64/4.91 ( ( nat_sum_decode @ ( nat_sum_encode @ X ) )
% 8.64/4.91 = X ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9434_sum__decode__inverse,axiom,
% 8.64/4.91 ! [N: nat] :
% 8.64/4.91 ( ( nat_sum_encode @ ( nat_sum_decode @ N ) )
% 8.64/4.91 = N ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9435_bij__sum__decode,axiom,
% 8.64/4.91 bij_be4790990086886966983at_nat @ nat_sum_decode @ top_top_set_nat @ top_to6661820994512907621at_nat ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9436_sum__decode__eq,axiom,
% 8.64/4.91 ! [X: nat,Y: nat] :
% 8.64/4.91 ( ( ( nat_sum_decode @ X )
% 8.64/4.91 = ( nat_sum_decode @ Y ) )
% 8.64/4.91 = ( X = Y ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9437_inj__sum__decode,axiom,
% 8.64/4.91 ! [A4: set_nat] : ( inj_on5701776251185195458at_nat @ nat_sum_decode @ A4 ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9438_surj__sum__decode,axiom,
% 8.64/4.91 ( ( image_678696785212003926at_nat @ nat_sum_decode @ top_top_set_nat )
% 8.64/4.91 = top_to6661820994512907621at_nat ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9439_nth__item_Opinduct,axiom,
% 8.64/4.91 ! [A0: nat,P2: nat > $o] :
% 8.64/4.91 ( ( accp_nat @ nth_item_rel @ A0 )
% 8.64/4.91 => ( ( ( accp_nat @ nth_item_rel @ zero_zero_nat )
% 8.64/4.91 => ( P2 @ zero_zero_nat ) )
% 8.64/4.91 => ( ! [N3: nat] :
% 8.64/4.91 ( ( accp_nat @ nth_item_rel @ ( suc @ N3 ) )
% 8.64/4.91 => ( ! [A6: nat,Aa: nat] :
% 8.64/4.91 ( ( ( nat_sum_decode @ N3 )
% 8.64/4.91 = ( sum_Inl_nat_nat @ A6 ) )
% 8.64/4.91 => ( ( ( nat_sum_decode @ A6 )
% 8.64/4.91 = ( sum_Inl_nat_nat @ Aa ) )
% 8.64/4.91 => ( P2 @ Aa ) ) )
% 8.64/4.91 => ( ! [A6: nat,B6: nat] :
% 8.64/4.91 ( ( ( nat_sum_decode @ N3 )
% 8.64/4.91 = ( sum_Inl_nat_nat @ A6 ) )
% 8.64/4.91 => ( ( ( nat_sum_decode @ A6 )
% 8.64/4.91 = ( sum_Inr_nat_nat @ B6 ) )
% 8.64/4.91 => ( P2 @ B6 ) ) )
% 8.64/4.91 => ( ! [B6: nat,Ba: nat,X5: nat,Y6: nat] :
% 8.64/4.91 ( ( ( nat_sum_decode @ N3 )
% 8.64/4.91 = ( sum_Inr_nat_nat @ B6 ) )
% 8.64/4.91 => ( ( ( nat_sum_decode @ B6 )
% 8.64/4.91 = ( sum_Inr_nat_nat @ Ba ) )
% 8.64/4.91 => ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 8.64/4.91 = ( nat_prod_decode @ Ba ) )
% 8.64/4.91 => ( P2 @ X5 ) ) ) )
% 8.64/4.91 => ( ! [B6: nat,Ba: nat,X5: nat,Y6: nat] :
% 8.64/4.91 ( ( ( nat_sum_decode @ N3 )
% 8.64/4.91 = ( sum_Inr_nat_nat @ B6 ) )
% 8.64/4.91 => ( ( ( nat_sum_decode @ B6 )
% 8.64/4.91 = ( sum_Inr_nat_nat @ Ba ) )
% 8.64/4.91 => ( ( ( product_Pair_nat_nat @ X5 @ Y6 )
% 8.64/4.91 = ( nat_prod_decode @ Ba ) )
% 8.64/4.91 => ( P2 @ Y6 ) ) ) )
% 8.64/4.91 => ( P2 @ ( suc @ N3 ) ) ) ) ) ) )
% 8.64/4.91 => ( P2 @ A0 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9440_int__decode__def,axiom,
% 8.64/4.91 ( nat_int_decode
% 8.64/4.91 = ( ^ [N4: nat] :
% 8.64/4.91 ( sum_ca7763040182479039464nt_nat @ semiri1314217659103216013at_int
% 8.64/4.91 @ ^ [B4: nat] : ( minus_minus_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ B4 ) ) @ one_one_int )
% 8.64/4.91 @ ( nat_sum_decode @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9441_sum__encode__def,axiom,
% 8.64/4.91 ( nat_sum_encode
% 8.64/4.91 = ( sum_ca6763686470577984908at_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 8.64/4.91 @ ^ [B4: nat] : ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9442_enat__def,axiom,
% 8.64/4.91 ( extended_enat2
% 8.64/4.91 = ( ^ [N4: nat] : ( extended_Abs_enat @ ( some_nat @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9443_Bseq__monoseq__convergent_H__dec,axiom,
% 8.64/4.91 ! [F2: nat > real,M5: nat] :
% 8.64/4.91 ( ( bfun_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( F2 @ ( plus_plus_nat @ N4 @ M5 ) )
% 8.64/4.91 @ at_top_nat )
% 8.64/4.91 => ( ! [M: nat,N3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ M5 @ M )
% 8.64/4.91 => ( ( ord_less_eq_nat @ M @ N3 )
% 8.64/4.91 => ( ord_less_eq_real @ ( F2 @ N3 ) @ ( F2 @ M ) ) ) )
% 8.64/4.91 => ( topolo7531315842566124627t_real @ F2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9444_Bseq__monoseq__convergent_H__inc,axiom,
% 8.64/4.91 ! [F2: nat > real,M5: nat] :
% 8.64/4.91 ( ( bfun_nat_real
% 8.64/4.91 @ ^ [N4: nat] : ( F2 @ ( plus_plus_nat @ N4 @ M5 ) )
% 8.64/4.91 @ at_top_nat )
% 8.64/4.91 => ( ! [M: nat,N3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ M5 @ M )
% 8.64/4.91 => ( ( ord_less_eq_nat @ M @ N3 )
% 8.64/4.91 => ( ord_less_eq_real @ ( F2 @ M ) @ ( F2 @ N3 ) ) ) )
% 8.64/4.91 => ( topolo7531315842566124627t_real @ F2 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9445_Bseq__mono__convergent,axiom,
% 8.64/4.91 ! [X8: nat > real] :
% 8.64/4.91 ( ( bfun_nat_real @ X8 @ at_top_nat )
% 8.64/4.91 => ( ! [M: nat,N3: nat] :
% 8.64/4.91 ( ( ord_less_eq_nat @ M @ N3 )
% 8.64/4.91 => ( ord_less_eq_real @ ( X8 @ M ) @ ( X8 @ N3 ) ) )
% 8.64/4.91 => ( topolo7531315842566124627t_real @ X8 ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9446_lcm__altdef__int,axiom,
% 8.64/4.91 ( gcd_lcm_int
% 8.64/4.91 = ( ^ [A5: int,B4: int] : ( divide_divide_int @ ( times_times_int @ ( abs_abs_int @ A5 ) @ ( abs_abs_int @ B4 ) ) @ ( gcd_gcd_int @ A5 @ B4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9447_prod__gcd__lcm__int,axiom,
% 8.64/4.91 ! [M2: int,N: int] :
% 8.64/4.91 ( ( times_times_int @ ( abs_abs_int @ M2 ) @ ( abs_abs_int @ N ) )
% 8.64/4.91 = ( times_times_int @ ( gcd_gcd_int @ M2 @ N ) @ ( gcd_lcm_int @ M2 @ N ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9448_lcm__0__iff__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ( gcd_lcm_nat @ M2 @ N )
% 8.64/4.91 = zero_zero_nat )
% 8.64/4.91 = ( ( M2 = zero_zero_nat )
% 8.64/4.91 | ( N = zero_zero_nat ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9449_lcm__1__iff__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ( gcd_lcm_nat @ M2 @ N )
% 8.64/4.91 = ( suc @ zero_zero_nat ) )
% 8.64/4.91 = ( ( M2
% 8.64/4.91 = ( suc @ zero_zero_nat ) )
% 8.64/4.91 & ( N
% 8.64/4.91 = ( suc @ zero_zero_nat ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9450_prod__gcd__lcm__nat,axiom,
% 8.64/4.91 ( times_times_nat
% 8.64/4.91 = ( ^ [M6: nat,N4: nat] : ( times_times_nat @ ( gcd_gcd_nat @ M6 @ N4 ) @ ( gcd_lcm_nat @ M6 @ N4 ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9451_lcm__pos__nat,axiom,
% 8.64/4.91 ! [M2: nat,N: nat] :
% 8.64/4.91 ( ( ord_less_nat @ zero_zero_nat @ M2 )
% 8.64/4.91 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.91 => ( ord_less_nat @ zero_zero_nat @ ( gcd_lcm_nat @ M2 @ N ) ) ) ) ).
% 8.64/4.91
% 8.64/4.91 thf(fact_9452_lcm__code__integer,axiom,
% 8.64/4.91 ( gcd_lcm_Code_integer
% 8.64/4.91 = ( ^ [A5: code_integer,B4: code_integer] : ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A5 ) @ ( abs_abs_Code_integer @ B4 ) ) @ ( gcd_gcd_Code_integer @ A5 @ B4 ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9453_lcm__nat__def,axiom,
% 8.64/4.92 ( gcd_lcm_nat
% 8.64/4.92 = ( ^ [X4: nat,Y4: nat] : ( divide_divide_nat @ ( times_times_nat @ X4 @ Y4 ) @ ( gcd_gcd_nat @ X4 @ Y4 ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9454_Lcm__eq__Max__nat,axiom,
% 8.64/4.92 ! [M5: set_nat] :
% 8.64/4.92 ( ( finite_finite_nat @ M5 )
% 8.64/4.92 => ( ( M5 != bot_bot_set_nat )
% 8.64/4.92 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 8.64/4.92 => ( ! [M: nat,N3: nat] :
% 8.64/4.92 ( ( member_nat @ M @ M5 )
% 8.64/4.92 => ( ( member_nat @ N3 @ M5 )
% 8.64/4.92 => ( member_nat @ ( gcd_lcm_nat @ M @ N3 ) @ M5 ) ) )
% 8.64/4.92 => ( ( gcd_Lcm_nat @ M5 )
% 8.64/4.92 = ( lattic8265883725875713057ax_nat @ M5 ) ) ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9455_Lcm__eq__0__I__nat,axiom,
% 8.64/4.92 ! [A4: set_nat] :
% 8.64/4.92 ( ( member_nat @ zero_zero_nat @ A4 )
% 8.64/4.92 => ( ( gcd_Lcm_nat @ A4 )
% 8.64/4.92 = zero_zero_nat ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9456_Lcm__0__iff__nat,axiom,
% 8.64/4.92 ! [A4: set_nat] :
% 8.64/4.92 ( ( finite_finite_nat @ A4 )
% 8.64/4.92 => ( ( ( gcd_Lcm_nat @ A4 )
% 8.64/4.92 = zero_zero_nat )
% 8.64/4.92 = ( member_nat @ zero_zero_nat @ A4 ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9457_Lcm__nat__infinite,axiom,
% 8.64/4.92 ! [M5: set_nat] :
% 8.64/4.92 ( ~ ( finite_finite_nat @ M5 )
% 8.64/4.92 => ( ( gcd_Lcm_nat @ M5 )
% 8.64/4.92 = zero_zero_nat ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9458_Lcm__nat__def,axiom,
% 8.64/4.92 ( gcd_Lcm_nat
% 8.64/4.92 = ( ^ [M9: set_nat] : ( if_nat @ ( finite_finite_nat @ M9 ) @ ( lattic7826324295020591184_F_nat @ gcd_lcm_nat @ one_one_nat @ M9 ) @ zero_zero_nat ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9459_unit__factor__simps_I1_J,axiom,
% 8.64/4.92 ( ( unit_f2748546683901255202or_nat @ zero_zero_nat )
% 8.64/4.92 = zero_zero_nat ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9460_unit__factor__simps_I2_J,axiom,
% 8.64/4.92 ! [N: nat] :
% 8.64/4.92 ( ( unit_f2748546683901255202or_nat @ ( suc @ N ) )
% 8.64/4.92 = one_one_nat ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9461_unit__factor__nat__def,axiom,
% 8.64/4.92 ( unit_f2748546683901255202or_nat
% 8.64/4.92 = ( ^ [N4: nat] : ( if_nat @ ( N4 = zero_zero_nat ) @ zero_zero_nat @ one_one_nat ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9462_times__num__def,axiom,
% 8.64/4.92 ( times_times_num
% 8.64/4.92 = ( ^ [M6: num,N4: num] : ( num_of_nat @ ( times_times_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9463_nat__of__num__code_I2_J,axiom,
% 8.64/4.92 ! [N: num] :
% 8.64/4.92 ( ( nat_of_num @ ( bit0 @ N ) )
% 8.64/4.92 = ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9464_less__eq__num__def,axiom,
% 8.64/4.92 ( ord_less_eq_num
% 8.64/4.92 = ( ^ [M6: num,N4: num] : ( ord_less_eq_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9465_less__num__def,axiom,
% 8.64/4.92 ( ord_less_num
% 8.64/4.92 = ( ^ [M6: num,N4: num] : ( ord_less_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9466_nat__of__num__inc,axiom,
% 8.64/4.92 ! [X: num] :
% 8.64/4.92 ( ( nat_of_num @ ( inc @ X ) )
% 8.64/4.92 = ( suc @ ( nat_of_num @ X ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9467_nat__of__num__mult,axiom,
% 8.64/4.92 ! [X: num,Y: num] :
% 8.64/4.92 ( ( nat_of_num @ ( times_times_num @ X @ Y ) )
% 8.64/4.92 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9468_nat__of__num__numeral,axiom,
% 8.64/4.92 nat_of_num = numeral_numeral_nat ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9469_num__eq__iff,axiom,
% 8.64/4.92 ( ( ^ [Y5: num,Z2: num] : ( Y5 = Z2 ) )
% 8.64/4.92 = ( ^ [X4: num,Y4: num] :
% 8.64/4.92 ( ( nat_of_num @ X4 )
% 8.64/4.92 = ( nat_of_num @ Y4 ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9470_nat__of__num__inverse,axiom,
% 8.64/4.92 ! [X: num] :
% 8.64/4.92 ( ( num_of_nat @ ( nat_of_num @ X ) )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9471_nat__of__num_Osimps_I2_J,axiom,
% 8.64/4.92 ! [X: num] :
% 8.64/4.92 ( ( nat_of_num @ ( bit0 @ X ) )
% 8.64/4.92 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9472_nat__of__num__pos,axiom,
% 8.64/4.92 ! [X: num] : ( ord_less_nat @ zero_zero_nat @ ( nat_of_num @ X ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9473_nat__of__num__neq__0,axiom,
% 8.64/4.92 ! [X: num] :
% 8.64/4.92 ( ( nat_of_num @ X )
% 8.64/4.92 != zero_zero_nat ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9474_nat__of__num__code_I1_J,axiom,
% 8.64/4.92 ( ( nat_of_num @ one )
% 8.64/4.92 = one_one_nat ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9475_nat__of__num__add,axiom,
% 8.64/4.92 ! [X: num,Y: num] :
% 8.64/4.92 ( ( nat_of_num @ ( plus_plus_num @ X @ Y ) )
% 8.64/4.92 = ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ Y ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9476_nat__of__num__sqr,axiom,
% 8.64/4.92 ! [X: num] :
% 8.64/4.92 ( ( nat_of_num @ ( sqr @ X ) )
% 8.64/4.92 = ( times_times_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9477_nat__of__num_Osimps_I1_J,axiom,
% 8.64/4.92 ( ( nat_of_num @ one )
% 8.64/4.92 = ( suc @ zero_zero_nat ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9478_nat__of__num_Osimps_I3_J,axiom,
% 8.64/4.92 ! [X: num] :
% 8.64/4.92 ( ( nat_of_num @ ( bit1 @ X ) )
% 8.64/4.92 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ X ) @ ( nat_of_num @ X ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9479_num__of__nat__inverse,axiom,
% 8.64/4.92 ! [N: nat] :
% 8.64/4.92 ( ( ord_less_nat @ zero_zero_nat @ N )
% 8.64/4.92 => ( ( nat_of_num @ ( num_of_nat @ N ) )
% 8.64/4.92 = N ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9480_nat__of__num__code_I3_J,axiom,
% 8.64/4.92 ! [N: num] :
% 8.64/4.92 ( ( nat_of_num @ ( bit1 @ N ) )
% 8.64/4.92 = ( suc @ ( plus_plus_nat @ ( nat_of_num @ N ) @ ( nat_of_num @ N ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9481_plus__num__def,axiom,
% 8.64/4.92 ( plus_plus_num
% 8.64/4.92 = ( ^ [M6: num,N4: num] : ( num_of_nat @ ( plus_plus_nat @ ( nat_of_num @ M6 ) @ ( nat_of_num @ N4 ) ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9482_natLeq__trans,axiom,
% 8.64/4.92 trans_nat @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9483_natLeq__antisym,axiom,
% 8.64/4.92 antisym_nat @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9484_VEBT__internal_Olesseq_Oelims_I3_J,axiom,
% 8.64/4.92 ! [X: option_nat,Xa2: option_nat] :
% 8.64/4.92 ( ~ ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 8.64/4.92 => ~ ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9485_VEBT__internal_Olesseq_Oelims_I2_J,axiom,
% 8.64/4.92 ! [X: option_nat,Xa2: option_nat] :
% 8.64/4.92 ( ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 8.64/4.92 => ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9486_VEBT__internal_Olesseq_Oelims_I1_J,axiom,
% 8.64/4.92 ! [X: option_nat,Xa2: option_nat,Y: $o] :
% 8.64/4.92 ( ( ( vEBT_VEBT_lesseq @ X @ Xa2 )
% 8.64/4.92 = Y )
% 8.64/4.92 => ( Y
% 8.64/4.92 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat @ X @ Xa2 ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9487_VEBT__internal_Olesseq_Osimps,axiom,
% 8.64/4.92 ( vEBT_VEBT_lesseq
% 8.64/4.92 = ( vEBT_V2881884560877996034ft_nat @ ord_less_eq_nat ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9488_integer__of__nat__0,axiom,
% 8.64/4.92 ( ( code_integer_of_nat @ zero_zero_nat )
% 8.64/4.92 = zero_z3403309356797280102nteger ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9489_natural__decr,axiom,
% 8.64/4.92 ! [N: code_natural] :
% 8.64/4.92 ( ( N != zero_z2226904508553997617atural )
% 8.64/4.92 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9490_times__natural_Orep__eq,axiom,
% 8.64/4.92 ! [X: code_natural,Xa2: code_natural] :
% 8.64/4.92 ( ( code_nat_of_natural @ ( times_2397367101498566445atural @ X @ Xa2 ) )
% 8.64/4.92 = ( times_times_nat @ ( code_nat_of_natural @ X ) @ ( code_nat_of_natural @ Xa2 ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9491_zero__natural_Orep__eq,axiom,
% 8.64/4.92 ( ( code_nat_of_natural @ zero_z2226904508553997617atural )
% 8.64/4.92 = zero_zero_nat ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9492_less__eq__natural_Orep__eq,axiom,
% 8.64/4.92 ( ord_le1926595141338095240atural
% 8.64/4.92 = ( ^ [X4: code_natural,Xa3: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X4 ) @ ( code_nat_of_natural @ Xa3 ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9493_next_Osimps,axiom,
% 8.64/4.92 ! [V2: code_natural,W2: code_natural] :
% 8.64/4.92 ( ( next @ ( produc3574140220909816553atural @ V2 @ W2 ) )
% 8.64/4.92 = ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( plus_p4538020629002901425atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ one_one_Code_natural ) ) @ one_one_Code_natural ) @ ( produc3574140220909816553atural @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ V2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( minus_shift @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ W2 @ ( numera5444537566228673987atural @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( numera5444537566228673987atural @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9494_Random_Orange__def,axiom,
% 8.64/4.92 ( range
% 8.64/4.92 = ( ^ [K3: code_natural] :
% 8.64/4.92 ( produc5538323210962509403atural
% 8.64/4.92 @ ( iterat8892046348760725948atural @ ( log @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ K3 )
% 8.64/4.92 @ ^ [L2: code_natural] :
% 8.64/4.92 ( produc5538323210962509403atural @ next
% 8.64/4.92 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V3 @ ( times_2397367101498566445atural @ L2 @ ( numera5444537566228673987atural @ ( bit1 @ ( bit0 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 8.64/4.92 @ one_one_Code_natural )
% 8.64/4.92 @ ^ [V3: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V3 @ K3 ) ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9495_Suc_Orep__eq,axiom,
% 8.64/4.92 ! [X: code_natural] :
% 8.64/4.92 ( ( code_nat_of_natural @ ( code_Suc @ X ) )
% 8.64/4.92 = ( suc @ ( code_nat_of_natural @ X ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9496_Suc_Oabs__eq,axiom,
% 8.64/4.92 ! [X: nat] :
% 8.64/4.92 ( ( code_Suc @ ( code_natural_of_nat @ X ) )
% 8.64/4.92 = ( code_natural_of_nat @ ( suc @ X ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9497_less__eq__natural_Oabs__eq,axiom,
% 8.64/4.92 ! [Xa2: nat,X: nat] :
% 8.64/4.92 ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa2 ) @ ( code_natural_of_nat @ X ) )
% 8.64/4.92 = ( ord_less_eq_nat @ Xa2 @ X ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9498_times__natural_Oabs__eq,axiom,
% 8.64/4.92 ! [Xa2: nat,X: nat] :
% 8.64/4.92 ( ( times_2397367101498566445atural @ ( code_natural_of_nat @ Xa2 ) @ ( code_natural_of_nat @ X ) )
% 8.64/4.92 = ( code_natural_of_nat @ ( times_times_nat @ Xa2 @ X ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9499_less__nat__rel,axiom,
% 8.64/4.92 ( ord_less_nat
% 8.64/4.92 = ( transi2163837189807498211lp_nat
% 8.64/4.92 @ ^ [M6: nat,N4: nat] :
% 8.64/4.92 ( N4
% 8.64/4.92 = ( suc @ M6 ) ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9500_zero__natural__def,axiom,
% 8.64/4.92 ( zero_z2226904508553997617atural
% 8.64/4.92 = ( code_natural_of_nat @ zero_zero_nat ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9501_Code__Numeral_OSuc__def,axiom,
% 8.64/4.92 ( code_Suc
% 8.64/4.92 = ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat @ suc ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9502_times__natural__def,axiom,
% 8.64/4.92 ( times_2397367101498566445atural
% 8.64/4.92 = ( map_fu6549440983881763648atural @ code_nat_of_natural @ ( map_fu1239815594074539274atural @ code_nat_of_natural @ code_natural_of_nat ) @ times_times_nat ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9503_typerep_Osize__neq,axiom,
% 8.64/4.92 ! [X: typerep] :
% 8.64/4.92 ( ( size_size_typerep @ X )
% 8.64/4.92 != zero_zero_nat ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9504_typerep_Osize_I2_J,axiom,
% 8.64/4.92 ! [X1: literal,X2: list_typerep] :
% 8.64/4.92 ( ( size_size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 8.64/4.92 = ( plus_plus_nat @ ( size_list_typerep @ size_size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9505_typerep_Osize__gen,axiom,
% 8.64/4.92 ! [X1: literal,X2: list_typerep] :
% 8.64/4.92 ( ( size_typerep @ ( typerep2 @ X1 @ X2 ) )
% 8.64/4.92 = ( plus_plus_nat @ ( size_list_typerep @ size_typerep @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9506_max__nat_Osemilattice__neutr__axioms,axiom,
% 8.64/4.92 semila9081495762789891438tr_nat @ ord_max_nat @ zero_zero_nat ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9507_gcd__nat_Osemilattice__neutr__axioms,axiom,
% 8.64/4.92 semila9081495762789891438tr_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9508_real__times__code,axiom,
% 8.64/4.92 ! [X: rat,Y: rat] :
% 8.64/4.92 ( ( times_times_real @ ( ratreal @ X ) @ ( ratreal @ Y ) )
% 8.64/4.92 = ( ratreal @ ( times_times_rat @ X @ Y ) ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9509_max__nat_Omonoid__axioms,axiom,
% 8.64/4.92 monoid_nat @ ord_max_nat @ zero_zero_nat ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9510_gcd__nat_Omonoid__axioms,axiom,
% 8.64/4.92 monoid_nat @ gcd_gcd_nat @ zero_zero_nat ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9511_natLeq__Card__order,axiom,
% 8.64/4.92 bNF_Ca1281551314933786834on_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) @ bNF_Ca8665028551170535155natLeq ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9512_card__of__nat,axiom,
% 8.64/4.92 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ top_top_set_nat ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 8.64/4.92
% 8.64/4.92 thf(fact_9513_card__of__Field__natLeq,axiom,
% 8.64/4.92 member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( bNF_Ca3793111618940312692of_nat @ ( field_nat @ bNF_Ca8665028551170535155natLeq ) ) @ bNF_Ca8665028551170535155natLeq ) @ bNF_We5258908940166488438at_nat ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 8.64/4.92 ! [X: int,Y: int] :
% 8.64/4.92 ( ( if_int @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 8.64/4.92 ! [X: int,Y: int] :
% 8.64/4.92 ( ( if_int @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 8.64/4.92 ! [X: nat,Y: nat] :
% 8.64/4.92 ( ( if_nat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 8.64/4.92 ! [X: nat,Y: nat] :
% 8.64/4.92 ( ( if_nat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 8.64/4.92 ! [X: num,Y: num] :
% 8.64/4.92 ( ( if_num @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 8.64/4.92 ! [X: num,Y: num] :
% 8.64/4.92 ( ( if_num @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 8.64/4.92 ! [X: rat,Y: rat] :
% 8.64/4.92 ( ( if_rat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 8.64/4.92 ! [X: rat,Y: rat] :
% 8.64/4.92 ( ( if_rat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 8.64/4.92 ! [X: real,Y: real] :
% 8.64/4.92 ( ( if_real @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 8.64/4.92 ! [X: real,Y: real] :
% 8.64/4.92 ( ( if_real @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 8.64/4.92 ! [X: complex,Y: complex] :
% 8.64/4.92 ( ( if_complex @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 8.64/4.92 ! [X: complex,Y: complex] :
% 8.64/4.92 ( ( if_complex @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 8.64/4.92 ! [X: extended_enat,Y: extended_enat] :
% 8.64/4.92 ( ( if_Extended_enat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 8.64/4.92 ! [X: extended_enat,Y: extended_enat] :
% 8.64/4.92 ( ( if_Extended_enat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.64/4.92 ! [X: code_integer,Y: code_integer] :
% 8.64/4.92 ( ( if_Code_integer @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 8.64/4.92 ! [X: code_integer,Y: code_integer] :
% 8.64/4.92 ( ( if_Code_integer @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: set_nat,Y: set_nat] :
% 8.64/4.92 ( ( if_set_nat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: set_nat,Y: set_nat] :
% 8.64/4.92 ( ( if_set_nat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 8.64/4.92 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 8.64/4.92 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 8.64/4.92 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 8.64/4.92 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: list_nat,Y: list_nat] :
% 8.64/4.92 ( ( if_list_nat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: list_nat,Y: list_nat] :
% 8.64/4.92 ( ( if_list_nat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: option_nat,Y: option_nat] :
% 8.64/4.92 ( ( if_option_nat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: option_nat,Y: option_nat] :
% 8.64/4.92 ( ( if_option_nat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.64/4.92 ! [X: option_num,Y: option_num] :
% 8.64/4.92 ( ( if_option_num @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 8.64/4.92 ! [X: option_num,Y: option_num] :
% 8.64/4.92 ( ( if_option_num @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 8.64/4.92 ( ( if_Sum_sum_nat_nat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Sum____Type__Osum_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: sum_sum_nat_nat,Y: sum_sum_nat_nat] :
% 8.64/4.92 ( ( if_Sum_sum_nat_nat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.64/4.92 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 8.64/4.92 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 8.64/4.92 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 8.64/4.92 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.64/4.92 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 8.64/4.92 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 8.64/4.92 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.64/4.92 ! [P2: $o] :
% 8.64/4.92 ( ( P2 = $true )
% 8.64/4.92 | ( P2 = $false ) ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.64/4.92 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.64/4.92 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 8.64/4.92 = Y ) ).
% 8.64/4.92
% 8.64/4.92 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 8.64/4.92 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 8.64/4.92 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 8.64/4.92 = X ) ).
% 8.64/4.92
% 8.64/4.92 thf(conj_0,conjecture,
% 8.64/4.92 ( info
% 8.64/4.92 = ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) ) ).
% 8.64/4.92 ------------------------
% 9.12/5.44 % (14822)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/4Mi)
% 9.12/5.44 % (14821)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/183Mi)
% 9.12/5.44 % (14823)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/27Mi)
% 9.12/5.44 % (14824)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/2Mi)
% 9.12/5.44 % (14825)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/2Mi)
% 9.12/5.44 % (14826)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/275Mi)
% 9.12/5.44 % (14827)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/18Mi)
% 9.12/5.44 % (14824)Instruction limit reached!
% 9.12/5.44 % (14824)------------------------------
% 9.12/5.44 % (14824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.44 % (14824)Termination reason: Unknown
% 9.12/5.44 % (14824)Termination phase: shuffling
% 9.12/5.44
% 9.12/5.44 % (14824)Memory used [KB]: 13176
% 9.12/5.44 % (14824)Time elapsed: 0.003 s
% 9.12/5.44 % (14824)Instructions burned: 2 (million)
% 9.12/5.44 % (14824)------------------------------
% 9.12/5.44 % (14824)------------------------------
% 9.12/5.44 % (14825)Instruction limit reached!
% 9.12/5.44 % (14825)------------------------------
% 9.12/5.44 % (14825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.44 % (14825)Termination reason: Unknown
% 9.12/5.44 % (14825)Termination phase: shuffling
% 9.12/5.44
% 9.12/5.44 % (14825)Memory used [KB]: 13176
% 9.12/5.44 % (14825)Time elapsed: 0.003 s
% 9.12/5.44 % (14825)Instructions burned: 2 (million)
% 9.12/5.44 % (14825)------------------------------
% 9.12/5.44 % (14825)------------------------------
% 9.12/5.45 % (14822)Instruction limit reached!
% 9.12/5.45 % (14822)------------------------------
% 9.12/5.45 % (14822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.45 % (14822)Termination reason: Unknown
% 9.12/5.45 % (14822)Termination phase: shuffling
% 9.12/5.45
% 9.12/5.45 % (14822)Memory used [KB]: 13304
% 9.12/5.45 % (14822)Time elapsed: 0.007 s
% 9.12/5.45 % (14822)Instructions burned: 4 (million)
% 9.12/5.45 % (14822)------------------------------
% 9.12/5.45 % (14822)------------------------------
% 9.12/5.46 % (14828)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/3Mi)
% 9.12/5.46 % (14829)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/37Mi)
% 9.12/5.46 % (14827)Instruction limit reached!
% 9.12/5.46 % (14827)------------------------------
% 9.12/5.46 % (14827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.46 % (14827)Termination reason: Unknown
% 9.12/5.46 % (14827)Termination phase: shuffling
% 9.12/5.46
% 9.12/5.46 % (14827)Memory used [KB]: 14072
% 9.12/5.46 % (14827)Time elapsed: 0.023 s
% 9.12/5.46 % (14827)Instructions burned: 18 (million)
% 9.12/5.46 % (14827)------------------------------
% 9.12/5.46 % (14827)------------------------------
% 9.12/5.46 % (14828)Instruction limit reached!
% 9.12/5.46 % (14828)------------------------------
% 9.12/5.46 % (14828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.46 % (14828)Termination reason: Unknown
% 9.12/5.46 % (14828)Termination phase: shuffling
% 9.12/5.46
% 9.12/5.46 % (14828)Memory used [KB]: 13176
% 9.12/5.46 % (14828)Time elapsed: 0.005 s
% 9.12/5.46 % (14828)Instructions burned: 3 (million)
% 9.12/5.46 % (14828)------------------------------
% 9.12/5.46 % (14828)------------------------------
% 9.12/5.46 % (14830)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/15Mi)
% 9.12/5.47 % (14823)Instruction limit reached!
% 9.12/5.47 % (14823)------------------------------
% 9.12/5.47 % (14823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.47 % (14823)Termination reason: Unknown
% 9.12/5.47 % (14823)Termination phase: shuffling
% 9.12/5.47
% 9.12/5.47 % (14823)Memory used [KB]: 14072
% 9.12/5.47 % (14823)Time elapsed: 0.030 s
% 9.12/5.47 % (14823)Instructions burned: 28 (million)
% 9.12/5.47 % (14823)------------------------------
% 9.12/5.47 % (14823)------------------------------
% 9.12/5.48 % (14831)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/3Mi)
% 9.12/5.48 % (14832)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/1041Mi)
% 9.12/5.48 % (14830)Instruction limit reached!
% 9.12/5.48 % (14830)------------------------------
% 9.12/5.48 % (14830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.48 % (14830)Termination reason: Unknown
% 9.12/5.48 % (14830)Termination phase: shuffling
% 9.12/5.48
% 9.12/5.48 % (14830)Memory used [KB]: 14072
% 9.12/5.48 % (14830)Time elapsed: 0.022 s
% 9.12/5.48 % (14830)Instructions burned: 16 (million)
% 9.12/5.48 % (14830)------------------------------
% 9.12/5.48 % (14830)------------------------------
% 9.12/5.49 % (14831)Instruction limit reached!
% 9.12/5.49 % (14831)------------------------------
% 9.12/5.49 % (14831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.49 % (14831)Termination reason: Unknown
% 9.12/5.49 % (14831)Termination phase: shuffling
% 9.12/5.49
% 9.12/5.49 % (14831)Memory used [KB]: 13176
% 9.12/5.49 % (14831)Time elapsed: 0.005 s
% 9.12/5.49 % (14831)Instructions burned: 3 (million)
% 9.12/5.49 % (14831)------------------------------
% 9.12/5.49 % (14831)------------------------------
% 9.12/5.49 % (14833)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/7Mi)
% 9.12/5.49 % (14829)Instruction limit reached!
% 9.12/5.49 % (14829)------------------------------
% 9.12/5.49 % (14829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/5.49 % (14829)Termination reason: Unknown
% 9.12/5.49 % (14829)Termination phase: shuffling
% 9.12/5.49
% 9.12/5.49 % (14829)Memory used [KB]: 14200
% 9.12/5.49 % (14829)Time elapsed: 0.034 s
% 9.12/5.49 % (14829)Instructions burned: 38 (million)
% 9.12/5.49 % (14829)------------------------------
% 9.12/5.49 % (14829)------------------------------
% 9.43/5.50 % (14833)Instruction limit reached!
% 9.43/5.50 % (14833)------------------------------
% 9.43/5.50 % (14833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.50 % (14833)Termination reason: Unknown
% 9.43/5.50 % (14833)Termination phase: shuffling
% 9.43/5.50
% 9.43/5.50 % (14833)Memory used [KB]: 13560
% 9.43/5.50 % (14833)Time elapsed: 0.011 s
% 9.43/5.50 % (14833)Instructions burned: 7 (million)
% 9.43/5.50 % (14833)------------------------------
% 9.43/5.50 % (14833)------------------------------
% 9.43/5.51 % (14834)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/16Mi)
% 9.43/5.51 % (14835)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/3Mi)
% 9.43/5.51 % (14836)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/3Mi)
% 9.43/5.51 % (14836)Instruction limit reached!
% 9.43/5.51 % (14836)------------------------------
% 9.43/5.51 % (14836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.51 % (14836)Termination reason: Unknown
% 9.43/5.51 % (14836)Termination phase: shuffling
% 9.43/5.51
% 9.43/5.51 % (14836)Memory used [KB]: 13304
% 9.43/5.51 % (14836)Time elapsed: 0.004 s
% 9.43/5.51 % (14836)Instructions burned: 3 (million)
% 9.43/5.51 % (14836)------------------------------
% 9.43/5.51 % (14836)------------------------------
% 9.43/5.51 % (14835)Instruction limit reached!
% 9.43/5.51 % (14835)------------------------------
% 9.43/5.51 % (14835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.51 % (14835)Termination reason: Unknown
% 9.43/5.51 % (14835)Termination phase: shuffling
% 9.43/5.51
% 9.43/5.51 % (14835)Memory used [KB]: 13176
% 9.43/5.51 % (14835)Time elapsed: 0.005 s
% 9.43/5.51 % (14835)Instructions burned: 3 (million)
% 9.43/5.51 % (14835)------------------------------
% 9.43/5.51 % (14835)------------------------------
% 9.43/5.52 % (14837)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/7Mi)
% 9.43/5.52 % (14838)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/3Mi)
% 9.43/5.52 % (14838)Instruction limit reached!
% 9.43/5.52 % (14838)------------------------------
% 9.43/5.52 % (14838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.52 % (14838)Termination reason: Unknown
% 9.43/5.52 % (14838)Termination phase: shuffling
% 9.43/5.52
% 9.43/5.52 % (14838)Memory used [KB]: 13304
% 9.43/5.52 % (14838)Time elapsed: 0.004 s
% 9.43/5.52 % (14838)Instructions burned: 3 (million)
% 9.43/5.52 % (14838)------------------------------
% 9.43/5.52 % (14838)------------------------------
% 9.43/5.53 % (14834)Instruction limit reached!
% 9.43/5.53 % (14834)------------------------------
% 9.43/5.53 % (14834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.53 % (14834)Termination reason: Unknown
% 9.43/5.53 % (14834)Termination phase: shuffling
% 9.43/5.53
% 9.43/5.53 % (14834)Memory used [KB]: 14072
% 9.43/5.53 % (14834)Time elapsed: 0.023 s
% 9.43/5.53 % (14834)Instructions burned: 16 (million)
% 9.43/5.53 % (14834)------------------------------
% 9.43/5.53 % (14834)------------------------------
% 9.43/5.53 % (14837)Instruction limit reached!
% 9.43/5.53 % (14837)------------------------------
% 9.43/5.53 % (14837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.53 % (14837)Termination reason: Unknown
% 9.43/5.53 % (14837)Termination phase: shuffling
% 9.43/5.53
% 9.43/5.53 % (14837)Memory used [KB]: 13560
% 9.43/5.53 % (14837)Time elapsed: 0.011 s
% 9.43/5.53 % (14837)Instructions burned: 7 (million)
% 9.43/5.53 % (14837)------------------------------
% 9.43/5.53 % (14837)------------------------------
% 9.43/5.53 % (14839)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/4Mi)
% 9.43/5.53 % (14840)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/18Mi)
% 9.43/5.53 % (14839)Instruction limit reached!
% 9.43/5.53 % (14839)------------------------------
% 9.43/5.53 % (14839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.53 % (14839)Termination reason: Unknown
% 9.43/5.53 % (14839)Termination phase: shuffling
% 9.43/5.53
% 9.43/5.53 % (14839)Memory used [KB]: 13304
% 9.43/5.53 % (14839)Time elapsed: 0.007 s
% 9.43/5.53 % (14839)Instructions burned: 4 (million)
% 9.43/5.53 % (14839)------------------------------
% 9.43/5.53 % (14839)------------------------------
% 9.43/5.55 % (14840)Instruction limit reached!
% 9.43/5.55 % (14840)------------------------------
% 9.43/5.55 % (14840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.55 % (14840)Termination reason: Unknown
% 9.43/5.55 % (14840)Termination phase: shuffling
% 9.43/5.55
% 9.43/5.55 % (14840)Memory used [KB]: 14072
% 9.43/5.55 % (14840)Time elapsed: 0.015 s
% 9.43/5.55 % (14840)Instructions burned: 18 (million)
% 9.43/5.55 % (14840)------------------------------
% 9.43/5.55 % (14840)------------------------------
% 9.43/5.55 % (14841)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/710Mi)
% 9.43/5.55 % (14842)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14485 for (2994ds/6Mi)
% 9.43/5.55 % (14843)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/902Mi)
% 9.43/5.55 % (14842)Instruction limit reached!
% 9.43/5.55 % (14842)------------------------------
% 9.43/5.55 % (14842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.55 % (14842)Termination reason: Unknown
% 9.43/5.55 % (14842)Termination phase: shuffling
% 9.43/5.55
% 9.43/5.55 % (14842)Memory used [KB]: 13432
% 9.43/5.55 % (14842)Time elapsed: 0.009 s
% 9.43/5.55 % (14842)Instructions burned: 6 (million)
% 9.43/5.55 % (14842)------------------------------
% 9.43/5.55 % (14842)------------------------------
% 9.43/5.56 % (14844)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/21Mi)
% 9.43/5.56 % (14821)Instruction limit reached!
% 9.43/5.56 % (14821)------------------------------
% 9.43/5.56 % (14821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.56 % (14821)Termination reason: Unknown
% 9.43/5.56 % (14821)Termination phase: shuffling
% 9.43/5.56
% 9.43/5.56 % (14821)Memory used [KB]: 16247
% 9.43/5.56 % (14821)Time elapsed: 0.126 s
% 9.43/5.56 % (14821)Instructions burned: 183 (million)
% 9.43/5.56 % (14821)------------------------------
% 9.43/5.56 % (14821)------------------------------
% 9.43/5.57 % (14844)Instruction limit reached!
% 9.43/5.57 % (14844)------------------------------
% 9.43/5.57 % (14844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.57 % (14844)Termination reason: Unknown
% 9.43/5.57 % (14844)Termination phase: shuffling
% 9.43/5.57
% 9.43/5.57 % (14844)Memory used [KB]: 14072
% 9.43/5.57 % (14844)Time elapsed: 0.016 s
% 9.43/5.57 % (14844)Instructions burned: 23 (million)
% 9.43/5.57 % (14844)------------------------------
% 9.43/5.57 % (14844)------------------------------
% 9.43/5.57 % (14845)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/5Mi)
% 9.43/5.58 % (14845)Instruction limit reached!
% 9.43/5.58 % (14845)------------------------------
% 9.43/5.58 % (14845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.58 % (14845)Termination reason: Unknown
% 9.43/5.58 % (14845)Termination phase: shuffling
% 9.43/5.58
% 9.43/5.58 % (14845)Memory used [KB]: 13432
% 9.43/5.58 % (14845)Time elapsed: 0.008 s
% 9.43/5.58 % (14845)Instructions burned: 5 (million)
% 9.43/5.58 % (14845)------------------------------
% 9.43/5.58 % (14845)------------------------------
% 9.43/5.58 % (14847)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/377Mi)
% 9.43/5.58 % (14846)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/6Mi)
% 9.43/5.59 % (14846)Instruction limit reached!
% 9.43/5.59 % (14846)------------------------------
% 9.43/5.59 % (14846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.43/5.59 % (14846)Termination reason: Unknown
% 9.43/5.59 % (14846)Termination phase: shuffling
% 9.43/5.59
% 9.43/5.59 % (14846)Memory used [KB]: 13432
% 9.43/5.59 % (14846)Time elapsed: 0.009 s
% 9.43/5.59 % (14846)Instructions burned: 6 (million)
% 9.43/5.59 % (14846)------------------------------
% 9.43/5.59 % (14846)------------------------------
% 9.43/5.60 % (14848)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/779Mi)
% 9.88/5.60 % (14849)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/19Mi)
% 9.88/5.61 % (14826)Instruction limit reached!
% 9.88/5.61 % (14826)------------------------------
% 9.88/5.61 % (14826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/5.61 % (14826)Termination reason: Unknown
% 9.88/5.61 % (14826)Termination phase: shuffling
% 9.88/5.61
% 9.88/5.61 % (14826)Memory used [KB]: 17526
% 9.88/5.61 % (14826)Time elapsed: 0.169 s
% 9.88/5.61 % (14826)Instructions burned: 277 (million)
% 9.88/5.61 % (14826)------------------------------
% 9.88/5.61 % (14826)------------------------------
% 9.88/5.62 % (14849)Instruction limit reached!
% 9.88/5.62 % (14849)------------------------------
% 9.88/5.62 % (14849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/5.62 % (14849)Termination reason: Unknown
% 9.88/5.62 % (14849)Termination phase: shuffling
% 9.88/5.62
% 9.88/5.62 % (14849)Memory used [KB]: 14072
% 9.88/5.62 % (14849)Time elapsed: 0.016 s
% 9.88/5.62 % (14849)Instructions burned: 20 (million)
% 9.88/5.62 % (14849)------------------------------
% 9.88/5.62 % (14849)------------------------------
% 9.88/5.62 % (14850)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/879Mi)
% 9.88/5.63 % (14851)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_14485 for (2993ds/17Mi)
% 9.88/5.64 % (14851)Instruction limit reached!
% 9.88/5.64 % (14851)------------------------------
% 9.88/5.64 % (14851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/5.64 % (14851)Termination reason: Unknown
% 9.88/5.64 % (14851)Termination phase: shuffling
% 9.88/5.64
% 9.88/5.64 % (14851)Memory used [KB]: 14072
% 9.88/5.64 % (14851)Time elapsed: 0.016 s
% 9.88/5.64 % (14851)Instructions burned: 19 (million)
% 9.88/5.64 % (14851)------------------------------
% 9.88/5.64 % (14851)------------------------------
% 9.88/5.66 % (14852)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_14485 for (2992ds/3Mi)
% 9.88/5.66 % (14852)Instruction limit reached!
% 9.88/5.66 % (14852)------------------------------
% 9.88/5.66 % (14852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/5.66 % (14852)Termination reason: Unknown
% 9.88/5.66 % (14852)Termination phase: shuffling
% 9.88/5.66
% 9.88/5.66 % (14852)Memory used [KB]: 13304
% 9.88/5.66 % (14852)Time elapsed: 0.004 s
% 9.88/5.66 % (14852)Instructions burned: 3 (million)
% 9.88/5.66 % (14852)------------------------------
% 9.88/5.66 % (14852)------------------------------
% 9.88/5.67 % (14853)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_14485 for (2992ds/30Mi)
% 9.88/5.69 % (14853)Instruction limit reached!
% 9.88/5.69 % (14853)------------------------------
% 9.88/5.69 % (14853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.88/5.69 % (14853)Termination reason: Unknown
% 9.88/5.69 % (14853)Termination phase: shuffling
% 9.88/5.69
% 9.88/5.69 % (14853)Memory used [KB]: 14072
% 9.88/5.69 % (14853)Time elapsed: 0.020 s
% 9.88/5.69 % (14853)Instructions burned: 30 (million)
% 9.88/5.69 % (14853)------------------------------
% 9.88/5.69 % (14853)------------------------------
% 10.16/5.70 % (14854)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_14485 for (2992ds/127Mi)
% 10.16/5.71 % (14847)Instruction limit reached!
% 10.16/5.71 % (14847)------------------------------
% 10.16/5.71 % (14847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.16/5.71 % (14847)Termination reason: Unknown
% 10.16/5.71 % (14847)Termination phase: shuffling
% 10.16/5.71
% 10.16/5.71 % (14847)Memory used [KB]: 18421
% 10.16/5.71 % (14847)Time elapsed: 0.131 s
% 10.16/5.71 % (14847)Instructions burned: 378 (million)
% 10.16/5.71 % (14847)------------------------------
% 10.16/5.71 % (14847)------------------------------
% 10.16/5.72 % (14855)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_14485 for (2992ds/100Mi)
% 10.16/5.76 % (14854)Instruction limit reached!
% 10.16/5.76 % (14854)------------------------------
% 10.16/5.76 % (14854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.16/5.76 % (14854)Termination reason: Unknown
% 10.16/5.76 % (14854)Termination phase: shuffling
% 10.16/5.76
% 10.16/5.76 % (14854)Memory used [KB]: 15479
% 10.16/5.76 % (14854)Time elapsed: 0.055 s
% 10.16/5.76 % (14854)Instructions burned: 128 (million)
% 10.16/5.76 % (14854)------------------------------
% 10.16/5.76 % (14854)------------------------------
% 10.16/5.76 % (14855)Instruction limit reached!
% 10.16/5.76 % (14855)------------------------------
% 10.16/5.76 % (14855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.16/5.76 % (14855)Termination reason: Unknown
% 10.16/5.76 % (14855)Termination phase: shuffling
% 10.16/5.76
% 10.16/5.76 % (14855)Memory used [KB]: 15095
% 10.16/5.76 % (14855)Time elapsed: 0.037 s
% 10.16/5.76 % (14855)Instructions burned: 101 (million)
% 10.16/5.76 % (14855)------------------------------
% 10.16/5.76 % (14855)------------------------------
% 10.16/5.77 % (14856)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_14485 for (2991ds/3Mi)
% 10.16/5.77 % (14857)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_14485 for (2991ds/20Mi)
% 10.16/5.77 % (14856)Instruction limit reached!
% 10.16/5.77 % (14856)------------------------------
% 10.16/5.77 % (14856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.16/5.77 % (14856)Termination reason: Unknown
% 10.16/5.77 % (14856)Termination phase: shuffling
% 10.16/5.77
% 10.16/5.77 % (14856)Memory used [KB]: 13304
% 10.16/5.77 % (14856)Time elapsed: 0.004 s
% 10.16/5.77 % (14856)Instructions burned: 3 (million)
% 10.16/5.77 % (14856)------------------------------
% 10.16/5.77 % (14856)------------------------------
% 10.16/5.78 % (14858)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_14485 for (2991ds/86Mi)
% 10.16/5.78 % (14857)Instruction limit reached!
% 10.16/5.78 % (14857)------------------------------
% 10.16/5.78 % (14857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.16/5.78 % (14857)Termination reason: Unknown
% 10.16/5.78 % (14857)Termination phase: shuffling
% 10.16/5.78
% 10.16/5.78 % (14857)Memory used [KB]: 14072
% 10.16/5.78 % (14857)Time elapsed: 0.015 s
% 10.16/5.78 % (14857)Instructions burned: 21 (million)
% 10.16/5.78 % (14857)------------------------------
% 10.16/5.78 % (14857)------------------------------
% 10.16/5.80 % (14859)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_14485 for (2991ds/107Mi)
% 10.46/5.81 % (14841)Instruction limit reached!
% 10.46/5.81 % (14841)------------------------------
% 10.46/5.81 % (14841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.81 % (14841)Termination reason: Unknown
% 10.46/5.81 % (14841)Termination phase: shuffling
% 10.46/5.81
% 10.46/5.81 % (14841)Memory used [KB]: 25074
% 10.46/5.81 % (14841)Time elapsed: 0.265 s
% 10.46/5.81 % (14841)Instructions burned: 712 (million)
% 10.46/5.81 % (14841)------------------------------
% 10.46/5.81 % (14841)------------------------------
% 10.46/5.82 % (14858)Instruction limit reached!
% 10.46/5.82 % (14858)------------------------------
% 10.46/5.82 % (14858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.82 % (14858)Termination reason: Unknown
% 10.46/5.82 % (14858)Termination phase: shuffling
% 10.46/5.82
% 10.46/5.82 % (14858)Memory used [KB]: 14967
% 10.46/5.82 % (14858)Time elapsed: 0.040 s
% 10.46/5.82 % (14858)Instructions burned: 86 (million)
% 10.46/5.82 % (14858)------------------------------
% 10.46/5.82 % (14858)------------------------------
% 10.46/5.82 % (14860)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_14485 for (2991ds/39Mi)
% 10.46/5.83 % (14861)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/448Mi)
% 10.46/5.84 % (14859)Instruction limit reached!
% 10.46/5.84 % (14859)------------------------------
% 10.46/5.84 % (14859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.84 % (14859)Termination reason: Unknown
% 10.46/5.84 % (14859)Termination phase: shuffling
% 10.46/5.84
% 10.46/5.84 % (14859)Memory used [KB]: 14967
% 10.46/5.84 % (14859)Time elapsed: 0.042 s
% 10.46/5.84 % (14859)Instructions burned: 107 (million)
% 10.46/5.84 % (14859)------------------------------
% 10.46/5.84 % (14859)------------------------------
% 10.46/5.84 % (14860)Instruction limit reached!
% 10.46/5.84 % (14860)------------------------------
% 10.46/5.84 % (14860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.84 % (14860)Termination reason: Unknown
% 10.46/5.84 % (14860)Termination phase: shuffling
% 10.46/5.84
% 10.46/5.84 % (14860)Memory used [KB]: 14328
% 10.46/5.84 % (14860)Time elapsed: 0.021 s
% 10.46/5.84 % (14860)Instructions burned: 40 (million)
% 10.46/5.84 % (14860)------------------------------
% 10.46/5.84 % (14860)------------------------------
% 10.46/5.85 % (14862)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/46Mi)
% 10.46/5.85 % (14848)Instruction limit reached!
% 10.46/5.85 % (14848)------------------------------
% 10.46/5.85 % (14848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.85 % (14848)Termination reason: Unknown
% 10.46/5.85 % (14848)Termination phase: shuffling
% 10.46/5.85
% 10.46/5.85 % (14848)Memory used [KB]: 26481
% 10.46/5.85 % (14848)Time elapsed: 0.254 s
% 10.46/5.85 % (14848)Instructions burned: 780 (million)
% 10.46/5.85 % (14848)------------------------------
% 10.46/5.85 % (14848)------------------------------
% 10.46/5.85 % (14863)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/98Mi)
% 10.46/5.86 % (14864)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/507Mi)
% 10.46/5.86 % (14832)Instruction limit reached!
% 10.46/5.86 % (14832)------------------------------
% 10.46/5.86 % (14832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.86 % (14832)Termination reason: Unknown
% 10.46/5.86 % (14832)Termination phase: shuffling
% 10.46/5.86
% 10.46/5.86 % (14832)Memory used [KB]: 34029
% 10.46/5.86 % (14832)Time elapsed: 0.381 s
% 10.46/5.86 % (14832)Instructions burned: 1042 (million)
% 10.46/5.86 % (14832)------------------------------
% 10.46/5.86 % (14832)------------------------------
% 10.46/5.87 % (14862)Instruction limit reached!
% 10.46/5.87 % (14862)------------------------------
% 10.46/5.87 % (14862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.87 % (14862)Termination reason: Unknown
% 10.46/5.87 % (14862)Termination phase: shuffling
% 10.46/5.87
% 10.46/5.87 % (14862)Memory used [KB]: 14328
% 10.46/5.87 % (14862)Time elapsed: 0.025 s
% 10.46/5.87 % (14862)Instructions burned: 48 (million)
% 10.46/5.87 % (14862)------------------------------
% 10.46/5.87 % (14862)------------------------------
% 10.46/5.88 % (14865)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/149Mi)
% 10.46/5.88 % (14866)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/39Mi)
% 10.46/5.89 % (14863)Instruction limit reached!
% 10.46/5.89 % (14863)------------------------------
% 10.46/5.89 % (14863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.46/5.89 % (14863)Termination reason: Unknown
% 10.46/5.89 % (14863)Termination phase: shuffling
% 10.46/5.89
% 10.46/5.89 % (14863)Memory used [KB]: 15223
% 10.46/5.89 % (14863)Time elapsed: 0.038 s
% 10.46/5.89 % (14863)Instructions burned: 100 (million)
% 10.46/5.89 % (14863)------------------------------
% 10.46/5.89 % (14863)------------------------------
% 11.64/5.90 % (14867)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/6Mi)
% 11.64/5.90 % (14866)Instruction limit reached!
% 11.64/5.90 % (14866)------------------------------
% 11.64/5.90 % (14866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.90 % (14866)Termination reason: Unknown
% 11.64/5.90 % (14866)Termination phase: shuffling
% 11.64/5.90
% 11.64/5.90 % (14866)Memory used [KB]: 14328
% 11.64/5.90 % (14866)Time elapsed: 0.022 s
% 11.64/5.90 % (14866)Instructions burned: 40 (million)
% 11.64/5.90 % (14866)------------------------------
% 11.64/5.90 % (14866)------------------------------
% 11.64/5.91 % (14843)Instruction limit reached!
% 11.64/5.91 % (14843)------------------------------
% 11.64/5.91 % (14843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.91 % (14843)Termination reason: Unknown
% 11.64/5.91 % (14843)Termination phase: Property scanning
% 11.64/5.91
% 11.64/5.91 % (14843)Memory used [KB]: 27504
% 11.64/5.91 % (14843)Time elapsed: 0.356 s
% 11.64/5.91 % (14843)Instructions burned: 903 (million)
% 11.64/5.91 % (14843)------------------------------
% 11.64/5.91 % (14843)------------------------------
% 11.64/5.91 % (14867)Instruction limit reached!
% 11.64/5.91 % (14867)------------------------------
% 11.64/5.91 % (14867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.91 % (14867)Termination reason: Unknown
% 11.64/5.91 % (14867)Termination phase: shuffling
% 11.64/5.91
% 11.64/5.91 % (14867)Memory used [KB]: 13432
% 11.64/5.91 % (14867)Time elapsed: 0.006 s
% 11.64/5.91 % (14867)Instructions burned: 6 (million)
% 11.64/5.91 % (14867)------------------------------
% 11.64/5.91 % (14867)------------------------------
% 11.64/5.91 % (14868)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/1087Mi)
% 11.64/5.92 % (14869)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/47Mi)
% 11.64/5.92 % (14870)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_14485 for (2990ds/44Mi)
% 11.64/5.94 % (14865)Instruction limit reached!
% 11.64/5.94 % (14865)------------------------------
% 11.64/5.94 % (14865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.94 % (14865)Termination reason: Unknown
% 11.64/5.94 % (14865)Termination phase: shuffling
% 11.64/5.94
% 11.64/5.94 % (14865)Memory used [KB]: 15735
% 11.64/5.94 % (14865)Time elapsed: 0.064 s
% 11.64/5.94 % (14865)Instructions burned: 150 (million)
% 11.64/5.94 % (14865)------------------------------
% 11.64/5.94 % (14865)------------------------------
% 11.64/5.94 % (14870)Instruction limit reached!
% 11.64/5.94 % (14870)------------------------------
% 11.64/5.94 % (14870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.94 % (14870)Termination reason: Unknown
% 11.64/5.94 % (14870)Termination phase: shuffling
% 11.64/5.94
% 11.64/5.94 % (14870)Memory used [KB]: 14328
% 11.64/5.94 % (14870)Time elapsed: 0.024 s
% 11.64/5.94 % (14870)Instructions burned: 45 (million)
% 11.64/5.94 % (14870)------------------------------
% 11.64/5.94 % (14870)------------------------------
% 11.64/5.94 % (14869)Instruction limit reached!
% 11.64/5.94 % (14869)------------------------------
% 11.64/5.94 % (14869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.94 % (14869)Termination reason: Unknown
% 11.64/5.94 % (14869)Termination phase: shuffling
% 11.64/5.94
% 11.64/5.94 % (14869)Memory used [KB]: 14456
% 11.64/5.94 % (14869)Time elapsed: 0.026 s
% 11.64/5.94 % (14869)Instructions burned: 49 (million)
% 11.64/5.94 % (14869)------------------------------
% 11.64/5.94 % (14869)------------------------------
% 11.64/5.95 % (14850)Instruction limit reached!
% 11.64/5.95 % (14850)------------------------------
% 11.64/5.95 % (14850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.95 % (14850)Termination reason: Unknown
% 11.64/5.95 % (14850)Termination phase: shuffling
% 11.64/5.95
% 11.64/5.95 % (14850)Memory used [KB]: 26993
% 11.64/5.95 % (14850)Time elapsed: 0.331 s
% 11.64/5.95 % (14850)Instructions burned: 879 (million)
% 11.64/5.95 % (14850)------------------------------
% 11.64/5.95 % (14850)------------------------------
% 11.64/5.95 % (14871)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/432Mi)
% 11.64/5.95 % (14872)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/62Mi)
% 11.64/5.95 % (14873)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/31Mi)
% 11.64/5.96 % (14874)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/96Mi)
% 11.64/5.97 % (14873)Instruction limit reached!
% 11.64/5.97 % (14873)------------------------------
% 11.64/5.97 % (14873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.97 % (14873)Termination reason: Unknown
% 11.64/5.97 % (14873)Termination phase: shuffling
% 11.64/5.97
% 11.64/5.97 % (14873)Memory used [KB]: 14072
% 11.64/5.97 % (14873)Time elapsed: 0.019 s
% 11.64/5.97 % (14873)Instructions burned: 32 (million)
% 11.64/5.97 % (14873)------------------------------
% 11.64/5.97 % (14873)------------------------------
% 11.64/5.98 % (14872)Instruction limit reached!
% 11.64/5.98 % (14872)------------------------------
% 11.64/5.98 % (14872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.98 % (14872)Termination reason: Unknown
% 11.64/5.98 % (14872)Termination phase: shuffling
% 11.64/5.98
% 11.64/5.98 % (14872)Memory used [KB]: 14583
% 11.64/5.98 % (14872)Time elapsed: 0.027 s
% 11.64/5.98 % (14872)Instructions burned: 62 (million)
% 11.64/5.98 % (14872)------------------------------
% 11.64/5.98 % (14872)------------------------------
% 11.64/5.98 % (14861)Instruction limit reached!
% 11.64/5.98 % (14861)------------------------------
% 11.64/5.98 % (14861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/5.98 % (14861)Termination reason: Unknown
% 11.64/5.98 % (14861)Termination phase: shuffling
% 11.64/5.98
% 11.64/5.98 % (14861)Memory used [KB]: 22003
% 11.64/5.98 % (14861)Time elapsed: 0.149 s
% 11.64/5.98 % (14861)Instructions burned: 449 (million)
% 11.64/5.98 % (14861)------------------------------
% 11.64/5.98 % (14861)------------------------------
% 11.64/5.98 % (14875)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/453Mi)
% 11.64/5.99 % (14877)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/83Mi)
% 11.64/6.00 % (14876)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/71Mi)
% 11.64/6.00 % (14874)Instruction limit reached!
% 11.64/6.00 % (14874)------------------------------
% 11.64/6.00 % (14874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.64/6.00 % (14874)Termination reason: Unknown
% 11.64/6.00 % (14874)Termination phase: shuffling
% 11.64/6.00
% 11.64/6.00 % (14874)Memory used [KB]: 15095
% 11.64/6.00 % (14874)Time elapsed: 0.041 s
% 11.64/6.00 % (14874)Instructions burned: 98 (million)
% 11.64/6.00 % (14874)------------------------------
% 11.64/6.00 % (14874)------------------------------
% 11.64/6.01 % (14878)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_14485 for (2989ds/11Mi)
% 13.26/6.02 % (14878)Instruction limit reached!
% 13.26/6.02 % (14878)------------------------------
% 13.26/6.02 % (14878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.02 % (14878)Termination reason: Unknown
% 13.26/6.02 % (14878)Termination phase: shuffling
% 13.26/6.02
% 13.26/6.02 % (14878)Memory used [KB]: 14072
% 13.26/6.02 % (14878)Time elapsed: 0.012 s
% 13.26/6.02 % (14878)Instructions burned: 12 (million)
% 13.26/6.02 % (14878)------------------------------
% 13.26/6.02 % (14878)------------------------------
% 13.26/6.03 % (14877)Instruction limit reached!
% 13.26/6.03 % (14877)------------------------------
% 13.26/6.03 % (14877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.03 % (14877)Termination reason: Unknown
% 13.26/6.03 % (14877)Termination phase: shuffling
% 13.26/6.03
% 13.26/6.03 % (14877)Memory used [KB]: 14967
% 13.26/6.03 % (14877)Time elapsed: 0.036 s
% 13.26/6.03 % (14877)Instructions burned: 84 (million)
% 13.26/6.03 % (14877)------------------------------
% 13.26/6.03 % (14877)------------------------------
% 13.26/6.03 % (14876)Instruction limit reached!
% 13.26/6.03 % (14876)------------------------------
% 13.26/6.03 % (14876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.03 % (14876)Termination reason: Unknown
% 13.26/6.03 % (14876)Termination phase: shuffling
% 13.26/6.03
% 13.26/6.03 % (14876)Memory used [KB]: 14711
% 13.26/6.03 % (14876)Time elapsed: 0.032 s
% 13.26/6.03 % (14876)Instructions burned: 71 (million)
% 13.26/6.03 % (14876)------------------------------
% 13.26/6.03 % (14876)------------------------------
% 13.26/6.04 % (14879)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/41Mi)
% 13.26/6.04 % (14880)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/6Mi)
% 13.26/6.04 % (14881)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/150Mi)
% 13.26/6.04 % (14864)Instruction limit reached!
% 13.26/6.04 % (14864)------------------------------
% 13.26/6.04 % (14864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.04 % (14864)Termination reason: Unknown
% 13.26/6.04 % (14864)Termination phase: shuffling
% 13.26/6.04
% 13.26/6.04 % (14864)Memory used [KB]: 20212
% 13.26/6.04 % (14864)Time elapsed: 0.182 s
% 13.26/6.04 % (14864)Instructions burned: 508 (million)
% 13.26/6.04 % (14864)------------------------------
% 13.26/6.04 % (14864)------------------------------
% 13.26/6.04 % (14880)Instruction limit reached!
% 13.26/6.04 % (14880)------------------------------
% 13.26/6.04 % (14880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.04 % (14880)Termination reason: Unknown
% 13.26/6.04 % (14880)Termination phase: shuffling
% 13.26/6.04
% 13.26/6.04 % (14880)Memory used [KB]: 13560
% 13.26/6.04 % (14880)Time elapsed: 0.007 s
% 13.26/6.04 % (14880)Instructions burned: 7 (million)
% 13.26/6.04 % (14880)------------------------------
% 13.26/6.04 % (14880)------------------------------
% 13.26/6.05 % (14882)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/343Mi)
% 13.26/6.05 % (14883)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/109Mi)
% 13.26/6.06 % (14879)Instruction limit reached!
% 13.26/6.06 % (14879)------------------------------
% 13.26/6.06 % (14879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.06 % (14879)Termination reason: Unknown
% 13.26/6.06 % (14879)Termination phase: shuffling
% 13.26/6.06
% 13.26/6.06 % (14879)Memory used [KB]: 14328
% 13.26/6.06 % (14879)Time elapsed: 0.022 s
% 13.26/6.06 % (14879)Instructions burned: 43 (million)
% 13.26/6.06 % (14879)------------------------------
% 13.26/6.06 % (14879)------------------------------
% 13.26/6.07 % (14884)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/253Mi)
% 13.26/6.08 % (14871)Instruction limit reached!
% 13.26/6.08 % (14871)------------------------------
% 13.26/6.08 % (14871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.08 % (14871)Termination reason: Unknown
% 13.26/6.08 % (14871)Termination phase: shuffling
% 13.26/6.08
% 13.26/6.08 % (14871)Memory used [KB]: 21875
% 13.26/6.08 % (14871)Time elapsed: 0.134 s
% 13.26/6.08 % (14871)Instructions burned: 432 (million)
% 13.26/6.08 % (14871)------------------------------
% 13.26/6.08 % (14871)------------------------------
% 13.26/6.10 % (14885)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/140Mi)
% 13.26/6.10 % (14883)Instruction limit reached!
% 13.26/6.10 % (14883)------------------------------
% 13.26/6.10 % (14883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.10 % (14883)Termination reason: Unknown
% 13.26/6.10 % (14883)Termination phase: shuffling
% 13.26/6.10
% 13.26/6.10 % (14883)Memory used [KB]: 15351
% 13.26/6.10 % (14883)Time elapsed: 0.045 s
% 13.26/6.10 % (14883)Instructions burned: 111 (million)
% 13.26/6.10 % (14883)------------------------------
% 13.26/6.10 % (14883)------------------------------
% 13.26/6.10 % (14881)Instruction limit reached!
% 13.26/6.10 % (14881)------------------------------
% 13.26/6.10 % (14881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.10 % (14881)Termination reason: Unknown
% 13.26/6.10 % (14881)Termination phase: shuffling
% 13.26/6.10
% 13.26/6.10 % (14881)Memory used [KB]: 15863
% 13.26/6.10 % (14881)Time elapsed: 0.059 s
% 13.26/6.10 % (14881)Instructions burned: 152 (million)
% 13.26/6.10 % (14881)------------------------------
% 13.26/6.10 % (14881)------------------------------
% 13.26/6.11 % (14886)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/614Mi)
% 13.26/6.11 % (14887)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_14485 for (2988ds/202Mi)
% 13.26/6.12 % (14875)Instruction limit reached!
% 13.26/6.12 % (14875)------------------------------
% 13.26/6.12 % (14875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/6.12 % (14875)Termination reason: Unknown
% 13.26/6.12 % (14875)Termination phase: shuffling
% 13.26/6.12
% 13.26/6.12 % (14875)Memory used [KB]: 22131
% 13.26/6.12 % (14875)Time elapsed: 0.139 s
% 13.26/6.12 % (14875)Instructions burned: 453 (million)
% 13.26/6.12 % (14875)------------------------------
% 13.26/6.12 % (14875)------------------------------
% 13.82/6.13 % (14888)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_14485 for (2987ds/339Mi)
% 13.82/6.15 % (14885)Instruction limit reached!
% 13.82/6.15 % (14885)------------------------------
% 13.82/6.15 % (14885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/6.15 % (14885)Termination reason: Unknown
% 13.82/6.15 % (14885)Termination phase: shuffling
% 13.82/6.15
% 13.82/6.15 % (14885)Memory used [KB]: 15607
% 13.82/6.15 % (14885)Time elapsed: 0.055 s
% 13.82/6.15 % (14885)Instructions burned: 142 (million)
% 13.82/6.15 % (14885)------------------------------
% 13.82/6.15 % (14885)------------------------------
% 13.82/6.16 % (14884)Instruction limit reached!
% 13.82/6.16 % (14884)------------------------------
% 13.82/6.16 % (14884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/6.16 % (14884)Termination reason: Unknown
% 13.82/6.16 % (14884)Termination phase: shuffling
% 13.82/6.16
% 13.82/6.16 % (14884)Memory used [KB]: 17398
% 13.82/6.16 % (14884)Time elapsed: 0.094 s
% 13.82/6.16 % (14884)Instructions burned: 255 (million)
% 13.82/6.16 % (14884)------------------------------
% 13.82/6.16 % (14884)------------------------------
% 13.82/6.16 % (14889)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_14485 for (2987ds/283Mi)
% 13.82/6.17 % (14882)Instruction limit reached!
% 13.82/6.17 % (14882)------------------------------
% 13.82/6.17 % (14882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/6.17 % (14882)Termination reason: Unknown
% 13.82/6.17 % (14882)Termination phase: shuffling
% 13.82/6.17
% 13.82/6.17 % (14882)Memory used [KB]: 18421
% 13.82/6.17 % (14882)Time elapsed: 0.122 s
% 13.82/6.17 % (14882)Instructions burned: 343 (million)
% 13.82/6.17 % (14882)------------------------------
% 13.82/6.17 % (14882)------------------------------
% 13.82/6.18 % (14890)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_14485 for (2987ds/134Mi)
% 13.82/6.18 % (14887)Instruction limit reached!
% 13.82/6.18 % (14887)------------------------------
% 13.82/6.18 % (14887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/6.18 % (14887)Termination reason: Unknown
% 13.82/6.18 % (14887)Termination phase: shuffling
% 13.82/6.18
% 13.82/6.18 % (14887)Memory used [KB]: 16630
% 13.82/6.18 % (14887)Time elapsed: 0.077 s
% 13.82/6.18 % (14887)Instructions burned: 202 (million)
% 13.82/6.18 % (14887)------------------------------
% 13.82/6.18 % (14887)------------------------------
% 13.82/6.19 % (14891)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_14485 for (2987ds/298Mi)
% 13.82/6.20 % (14892)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_14485 for (2987ds/192Mi)
% 14.27/6.25 % (14889)Instruction limit reached!
% 14.27/6.25 % (14889)------------------------------
% 14.27/6.25 % (14889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.27/6.25 % (14889)Termination reason: Unknown
% 14.27/6.25 % (14889)Termination phase: shuffling
% 14.27/6.25
% 14.27/6.25 % (14889)Memory used [KB]: 19701
% 14.27/6.25 % (14889)Time elapsed: 0.089 s
% 14.27/6.25 % (14889)Instructions burned: 284 (million)
% 14.27/6.25 % (14889)------------------------------
% 14.27/6.25 % (14889)------------------------------
% 14.27/6.25 % (14888)Instruction limit reached!
% 14.27/6.25 % (14888)------------------------------
% 14.27/6.25 % (14888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.27/6.25 % (14888)Termination reason: Unknown
% 14.27/6.25 % (14888)Termination phase: shuffling
% 14.27/6.25
% 14.27/6.25 % (14888)Memory used [KB]: 18166
% 14.27/6.25 % (14888)Time elapsed: 0.119 s
% 14.27/6.25 % (14888)Instructions burned: 339 (million)
% 14.27/6.25 % (14888)------------------------------
% 14.27/6.25 % (14888)------------------------------
% 14.27/6.26 % (14890)Instruction limit reached!
% 14.27/6.26 % (14890)------------------------------
% 14.27/6.26 % (14890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.27/6.26 % (14890)Termination reason: Unknown
% 14.27/6.26 % (14890)Termination phase: shuffling
% 14.27/6.26
% 14.27/6.26 % (14890)Memory used [KB]: 15351
% 14.27/6.26 % (14890)Time elapsed: 0.081 s
% 14.27/6.26 % (14890)Instructions burned: 134 (million)
% 14.27/6.26 % (14890)------------------------------
% 14.27/6.26 % (14890)------------------------------
% 14.27/6.26 % (14893)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/258Mi)
% 14.27/6.26 % (14894)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/90Mi)
% 14.27/6.27 % (14892)Instruction limit reached!
% 14.27/6.27 % (14892)------------------------------
% 14.27/6.27 % (14892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.27/6.27 % (14892)Termination reason: Unknown
% 14.27/6.27 % (14892)Termination phase: shuffling
% 14.27/6.27
% 14.27/6.27 % (14892)Memory used [KB]: 16375
% 14.27/6.27 % (14892)Time elapsed: 0.071 s
% 14.27/6.27 % (14892)Instructions burned: 194 (million)
% 14.27/6.27 % (14892)------------------------------
% 14.27/6.27 % (14892)------------------------------
% 14.27/6.27 % (14895)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/231Mi)
% 14.27/6.27 % (14868)Instruction limit reached!
% 14.27/6.27 % (14868)------------------------------
% 14.27/6.27 % (14868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.27/6.27 % (14868)Termination reason: Unknown
% 14.27/6.27 % (14868)Termination phase: Property scanning
% 14.27/6.27
% 14.27/6.27 % (14868)Memory used [KB]: 27376
% 14.27/6.27 % (14868)Time elapsed: 0.362 s
% 14.27/6.27 % (14868)Instructions burned: 1088 (million)
% 14.27/6.27 % (14868)------------------------------
% 14.27/6.27 % (14868)------------------------------
% 14.27/6.28 % (14896)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/458Mi)
% 14.27/6.28 % (14891)Instruction limit reached!
% 14.27/6.28 % (14891)------------------------------
% 14.27/6.28 % (14891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.27/6.28 % (14891)Termination reason: Unknown
% 14.27/6.28 % (14891)Termination phase: shuffling
% 14.27/6.28
% 14.27/6.28 % (14891)Memory used [KB]: 19957
% 14.27/6.28 % (14891)Time elapsed: 0.093 s
% 14.27/6.28 % (14891)Instructions burned: 299 (million)
% 14.27/6.28 % (14891)------------------------------
% 14.27/6.28 % (14891)------------------------------
% 14.27/6.29 % (14897)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/31Mi)
% 14.27/6.29 % (14898)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/297Mi)
% 14.88/6.30 % (14894)Instruction limit reached!
% 14.88/6.30 % (14894)------------------------------
% 14.88/6.30 % (14894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/6.30 % (14894)Termination reason: Unknown
% 14.88/6.30 % (14894)Termination phase: shuffling
% 14.88/6.30
% 14.88/6.30 % (14894)Memory used [KB]: 14711
% 14.88/6.30 % (14894)Time elapsed: 0.037 s
% 14.88/6.30 % (14894)Instructions burned: 91 (million)
% 14.88/6.30 % (14894)------------------------------
% 14.88/6.30 % (14894)------------------------------
% 14.88/6.31 % (14897)Instruction limit reached!
% 14.88/6.31 % (14897)------------------------------
% 14.88/6.31 % (14897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/6.31 % (14897)Termination reason: Unknown
% 14.88/6.31 % (14897)Termination phase: shuffling
% 14.88/6.31
% 14.88/6.31 % (14897)Memory used [KB]: 14072
% 14.88/6.31 % (14897)Time elapsed: 0.020 s
% 14.88/6.31 % (14897)Instructions burned: 32 (million)
% 14.88/6.31 % (14897)------------------------------
% 14.88/6.31 % (14897)------------------------------
% 14.88/6.31 % (14899)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/987Mi)
% 14.88/6.32 % (14900)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/182Mi)
% 14.88/6.32 % (14886)Instruction limit reached!
% 14.88/6.32 % (14886)------------------------------
% 14.88/6.32 % (14886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/6.32 % (14886)Termination reason: Unknown
% 14.88/6.32 % (14886)Termination phase: shuffling
% 14.88/6.32
% 14.88/6.32 % (14886)Memory used [KB]: 23922
% 14.88/6.32 % (14886)Time elapsed: 0.216 s
% 14.88/6.32 % (14886)Instructions burned: 615 (million)
% 14.88/6.32 % (14886)------------------------------
% 14.88/6.32 % (14886)------------------------------
% 14.88/6.34 % (14901)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_14485 for (2986ds/182Mi)
% 14.88/6.35 % (14895)Instruction limit reached!
% 14.88/6.35 % (14895)------------------------------
% 14.88/6.35 % (14895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/6.35 % (14895)Termination reason: Unknown
% 14.88/6.35 % (14895)Termination phase: shuffling
% 14.88/6.35
% 14.88/6.35 % (14895)Memory used [KB]: 17014
% 14.88/6.35 % (14895)Time elapsed: 0.083 s
% 14.88/6.35 % (14895)Instructions burned: 234 (million)
% 14.88/6.35 % (14895)------------------------------
% 14.88/6.35 % (14895)------------------------------
% 14.88/6.36 % (14893)Instruction limit reached!
% 14.88/6.36 % (14893)------------------------------
% 14.88/6.36 % (14893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/6.36 % (14893)Termination reason: Unknown
% 14.88/6.36 % (14893)Termination phase: shuffling
% 14.88/6.36
% 14.88/6.36 % (14893)Memory used [KB]: 17270
% 14.88/6.36 % (14893)Time elapsed: 0.096 s
% 14.88/6.36 % (14893)Instructions burned: 260 (million)
% 14.88/6.36 % (14893)------------------------------
% 14.88/6.36 % (14893)------------------------------
% 14.88/6.37 % (14902)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_14485 for (2985ds/154Mi)
% 14.88/6.37 % (14903)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_14485 for (2985ds/79Mi)
% 14.88/6.38 % (14898)Instruction limit reached!
% 14.88/6.38 % (14898)------------------------------
% 14.88/6.38 % (14898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/6.38 % (14898)Termination reason: Unknown
% 14.88/6.38 % (14898)Termination phase: shuffling
% 14.88/6.38
% 14.88/6.38 % (14898)Memory used [KB]: 20084
% 14.88/6.38 % (14898)Time elapsed: 0.096 s
% 14.88/6.38 % (14898)Instructions burned: 299 (million)
% 14.88/6.38 % (14898)------------------------------
% 14.88/6.38 % (14898)------------------------------
% 14.88/6.39 % (14900)Instruction limit reached!
% 14.88/6.39 % (14900)------------------------------
% 14.88/6.39 % (14900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.88/6.39 % (14900)Termination reason: Unknown
% 14.88/6.39 % (14900)Termination phase: shuffling
% 14.88/6.39
% 14.88/6.39 % (14900)Memory used [KB]: 16247
% 14.88/6.39 % (14900)Time elapsed: 0.070 s
% 14.88/6.39 % (14900)Instructions burned: 184 (million)
% 14.88/6.39 % (14900)------------------------------
% 14.88/6.39 % (14900)------------------------------
% 15.58/6.40 % (14905)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_14485 for (2985ds/114Mi)
% 15.58/6.40 % (14903)Instruction limit reached!
% 15.58/6.40 % (14903)------------------------------
% 15.58/6.40 % (14903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.40 % (14903)Termination reason: Unknown
% 15.58/6.40 % (14903)Termination phase: shuffling
% 15.58/6.40
% 15.58/6.40 % (14903)Memory used [KB]: 14839
% 15.58/6.40 % (14903)Time elapsed: 0.034 s
% 15.58/6.40 % (14903)Instructions burned: 79 (million)
% 15.58/6.40 % (14903)------------------------------
% 15.58/6.40 % (14903)------------------------------
% 15.58/6.41 % (14901)Instruction limit reached!
% 15.58/6.41 % (14901)------------------------------
% 15.58/6.41 % (14901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.41 % (14901)Termination reason: Unknown
% 15.58/6.41 % (14901)Termination phase: shuffling
% 15.58/6.41
% 15.58/6.41 % (14901)Memory used [KB]: 16375
% 15.58/6.41 % (14901)Time elapsed: 0.070 s
% 15.58/6.41 % (14901)Instructions burned: 182 (million)
% 15.58/6.41 % (14901)------------------------------
% 15.58/6.41 % (14901)------------------------------
% 15.58/6.41 % (14904)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_14485 for (2985ds/216Mi)
% 15.58/6.41 % (14906)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_14485 for (2985ds/922Mi)
% 15.58/6.42 % (14907)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_14485 for (2985ds/182Mi)
% 15.58/6.42 % (14902)Instruction limit reached!
% 15.58/6.42 % (14902)------------------------------
% 15.58/6.42 % (14902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.42 % (14902)Termination reason: Unknown
% 15.58/6.42 % (14902)Termination phase: shuffling
% 15.58/6.42
% 15.58/6.42 % (14902)Memory used [KB]: 15991
% 15.58/6.42 % (14902)Time elapsed: 0.058 s
% 15.58/6.42 % (14902)Instructions burned: 156 (million)
% 15.58/6.42 % (14902)------------------------------
% 15.58/6.42 % (14902)------------------------------
% 15.58/6.43 % (14908)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_14485 for (2985ds/164Mi)
% 15.58/6.44 % (14896)Instruction limit reached!
% 15.58/6.44 % (14896)------------------------------
% 15.58/6.44 % (14896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.44 % (14896)Termination reason: Unknown
% 15.58/6.44 % (14896)Termination phase: shuffling
% 15.58/6.44
% 15.58/6.44 % (14896)Memory used [KB]: 19701
% 15.58/6.44 % (14896)Time elapsed: 0.162 s
% 15.58/6.44 % (14896)Instructions burned: 460 (million)
% 15.58/6.44 % (14896)------------------------------
% 15.58/6.44 % (14896)------------------------------
% 15.58/6.44 % (14905)Instruction limit reached!
% 15.58/6.44 % (14905)------------------------------
% 15.58/6.44 % (14905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.44 % (14905)Termination reason: Unknown
% 15.58/6.44 % (14905)Termination phase: shuffling
% 15.58/6.44
% 15.58/6.44 % (14905)Memory used [KB]: 15223
% 15.58/6.44 % (14905)Time elapsed: 0.046 s
% 15.58/6.44 % (14905)Instructions burned: 116 (million)
% 15.58/6.44 % (14905)------------------------------
% 15.58/6.44 % (14905)------------------------------
% 15.58/6.45 % (14909)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_14485 for (2984ds/50Mi)
% 15.58/6.45 % (14910)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_14485 for (2984ds/368Mi)
% 15.58/6.47 % (14909)Instruction limit reached!
% 15.58/6.47 % (14909)------------------------------
% 15.58/6.47 % (14909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.47 % (14909)Termination reason: Unknown
% 15.58/6.47 % (14909)Termination phase: shuffling
% 15.58/6.47
% 15.58/6.47 % (14909)Memory used [KB]: 14328
% 15.58/6.47 % (14909)Time elapsed: 0.024 s
% 15.58/6.47 % (14909)Instructions burned: 51 (million)
% 15.58/6.47 % (14909)------------------------------
% 15.58/6.47 % (14909)------------------------------
% 15.58/6.48 % (14907)Instruction limit reached!
% 15.58/6.48 % (14907)------------------------------
% 15.58/6.48 % (14907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.48 % (14907)Termination reason: Unknown
% 15.58/6.48 % (14907)Termination phase: shuffling
% 15.58/6.48
% 15.58/6.48 % (14907)Memory used [KB]: 16375
% 15.58/6.48 % (14907)Time elapsed: 0.061 s
% 15.58/6.48 % (14907)Instructions burned: 185 (million)
% 15.58/6.48 % (14907)------------------------------
% 15.58/6.48 % (14907)------------------------------
% 15.58/6.48 % (14911)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_14485 for (2984ds/1021Mi)
% 15.58/6.48 % (14904)Instruction limit reached!
% 15.58/6.48 % (14904)------------------------------
% 15.58/6.48 % (14904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.48 % (14904)Termination reason: Unknown
% 15.58/6.48 % (14904)Termination phase: shuffling
% 15.58/6.48
% 15.58/6.48 % (14904)Memory used [KB]: 16758
% 15.58/6.48 % (14904)Time elapsed: 0.081 s
% 15.58/6.48 % (14904)Instructions burned: 216 (million)
% 15.58/6.48 % (14904)------------------------------
% 15.58/6.48 % (14904)------------------------------
% 15.58/6.49 % (14912)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_14485 for (2984ds/267Mi)
% 15.58/6.49 % (14908)Instruction limit reached!
% 15.58/6.49 % (14908)------------------------------
% 15.58/6.49 % (14908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.58/6.49 % (14908)Termination reason: Unknown
% 15.58/6.49 % (14908)Termination phase: shuffling
% 15.58/6.49
% 15.58/6.49 % (14908)Memory used [KB]: 15991
% 15.58/6.49 % (14908)Time elapsed: 0.060 s
% 15.58/6.49 % (14908)Instructions burned: 164 (million)
% 15.58/6.49 % (14908)------------------------------
% 15.58/6.49 % (14908)------------------------------
% 15.58/6.50 % (14913)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_14485 for (2984ds/204Mi)
% 16.27/6.51 % (14914)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_14485 for (2984ds/26Mi)
% 16.27/6.52 % (14914)Instruction limit reached!
% 16.27/6.52 % (14914)------------------------------
% 16.27/6.52 % (14914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.27/6.52 % (14914)Termination reason: Unknown
% 16.27/6.52 % (14914)Termination phase: shuffling
% 16.27/6.52
% 16.27/6.52 % (14914)Memory used [KB]: 14200
% 16.27/6.52 % (14914)Time elapsed: 0.019 s
% 16.27/6.52 % (14914)Instructions burned: 29 (million)
% 16.27/6.52 % (14914)------------------------------
% 16.27/6.52 % (14914)------------------------------
% 16.27/6.53 % (14915)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_14485 for (2983ds/53Mi)
% 16.27/6.56 % (14915)Instruction limit reached!
% 16.27/6.56 % (14915)------------------------------
% 16.27/6.56 % (14915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.27/6.56 % (14915)Termination reason: Unknown
% 16.27/6.56 % (14915)Termination phase: shuffling
% 16.27/6.56
% 16.27/6.56 % (14915)Memory used [KB]: 14456
% 16.27/6.56 % (14915)Time elapsed: 0.027 s
% 16.27/6.56 % (14915)Instructions burned: 54 (million)
% 16.27/6.56 % (14915)------------------------------
% 16.27/6.56 % (14915)------------------------------
% 16.27/6.57 % (14913)Instruction limit reached!
% 16.27/6.57 % (14913)------------------------------
% 16.27/6.57 % (14913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.27/6.57 % (14913)Termination reason: Unknown
% 16.27/6.57 % (14913)Termination phase: shuffling
% 16.27/6.57
% 16.27/6.57 % (14913)Memory used [KB]: 16502
% 16.27/6.57 % (14913)Time elapsed: 0.077 s
% 16.27/6.57 % (14913)Instructions burned: 206 (million)
% 16.27/6.57 % (14913)------------------------------
% 16.27/6.57 % (14913)------------------------------
% 16.27/6.57 % (14912)Instruction limit reached!
% 16.27/6.57 % (14912)------------------------------
% 16.27/6.57 % (14912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.27/6.57 % (14912)Termination reason: Unknown
% 16.27/6.57 % (14912)Termination phase: shuffling
% 16.27/6.57
% 16.27/6.57 % (14912)Memory used [KB]: 19573
% 16.27/6.57 % (14912)Time elapsed: 0.087 s
% 16.27/6.57 % (14912)Instructions burned: 268 (million)
% 16.27/6.57 % (14912)------------------------------
% 16.27/6.57 % (14912)------------------------------
% 16.27/6.57 % (14916)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_14485 for (2983ds/4436Mi)
% 16.27/6.58 % (14917)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_14485 for (2983ds/1539Mi)
% 16.27/6.58 % (14910)Instruction limit reached!
% 16.27/6.58 % (14910)------------------------------
% 16.27/6.58 % (14910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.27/6.58 % (14910)Termination reason: Unknown
% 16.27/6.58 % (14910)Termination phase: shuffling
% 16.27/6.58
% 16.27/6.58 % (14910)Memory used [KB]: 18677
% 16.27/6.58 % (14910)Time elapsed: 0.131 s
% 16.27/6.58 % (14910)Instructions burned: 368 (million)
% 16.27/6.58 % (14910)------------------------------
% 16.27/6.58 % (14910)------------------------------
% 16.27/6.58 % (14918)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_14485 for (2983ds/408Mi)
% 16.27/6.59 % (14919)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_14485 for (2983ds/5205Mi)
% 16.66/6.61 % (14899)Instruction limit reached!
% 16.66/6.61 % (14899)------------------------------
% 16.66/6.61 % (14899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.66/6.61 % (14899)Termination reason: Unknown
% 16.66/6.61 % (14899)Termination phase: shuffling
% 16.66/6.61
% 16.66/6.61 % (14899)Memory used [KB]: 33261
% 16.66/6.61 % (14899)Time elapsed: 0.299 s
% 16.66/6.61 % (14899)Instructions burned: 988 (million)
% 16.66/6.61 % (14899)------------------------------
% 16.66/6.61 % (14899)------------------------------
% 16.66/6.62 % (14920)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_14485 for (2983ds/1913Mi)
% 16.97/6.73 % (14918)Instruction limit reached!
% 16.97/6.73 % (14918)------------------------------
% 16.97/6.73 % (14918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.97/6.73 % (14918)Termination reason: Unknown
% 16.97/6.73 % (14918)Termination phase: shuffling
% 16.97/6.73
% 16.97/6.73 % (14918)Memory used [KB]: 19445
% 16.97/6.73 % (14918)Time elapsed: 0.144 s
% 16.97/6.73 % (14918)Instructions burned: 410 (million)
% 16.97/6.73 % (14918)------------------------------
% 16.97/6.73 % (14918)------------------------------
% 16.97/6.73 % (14906)Instruction limit reached!
% 16.97/6.73 % (14906)------------------------------
% 16.97/6.73 % (14906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.97/6.73 % (14906)Termination reason: Unknown
% 16.97/6.73 % (14906)Termination phase: Property scanning
% 16.97/6.73
% 16.97/6.73 % (14906)Memory used [KB]: 27504
% 16.97/6.73 % (14906)Time elapsed: 0.319 s
% 16.97/6.73 % (14906)Instructions burned: 925 (million)
% 16.97/6.73 % (14906)------------------------------
% 16.97/6.73 % (14906)------------------------------
% 16.97/6.74 % (14921)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_14485 for (2981ds/4350Mi)
% 16.97/6.74 % (14922)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_14485 for (2981ds/68Mi)
% 16.97/6.77 % (14922)Instruction limit reached!
% 16.97/6.77 % (14922)------------------------------
% 16.97/6.77 % (14922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.97/6.77 % (14922)Termination reason: Unknown
% 16.97/6.77 % (14922)Termination phase: shuffling
% 16.97/6.77
% 16.97/6.77 % (14922)Memory used [KB]: 14711
% 16.97/6.77 % (14922)Time elapsed: 0.031 s
% 16.97/6.77 % (14922)Instructions burned: 69 (million)
% 16.97/6.77 % (14922)------------------------------
% 16.97/6.77 % (14922)------------------------------
% 16.97/6.78 % (14923)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_14485 for (2981ds/358Mi)
% 17.51/6.83 % (14911)Instruction limit reached!
% 17.51/6.83 % (14911)------------------------------
% 17.51/6.83 % (14911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/6.83 % (14911)Termination reason: Unknown
% 17.51/6.83 % (14911)Termination phase: Property scanning
% 17.51/6.83
% 17.51/6.83 % (14911)Memory used [KB]: 27504
% 17.51/6.83 % (14911)Time elapsed: 0.348 s
% 17.51/6.83 % (14911)Instructions burned: 1022 (million)
% 17.51/6.83 % (14911)------------------------------
% 17.51/6.83 % (14911)------------------------------
% 17.51/6.84 % (14924)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_14485 for (2980ds/31Mi)
% 17.51/6.86 % (14924)Instruction limit reached!
% 17.51/6.86 % (14924)------------------------------
% 17.51/6.86 % (14924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.51/6.86 % (14924)Termination reason: Unknown
% 17.51/6.86 % (14924)Termination phase: shuffling
% 17.51/6.86
% 17.51/6.86 % (14924)Memory used [KB]: 14072
% 17.51/6.86 % (14924)Time elapsed: 0.020 s
% 17.51/6.86 % (14924)Instructions burned: 33 (million)
% 17.51/6.86 % (14924)------------------------------
% 17.51/6.86 % (14924)------------------------------
% 17.51/6.87 % (14925)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_14485 for (2980ds/279Mi)
% 17.90/6.91 % (14923)Instruction limit reached!
% 17.90/6.91 % (14923)------------------------------
% 17.90/6.91 % (14923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.90/6.91 % (14923)Termination reason: Unknown
% 17.90/6.91 % (14923)Termination phase: shuffling
% 17.90/6.91
% 17.90/6.91 % (14923)Memory used [KB]: 18549
% 17.90/6.91 % (14923)Time elapsed: 0.126 s
% 17.90/6.91 % (14923)Instructions burned: 358 (million)
% 17.90/6.91 % (14923)------------------------------
% 17.90/6.91 % (14923)------------------------------
% 17.90/6.92 % (14926)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_14485 for (2980ds/258Mi)
% 17.90/6.96 % (14925)Instruction limit reached!
% 17.90/6.96 % (14925)------------------------------
% 17.90/6.96 % (14925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.90/6.96 % (14925)Termination reason: Unknown
% 17.90/6.96 % (14925)Termination phase: shuffling
% 17.90/6.96
% 17.90/6.96 % (14925)Memory used [KB]: 19829
% 17.90/6.96 % (14925)Time elapsed: 0.089 s
% 17.90/6.96 % (14925)Instructions burned: 282 (million)
% 17.90/6.96 % (14925)------------------------------
% 17.90/6.96 % (14925)------------------------------
% 17.90/6.97 % (14927)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_14485 for (2979ds/26Mi)
% 17.90/6.99 % (14927)Instruction limit reached!
% 17.90/6.99 % (14927)------------------------------
% 17.90/6.99 % (14927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.90/6.99 % (14927)Termination reason: Unknown
% 17.90/6.99 % (14927)Termination phase: shuffling
% 17.90/6.99
% 17.90/6.99 % (14927)Memory used [KB]: 14200
% 17.90/6.99 % (14927)Time elapsed: 0.017 s
% 17.90/6.99 % (14927)Instructions burned: 26 (million)
% 17.90/6.99 % (14927)------------------------------
% 17.90/6.99 % (14927)------------------------------
% 17.90/7.00 % (14928)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_14485 for (2979ds/995Mi)
% 17.90/7.01 % (14926)Instruction limit reached!
% 17.90/7.01 % (14926)------------------------------
% 17.90/7.01 % (14926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.90/7.01 % (14926)Termination reason: Unknown
% 17.90/7.01 % (14926)Termination phase: shuffling
% 17.90/7.01
% 17.90/7.01 % (14926)Memory used [KB]: 17270
% 17.90/7.01 % (14926)Time elapsed: 0.092 s
% 17.90/7.01 % (14926)Instructions burned: 258 (million)
% 17.90/7.01 % (14926)------------------------------
% 17.90/7.01 % (14926)------------------------------
% 20.10/7.02 % (14929)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_14485 for (2979ds/373Mi)
% 20.10/7.06 % (14917)Instruction limit reached!
% 20.10/7.06 % (14917)------------------------------
% 20.10/7.06 % (14917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.10/7.06 % (14917)Termination reason: Unknown
% 20.10/7.06 % (14917)Termination phase: Property scanning
% 20.10/7.06
% 20.10/7.06 % (14917)Memory used [KB]: 27376
% 20.10/7.06 % (14917)Time elapsed: 0.477 s
% 20.10/7.06 % (14917)Instructions burned: 1540 (million)
% 20.10/7.06 % (14917)------------------------------
% 20.10/7.06 % (14917)------------------------------
% 20.10/7.07 % (14930)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_14485 for (2978ds/253Mi)
% 20.77/7.15 % (14929)Instruction limit reached!
% 20.77/7.15 % (14929)------------------------------
% 20.77/7.15 % (14929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.77/7.15 % (14929)Termination reason: Unknown
% 20.77/7.15 % (14929)Termination phase: shuffling
% 20.77/7.15
% 20.77/7.15 % (14929)Memory used [KB]: 18677
% 20.77/7.15 % (14929)Time elapsed: 0.133 s
% 20.77/7.15 % (14929)Instructions burned: 374 (million)
% 20.77/7.15 % (14929)------------------------------
% 20.77/7.15 % (14929)------------------------------
% 20.77/7.15 % (14930)Instruction limit reached!
% 20.77/7.15 % (14930)------------------------------
% 20.77/7.15 % (14930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.77/7.15 % (14930)Termination reason: Unknown
% 20.77/7.15 % (14930)Termination phase: shuffling
% 20.77/7.15
% 20.77/7.15 % (14930)Memory used [KB]: 19317
% 20.77/7.15 % (14930)Time elapsed: 0.084 s
% 20.77/7.15 % (14930)Instructions burned: 256 (million)
% 20.77/7.15 % (14930)------------------------------
% 20.77/7.15 % (14930)------------------------------
% 20.77/7.16 % (14931)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_14485 for (2977ds/832Mi)
% 20.77/7.17 % (14932)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_14485 for (2977ds/668Mi)
% 21.45/7.22 % (14920)Instruction limit reached!
% 21.45/7.22 % (14920)------------------------------
% 21.45/7.22 % (14920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.45/7.22 % (14920)Termination reason: Unknown
% 21.45/7.22 % (14920)Termination phase: SInE selection
% 21.45/7.22
% 21.45/7.22 % (14920)Memory used [KB]: 28400
% 21.45/7.22 % (14920)Time elapsed: 0.598 s
% 21.45/7.22 % (14920)Instructions burned: 1914 (million)
% 21.45/7.22 % (14920)------------------------------
% 21.45/7.22 % (14920)------------------------------
% 21.45/7.23 % (14933)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_14485 for (2977ds/40Mi)
% 21.45/7.25 % (14933)Instruction limit reached!
% 21.45/7.25 % (14933)------------------------------
% 21.45/7.25 % (14933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.45/7.25 % (14933)Termination reason: Unknown
% 21.45/7.25 % (14933)Termination phase: shuffling
% 21.45/7.25
% 21.45/7.25 % (14933)Memory used [KB]: 14328
% 21.45/7.25 % (14933)Time elapsed: 0.021 s
% 21.45/7.25 % (14933)Instructions burned: 40 (million)
% 21.45/7.25 % (14933)------------------------------
% 21.45/7.25 % (14933)------------------------------
% 21.45/7.26 % (14934)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_14485 for (2976ds/294Mi)
% 21.45/7.29 % (14921)Refutation not found, incomplete strategy
% 21.45/7.29 % (14921)------------------------------
% 21.45/7.29 % (14921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.45/7.29 % (14921)Termination reason: Refutation not found, incomplete strategy
% 21.45/7.29
% 21.45/7.29
% 21.45/7.29 % (14921)Memory used [KB]: 32238
% 21.45/7.29 % (14921)Time elapsed: 0.552 s
% 21.45/7.29 % (14921)Instructions burned: 1750 (million)
% 21.45/7.29 % (14921)------------------------------
% 21.45/7.29 % (14921)------------------------------
% 21.45/7.29 % (14928)Instruction limit reached!
% 21.45/7.29 % (14928)------------------------------
% 21.45/7.29 % (14928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.45/7.29 % (14928)Termination reason: Unknown
% 21.45/7.29 % (14928)Termination phase: shuffling
% 21.45/7.29
% 21.45/7.29 % (14928)Memory used [KB]: 33389
% 21.45/7.29 % (14928)Time elapsed: 0.298 s
% 21.45/7.29 % (14928)Instructions burned: 996 (million)
% 21.45/7.29 % (14928)------------------------------
% 21.45/7.29 % (14928)------------------------------
% 21.63/7.30 % (14935)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_14485 for (2976ds/187Mi)
% 21.63/7.31 % (14936)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_14485 for (2976ds/371Mi)
% 21.63/7.35 % (14934)Instruction limit reached!
% 21.63/7.35 % (14934)------------------------------
% 21.63/7.35 % (14934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.63/7.35 % (14934)Termination reason: Unknown
% 21.63/7.35 % (14934)Termination phase: shuffling
% 21.63/7.35
% 21.63/7.35 % (14934)Memory used [KB]: 19957
% 21.63/7.35 % (14934)Time elapsed: 0.092 s
% 21.63/7.35 % (14934)Instructions burned: 294 (million)
% 21.63/7.35 % (14934)------------------------------
% 21.63/7.35 % (14934)------------------------------
% 21.63/7.36 % (14932)Instruction limit reached!
% 21.63/7.36 % (14932)------------------------------
% 21.63/7.36 % (14932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.63/7.36 % (14932)Termination reason: Unknown
% 21.63/7.36 % (14932)Termination phase: shuffling
% 21.63/7.36
% 21.63/7.36 % (14932)Memory used [KB]: 25074
% 21.63/7.36 % (14932)Time elapsed: 0.199 s
% 21.63/7.36 % (14932)Instructions burned: 669 (million)
% 21.63/7.36 % (14932)------------------------------
% 21.63/7.36 % (14932)------------------------------
% 21.63/7.36 % (14937)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_14485 for (2975ds/1827Mi)
% 21.63/7.37 % (14935)Instruction limit reached!
% 21.63/7.37 % (14935)------------------------------
% 21.63/7.37 % (14935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.63/7.37 % (14935)Termination reason: Unknown
% 21.63/7.37 % (14935)Termination phase: shuffling
% 21.63/7.37
% 21.63/7.37 % (14935)Memory used [KB]: 16119
% 21.63/7.37 % (14935)Time elapsed: 0.069 s
% 21.63/7.37 % (14935)Instructions burned: 187 (million)
% 21.63/7.37 % (14935)------------------------------
% 21.63/7.37 % (14935)------------------------------
% 21.63/7.38 % (14938)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_14485 for (2975ds/70Mi)
% 21.63/7.38 % (14939)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_14485 for (2975ds/316Mi)
% 22.52/7.40 % (14938)Instruction limit reached!
% 22.52/7.40 % (14938)------------------------------
% 22.52/7.40 % (14938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.52/7.40 % (14938)Termination reason: Unknown
% 22.52/7.40 % (14938)Termination phase: shuffling
% 22.52/7.40
% 22.52/7.40 % (14938)Memory used [KB]: 14711
% 22.52/7.40 % (14938)Time elapsed: 0.030 s
% 22.52/7.40 % (14938)Instructions burned: 72 (million)
% 22.52/7.40 % (14938)------------------------------
% 22.52/7.40 % (14938)------------------------------
% 22.52/7.42 % (14940)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_14485 for (2975ds/932Mi)
% 22.52/7.44 % (14936)Instruction limit reached!
% 22.52/7.44 % (14936)------------------------------
% 22.52/7.44 % (14936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.52/7.44 % (14936)Termination reason: Unknown
% 22.52/7.44 % (14936)Termination phase: shuffling
% 22.52/7.44
% 22.52/7.44 % (14936)Memory used [KB]: 18549
% 22.52/7.44 % (14936)Time elapsed: 0.132 s
% 22.52/7.44 % (14936)Instructions burned: 373 (million)
% 22.52/7.44 % (14936)------------------------------
% 22.52/7.44 % (14936)------------------------------
% 22.52/7.45 % (14941)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_14485 for (2974ds/4714Mi)
% 22.52/7.45 % (14931)Instruction limit reached!
% 22.52/7.45 % (14931)------------------------------
% 22.52/7.45 % (14931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.52/7.45 % (14931)Termination reason: Unknown
% 22.52/7.45 % (14931)Termination phase: shuffling
% 22.52/7.45
% 22.52/7.45 % (14931)Memory used [KB]: 26609
% 22.52/7.45 % (14931)Time elapsed: 0.290 s
% 22.52/7.45 % (14931)Instructions burned: 832 (million)
% 22.52/7.45 % (14931)------------------------------
% 22.52/7.45 % (14931)------------------------------
% 22.52/7.47 % (14942)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_14485 for (2974ds/8250Mi)
% 22.52/7.49 % (14939)Instruction limit reached!
% 22.52/7.49 % (14939)------------------------------
% 22.52/7.49 % (14939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.52/7.49 % (14939)Termination reason: Unknown
% 22.52/7.49 % (14939)Termination phase: shuffling
% 22.52/7.49
% 22.52/7.49 % (14939)Memory used [KB]: 20212
% 22.52/7.49 % (14939)Time elapsed: 0.102 s
% 22.52/7.49 % (14939)Instructions burned: 317 (million)
% 22.52/7.49 % (14939)------------------------------
% 22.52/7.49 % (14939)------------------------------
% 23.32/7.50 % (14943)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_14485 for (2974ds/770Mi)
% 23.52/7.69 % (14940)Instruction limit reached!
% 23.52/7.69 % (14940)------------------------------
% 23.52/7.69 % (14940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.52/7.69 % (14940)Termination reason: Unknown
% 23.52/7.69 % (14940)Termination phase: shuffling
% 23.52/7.69
% 23.52/7.69 % (14940)Memory used [KB]: 32622
% 23.52/7.69 % (14940)Time elapsed: 0.278 s
% 23.52/7.69 % (14940)Instructions burned: 935 (million)
% 23.52/7.69 % (14940)------------------------------
% 23.52/7.69 % (14940)------------------------------
% 24.03/7.71 % (14944)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_14485 for (2972ds/794Mi)
% 24.03/7.75 % (14943)Instruction limit reached!
% 24.03/7.75 % (14943)------------------------------
% 24.03/7.75 % (14943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.03/7.75 % (14943)Termination reason: Unknown
% 24.03/7.75 % (14943)Termination phase: shuffling
% 24.03/7.75
% 24.03/7.75 % (14943)Memory used [KB]: 25458
% 24.03/7.75 % (14943)Time elapsed: 0.258 s
% 24.03/7.75 % (14943)Instructions burned: 770 (million)
% 24.03/7.75 % (14943)------------------------------
% 24.03/7.75 % (14943)------------------------------
% 24.03/7.77 % (14945)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_14485 for (2971ds/464Mi)
% 24.69/7.93 % (14945)Instruction limit reached!
% 24.69/7.93 % (14945)------------------------------
% 24.69/7.93 % (14945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/7.93 % (14945)Termination reason: Unknown
% 24.69/7.93 % (14945)Termination phase: shuffling
% 24.69/7.93
% 24.69/7.93 % (14945)Memory used [KB]: 19829
% 24.69/7.93 % (14945)Time elapsed: 0.164 s
% 24.69/7.93 % (14945)Instructions burned: 464 (million)
% 24.69/7.93 % (14945)------------------------------
% 24.69/7.93 % (14945)------------------------------
% 24.69/7.94 % (14946)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_14485 for (2969ds/1376Mi)
% 24.69/7.94 % (14937)Instruction limit reached!
% 24.69/7.94 % (14937)------------------------------
% 24.69/7.94 % (14937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/7.94 % (14937)Termination reason: Unknown
% 24.69/7.94 % (14937)Termination phase: Preprocessing 3
% 24.69/7.94
% 24.69/7.94 % (14937)Memory used [KB]: 33517
% 24.69/7.94 % (14937)Time elapsed: 0.583 s
% 24.69/7.94 % (14937)Instructions burned: 1827 (million)
% 24.69/7.94 % (14937)------------------------------
% 24.69/7.94 % (14937)------------------------------
% 24.69/7.96 % (14947)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_14485 for (2969ds/906Mi)
% 24.69/7.98 % (14944)Instruction limit reached!
% 24.69/7.98 % (14944)------------------------------
% 24.69/7.98 % (14944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/7.98 % (14944)Termination reason: Unknown
% 24.69/7.98 % (14944)Termination phase: shuffling
% 24.69/7.98
% 24.69/7.98 % (14944)Memory used [KB]: 25841
% 24.69/7.98 % (14944)Time elapsed: 0.274 s
% 24.69/7.98 % (14944)Instructions burned: 796 (million)
% 24.69/7.98 % (14944)------------------------------
% 24.69/7.98 % (14944)------------------------------
% 24.69/7.99 % (14948)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_14485 for (2969ds/434Mi)
% 24.69/8.02 % (14919)Instruction limit reached!
% 24.69/8.02 % (14919)------------------------------
% 24.69/8.02 % (14919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.69/8.02 % (14919)Termination reason: Unknown
% 24.69/8.02 % (14919)Termination phase: Property scanning
% 24.69/8.02
% 24.69/8.02 % (14919)Memory used [KB]: 59743
% 24.69/8.02 % (14919)Time elapsed: 1.425 s
% 24.69/8.02 % (14919)Instructions burned: 5207 (million)
% 24.69/8.02 % (14919)------------------------------
% 24.69/8.02 % (14919)------------------------------
% 25.89/8.03 % (14949)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_14485 for (2969ds/865Mi)
% 25.89/8.05 % (14916)Instruction limit reached!
% 25.89/8.05 % (14916)------------------------------
% 25.89/8.05 % (14916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.89/8.05 % (14916)Termination reason: Unknown
% 25.89/8.05 % (14916)Termination phase: Saturation
% 25.89/8.05
% 25.89/8.05 % (14916)Memory used [KB]: 34413
% 25.89/8.05 % (14916)Time elapsed: 1.478 s
% 25.89/8.05 % (14916)Instructions burned: 4437 (million)
% 25.89/8.05 % (14916)------------------------------
% 25.89/8.05 % (14916)------------------------------
% 25.89/8.06 % (14950)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_14485 for (2968ds/593Mi)
% 27.88/8.14 % (14948)Instruction limit reached!
% 27.88/8.14 % (14948)------------------------------
% 27.88/8.14 % (14948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.88/8.14 % (14948)Termination reason: Unknown
% 27.88/8.14 % (14948)Termination phase: shuffling
% 27.88/8.14
% 27.88/8.14 % (14948)Memory used [KB]: 19701
% 27.88/8.14 % (14948)Time elapsed: 0.154 s
% 27.88/8.14 % (14948)Instructions burned: 435 (million)
% 27.88/8.14 % (14948)------------------------------
% 27.88/8.14 % (14948)------------------------------
% 27.88/8.16 % (14951)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_14485 for (2967ds/443Mi)
% 28.19/8.24 % (14950)Instruction limit reached!
% 28.19/8.24 % (14950)------------------------------
% 28.19/8.24 % (14950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.19/8.24 % (14950)Termination reason: Unknown
% 28.19/8.24 % (14950)Termination phase: shuffling
% 28.19/8.24
% 28.19/8.24 % (14950)Memory used [KB]: 24050
% 28.19/8.24 % (14950)Time elapsed: 0.177 s
% 28.19/8.24 % (14950)Instructions burned: 593 (million)
% 28.19/8.24 % (14950)------------------------------
% 28.19/8.24 % (14950)------------------------------
% 28.19/8.25 % (14952)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_14485 for (2966ds/594Mi)
% 28.19/8.26 % (14947)Instruction limit reached!
% 28.19/8.26 % (14947)------------------------------
% 28.19/8.26 % (14947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.19/8.26 % (14947)Termination reason: Unknown
% 28.19/8.26 % (14947)Termination phase: shuffling
% 28.19/8.26
% 28.19/8.26 % (14947)Memory used [KB]: 27249
% 28.19/8.26 % (14947)Time elapsed: 0.308 s
% 28.19/8.26 % (14947)Instructions burned: 908 (million)
% 28.19/8.26 % (14947)------------------------------
% 28.19/8.26 % (14947)------------------------------
% 28.19/8.28 % (14953)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_14485 for (2966ds/327Mi)
% 28.19/8.29 % (14949)Instruction limit reached!
% 28.19/8.29 % (14949)------------------------------
% 28.19/8.29 % (14949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.19/8.29 % (14949)Termination reason: Unknown
% 28.19/8.29 % (14949)Termination phase: shuffling
% 28.19/8.29
% 28.19/8.29 % (14949)Memory used [KB]: 31726
% 28.19/8.29 % (14949)Time elapsed: 0.259 s
% 28.19/8.29 % (14949)Instructions burned: 866 (million)
% 28.19/8.29 % (14949)------------------------------
% 28.19/8.29 % (14949)------------------------------
% 29.06/8.30 % (14954)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_14485 for (2966ds/5411Mi)
% 29.06/8.31 % (14951)Instruction limit reached!
% 29.06/8.31 % (14951)------------------------------
% 29.06/8.31 % (14951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/8.31 % (14951)Termination reason: Unknown
% 29.06/8.31 % (14951)Termination phase: shuffling
% 29.06/8.31
% 29.06/8.31 % (14951)Memory used [KB]: 19445
% 29.06/8.31 % (14951)Time elapsed: 0.152 s
% 29.06/8.31 % (14951)Instructions burned: 443 (million)
% 29.06/8.31 % (14951)------------------------------
% 29.06/8.31 % (14951)------------------------------
% 29.06/8.32 % (14955)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_14485 for (2966ds/1762Mi)
% 29.06/8.35 % (14946)Instruction limit reached!
% 29.06/8.35 % (14946)------------------------------
% 29.06/8.35 % (14946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/8.35 % (14946)Termination reason: Unknown
% 29.06/8.35 % (14946)Termination phase: shuffling
% 29.06/8.35
% 29.06/8.35 % (14946)Memory used [KB]: 38378
% 29.06/8.35 % (14946)Time elapsed: 0.407 s
% 29.06/8.35 % (14946)Instructions burned: 1377 (million)
% 29.06/8.35 % (14946)------------------------------
% 29.06/8.35 % (14946)------------------------------
% 29.06/8.36 % (14956)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_14485 for (2965ds/96Mi)
% 29.06/8.39 % (14953)Instruction limit reached!
% 29.06/8.39 % (14953)------------------------------
% 29.06/8.39 % (14953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/8.39 % (14953)Termination reason: Unknown
% 29.06/8.39 % (14953)Termination phase: shuffling
% 29.06/8.39
% 29.06/8.39 % (14953)Memory used [KB]: 18166
% 29.06/8.39 % (14953)Time elapsed: 0.116 s
% 29.06/8.39 % (14953)Instructions burned: 328 (million)
% 29.06/8.39 % (14953)------------------------------
% 29.06/8.39 % (14953)------------------------------
% 29.06/8.39 % (14956)Instruction limit reached!
% 29.06/8.39 % (14956)------------------------------
% 29.06/8.39 % (14956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.06/8.39 % (14956)Termination reason: Unknown
% 29.06/8.39 % (14956)Termination phase: shuffling
% 29.06/8.39
% 29.06/8.39 % (14956)Memory used [KB]: 15095
% 29.06/8.39 % (14956)Time elapsed: 0.036 s
% 29.06/8.39 % (14956)Instructions burned: 97 (million)
% 29.06/8.39 % (14956)------------------------------
% 29.06/8.39 % (14956)------------------------------
% 29.64/8.40 % (14957)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_14485 for (2965ds/503Mi)
% 29.64/8.41 % (14958)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_14485 for (2965ds/90Mi)
% 29.64/8.44 % (14958)Instruction limit reached!
% 29.64/8.44 % (14958)------------------------------
% 29.64/8.44 % (14958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.64/8.44 % (14958)Termination reason: Unknown
% 29.64/8.44 % (14958)Termination phase: shuffling
% 29.64/8.44
% 29.64/8.44 % (14958)Memory used [KB]: 15095
% 29.64/8.44 % (14958)Time elapsed: 0.039 s
% 29.64/8.44 % (14958)Instructions burned: 92 (million)
% 29.64/8.44 % (14958)------------------------------
% 29.64/8.44 % (14958)------------------------------
% 29.64/8.46 % (14952)Instruction limit reached!
% 29.64/8.46 % (14952)------------------------------
% 29.64/8.46 % (14952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.64/8.46 % (14952)Termination reason: Unknown
% 29.64/8.46 % (14952)Termination phase: shuffling
% 29.64/8.46
% 29.64/8.46 % (14952)Memory used [KB]: 23411
% 29.64/8.46 % (14952)Time elapsed: 0.206 s
% 29.64/8.46 % (14952)Instructions burned: 596 (million)
% 29.64/8.46 % (14952)------------------------------
% 29.64/8.46 % (14952)------------------------------
% 29.64/8.46 % (14959)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_14485 for (2964ds/593Mi)
% 29.64/8.47 % (14960)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_14485 for (2964ds/1512Mi)
% 30.10/8.57 % (14957)Instruction limit reached!
% 30.10/8.57 % (14957)------------------------------
% 30.10/8.57 % (14957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.10/8.57 % (14957)Termination reason: Unknown
% 30.10/8.57 % (14957)Termination phase: shuffling
% 30.10/8.57
% 30.10/8.57 % (14957)Memory used [KB]: 19957
% 30.10/8.57 % (14957)Time elapsed: 0.171 s
% 30.10/8.57 % (14957)Instructions burned: 504 (million)
% 30.10/8.57 % (14957)------------------------------
% 30.10/8.57 % (14957)------------------------------
% 30.10/8.59 % (14961)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_14485 for (2963ds/569Mi)
% 30.49/8.66 % (14959)Instruction limit reached!
% 30.49/8.66 % (14959)------------------------------
% 30.49/8.66 % (14959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.49/8.66 % (14959)Termination reason: Unknown
% 30.49/8.66 % (14959)Termination phase: shuffling
% 30.49/8.66
% 30.49/8.66 % (14959)Memory used [KB]: 23283
% 30.49/8.66 % (14959)Time elapsed: 0.205 s
% 30.49/8.66 % (14959)Instructions burned: 593 (million)
% 30.49/8.66 % (14959)------------------------------
% 30.49/8.66 % (14959)------------------------------
% 30.49/8.67 % (14962)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_14485 for (2962ds/501Mi)
% 30.91/8.73 % (14941)Instruction limit reached!
% 30.91/8.73 % (14941)------------------------------
% 30.91/8.73 % (14941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/8.73 % (14941)Termination reason: Unknown
% 30.91/8.73 % (14941)Termination phase: Function definition elimination
% 30.91/8.73
% 30.91/8.73 % (14941)Memory used [KB]: 56544
% 30.91/8.73 % (14941)Time elapsed: 1.278 s
% 30.91/8.73 % (14941)Instructions burned: 4717 (million)
% 30.91/8.73 % (14941)------------------------------
% 30.91/8.73 % (14941)------------------------------
% 30.91/8.74 % (14963)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_14485 for (2961ds/562Mi)
% 30.91/8.76 % (14961)Instruction limit reached!
% 30.91/8.76 % (14961)------------------------------
% 30.91/8.76 % (14961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.91/8.76 % (14961)Termination reason: Unknown
% 30.91/8.76 % (14961)Termination phase: shuffling
% 30.91/8.76
% 30.91/8.76 % (14961)Memory used [KB]: 23666
% 30.91/8.76 % (14961)Time elapsed: 0.172 s
% 30.91/8.76 % (14961)Instructions burned: 570 (million)
% 30.91/8.76 % (14961)------------------------------
% 30.91/8.76 % (14961)------------------------------
% 30.91/8.77 % (14964)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_14485 for (2961ds/406Mi)
% 31.24/8.83 % (14955)Instruction limit reached!
% 31.24/8.83 % (14955)------------------------------
% 31.24/8.83 % (14955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/8.83 % (14955)Termination reason: Unknown
% 31.24/8.83 % (14955)Termination phase: Property scanning
% 31.24/8.83
% 31.24/8.83 % (14955)Memory used [KB]: 41960
% 31.24/8.83 % (14955)Time elapsed: 0.517 s
% 31.24/8.83 % (14955)Instructions burned: 1763 (million)
% 31.24/8.83 % (14955)------------------------------
% 31.24/8.83 % (14955)------------------------------
% 31.24/8.84 % (14962)Instruction limit reached!
% 31.24/8.84 % (14962)------------------------------
% 31.24/8.84 % (14962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/8.84 % (14962)Termination reason: Unknown
% 31.24/8.84 % (14962)Termination phase: shuffling
% 31.24/8.84
% 31.24/8.84 % (14962)Memory used [KB]: 20084
% 31.24/8.84 % (14962)Time elapsed: 0.171 s
% 31.24/8.84 % (14962)Instructions burned: 502 (million)
% 31.24/8.84 % (14962)------------------------------
% 31.24/8.84 % (14962)------------------------------
% 31.24/8.85 % (14965)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_14485 for (2960ds/582Mi)
% 31.24/8.85 % (14966)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_14485 for (2960ds/456Mi)
% 31.24/8.87 % (14954)Refutation not found, incomplete strategy
% 31.24/8.87 % (14954)------------------------------
% 31.24/8.87 % (14954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.24/8.87 % (14954)Termination reason: Refutation not found, incomplete strategy
% 31.24/8.87
% 31.24/8.87
% 31.24/8.87 % (14954)Memory used [KB]: 33133
% 31.24/8.87 % (14954)Time elapsed: 0.565 s
% 31.24/8.87 % (14954)Instructions burned: 1786 (million)
% 31.24/8.87 % (14954)------------------------------
% 31.24/8.87 % (14954)------------------------------
% 31.24/8.88 % (14967)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_14485 for (2960ds/393Mi)
% 32.63/8.91 % (14964)Instruction limit reached!
% 32.63/8.91 % (14964)------------------------------
% 32.63/8.91 % (14964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.63/8.91 % (14964)Termination reason: Unknown
% 32.63/8.91 % (14964)Termination phase: shuffling
% 32.63/8.91
% 32.63/8.91 % (14964)Memory used [KB]: 19061
% 32.63/8.91 % (14964)Time elapsed: 0.141 s
% 32.63/8.91 % (14964)Instructions burned: 406 (million)
% 32.63/8.91 % (14964)------------------------------
% 32.63/8.91 % (14964)------------------------------
% 32.63/8.91 % (14963)Instruction limit reached!
% 32.63/8.91 % (14963)------------------------------
% 32.63/8.91 % (14963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.63/8.91 % (14963)Termination reason: Unknown
% 32.63/8.91 % (14963)Termination phase: shuffling
% 32.63/8.91
% 32.63/8.91 % (14963)Memory used [KB]: 23539
% 32.63/8.91 % (14963)Time elapsed: 0.169 s
% 32.63/8.91 % (14963)Instructions burned: 562 (million)
% 32.63/8.91 % (14963)------------------------------
% 32.63/8.91 % (14963)------------------------------
% 32.63/8.92 % (14969)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_14485 for (2960ds/3373Mi)
% 32.63/8.93 % (14968)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_14485 for (2960ds/1335Mi)
% 32.63/8.95 % (14960)Instruction limit reached!
% 32.63/8.95 % (14960)------------------------------
% 32.63/8.95 % (14960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.63/8.95 % (14960)Termination reason: Unknown
% 32.63/8.95 % (14960)Termination phase: Property scanning
% 32.63/8.95
% 32.63/8.95 % (14960)Memory used [KB]: 29679
% 32.63/8.95 % (14960)Time elapsed: 0.485 s
% 32.63/8.95 % (14960)Instructions burned: 1512 (million)
% 32.63/8.95 % (14960)------------------------------
% 32.63/8.95 % (14960)------------------------------
% 32.63/8.96 % (14970)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_14485 for (2959ds/474Mi)
% 32.63/9.00 % (14967)Instruction limit reached!
% 32.63/9.00 % (14967)------------------------------
% 32.63/9.00 % (14967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.63/9.00 % (14967)Termination reason: Unknown
% 32.63/9.00 % (14967)Termination phase: shuffling
% 32.63/9.00
% 32.63/9.00 % (14967)Memory used [KB]: 21364
% 32.63/9.00 % (14967)Time elapsed: 0.122 s
% 32.63/9.00 % (14967)Instructions burned: 393 (million)
% 32.63/9.00 % (14967)------------------------------
% 32.63/9.00 % (14967)------------------------------
% 32.63/9.01 % (14966)Instruction limit reached!
% 32.63/9.01 % (14966)------------------------------
% 32.63/9.01 % (14966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.63/9.01 % (14966)Termination reason: Unknown
% 32.63/9.01 % (14966)Termination phase: shuffling
% 32.63/9.01
% 32.63/9.01 % (14966)Memory used [KB]: 19573
% 32.63/9.01 % (14966)Time elapsed: 0.159 s
% 32.63/9.01 % (14966)Instructions burned: 457 (million)
% 32.63/9.01 % (14966)------------------------------
% 32.63/9.01 % (14966)------------------------------
% 32.63/9.01 % (14971)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_14485 for (2959ds/157Mi)
% 34.31/9.02 % (14972)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_14485 for (2959ds/590Mi)
% 34.31/9.05 % (14965)Instruction limit reached!
% 34.31/9.05 % (14965)------------------------------
% 34.31/9.05 % (14965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.31/9.05 % (14965)Termination reason: Unknown
% 34.31/9.05 % (14965)Termination phase: shuffling
% 34.31/9.05
% 34.31/9.05 % (14965)Memory used [KB]: 21492
% 34.31/9.05 % (14965)Time elapsed: 0.206 s
% 34.31/9.05 % (14965)Instructions burned: 584 (million)
% 34.31/9.05 % (14965)------------------------------
% 34.31/9.05 % (14965)------------------------------
% 34.31/9.06 % (14973)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_14485 for (2958ds/104Mi)
% 34.31/9.07 % (14971)Instruction limit reached!
% 34.31/9.07 % (14971)------------------------------
% 34.31/9.07 % (14971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.31/9.07 % (14971)Termination reason: Unknown
% 34.31/9.07 % (14971)Termination phase: shuffling
% 34.31/9.07
% 34.31/9.07 % (14971)Memory used [KB]: 15991
% 34.31/9.07 % (14971)Time elapsed: 0.054 s
% 34.31/9.07 % (14971)Instructions burned: 159 (million)
% 34.31/9.07 % (14971)------------------------------
% 34.31/9.07 % (14971)------------------------------
% 34.31/9.08 % (14974)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_14485 for (2958ds/414Mi)
% 34.31/9.11 % (14973)Instruction limit reached!
% 34.31/9.11 % (14973)------------------------------
% 34.31/9.11 % (14973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.31/9.11 % (14973)Termination reason: Unknown
% 34.31/9.11 % (14973)Termination phase: shuffling
% 34.31/9.11
% 34.31/9.11 % (14973)Memory used [KB]: 15223
% 34.31/9.11 % (14973)Time elapsed: 0.045 s
% 34.31/9.11 % (14973)Instructions burned: 105 (million)
% 34.31/9.11 % (14973)------------------------------
% 34.31/9.11 % (14973)------------------------------
% 34.31/9.11 % (14970)Instruction limit reached!
% 34.31/9.11 % (14970)------------------------------
% 34.31/9.11 % (14970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.31/9.11 % (14970)Termination reason: Unknown
% 34.31/9.11 % (14970)Termination phase: shuffling
% 34.31/9.11
% 34.31/9.11 % (14970)Memory used [KB]: 22387
% 34.31/9.11 % (14970)Time elapsed: 0.146 s
% 34.31/9.11 % (14970)Instructions burned: 475 (million)
% 34.31/9.11 % (14970)------------------------------
% 34.31/9.11 % (14970)------------------------------
% 34.31/9.12 % (14975)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_14485 for (2958ds/715Mi)
% 34.31/9.12 % (14976)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_14485 for (2958ds/961Mi)
% 34.88/9.13 % (14942)First to succeed.
% 34.88/9.15 % (14942)Refutation found. Thanks to Tanya!
% 34.88/9.15 % SZS status ContradictoryAxioms for DTF2THF_14485
% 34.88/9.15 % SZS output start Proof for DTF2THF_14485
% 34.88/9.15 thf(type_def_5, type, real: $tType).
% 34.88/9.15 thf(type_def_6, type, int: $tType).
% 34.88/9.15 thf(type_def_8, type, set_nat: $tType).
% 34.88/9.15 thf(type_def_9, type, set_Pr1261947904930325089at_nat: $tType).
% 34.88/9.15 thf(type_def_10, type, set_Pr4811707699266497531nteger: $tType).
% 34.88/9.15 thf(type_def_11, type, code_integer: $tType).
% 34.88/9.15 thf(type_def_12, type, nat: $tType).
% 34.88/9.15 thf(type_def_13, type, num: $tType).
% 34.88/9.15 thf(type_def_14, type, rat: $tType).
% 34.88/9.15 thf(type_def_15, type, set_Pr958786334691620121nt_int: $tType).
% 34.88/9.15 thf(type_def_16, type, product_prod_nat_nat: $tType).
% 34.88/9.15 thf(type_def_17, type, product_prod_int_int: $tType).
% 34.88/9.15 thf(type_def_18, type, set_Pr4329608150637261639at_nat: $tType).
% 34.88/9.15 thf(type_def_19, type, complex: $tType).
% 34.88/9.15 thf(type_def_20, type, code_natural: $tType).
% 34.88/9.15 thf(type_def_21, type, option_num: $tType).
% 34.88/9.15 thf(type_def_22, type, produc8923325533196201883nteger: $tType).
% 34.88/9.15 thf(type_def_23, type, set_set_nat: $tType).
% 34.88/9.15 thf(type_def_24, type, filter_real: $tType).
% 34.88/9.15 thf(type_def_25, type, extended_enat: $tType).
% 34.88/9.15 thf(type_def_26, type, option_nat: $tType).
% 34.88/9.15 thf(type_def_27, type, filter_nat: $tType).
% 34.88/9.15 thf(type_def_28, type, filter1242075044329608583at_nat: $tType).
% 34.88/9.15 thf(type_def_29, type, set_o: $tType).
% 34.88/9.15 thf(type_def_30, type, set_complex: $tType).
% 34.88/9.15 thf(type_def_31, type, set_int: $tType).
% 34.88/9.15 thf(type_def_32, type, set_list_o: $tType).
% 34.88/9.15 thf(type_def_33, type, set_list_complex: $tType).
% 34.88/9.15 thf(type_def_34, type, set_list_int: $tType).
% 34.88/9.15 thf(type_def_35, type, set_list_list_nat: $tType).
% 34.88/9.15 thf(type_def_36, type, set_list_nat: $tType).
% 34.88/9.15 thf(type_def_37, type, set_list_set_nat: $tType).
% 34.88/9.15 thf(type_def_38, type, set_list_VEBT_VEBT: $tType).
% 34.88/9.15 thf(type_def_39, type, set_real: $tType).
% 34.88/9.15 thf(type_def_40, type, set_VEBT_VEBT: $tType).
% 34.88/9.15 thf(type_def_41, type, set_num: $tType).
% 34.88/9.15 thf(type_def_42, type, set_rat: $tType).
% 34.88/9.15 thf(type_def_43, type, list_nat: $tType).
% 34.88/9.15 thf(type_def_44, type, sum_sum_nat_nat: $tType).
% 34.88/9.15 thf(type_def_45, type, set_Sum_sum_nat_nat: $tType).
% 34.88/9.15 thf(type_def_46, type, char: $tType).
% 34.88/9.15 thf(type_def_47, type, set_Pr8693737435421807431at_nat: $tType).
% 34.88/9.15 thf(type_def_48, type, vEBT_VEBT: $tType).
% 34.88/9.15 thf(type_def_49, type, list_o: $tType).
% 34.88/9.15 thf(type_def_50, type, list_list_o: $tType).
% 34.88/9.15 thf(type_def_51, type, list_list_int: $tType).
% 34.88/9.15 thf(type_def_52, type, list_int: $tType).
% 34.88/9.15 thf(type_def_53, type, list_list_nat: $tType).
% 34.88/9.15 thf(type_def_54, type, list_list_VEBT_VEBT: $tType).
% 34.88/9.15 thf(type_def_55, type, list_VEBT_VEBT: $tType).
% 34.88/9.15 thf(type_def_56, type, list_complex: $tType).
% 34.88/9.15 thf(type_def_57, type, list_real: $tType).
% 34.88/9.15 thf(type_def_58, type, list_set_nat: $tType).
% 34.88/9.15 thf(type_def_59, type, list_P6011104703257516679at_nat: $tType).
% 34.88/9.15 thf(type_def_60, type, list_P7333126701944960589_nat_o: $tType).
% 34.88/9.15 thf(type_def_61, type, list_P3521021558325789923at_int: $tType).
% 34.88/9.15 thf(type_def_62, type, list_P5647936690300460905T_VEBT: $tType).
% 34.88/9.15 thf(type_def_63, type, option_o: $tType).
% 34.88/9.15 thf(type_def_64, type, option_int: $tType).
% 34.88/9.15 thf(type_def_65, type, list_num: $tType).
% 34.88/9.15 thf(type_def_66, type, option4927543243414619207at_nat: $tType).
% 34.88/9.15 thf(type_def_67, type, option_VEBT_VEBT: $tType).
% 34.88/9.15 thf(type_def_68, type, set_Product_prod_o_o: $tType).
% 34.88/9.15 thf(type_def_69, type, set_Pr6227168374412355847list_o: $tType).
% 34.88/9.15 thf(type_def_70, type, set_Pr7565137564259432987nteger: $tType).
% 34.88/9.15 thf(type_def_71, type, set_Pr765067013931698361st_int: $tType).
% 34.88/9.15 thf(type_def_72, type, set_Pr3451248702717554689st_nat: $tType).
% 34.88/9.15 thf(type_def_73, type, set_Pr1542805901266377927at_nat: $tType).
% 34.88/9.15 thf(type_def_74, type, set_Pr4333006031979791559at_nat: $tType).
% 34.88/9.15 thf(type_def_75, type, set_Pr6192946355708809607T_VEBT: $tType).
% 34.88/9.15 thf(type_def_76, type, set_Pr1916528119006554503T_VEBT: $tType).
% 34.88/9.15 thf(type_def_77, type, list_C4705013386053401436er_nat: $tType).
% 34.88/9.15 thf(type_def_78, type, list_int_nat: $tType).
% 34.88/9.15 thf(type_def_79, type, list_nat_nat: $tType).
% 34.88/9.15 thf(type_def_80, type, list_P9162950289778280392at_nat: $tType).
% 34.88/9.15 thf(type_def_81, type, list_s9130966667114977576at_nat: $tType).
% 34.88/9.15 thf(type_def_82, type, list_Code_integer: $tType).
% 34.88/9.15 thf(type_def_83, type, list_P5578671422887162913nteger: $tType).
% 34.88/9.15 thf(type_def_84, type, list_P5707943133018811711nt_int: $tType).
% 34.88/9.15 thf(type_def_85, type, produc859450856879609959at_nat: $tType).
% 34.88/9.15 thf(type_def_86, type, list_P8469869581646625389at_nat: $tType).
% 34.88/9.15 thf(type_def_87, type, produc3843707927480180839at_nat: $tType).
% 34.88/9.15 thf(type_def_88, type, list_P5464809261938338413at_nat: $tType).
% 34.88/9.15 thf(type_def_89, type, list_s1210847774152347623at_nat: $tType).
% 34.88/9.15 thf(type_def_90, type, set_Code_integer: $tType).
% 34.88/9.15 thf(type_def_91, type, list_P3924974545808530565omplex: $tType).
% 34.88/9.15 thf(type_def_92, type, set_Pr5421754520313593387omplex: $tType).
% 34.88/9.15 thf(type_def_93, type, list_P5232166724548748803o_real: $tType).
% 34.88/9.15 thf(type_def_94, type, set_Pr6573716822653411497o_real: $tType).
% 34.88/9.15 thf(type_def_95, type, list_P7495141550334521929T_VEBT: $tType).
% 34.88/9.15 thf(type_def_96, type, set_Pr7543698050874017315T_VEBT: $tType).
% 34.88/9.15 thf(type_def_97, type, list_P7942624414058669295plex_o: $tType).
% 34.88/9.15 thf(type_def_98, type, set_Pr216032351708956309plex_o: $tType).
% 34.88/9.15 thf(type_def_99, type, list_P7664491975274850627omplex: $tType).
% 34.88/9.15 thf(type_def_100, type, set_Pr5085853215250843933omplex: $tType).
% 34.88/9.15 thf(type_def_101, type, list_P2206113689347244737ex_int: $tType).
% 34.88/9.15 thf(type_def_102, type, set_Pr2254670189886740123ex_int: $tType).
% 34.88/9.15 thf(type_def_103, type, list_P4696196834278971493ex_nat: $tType).
% 34.88/9.15 thf(type_def_104, type, set_Pr4744753334818466879ex_nat: $tType).
% 34.88/9.15 thf(type_def_105, type, list_P7647014805210017729x_real: $tType).
% 34.88/9.15 thf(type_def_106, type, set_Pr1133549439701694107x_real: $tType).
% 34.88/9.15 thf(type_def_107, type, list_P7977503562704621835T_VEBT: $tType).
% 34.88/9.15 thf(type_def_108, type, set_Pr4085867452638698417T_VEBT: $tType).
% 34.88/9.15 thf(type_def_109, type, list_P1797514011394873281omplex: $tType).
% 34.88/9.15 thf(type_def_110, type, set_Pr1846070511934368667omplex: $tType).
% 34.88/9.15 thf(type_def_111, type, list_P6863124054624500543t_real: $tType).
% 34.88/9.15 thf(type_def_112, type, set_Pr3538720872664544793t_real: $tType).
% 34.88/9.15 thf(type_def_113, type, list_P3595434254542482545real_o: $tType).
% 34.88/9.15 thf(type_def_114, type, set_Pr4936984352647145239real_o: $tType).
% 34.88/9.15 thf(type_def_115, type, list_P3881527313128557121omplex: $tType).
% 34.88/9.15 thf(type_def_116, type, set_Pr6591433984475009307omplex: $tType).
% 34.88/9.15 thf(type_def_117, type, list_P4344331454722006975al_int: $tType).
% 34.88/9.15 thf(type_def_118, type, set_Pr1019928272762051225al_int: $tType).
% 34.88/9.15 thf(type_def_119, type, list_P6834414599653733731al_nat: $tType).
% 34.88/9.15 thf(type_def_120, type, set_Pr3510011417693777981al_nat: $tType).
% 34.88/9.15 thf(type_def_121, type, list_P8689742595348180415l_real: $tType).
% 34.88/9.15 thf(type_def_122, type, set_Pr6218003697084177305l_real: $tType).
% 34.88/9.15 thf(type_def_123, type, list_P877281246627933069T_VEBT: $tType).
% 34.88/9.15 thf(type_def_124, type, set_Pr6019664923565264691T_VEBT: $tType).
% 34.88/9.15 thf(type_def_125, type, list_P6254988961118846195et_nat: $tType).
% 34.88/9.15 thf(type_def_126, type, set_Pr5488025237498180813et_nat: $tType).
% 34.88/9.15 thf(type_def_127, type, list_P3126845725202233233VEBT_o: $tType).
% 34.88/9.15 thf(type_def_128, type, set_Pr3175402225741728619VEBT_o: $tType).
% 34.88/9.15 thf(type_def_129, type, list_P4108580160459392801omplex: $tType).
% 34.88/9.15 thf(type_def_130, type, set_Pr216944050393469383omplex: $tType).
% 34.88/9.15 thf(type_def_131, type, list_P4547456442757143711BT_int: $tType).
% 34.88/9.15 thf(type_def_132, type, set_Pr5066593544530342725BT_int: $tType).
% 34.88/9.15 thf(type_def_133, type, list_P7037539587688870467BT_nat: $tType).
% 34.88/9.15 thf(type_def_134, type, set_Pr7556676689462069481BT_nat: $tType).
% 34.88/9.15 thf(type_def_135, type, list_P2623026923184700063T_real: $tType).
% 34.88/9.15 thf(type_def_136, type, set_Pr7765410600122031685T_real: $tType).
% 34.88/9.15 thf(type_def_137, type, list_P7413028617227757229T_VEBT: $tType).
% 34.88/9.15 thf(type_def_138, type, set_se7855581050983116737at_nat: $tType).
% 34.88/9.15 thf(type_def_139, type, typerep: $tType).
% 34.88/9.15 thf(type_def_140, type, list_typerep: $tType).
% 34.88/9.15 thf(type_def_141, type, produc8243902056947475879T_VEBT: $tType).
% 34.88/9.15 thf(type_def_142, type, set_Pr8834758594704517033_o_int: $tType).
% 34.88/9.15 thf(type_def_143, type, set_Pr5001190662893202239st_int: $tType).
% 34.88/9.15 thf(type_def_144, type, set_Pr2101469702781467981_o_nat: $tType).
% 34.88/9.15 thf(type_def_145, type, set_Pr591367044826345187st_nat: $tType).
% 34.88/9.15 thf(type_def_146, type, set_Pr5170412164475753123T_VEBT: $tType).
% 34.88/9.15 thf(type_def_147, type, set_Pr3149072824959771635_nat_o: $tType).
% 34.88/9.15 thf(type_def_148, type, set_Pr1150278048023938153list_o: $tType).
% 34.88/9.15 thf(type_def_149, type, set_Pr6167073792073659919T_VEBT: $tType).
% 34.88/9.15 thf(type_def_150, type, set_Pr1262583345697558789T_VEBT: $tType).
% 34.88/9.15 thf(type_def_151, type, set_Pr7508168486584781291list_o: $tType).
% 34.88/9.15 thf(type_def_152, type, set_Pr4080907618048478043st_int: $tType).
% 34.88/9.15 thf(type_def_153, type, set_Pr8894456036836396799st_nat: $tType).
% 34.88/9.15 thf(type_def_154, type, list_P4002435161011370285od_o_o: $tType).
% 34.88/9.15 thf(type_def_155, type, product_prod_o_o: $tType).
% 34.88/9.15 thf(type_def_156, type, list_P3795440434834930179_o_int: $tType).
% 34.88/9.15 thf(type_def_157, type, product_prod_o_int: $tType).
% 34.88/9.15 thf(type_def_158, type, list_P6285523579766656935_o_nat: $tType).
% 34.88/9.15 thf(type_def_159, type, product_prod_o_nat: $tType).
% 34.88/9.15 thf(type_def_160, type, produc2504756804600209347T_VEBT: $tType).
% 34.88/9.15 thf(type_def_161, type, product_prod_nat_o: $tType).
% 34.88/9.15 thf(type_def_162, type, product_prod_nat_int: $tType).
% 34.88/9.15 thf(type_def_163, type, produc8025551001238799321T_VEBT: $tType).
% 34.88/9.15 thf(type_def_164, type, produc334124729049499915VEBT_o: $tType).
% 34.88/9.15 thf(type_def_165, type, produc4894624898956917775BT_int: $tType).
% 34.88/9.15 thf(type_def_166, type, produc9072475918466114483BT_nat: $tType).
% 34.88/9.15 thf(type_def_167, type, set_char: $tType).
% 34.88/9.15 thf(type_def_168, type, produc4953844613479565601on_nat: $tType).
% 34.88/9.15 thf(type_def_169, type, produc2233624965454879586on_nat: $tType).
% 34.88/9.15 thf(type_def_170, type, produc7248412053542808358at_nat: $tType).
% 34.88/9.15 thf(type_def_171, type, produc4471711990508489141at_nat: $tType).
% 34.88/9.15 thf(type_def_172, type, produc8306885398267862888on_nat: $tType).
% 34.88/9.15 thf(type_def_173, type, produc3447558737645232053on_num: $tType).
% 34.88/9.15 thf(type_def_174, type, produc7036089656553540234on_num: $tType).
% 34.88/9.15 thf(type_def_175, type, produc1193250871479095198on_num: $tType).
% 34.88/9.15 thf(type_def_176, type, produc6121120109295599847at_nat: $tType).
% 34.88/9.15 thf(type_def_177, type, produc5491161045314408544at_nat: $tType).
% 34.88/9.15 thf(type_def_178, type, produc5542196010084753463at_nat: $tType).
% 34.88/9.15 thf(type_def_179, type, produc648051720047351925omplex: $tType).
% 34.88/9.15 thf(type_def_180, type, product_prod_o_real: $tType).
% 34.88/9.15 thf(type_def_181, type, produc7822875418678951345atural: $tType).
% 34.88/9.15 thf(type_def_182, type, produc5835291356934675326atural: $tType).
% 34.88/9.15 thf(type_def_183, type, produc6088675342482847199plex_o: $tType).
% 34.88/9.15 thf(type_def_184, type, produc4411394909380815293omplex: $tType).
% 34.88/9.15 thf(type_def_185, type, produc6845221339535797307ex_int: $tType).
% 34.88/9.15 thf(type_def_186, type, produc1799700322190218207ex_nat: $tType).
% 34.88/9.15 thf(type_def_187, type, produc8892588492097263291x_real: $tType).
% 34.88/9.15 thf(type_def_188, type, produc7151440242714718331T_VEBT: $tType).
% 34.88/9.15 thf(type_def_189, type, produc5838698208256999739omplex: $tType).
% 34.88/9.15 thf(type_def_190, type, produc679980390762269497t_real: $tType).
% 34.88/9.15 thf(type_def_191, type, produc7102631898165422375list_o: $tType).
% 34.88/9.15 thf(type_def_192, type, produc1713839591385758857st_int: $tType).
% 34.88/9.15 thf(type_def_193, type, produc4203922736317485613st_nat: $tType).
% 34.88/9.15 thf(type_def_194, type, produc1922972420619397443T_VEBT: $tType).
% 34.88/9.15 thf(type_def_195, type, produc862207588354017979nteger: $tType).
% 34.88/9.15 thf(type_def_196, type, produc1186641810826059865st_int: $tType).
% 34.88/9.15 thf(type_def_197, type, produc149729814636038835list_o: $tType).
% 34.88/9.15 thf(type_def_198, type, produc1828647624359046049st_nat: $tType).
% 34.88/9.15 thf(type_def_199, type, produc872621073311890639T_VEBT: $tType).
% 34.88/9.15 thf(type_def_200, type, produc6392793444374437607at_nat: $tType).
% 34.88/9.15 thf(type_def_201, type, produc424102278133772007at_nat: $tType).
% 34.88/9.15 thf(type_def_202, type, produc3962069817607390347list_o: $tType).
% 34.88/9.15 thf(type_def_203, type, produc7831203938951381541st_int: $tType).
% 34.88/9.15 thf(type_def_204, type, produc1097915047028332489st_nat: $tType).
% 34.88/9.15 thf(type_def_205, type, produc9211091688327510695T_VEBT: $tType).
% 34.88/9.15 thf(type_def_206, type, product_prod_real_o: $tType).
% 34.88/9.15 thf(type_def_207, type, produc6979889472282505531omplex: $tType).
% 34.88/9.15 thf(type_def_208, type, produc8786904178792722361al_int: $tType).
% 34.88/9.15 thf(type_def_209, type, produc3741383161447143261al_nat: $tType).
% 34.88/9.15 thf(type_def_210, type, produc2422161461964618553l_real: $tType).
% 34.88/9.15 thf(type_def_211, type, produc3757001726724277373T_VEBT: $tType).
% 34.88/9.15 thf(type_def_212, type, produc7819656566062154093et_nat: $tType).
% 34.88/9.15 thf(type_def_213, type, produc8380087813684007313omplex: $tType).
% 34.88/9.15 thf(type_def_214, type, produc7272778201969148633d_enat: $tType).
% 34.88/9.15 thf(type_def_215, type, produc5170161368751668367T_real: $tType).
% 34.88/9.15 thf(type_def_216, type, literal: $tType).
% 34.88/9.15 thf(func_def_0, type, produc5542196010084753463at_nat: $tType).
% 34.88/9.15 thf(func_def_1, type, produc5491161045314408544at_nat: $tType).
% 34.88/9.15 thf(func_def_2, type, set_Pr4333006031979791559at_nat: $tType).
% 34.88/9.15 thf(func_def_3, type, produc424102278133772007at_nat: $tType).
% 34.88/9.15 thf(func_def_4, type, set_Pr1542805901266377927at_nat: $tType).
% 34.88/9.15 thf(func_def_5, type, list_P5464809261938338413at_nat: $tType).
% 34.88/9.15 thf(func_def_6, type, set_Pr4329608150637261639at_nat: $tType).
% 34.88/9.15 thf(func_def_7, type, produc1193250871479095198on_num: $tType).
% 34.88/9.15 thf(func_def_8, type, produc8306885398267862888on_nat: $tType).
% 34.88/9.15 thf(func_def_9, type, produc6121120109295599847at_nat: $tType).
% 34.88/9.15 thf(func_def_10, type, produc4471711990508489141at_nat: $tType).
% 34.88/9.15 thf(func_def_11, type, produc6392793444374437607at_nat: $tType).
% 34.88/9.15 thf(func_def_12, type, produc7036089656553540234on_num: $tType).
% 34.88/9.15 thf(func_def_13, type, produc2233624965454879586on_nat: $tType).
% 34.88/9.15 thf(func_def_14, type, produc3843707927480180839at_nat: $tType).
% 34.88/9.15 thf(func_def_15, type, list_P8469869581646625389at_nat: $tType).
% 34.88/9.15 thf(func_def_16, type, set_Pr8693737435421807431at_nat: $tType).
% 34.88/9.15 thf(func_def_17, type, produc5835291356934675326atural: $tType).
% 34.88/9.15 thf(func_def_18, type, set_Pr1916528119006554503T_VEBT: $tType).
% 34.88/9.15 thf(func_def_19, type, produc859450856879609959at_nat: $tType).
% 34.88/9.15 thf(func_def_20, type, set_Pr7565137564259432987nteger: $tType).
% 34.88/9.15 thf(func_def_21, type, produc9211091688327510695T_VEBT: $tType).
% 34.88/9.15 thf(func_def_22, type, set_Pr8894456036836396799st_nat: $tType).
% 34.88/9.15 thf(func_def_23, type, set_Pr4080907618048478043st_int: $tType).
% 34.88/9.15 thf(func_def_24, type, set_Pr1262583345697558789T_VEBT: $tType).
% 34.88/9.15 thf(func_def_25, type, produc862207588354017979nteger: $tType).
% 34.88/9.15 thf(func_def_26, type, set_Pr7508168486584781291list_o: $tType).
% 34.88/9.15 thf(func_def_27, type, set_Pr5170412164475753123T_VEBT: $tType).
% 34.88/9.15 thf(func_def_28, type, list_s9130966667114977576at_nat: $tType).
% 34.88/9.15 thf(func_def_29, type, produc1097915047028332489st_nat: $tType).
% 34.88/9.15 thf(func_def_30, type, produc7831203938951381541st_int: $tType).
% 34.88/9.15 thf(func_def_31, type, produc872621073311890639T_VEBT: $tType).
% 34.88/9.15 thf(func_def_32, type, set_Pr3451248702717554689st_nat: $tType).
% 34.88/9.15 thf(func_def_33, type, set_Pr765067013931698361st_int: $tType).
% 34.88/9.15 thf(func_def_34, type, list_P7413028617227757229T_VEBT: $tType).
% 34.88/9.15 thf(func_def_35, type, set_Pr6192946355708809607T_VEBT: $tType).
% 34.88/9.15 thf(func_def_36, type, list_P6254988961118846195et_nat: $tType).
% 34.88/9.15 thf(func_def_37, type, list_P5578671422887162913nteger: $tType).
% 34.88/9.15 thf(func_def_38, type, set_Pr5488025237498180813et_nat: $tType).
% 34.88/9.15 thf(func_def_39, type, set_Pr4811707699266497531nteger: $tType).
% 34.88/9.15 thf(func_def_40, type, produc3447558737645232053on_num: $tType).
% 34.88/9.15 thf(func_def_41, type, produc4953844613479565601on_nat: $tType).
% 34.88/9.15 thf(func_def_42, type, produc3962069817607390347list_o: $tType).
% 34.88/9.15 thf(func_def_43, type, produc1922972420619397443T_VEBT: $tType).
% 34.88/9.15 thf(func_def_44, type, set_Pr1150278048023938153list_o: $tType).
% 34.88/9.15 thf(func_def_45, type, set_Pr591367044826345187st_nat: $tType).
% 34.88/9.15 thf(func_def_46, type, set_Pr5001190662893202239st_int: $tType).
% 34.88/9.15 thf(func_def_47, type, produc7248412053542808358at_nat: $tType).
% 34.88/9.15 thf(func_def_48, type, list_P4108580160459392801omplex: $tType).
% 34.88/9.15 thf(func_def_49, type, list_P7977503562704621835T_VEBT: $tType).
% 34.88/9.15 thf(func_def_50, type, set_Pr216944050393469383omplex: $tType).
% 34.88/9.15 thf(func_def_51, type, set_Pr4085867452638698417T_VEBT: $tType).
% 34.88/9.15 thf(func_def_52, type, list_P9162950289778280392at_nat: $tType).
% 34.88/9.15 thf(func_def_53, type, list_P2623026923184700063T_real: $tType).
% 34.88/9.15 thf(func_def_54, type, list_P877281246627933069T_VEBT: $tType).
% 34.88/9.15 thf(func_def_55, type, produc1828647624359046049st_nat: $tType).
% 34.88/9.15 thf(func_def_56, type, produc1186641810826059865st_int: $tType).
% 34.88/9.15 thf(func_def_57, type, set_Pr7765410600122031685T_real: $tType).
% 34.88/9.15 thf(func_def_58, type, set_Pr6019664923565264691T_VEBT: $tType).
% 34.88/9.15 thf(func_def_59, type, list_P7037539587688870467BT_nat: $tType).
% 34.88/9.15 thf(func_def_60, type, list_P4547456442757143711BT_int: $tType).
% 34.88/9.15 thf(func_def_61, type, list_P5647936690300460905T_VEBT: $tType).
% 34.88/9.15 thf(func_def_62, type, set_Pr6227168374412355847list_o: $tType).
% 34.88/9.15 thf(func_def_63, type, produc8243902056947475879T_VEBT: $tType).
% 34.88/9.15 thf(func_def_64, type, list_s1210847774152347623at_nat: $tType).
% 34.88/9.15 thf(func_def_65, type, list_P7664491975274850627omplex: $tType).
% 34.88/9.15 thf(func_def_66, type, set_Pr7556676689462069481BT_nat: $tType).
% 34.88/9.15 thf(func_def_67, type, set_Pr5066593544530342725BT_int: $tType).
% 34.88/9.15 thf(func_def_68, type, set_Pr6167073792073659919T_VEBT: $tType).
% 34.88/9.15 thf(func_def_69, type, set_se7855581050983116737at_nat: $tType).
% 34.88/9.15 thf(func_def_70, type, set_Pr5085853215250843933omplex: $tType).
% 34.88/9.15 thf(func_def_71, type, produc7819656566062154093et_nat: $tType).
% 34.88/9.15 thf(func_def_72, type, produc7822875418678951345atural: $tType).
% 34.88/9.15 thf(func_def_73, type, produc8923325533196201883nteger: $tType).
% 34.88/9.15 thf(func_def_74, type, produc7272778201969148633d_enat: $tType).
% 34.88/9.15 thf(func_def_75, type, list_P3881527313128557121omplex: $tType).
% 34.88/9.15 thf(func_def_76, type, list_P7647014805210017729x_real: $tType).
% 34.88/9.15 thf(func_def_77, type, produc149729814636038835list_o: $tType).
% 34.88/9.15 thf(func_def_78, type, produc4203922736317485613st_nat: $tType).
% 34.88/9.15 thf(func_def_79, type, produc1713839591385758857st_int: $tType).
% 34.88/9.15 thf(func_def_80, type, set_Pr6591433984475009307omplex: $tType).
% 34.88/9.15 thf(func_def_81, type, set_Pr1133549439701694107x_real: $tType).
% 34.88/9.15 thf(func_def_82, type, list_P3126845725202233233VEBT_o: $tType).
% 34.88/9.15 thf(func_def_83, type, list_P1797514011394873281omplex: $tType).
% 34.88/9.15 thf(func_def_84, type, list_P4696196834278971493ex_nat: $tType).
% 34.88/9.15 thf(func_def_85, type, list_P2206113689347244737ex_int: $tType).
% 34.88/9.15 thf(func_def_86, type, list_P7495141550334521929T_VEBT: $tType).
% 34.88/9.15 thf(func_def_87, type, produc8380087813684007313omplex: $tType).
% 34.88/9.15 thf(func_def_88, type, produc7151440242714718331T_VEBT: $tType).
% 34.88/9.15 thf(func_def_89, type, set_Pr3175402225741728619VEBT_o: $tType).
% 34.88/9.15 thf(func_def_90, type, set_Pr1846070511934368667omplex: $tType).
% 34.88/9.15 thf(func_def_91, type, set_Pr4744753334818466879ex_nat: $tType).
% 34.88/9.15 thf(func_def_92, type, set_Pr2254670189886740123ex_int: $tType).
% 34.88/9.15 thf(func_def_93, type, set_Pr7543698050874017315T_VEBT: $tType).
% 34.88/9.15 thf(func_def_94, type, option4927543243414619207at_nat: $tType).
% 34.88/9.15 thf(func_def_95, type, list_P8689742595348180415l_real: $tType).
% 34.88/9.15 thf(func_def_96, type, filter1242075044329608583at_nat: $tType).
% 34.88/9.15 thf(func_def_97, type, set_Pr6218003697084177305l_real: $tType).
% 34.88/9.15 thf(func_def_98, type, list_P6834414599653733731al_nat: $tType).
% 34.88/9.15 thf(func_def_99, type, list_P4344331454722006975al_int: $tType).
% 34.88/9.15 thf(func_def_100, type, list_P6863124054624500543t_real: $tType).
% 34.88/9.15 thf(func_def_101, type, produc5170161368751668367T_real: $tType).
% 34.88/9.15 thf(func_def_102, type, produc3757001726724277373T_VEBT: $tType).
% 34.88/9.15 thf(func_def_103, type, set_Pr3510011417693777981al_nat: $tType).
% 34.88/9.15 thf(func_def_104, type, set_Pr1019928272762051225al_int: $tType).
% 34.88/9.15 thf(func_def_105, type, set_Pr3538720872664544793t_real: $tType).
% 34.88/9.15 thf(func_def_106, type, produc7102631898165422375list_o: $tType).
% 34.88/9.15 thf(func_def_107, type, list_P6011104703257516679at_nat: $tType).
% 34.88/9.15 thf(func_def_108, type, list_P3521021558325789923at_int: $tType).
% 34.88/9.15 thf(func_def_109, type, list_P5707943133018811711nt_int: $tType).
% 34.88/9.15 thf(func_def_110, type, produc9072475918466114483BT_nat: $tType).
% 34.88/9.15 thf(func_def_111, type, produc4894624898956917775BT_int: $tType).
% 34.88/9.15 thf(func_def_112, type, produc8025551001238799321T_VEBT: $tType).
% 34.88/9.15 thf(func_def_113, type, list_P7942624414058669295plex_o: $tType).
% 34.88/9.15 thf(func_def_114, type, list_P3924974545808530565omplex: $tType).
% 34.88/9.15 thf(func_def_115, type, set_Pr1261947904930325089at_nat: $tType).
% 34.88/9.15 thf(func_def_116, type, set_Pr958786334691620121nt_int: $tType).
% 34.88/9.15 thf(func_def_117, type, produc4411394909380815293omplex: $tType).
% 34.88/9.15 thf(func_def_118, type, set_Pr216032351708956309plex_o: $tType).
% 34.88/9.15 thf(func_def_119, type, set_Pr5421754520313593387omplex: $tType).
% 34.88/9.15 thf(func_def_120, type, list_C4705013386053401436er_nat: $tType).
% 34.88/9.15 thf(func_def_121, type, set_Sum_sum_nat_nat: $tType).
% 34.88/9.15 thf(func_def_122, type, list_P3595434254542482545real_o: $tType).
% 34.88/9.15 thf(func_def_123, type, list_P5232166724548748803o_real: $tType).
% 34.88/9.15 thf(func_def_124, type, produc6979889472282505531omplex: $tType).
% 34.88/9.15 thf(func_def_125, type, produc8892588492097263291x_real: $tType).
% 34.88/9.15 thf(func_def_126, type, list_list_VEBT_VEBT: $tType).
% 34.88/9.15 thf(func_def_127, type, set_Pr4936984352647145239real_o: $tType).
% 34.88/9.15 thf(func_def_128, type, set_Pr6573716822653411497o_real: $tType).
% 34.88/9.15 thf(func_def_129, type, set_list_list_nat: $tType).
% 34.88/9.15 thf(func_def_130, type, list_P7333126701944960589_nat_o: $tType).
% 34.88/9.15 thf(func_def_131, type, list_P6285523579766656935_o_nat: $tType).
% 34.88/9.15 thf(func_def_132, type, list_P3795440434834930179_o_int: $tType).
% 34.88/9.15 thf(func_def_133, type, set_list_VEBT_VEBT: $tType).
% 34.88/9.15 thf(func_def_134, type, produc334124729049499915VEBT_o: $tType).
% 34.88/9.15 thf(func_def_135, type, produc5838698208256999739omplex: $tType).
% 34.88/9.15 thf(func_def_136, type, produc1799700322190218207ex_nat: $tType).
% 34.88/9.15 thf(func_def_137, type, produc6845221339535797307ex_int: $tType).
% 34.88/9.15 thf(func_def_138, type, produc2504756804600209347T_VEBT: $tType).
% 34.88/9.15 thf(func_def_139, type, set_Pr3149072824959771635_nat_o: $tType).
% 34.88/9.15 thf(func_def_140, type, set_Pr2101469702781467981_o_nat: $tType).
% 34.88/9.15 thf(func_def_141, type, set_Pr8834758594704517033_o_int: $tType).
% 34.88/9.15 thf(func_def_142, type, set_list_set_nat: $tType).
% 34.88/9.15 thf(func_def_143, type, produc2422161461964618553l_real: $tType).
% 34.88/9.15 thf(func_def_144, type, produc3741383161447143261al_nat: $tType).
% 34.88/9.15 thf(func_def_145, type, produc8786904178792722361al_int: $tType).
% 34.88/9.15 thf(func_def_146, type, produc679980390762269497t_real: $tType).
% 34.88/9.15 thf(func_def_147, type, product_prod_nat_nat: $tType).
% 34.88/9.15 thf(func_def_148, type, product_prod_nat_int: $tType).
% 34.88/9.15 thf(func_def_149, type, product_prod_int_int: $tType).
% 34.88/9.15 thf(func_def_150, type, list_P4002435161011370285od_o_o: $tType).
% 34.88/9.15 thf(func_def_151, type, set_list_complex: $tType).
% 34.88/9.15 thf(func_def_152, type, produc6088675342482847199plex_o: $tType).
% 34.88/9.15 thf(func_def_153, type, produc648051720047351925omplex: $tType).
% 34.88/9.15 thf(func_def_154, type, set_Product_prod_o_o: $tType).
% 34.88/9.15 thf(func_def_155, type, list_nat_nat: $tType).
% 34.88/9.15 thf(func_def_156, type, list_int_nat: $tType).
% 34.88/9.15 thf(func_def_157, type, option_VEBT_VEBT: $tType).
% 34.88/9.15 thf(func_def_158, type, sum_sum_nat_nat: $tType).
% 34.88/9.15 thf(func_def_159, type, product_prod_real_o: $tType).
% 34.88/9.15 thf(func_def_160, type, product_prod_o_real: $tType).
% 34.88/9.15 thf(func_def_161, type, list_list_nat: $tType).
% 34.88/9.15 thf(func_def_162, type, list_list_int: $tType).
% 34.88/9.15 thf(func_def_163, type, list_VEBT_VEBT: $tType).
% 34.88/9.15 thf(func_def_164, type, set_list_nat: $tType).
% 34.88/9.15 thf(func_def_165, type, set_list_int: $tType).
% 34.88/9.15 thf(func_def_166, type, product_prod_nat_o: $tType).
% 34.88/9.15 thf(func_def_167, type, product_prod_o_nat: $tType).
% 34.88/9.15 thf(func_def_168, type, product_prod_o_int: $tType).
% 34.88/9.15 thf(func_def_169, type, list_set_nat: $tType).
% 34.88/9.15 thf(func_def_170, type, list_Code_integer: $tType).
% 34.88/9.15 thf(func_def_171, type, set_VEBT_VEBT: $tType).
% 34.88/9.15 thf(func_def_172, type, set_set_nat: $tType).
% 34.88/9.15 thf(func_def_173, type, set_Code_integer: $tType).
% 34.88/9.15 thf(func_def_174, type, list_list_o: $tType).
% 34.88/9.15 thf(func_def_175, type, list_typerep: $tType).
% 34.88/9.15 thf(func_def_176, type, list_complex: $tType).
% 34.88/9.15 thf(func_def_177, type, set_list_o: $tType).
% 34.88/9.15 thf(func_def_178, type, product_prod_o_o: $tType).
% 34.88/9.15 thf(func_def_179, type, set_complex: $tType).
% 34.88/9.15 thf(func_def_180, type, filter_real: $tType).
% 34.88/9.15 thf(func_def_181, type, option_num: $tType).
% 34.88/9.15 thf(func_def_182, type, option_nat: $tType).
% 34.88/9.15 thf(func_def_183, type, option_int: $tType).
% 34.88/9.15 thf(func_def_184, type, filter_nat: $tType).
% 34.88/9.15 thf(func_def_185, type, set_char: $tType).
% 34.88/9.15 thf(func_def_186, type, list_real: $tType).
% 34.88/9.15 thf(func_def_187, type, set_real: $tType).
% 34.88/9.15 thf(func_def_188, type, list_num: $tType).
% 34.88/9.15 thf(func_def_189, type, list_nat: $tType).
% 34.88/9.15 thf(func_def_190, type, list_int: $tType).
% 34.88/9.15 thf(func_def_191, type, vEBT_VEBT: $tType).
% 34.88/9.15 thf(func_def_192, type, set_rat: $tType).
% 34.88/9.15 thf(func_def_193, type, set_num: $tType).
% 34.88/9.15 thf(func_def_194, type, set_nat: $tType).
% 34.88/9.15 thf(func_def_195, type, set_int: $tType).
% 34.88/9.15 thf(func_def_196, type, code_natural: $tType).
% 34.88/9.15 thf(func_def_197, type, code_integer: $tType).
% 34.88/9.15 thf(func_def_198, type, option_o: $tType).
% 34.88/9.15 thf(func_def_199, type, extended_enat: $tType).
% 34.88/9.15 thf(func_def_200, type, list_o: $tType).
% 34.88/9.15 thf(func_def_201, type, typerep: $tType).
% 34.88/9.15 thf(func_def_202, type, complex: $tType).
% 34.88/9.15 thf(func_def_203, type, literal: $tType).
% 34.88/9.15 thf(func_def_204, type, set_o: $tType).
% 34.88/9.15 thf(func_def_205, type, char: $tType).
% 34.88/9.15 thf(func_def_206, type, real: $tType).
% 34.88/9.15 thf(func_def_207, type, rat: $tType).
% 34.88/9.15 thf(func_def_208, type, num: $tType).
% 34.88/9.15 thf(func_def_209, type, nat: $tType).
% 34.88/9.15 thf(func_def_210, type, int: $tType).
% 34.88/9.15 thf(func_def_211, type, archim7802044766580827645g_real: real > int).
% 34.88/9.15 thf(func_def_212, type, archim6058952711729229775r_real: real > int).
% 34.88/9.15 thf(func_def_213, type, bNF_Ca3793111618940312692of_nat: set_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_214, type, bNF_Ca1281551314933786834on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_215, type, bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_216, type, bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_217, type, bNF_Ca8987285221972644271er_int: set_Pr4811707699266497531nteger > (code_integer > int) > $o).
% 34.88/9.15 thf(func_def_218, type, bNF_Ca8989775692481694547er_nat: set_Pr4811707699266497531nteger > (code_integer > nat) > $o).
% 34.88/9.15 thf(func_def_219, type, bNF_Ca5547107478637473181er_num: set_Pr4811707699266497531nteger > (code_integer > num) > $o).
% 34.88/9.15 thf(func_def_220, type, bNF_Ca8354645632395198811er_rat: set_Pr4811707699266497531nteger > (code_integer > rat) > $o).
% 34.88/9.15 thf(func_def_221, type, bNF_Ca1968104039914474786nt_nat: set_Pr958786334691620121nt_int > (int > nat) > $o).
% 34.88/9.15 thf(func_def_222, type, bNF_Ca7748807862925029228nt_num: set_Pr958786334691620121nt_int > (int > num) > $o).
% 34.88/9.15 thf(func_def_223, type, bNF_Ca1332973979827979050nt_rat: set_Pr958786334691620121nt_int > (int > rat) > $o).
% 34.88/9.15 thf(func_def_224, type, bNF_Ca968750328013420230at_nat: set_Pr1261947904930325089at_nat > (nat > nat) > $o).
% 34.88/9.15 thf(func_def_225, type, bNF_Ca6749454151023974672at_num: set_Pr1261947904930325089at_nat > (nat > num) > $o).
% 34.88/9.15 thf(func_def_226, type, bNF_Ca333620267926924494at_rat: set_Pr1261947904930325089at_nat > (nat > rat) > $o).
% 34.88/9.15 thf(func_def_227, type, bNF_re1962705104956426057at_rat: ((nat > rat) > (nat > rat) > $o) > (((nat > rat) > nat > rat) > ((nat > rat) > nat > rat) > $o) > ((nat > rat) > (nat > rat) > nat > rat) > ((nat > rat) > (nat > rat) > nat > rat) > $o).
% 34.88/9.15 thf(func_def_228, type, bNF_re895249473297799549at_rat: ((nat > rat) > (nat > rat) > $o) > ((nat > rat) > (nat > rat) > $o) > ((nat > rat) > nat > rat) > ((nat > rat) > nat > rat) > $o).
% 34.88/9.15 thf(func_def_229, type, bNF_re728719798268516973at_o_o: ((nat > rat) > (nat > rat) > $o) > ($o > $o > $o) > ((nat > rat) > $o) > ((nat > rat) > $o) > $o).
% 34.88/9.15 thf(func_def_230, type, bNF_re4695409256820837752l_real: ((nat > rat) > real > $o) > (((nat > rat) > nat > rat) > (real > real) > $o) > ((nat > rat) > (nat > rat) > nat > rat) > (real > real > real) > $o).
% 34.88/9.15 thf(func_def_231, type, bNF_re3023117138289059399t_real: ((nat > rat) > real > $o) > ((nat > rat) > real > $o) > ((nat > rat) > nat > rat) > (real > real) > $o).
% 34.88/9.15 thf(func_def_232, type, bNF_re4297313714947099218al_o_o: ((nat > rat) > real > $o) > ($o > $o > $o) > ((nat > rat) > $o) > (real > $o) > $o).
% 34.88/9.15 thf(func_def_233, type, bNF_re711492959462206631nt_int: (int > int > $o) > ((int > int) > (int > int) > $o) > (int > int > int) > (int > int > int) > $o).
% 34.88/9.15 thf(func_def_234, type, bNF_re4712519889275205905nt_int: (int > int > $o) > (int > int > $o) > (int > int) > (int > int) > $o).
% 34.88/9.15 thf(func_def_235, type, bNF_re578469030762574527_nat_o: (nat > nat > $o) > ((nat > $o) > (nat > $o) > $o) > (nat > nat > $o) > (nat > nat > $o) > $o).
% 34.88/9.15 thf(func_def_236, type, bNF_re1345281282404953727at_nat: (nat > nat > $o) > ((nat > nat) > (nat > nat) > $o) > (nat > nat > nat) > (nat > nat > nat) > $o).
% 34.88/9.15 thf(func_def_237, type, bNF_re4705727531993890431at_o_o: (nat > nat > $o) > ($o > $o > $o) > (nat > $o) > (nat > $o) > $o).
% 34.88/9.15 thf(func_def_238, type, bNF_re5653821019739307937at_nat: (nat > nat > $o) > (nat > nat > $o) > (nat > nat) > (nat > nat) > $o).
% 34.88/9.15 thf(func_def_239, type, bNF_re6830278522597306478at_int: (nat > nat > $o) > (product_prod_nat_nat > int > $o) > (nat > product_prod_nat_nat) > (nat > int) > $o).
% 34.88/9.15 thf(func_def_240, type, bNF_re5228765855967844073nt_int: (product_prod_int_int > product_prod_int_int > $o) > ((product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > $o) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > $o).
% 34.88/9.15 thf(func_def_241, type, bNF_re8699439704749558557nt_o_o: (product_prod_int_int > product_prod_int_int > $o) > ($o > $o > $o) > (product_prod_int_int > $o) > (product_prod_int_int > $o) > $o).
% 34.88/9.15 thf(func_def_242, type, bNF_re7145576690424134365nt_int: (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int > $o) > (product_prod_int_int > product_prod_int_int) > (product_prod_int_int > product_prod_int_int) > $o).
% 34.88/9.15 thf(func_def_243, type, bNF_re7627151682743391978at_rat: (product_prod_int_int > rat > $o) > ((product_prod_int_int > product_prod_int_int) > (rat > rat) > $o) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > (rat > rat > rat) > $o).
% 34.88/9.15 thf(func_def_244, type, bNF_re1494630372529172596at_o_o: (product_prod_int_int > rat > $o) > ($o > $o > $o) > (product_prod_int_int > $o) > (rat > $o) > $o).
% 34.88/9.15 thf(func_def_245, type, bNF_re8279943556446156061nt_rat: (product_prod_int_int > rat > $o) > (product_prod_int_int > rat > $o) > (product_prod_int_int > product_prod_int_int) > (rat > rat) > $o).
% 34.88/9.15 thf(func_def_246, type, bNF_re717283939379294677_int_o: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > $o) > (int > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (int > int > $o) > $o).
% 34.88/9.15 thf(func_def_247, type, bNF_re7408651293131936558nt_int: (product_prod_nat_nat > int > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (int > int > int) > $o).
% 34.88/9.15 thf(func_def_248, type, bNF_re6644619430987730960nt_o_o: (product_prod_nat_nat > int > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (int > $o) > $o).
% 34.88/9.15 thf(func_def_249, type, bNF_re7400052026677387805at_int: (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > int > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (int > int) > $o).
% 34.88/9.15 thf(func_def_250, type, bNF_re4202695980764964119_nat_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > $o).
% 34.88/9.15 thf(func_def_251, type, bNF_re3099431351363272937at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > ((product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > $o).
% 34.88/9.15 thf(func_def_252, type, bNF_re3666534408544137501at_o_o: (product_prod_nat_nat > product_prod_nat_nat > $o) > ($o > $o > $o) > (product_prod_nat_nat > $o) > (product_prod_nat_nat > $o) > $o).
% 34.88/9.15 thf(func_def_253, type, bNF_re2241393799969408733at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > (product_prod_nat_nat > product_prod_nat_nat) > (product_prod_nat_nat > product_prod_nat_nat) > $o).
% 34.88/9.15 thf(func_def_254, type, bNF_We5258908940166488438at_nat: set_Pr4329608150637261639at_nat).
% 34.88/9.15 thf(func_def_255, type, bNF_We3818239936649020644el_nat: set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_256, type, binomial: nat > nat > nat).
% 34.88/9.15 thf(func_def_257, type, gbinom8545251970709558553nteger: code_integer > nat > code_integer).
% 34.88/9.15 thf(func_def_258, type, gbinomial_complex: complex > nat > complex).
% 34.88/9.15 thf(func_def_259, type, gbinomial_int: int > nat > int).
% 34.88/9.15 thf(func_def_260, type, gbinomial_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_261, type, gbinomial_rat: rat > nat > rat).
% 34.88/9.15 thf(func_def_262, type, gbinomial_real: real > nat > real).
% 34.88/9.15 thf(func_def_263, type, bit_and_int_rel: product_prod_int_int > product_prod_int_int > $o).
% 34.88/9.15 thf(func_def_264, type, bit_concat_bit: nat > int > int > int).
% 34.88/9.15 thf(func_def_265, type, bit_ri7919022796975470100ot_int: int > int).
% 34.88/9.15 thf(func_def_266, type, bit_ri6519982836138164636nteger: nat > code_integer > code_integer).
% 34.88/9.15 thf(func_def_267, type, bit_ri631733984087533419it_int: nat > int > int).
% 34.88/9.15 thf(func_def_268, type, bit_se3949692690581998587nteger: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_269, type, bit_se725231765392027082nd_int: int > int > int).
% 34.88/9.15 thf(func_def_270, type, bit_se727722235901077358nd_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_271, type, bit_se8568078237143864401it_int: nat > int > int).
% 34.88/9.15 thf(func_def_272, type, bit_se8570568707652914677it_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_273, type, bit_se1345352211410354436nteger: nat > code_integer > code_integer).
% 34.88/9.15 thf(func_def_274, type, bit_se168947363167071951atural: nat > code_natural > code_natural).
% 34.88/9.15 thf(func_def_275, type, bit_se2159334234014336723it_int: nat > int > int).
% 34.88/9.15 thf(func_def_276, type, bit_se2161824704523386999it_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_277, type, bit_se2002935070580805687sk_nat: nat > nat).
% 34.88/9.15 thf(func_def_278, type, bit_se1409905431419307370or_int: int > int > int).
% 34.88/9.15 thf(func_def_279, type, bit_se1412395901928357646or_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_280, type, bit_se545348938243370406it_int: nat > int > int).
% 34.88/9.15 thf(func_def_281, type, bit_se547839408752420682it_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_282, type, bit_se2793503036327961859nteger: nat > code_integer > code_integer).
% 34.88/9.15 thf(func_def_283, type, bit_se1617098188084679374atural: nat > code_natural > code_natural).
% 34.88/9.15 thf(func_def_284, type, bit_se7879613467334960850it_int: nat > int > int).
% 34.88/9.15 thf(func_def_285, type, bit_se7882103937844011126it_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_286, type, bit_se2923211474154528505it_int: nat > int > int).
% 34.88/9.15 thf(func_def_287, type, bit_se2925701944663578781it_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_288, type, bit_se7083795435491715335atural: nat > code_natural > code_natural).
% 34.88/9.15 thf(func_def_289, type, bit_se4203085406695923979it_int: nat > int > int).
% 34.88/9.15 thf(func_def_290, type, bit_se4205575877204974255it_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_291, type, bit_se6526347334894502574or_int: int > int > int).
% 34.88/9.15 thf(func_def_292, type, bit_se6528837805403552850or_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_293, type, bit_se1146084159140164899it_int: int > nat > $o).
% 34.88/9.15 thf(func_def_294, type, bit_se1148574629649215175it_nat: nat > nat > $o).
% 34.88/9.15 thf(func_def_295, type, bit_take_bit_num: nat > num > option_num).
% 34.88/9.15 thf(func_def_296, type, code_Suc: code_natural > code_natural).
% 34.88/9.15 thf(func_def_297, type, code_divmod_abs: code_integer > code_integer > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_298, type, code_divmod_integer: code_integer > code_integer > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_299, type, code_int_of_integer: code_integer > int).
% 34.88/9.15 thf(func_def_300, type, code_integer_of_int: int > code_integer).
% 34.88/9.15 thf(func_def_301, type, code_integer_of_nat: nat > code_integer).
% 34.88/9.15 thf(func_def_302, type, code_nat_of_integer: code_integer > nat).
% 34.88/9.15 thf(func_def_303, type, code_nat_of_natural: code_natural > nat).
% 34.88/9.15 thf(func_def_304, type, code_natural_of_nat: nat > code_natural).
% 34.88/9.15 thf(func_def_305, type, comple7806235888213564991et_nat: set_set_nat > set_nat).
% 34.88/9.15 thf(func_def_306, type, complete_Sup_Sup_nat: set_nat > nat).
% 34.88/9.15 thf(func_def_307, type, comple7399068483239264473et_nat: set_set_nat > set_nat).
% 34.88/9.15 thf(func_def_308, type, arg: complex > real).
% 34.88/9.15 thf(func_def_309, type, cis: real > complex).
% 34.88/9.15 thf(func_def_310, type, cnj: complex > complex).
% 34.88/9.15 thf(func_def_311, type, complex2: real > real > complex).
% 34.88/9.15 thf(func_def_312, type, im: complex > real).
% 34.88/9.15 thf(func_def_313, type, re: complex > real).
% 34.88/9.15 thf(func_def_314, type, csqrt: complex > complex).
% 34.88/9.15 thf(func_def_315, type, imaginary_unit: complex).
% 34.88/9.15 thf(func_def_316, type, rcis: real > real > complex).
% 34.88/9.15 thf(func_def_317, type, nat_to_rat_surj: nat > rat).
% 34.88/9.15 thf(func_def_318, type, nth_item_rel: nat > nat > $o).
% 34.88/9.15 thf(func_def_319, type, differ6690327859849518006l_real: (real > real) > filter_real > $o).
% 34.88/9.15 thf(func_def_320, type, has_fi5821293074295781190e_real: (real > real) > real > filter_real > $o).
% 34.88/9.15 thf(func_def_321, type, adjust_div: product_prod_int_int > int).
% 34.88/9.15 thf(func_def_322, type, adjust_mod: int > int > int).
% 34.88/9.15 thf(func_def_323, type, divmod_nat: nat > nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_324, type, eucl_rel_int: int > int > product_prod_int_int > $o).
% 34.88/9.15 thf(func_def_325, type, unique5706413561485394159nteger: produc8923325533196201883nteger > $o).
% 34.88/9.15 thf(func_def_326, type, unique6319869463603278526ux_int: product_prod_int_int > $o).
% 34.88/9.15 thf(func_def_327, type, unique6322359934112328802ux_nat: product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_328, type, unique3479559517661332726nteger: num > num > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_329, type, unique5052692396658037445od_int: num > num > product_prod_int_int).
% 34.88/9.15 thf(func_def_330, type, unique5055182867167087721od_nat: num > num > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_331, type, unique4921790084139445826nteger: num > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_332, type, unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int).
% 34.88/9.15 thf(func_def_333, type, unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_334, type, extended_eSuc: extended_enat > extended_enat).
% 34.88/9.15 thf(func_def_335, type, extended_enat2: nat > extended_enat).
% 34.88/9.15 thf(func_def_336, type, extended_Abs_enat: option_nat > extended_enat).
% 34.88/9.15 thf(func_def_337, type, extended_case_enat_o: (nat > $o) > $o > extended_enat > $o).
% 34.88/9.15 thf(func_def_338, type, extend3600170679010898289d_enat: (nat > extended_enat) > extended_enat > extended_enat > extended_enat).
% 34.88/9.15 thf(func_def_339, type, extend5688581933313929465d_enat: extended_enat).
% 34.88/9.15 thf(func_def_340, type, comm_s8582702949713902594nteger: code_integer > nat > code_integer).
% 34.88/9.15 thf(func_def_341, type, comm_s2602460028002588243omplex: complex > nat > complex).
% 34.88/9.15 thf(func_def_342, type, comm_s4660882817536571857er_int: int > nat > int).
% 34.88/9.15 thf(func_def_343, type, comm_s4663373288045622133er_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_344, type, comm_s4028243227959126397er_rat: rat > nat > rat).
% 34.88/9.15 thf(func_def_345, type, comm_s7457072308508201937r_real: real > nat > real).
% 34.88/9.15 thf(func_def_346, type, semiri3624122377584611663nteger: nat > code_integer).
% 34.88/9.15 thf(func_def_347, type, semiri2447717529341329178atural: nat > code_natural).
% 34.88/9.15 thf(func_def_348, type, semiri5044797733671781792omplex: nat > complex).
% 34.88/9.15 thf(func_def_349, type, semiri4449623510593786356d_enat: nat > extended_enat).
% 34.88/9.15 thf(func_def_350, type, semiri1406184849735516958ct_int: nat > int).
% 34.88/9.15 thf(func_def_351, type, semiri1408675320244567234ct_nat: nat > nat).
% 34.88/9.15 thf(func_def_352, type, semiri773545260158071498ct_rat: nat > rat).
% 34.88/9.15 thf(func_def_353, type, semiri2265585572941072030t_real: nat > real).
% 34.88/9.15 thf(func_def_354, type, invers8013647133539491842omplex: complex > complex).
% 34.88/9.15 thf(func_def_355, type, inverse_inverse_rat: rat > rat).
% 34.88/9.15 thf(func_def_356, type, inverse_inverse_real: real > real).
% 34.88/9.15 thf(func_def_357, type, at_bot_real: filter_real).
% 34.88/9.15 thf(func_def_358, type, at_top_nat: filter_nat).
% 34.88/9.15 thf(func_def_359, type, at_top_real: filter_real).
% 34.88/9.15 thf(func_def_360, type, eventually_nat: (nat > $o) > filter_nat > $o).
% 34.88/9.15 thf(func_def_361, type, eventu1038000079068216329at_nat: (product_prod_nat_nat > $o) > filter1242075044329608583at_nat > $o).
% 34.88/9.15 thf(func_def_362, type, filterlim_nat_nat: (nat > nat) > filter_nat > filter_nat > $o).
% 34.88/9.15 thf(func_def_363, type, filterlim_nat_real: (nat > real) > filter_real > filter_nat > $o).
% 34.88/9.15 thf(func_def_364, type, filterlim_real_real: (real > real) > filter_real > filter_real > $o).
% 34.88/9.15 thf(func_def_365, type, prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat).
% 34.88/9.15 thf(func_def_366, type, finite_card_o: set_o > nat).
% 34.88/9.15 thf(func_def_367, type, finite_card_complex: set_complex > nat).
% 34.88/9.15 thf(func_def_368, type, finite_card_int: set_int > nat).
% 34.88/9.15 thf(func_def_369, type, finite_card_list_o: set_list_o > nat).
% 34.88/9.15 thf(func_def_370, type, finite5120063068150530198omplex: set_list_complex > nat).
% 34.88/9.15 thf(func_def_371, type, finite_card_list_int: set_list_int > nat).
% 34.88/9.15 thf(func_def_372, type, finite7325466520557071688st_nat: set_list_list_nat > nat).
% 34.88/9.15 thf(func_def_373, type, finite_card_list_nat: set_list_nat > nat).
% 34.88/9.15 thf(func_def_374, type, finite5631907774883551598et_nat: set_list_set_nat > nat).
% 34.88/9.15 thf(func_def_375, type, finite5915292604075114978T_VEBT: set_list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_376, type, finite_card_nat: set_nat > nat).
% 34.88/9.15 thf(func_def_377, type, finite711546835091564841at_nat: set_Pr1261947904930325089at_nat > nat).
% 34.88/9.15 thf(func_def_378, type, finite_card_real: set_real > nat).
% 34.88/9.15 thf(func_def_379, type, finite_card_set_nat: set_set_nat > nat).
% 34.88/9.15 thf(func_def_380, type, finite7802652506058667612T_VEBT: set_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_381, type, finite_finite_o: set_o > $o).
% 34.88/9.15 thf(func_def_382, type, finite3207457112153483333omplex: set_complex > $o).
% 34.88/9.15 thf(func_def_383, type, finite_finite_int: set_int > $o).
% 34.88/9.15 thf(func_def_384, type, finite_finite_list_o: set_list_o > $o).
% 34.88/9.15 thf(func_def_385, type, finite8712137658972009173omplex: set_list_complex > $o).
% 34.88/9.15 thf(func_def_386, type, finite3922522038869484883st_int: set_list_int > $o).
% 34.88/9.15 thf(func_def_387, type, finite8100373058378681591st_nat: set_list_nat > $o).
% 34.88/9.15 thf(func_def_388, type, finite3004134309566078307T_VEBT: set_list_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_389, type, finite_finite_nat: set_nat > $o).
% 34.88/9.15 thf(func_def_390, type, finite_finite_num: set_num > $o).
% 34.88/9.15 thf(func_def_391, type, finite6177210948735845034at_nat: set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_392, type, finite_finite_rat: set_rat > $o).
% 34.88/9.15 thf(func_def_393, type, finite_finite_real: set_real > $o).
% 34.88/9.15 thf(func_def_394, type, finite1152437895449049373et_nat: set_set_nat > $o).
% 34.88/9.15 thf(func_def_395, type, finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_396, type, bij_be1856998921033663316omplex: (complex > complex) > set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_397, type, bij_betw_int_nat: (int > nat) > set_int > set_nat > $o).
% 34.88/9.15 thf(func_def_398, type, bij_be8532844293280997160at_nat: (list_nat > nat) > set_list_nat > set_nat > $o).
% 34.88/9.15 thf(func_def_399, type, bij_betw_nat_complex: (nat > complex) > set_nat > set_complex > $o).
% 34.88/9.15 thf(func_def_400, type, bij_betw_nat_int: (nat > int) > set_nat > set_int > $o).
% 34.88/9.15 thf(func_def_401, type, bij_be6293887246118711976st_nat: (nat > list_nat) > set_nat > set_list_nat > $o).
% 34.88/9.15 thf(func_def_402, type, bij_betw_nat_nat: (nat > nat) > set_nat > set_nat > $o).
% 34.88/9.15 thf(func_def_403, type, bij_be8693218025023041337at_nat: (nat > product_prod_nat_nat) > set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_404, type, bij_be4790990086886966983at_nat: (nat > sum_sum_nat_nat) > set_nat > set_Sum_sum_nat_nat > $o).
% 34.88/9.15 thf(func_def_405, type, bij_be5333170631980326235at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > set_nat > $o).
% 34.88/9.15 thf(func_def_406, type, bij_be5432664580149595207at_nat: (sum_sum_nat_nat > nat) > set_Sum_sum_nat_nat > set_nat > $o).
% 34.88/9.15 thf(func_def_407, type, comp_C8797469213163452608nteger: ((code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_408, type, comp_C1593894019821074884nteger: (code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger) > (code_integer > code_integer) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_409, type, comp_nat_nat_nat: (nat > nat) > (nat > nat) > nat > nat).
% 34.88/9.15 thf(func_def_410, type, id_o: $o > $o).
% 34.88/9.15 thf(func_def_411, type, id_nat: nat > nat).
% 34.88/9.15 thf(func_def_412, type, inj_on_int_nat: (int > nat) > set_int > $o).
% 34.88/9.15 thf(func_def_413, type, inj_on_list_nat_nat: (list_nat > nat) > set_list_nat > $o).
% 34.88/9.15 thf(func_def_414, type, inj_on_nat_int: (nat > int) > set_nat > $o).
% 34.88/9.15 thf(func_def_415, type, inj_on_nat_list_nat: (nat > list_nat) > set_nat > $o).
% 34.88/9.15 thf(func_def_416, type, inj_on_nat_nat: (nat > nat) > set_nat > $o).
% 34.88/9.15 thf(func_def_417, type, inj_on5538052773655684606at_nat: (nat > product_prod_nat_nat) > set_nat > $o).
% 34.88/9.15 thf(func_def_418, type, inj_on_nat_char: (nat > char) > set_nat > $o).
% 34.88/9.15 thf(func_def_419, type, inj_on5701776251185195458at_nat: (nat > sum_sum_nat_nat) > set_nat > $o).
% 34.88/9.15 thf(func_def_420, type, inj_on2178005380612969504at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_421, type, inj_on_real_real: (real > real) > set_real > $o).
% 34.88/9.15 thf(func_def_422, type, inj_on_set_nat_nat: (set_nat > nat) > set_set_nat > $o).
% 34.88/9.15 thf(func_def_423, type, inj_on6343450744447823682at_nat: (sum_sum_nat_nat > nat) > set_Sum_sum_nat_nat > $o).
% 34.88/9.15 thf(func_def_424, type, map_fu6549440983881763648atural: (code_natural > nat) > ((nat > nat) > code_natural > code_natural) > (nat > nat > nat) > code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_425, type, map_fu1239815594074539274atural: (code_natural > nat) > (nat > code_natural) > (nat > nat) > code_natural > code_natural).
% 34.88/9.15 thf(func_def_426, type, map_fu434086159418415080_int_o: (int > product_prod_nat_nat) > ((product_prod_nat_nat > $o) > int > $o) > (product_prod_nat_nat > product_prod_nat_nat > $o) > int > int > $o).
% 34.88/9.15 thf(func_def_427, type, map_fu4960017516451851995nt_int: (int > product_prod_nat_nat) > ((product_prod_nat_nat > product_prod_nat_nat) > int > int) > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > int > int > int).
% 34.88/9.15 thf(func_def_428, type, map_fu4826362097070443709at_o_o: (int > product_prod_nat_nat) > ($o > $o) > (product_prod_nat_nat > $o) > int > $o).
% 34.88/9.15 thf(func_def_429, type, map_fu3667384564859982768at_int: (int > product_prod_nat_nat) > (product_prod_nat_nat > int) > (product_prod_nat_nat > product_prod_nat_nat) > int > int).
% 34.88/9.15 thf(func_def_430, type, map_fu4333342158222067775at_rat: (rat > product_prod_int_int) > ((product_prod_int_int > product_prod_int_int) > rat > rat) > (product_prod_int_int > product_prod_int_int > product_prod_int_int) > rat > rat > rat).
% 34.88/9.15 thf(func_def_431, type, map_fu898904425404107465nt_o_o: (rat > product_prod_int_int) > ($o > $o) > (product_prod_int_int > $o) > rat > $o).
% 34.88/9.15 thf(func_def_432, type, map_fu5673905371560938248nt_rat: (rat > product_prod_int_int) > (product_prod_int_int > rat) > (product_prod_int_int > product_prod_int_int) > rat > rat).
% 34.88/9.15 thf(func_def_433, type, map_fu1856342031159181835at_o_o: (real > nat > rat) > ($o > $o) > ((nat > rat) > $o) > real > $o).
% 34.88/9.15 thf(func_def_434, type, the_in5290026491893676941l_real: set_real > (real > real) > real > real).
% 34.88/9.15 thf(func_def_435, type, fun_pair_leq: set_Pr8693737435421807431at_nat).
% 34.88/9.15 thf(func_def_436, type, fun_pair_less: set_Pr8693737435421807431at_nat).
% 34.88/9.15 thf(func_def_437, type, gcd_Gcd_int: set_int > int).
% 34.88/9.15 thf(func_def_438, type, gcd_Gcd_nat: set_nat > nat).
% 34.88/9.15 thf(func_def_439, type, gcd_Lcm_nat: set_nat > nat).
% 34.88/9.15 thf(func_def_440, type, bezw: nat > nat > product_prod_int_int).
% 34.88/9.15 thf(func_def_441, type, bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_442, type, gcd_gcd_Code_integer: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_443, type, gcd_gcd_int: int > int > int).
% 34.88/9.15 thf(func_def_444, type, gcd_gcd_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_445, type, gcd_lcm_Code_integer: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_446, type, gcd_lcm_int: int > int > int).
% 34.88/9.15 thf(func_def_447, type, gcd_lcm_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_448, type, gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_449, type, semiri4256215615220890538in_int: set_int > int).
% 34.88/9.15 thf(func_def_450, type, semiri4258706085729940814in_nat: set_nat > nat).
% 34.88/9.15 thf(func_def_451, type, abs_abs_Code_integer: code_integer > code_integer).
% 34.88/9.15 thf(func_def_452, type, abs_abs_complex: complex > complex).
% 34.88/9.15 thf(func_def_453, type, abs_abs_int: int > int).
% 34.88/9.15 thf(func_def_454, type, abs_abs_rat: rat > rat).
% 34.88/9.15 thf(func_def_455, type, abs_abs_real: real > real).
% 34.88/9.15 thf(func_def_456, type, minus_8373710615458151222nteger: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_457, type, minus_7197305767214868737atural: code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_458, type, minus_minus_complex: complex > complex > complex).
% 34.88/9.15 thf(func_def_459, type, minus_3235023915231533773d_enat: extended_enat > extended_enat > extended_enat).
% 34.88/9.15 thf(func_def_460, type, minus_minus_int: int > int > int).
% 34.88/9.15 thf(func_def_461, type, minus_minus_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_462, type, minus_minus_rat: rat > rat > rat).
% 34.88/9.15 thf(func_def_463, type, minus_minus_real: real > real > real).
% 34.88/9.15 thf(func_def_464, type, minus_minus_set_o: set_o > set_o > set_o).
% 34.88/9.15 thf(func_def_465, type, minus_811609699411566653omplex: set_complex > set_complex > set_complex).
% 34.88/9.15 thf(func_def_466, type, minus_minus_set_int: set_int > set_int > set_int).
% 34.88/9.15 thf(func_def_467, type, minus_7954133019191499631st_nat: set_list_nat > set_list_nat > set_list_nat).
% 34.88/9.15 thf(func_def_468, type, minus_minus_set_nat: set_nat > set_nat > set_nat).
% 34.88/9.15 thf(func_def_469, type, minus_1356011639430497352at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_470, type, minus_minus_set_real: set_real > set_real > set_real).
% 34.88/9.15 thf(func_def_471, type, minus_2163939370556025621et_nat: set_set_nat > set_set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_472, type, minus_5127226145743854075T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 34.88/9.15 thf(func_def_473, type, monoid_nat: (nat > nat > nat) > nat > $o).
% 34.88/9.15 thf(func_def_474, type, one_one_Code_integer: code_integer).
% 34.88/9.15 thf(func_def_475, type, one_one_Code_natural: code_natural).
% 34.88/9.15 thf(func_def_476, type, one_one_complex: complex).
% 34.88/9.15 thf(func_def_477, type, one_on7984719198319812577d_enat: extended_enat).
% 34.88/9.15 thf(func_def_478, type, one_one_int: int).
% 34.88/9.15 thf(func_def_479, type, one_one_nat: nat).
% 34.88/9.15 thf(func_def_480, type, one_one_rat: rat).
% 34.88/9.15 thf(func_def_481, type, one_one_real: real).
% 34.88/9.15 thf(func_def_482, type, plus_p5714425477246183910nteger: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_483, type, plus_p4538020629002901425atural: code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_484, type, plus_plus_complex: complex > complex > complex).
% 34.88/9.15 thf(func_def_485, type, plus_p3455044024723400733d_enat: extended_enat > extended_enat > extended_enat).
% 34.88/9.15 thf(func_def_486, type, plus_plus_int: int > int > int).
% 34.88/9.15 thf(func_def_487, type, plus_plus_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_488, type, plus_plus_num: num > num > num).
% 34.88/9.15 thf(func_def_489, type, plus_plus_rat: rat > rat > rat).
% 34.88/9.15 thf(func_def_490, type, plus_plus_real: real > real > real).
% 34.88/9.15 thf(func_def_491, type, sgn_sgn_Code_integer: code_integer > code_integer).
% 34.88/9.15 thf(func_def_492, type, sgn_sgn_int: int > int).
% 34.88/9.15 thf(func_def_493, type, sgn_sgn_rat: rat > rat).
% 34.88/9.15 thf(func_def_494, type, sgn_sgn_real: real > real).
% 34.88/9.15 thf(func_def_495, type, times_3573771949741848930nteger: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_496, type, times_2397367101498566445atural: code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_497, type, times_times_complex: complex > complex > complex).
% 34.88/9.15 thf(func_def_498, type, times_7803423173614009249d_enat: extended_enat > extended_enat > extended_enat).
% 34.88/9.15 thf(func_def_499, type, times_times_int: int > int > int).
% 34.88/9.15 thf(func_def_500, type, times_times_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_501, type, times_times_num: num > num > num).
% 34.88/9.15 thf(func_def_502, type, times_times_rat: rat > rat > rat).
% 34.88/9.15 thf(func_def_503, type, times_times_real: real > real > real).
% 34.88/9.15 thf(func_def_504, type, uminus1351360451143612070nteger: code_integer > code_integer).
% 34.88/9.15 thf(func_def_505, type, uminus1482373934393186551omplex: complex > complex).
% 34.88/9.15 thf(func_def_506, type, uminus_uminus_int: int > int).
% 34.88/9.15 thf(func_def_507, type, uminus_uminus_rat: rat > rat).
% 34.88/9.15 thf(func_def_508, type, uminus_uminus_real: real > real).
% 34.88/9.15 thf(func_def_509, type, uminus8566677241136511917omplex: set_complex > set_complex).
% 34.88/9.15 thf(func_def_510, type, uminus1532241313380277803et_int: set_int > set_int).
% 34.88/9.15 thf(func_def_511, type, uminus5710092332889474511et_nat: set_nat > set_nat).
% 34.88/9.15 thf(func_def_512, type, uminus6524753893492686040at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_513, type, uminus612125837232591019t_real: set_real > set_real).
% 34.88/9.15 thf(func_def_514, type, zero_z3403309356797280102nteger: code_integer).
% 34.88/9.15 thf(func_def_515, type, zero_z2226904508553997617atural: code_natural).
% 34.88/9.15 thf(func_def_516, type, zero_zero_complex: complex).
% 34.88/9.15 thf(func_def_517, type, zero_z5237406670263579293d_enat: extended_enat).
% 34.88/9.15 thf(func_def_518, type, zero_zero_int: int).
% 34.88/9.15 thf(func_def_519, type, zero_zero_nat: nat).
% 34.88/9.15 thf(func_def_520, type, zero_zero_rat: rat).
% 34.88/9.15 thf(func_def_521, type, zero_zero_real: real).
% 34.88/9.15 thf(func_def_522, type, groups8507830703676809646_o_nat: ($o > nat) > set_o > nat).
% 34.88/9.15 thf(func_def_523, type, groups6621422865394947399nteger: (complex > code_integer) > set_complex > code_integer).
% 34.88/9.15 thf(func_def_524, type, groups7754918857620584856omplex: (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_525, type, groups5690904116761175830ex_int: (complex > int) > set_complex > int).
% 34.88/9.15 thf(func_def_526, type, groups5693394587270226106ex_nat: (complex > nat) > set_complex > nat).
% 34.88/9.15 thf(func_def_527, type, groups5058264527183730370ex_rat: (complex > rat) > set_complex > rat).
% 34.88/9.15 thf(func_def_528, type, groups5808333547571424918x_real: (complex > real) > set_complex > real).
% 34.88/9.15 thf(func_def_529, type, groups7873554091576472773nteger: (int > code_integer) > set_int > code_integer).
% 34.88/9.15 thf(func_def_530, type, groups3049146728041665814omplex: (int > complex) > set_int > complex).
% 34.88/9.15 thf(func_def_531, type, groups4538972089207619220nt_int: (int > int) > set_int > int).
% 34.88/9.15 thf(func_def_532, type, groups4541462559716669496nt_nat: (int > nat) > set_int > nat).
% 34.88/9.15 thf(func_def_533, type, groups3906332499630173760nt_rat: (int > rat) > set_int > rat).
% 34.88/9.15 thf(func_def_534, type, groups8778361861064173332t_real: (int > real) > set_int > real).
% 34.88/9.15 thf(func_def_535, type, groups6529277132148336714omplex: (list_nat > complex) > set_list_nat > complex).
% 34.88/9.15 thf(func_def_536, type, groups4396056296759096172at_nat: (list_nat > nat) > set_list_nat > nat).
% 34.88/9.15 thf(func_def_537, type, groups8399112307953289288t_real: (list_nat > real) > set_list_nat > real).
% 34.88/9.15 thf(func_def_538, type, groups7501900531339628137nteger: (nat > code_integer) > set_nat > code_integer).
% 34.88/9.15 thf(func_def_539, type, groups2073611262835488442omplex: (nat > complex) > set_nat > complex).
% 34.88/9.15 thf(func_def_540, type, groups7108830773950497114d_enat: (nat > extended_enat) > set_nat > extended_enat).
% 34.88/9.15 thf(func_def_541, type, groups3539618377306564664at_int: (nat > int) > set_nat > int).
% 34.88/9.15 thf(func_def_542, type, groups3542108847815614940at_nat: (nat > nat) > set_nat > nat).
% 34.88/9.15 thf(func_def_543, type, groups2906978787729119204at_rat: (nat > rat) > set_nat > rat).
% 34.88/9.15 thf(func_def_544, type, groups6591440286371151544t_real: (nat > real) > set_nat > real).
% 34.88/9.15 thf(func_def_545, type, groups7713935264441627589nteger: (real > code_integer) > set_real > code_integer).
% 34.88/9.15 thf(func_def_546, type, groups5754745047067104278omplex: (real > complex) > set_real > complex).
% 34.88/9.15 thf(func_def_547, type, groups1932886352136224148al_int: (real > int) > set_real > int).
% 34.88/9.15 thf(func_def_548, type, groups1935376822645274424al_nat: (real > nat) > set_real > nat).
% 34.88/9.15 thf(func_def_549, type, groups1300246762558778688al_rat: (real > rat) > set_real > rat).
% 34.88/9.15 thf(func_def_550, type, groups8097168146408367636l_real: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_551, type, groups8255218700646806128omplex: (set_nat > complex) > set_set_nat > complex).
% 34.88/9.15 thf(func_def_552, type, groups8294997508430121362at_nat: (set_nat > nat) > set_set_nat > nat).
% 34.88/9.15 thf(func_def_553, type, groups5107569545109728110t_real: (set_nat > real) > set_set_nat > real).
% 34.88/9.15 thf(func_def_554, type, groups771621172384141258BT_nat: (vEBT_VEBT > nat) > set_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_555, type, groups8682486955453173170nteger: (complex > code_integer) > set_complex > code_integer).
% 34.88/9.15 thf(func_def_556, type, groups3708469109370488835omplex: (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_557, type, groups858564598930262913ex_int: (complex > int) > set_complex > int).
% 34.88/9.15 thf(func_def_558, type, groups861055069439313189ex_nat: (complex > nat) > set_complex > nat).
% 34.88/9.15 thf(func_def_559, type, groups225925009352817453ex_rat: (complex > rat) > set_complex > rat).
% 34.88/9.15 thf(func_def_560, type, groups766887009212190081x_real: (complex > real) > set_complex > real).
% 34.88/9.15 thf(func_def_561, type, groups3827104343326376752nteger: (int > code_integer) > set_int > code_integer).
% 34.88/9.15 thf(func_def_562, type, groups7440179247065528705omplex: (int > complex) > set_int > complex).
% 34.88/9.15 thf(func_def_563, type, groups1705073143266064639nt_int: (int > int) > set_int > int).
% 34.88/9.15 thf(func_def_564, type, groups1707563613775114915nt_nat: (int > nat) > set_int > nat).
% 34.88/9.15 thf(func_def_565, type, groups1072433553688619179nt_rat: (int > rat) > set_int > rat).
% 34.88/9.15 thf(func_def_566, type, groups2316167850115554303t_real: (int > real) > set_int > real).
% 34.88/9.15 thf(func_def_567, type, groups3455450783089532116nteger: (nat > code_integer) > set_nat > code_integer).
% 34.88/9.15 thf(func_def_568, type, groups6464643781859351333omplex: (nat > complex) > set_nat > complex).
% 34.88/9.15 thf(func_def_569, type, groups705719431365010083at_int: (nat > int) > set_nat > int).
% 34.88/9.15 thf(func_def_570, type, groups708209901874060359at_nat: (nat > nat) > set_nat > nat).
% 34.88/9.15 thf(func_def_571, type, groups73079841787564623at_rat: (nat > rat) > set_nat > rat).
% 34.88/9.15 thf(func_def_572, type, groups129246275422532515t_real: (nat > real) > set_nat > real).
% 34.88/9.15 thf(func_def_573, type, groups8110221916422527690omplex: (product_prod_nat_nat > complex) > set_Pr1261947904930325089at_nat > complex).
% 34.88/9.15 thf(func_def_574, type, groups6225526099057966256nteger: (real > code_integer) > set_real > code_integer).
% 34.88/9.15 thf(func_def_575, type, groups713298508707869441omplex: (real > complex) > set_real > complex).
% 34.88/9.15 thf(func_def_576, type, groups4694064378042380927al_int: (real > int) > set_real > int).
% 34.88/9.15 thf(func_def_577, type, groups4696554848551431203al_nat: (real > nat) > set_real > nat).
% 34.88/9.15 thf(func_def_578, type, groups4061424788464935467al_rat: (real > rat) > set_real > rat).
% 34.88/9.15 thf(func_def_579, type, groups1681761925125756287l_real: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_580, type, groups9116527308978886569_o_int: ($o > int) > int > list_o > int).
% 34.88/9.15 thf(func_def_581, type, groups4561878855575611511st_nat: list_nat > nat).
% 34.88/9.15 thf(func_def_582, type, the_real: (real > $o) > real).
% 34.88/9.15 thf(func_def_583, type, if_Code_integer: $o > code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_584, type, if_complex: $o > complex > complex > complex).
% 34.88/9.15 thf(func_def_585, type, if_Extended_enat: $o > extended_enat > extended_enat > extended_enat).
% 34.88/9.15 thf(func_def_586, type, if_int: $o > int > int > int).
% 34.88/9.15 thf(func_def_587, type, if_list_nat: $o > list_nat > list_nat > list_nat).
% 34.88/9.15 thf(func_def_588, type, if_nat: $o > nat > nat > nat).
% 34.88/9.15 thf(func_def_589, type, if_num: $o > num > num > num).
% 34.88/9.15 thf(func_def_590, type, if_option_nat: $o > option_nat > option_nat > option_nat).
% 34.88/9.15 thf(func_def_591, type, if_option_num: $o > option_num > option_num > option_num).
% 34.88/9.15 thf(func_def_592, type, if_Pro6119634080678213985nteger: $o > produc8923325533196201883nteger > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_593, type, if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int).
% 34.88/9.15 thf(func_def_594, type, if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_595, type, if_rat: $o > rat > rat > rat).
% 34.88/9.15 thf(func_def_596, type, if_real: $o > real > real > real).
% 34.88/9.15 thf(func_def_597, type, if_set_nat: $o > set_nat > set_nat > set_nat).
% 34.88/9.15 thf(func_def_598, type, if_Sum_sum_nat_nat: $o > sum_sum_nat_nat > sum_sum_nat_nat > sum_sum_nat_nat).
% 34.88/9.15 thf(func_def_599, type, if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_600, type, infini8530281810654367211te_nat: set_nat > nat > nat).
% 34.88/9.15 thf(func_def_601, type, abs_Integ: product_prod_nat_nat > int).
% 34.88/9.15 thf(func_def_602, type, rep_Integ: int > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_603, type, intrel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_604, type, nat2: int > nat).
% 34.88/9.15 thf(func_def_605, type, pcr_int: product_prod_nat_nat > int > $o).
% 34.88/9.15 thf(func_def_606, type, ring_1_Ints_real: set_real).
% 34.88/9.15 thf(func_def_607, type, ring_1_of_int_rat: int > rat).
% 34.88/9.15 thf(func_def_608, type, ring_1_of_int_real: int > real).
% 34.88/9.15 thf(func_def_609, type, inf_inf_int: int > int > int).
% 34.88/9.15 thf(func_def_610, type, inf_inf_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_611, type, inf_inf_rat: rat > rat > rat).
% 34.88/9.15 thf(func_def_612, type, inf_inf_set_complex: set_complex > set_complex > set_complex).
% 34.88/9.15 thf(func_def_613, type, inf_inf_set_int: set_int > set_int > set_int).
% 34.88/9.15 thf(func_def_614, type, inf_inf_set_nat: set_nat > set_nat > set_nat).
% 34.88/9.15 thf(func_def_615, type, inf_inf_set_num: set_num > set_num > set_num).
% 34.88/9.15 thf(func_def_616, type, inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_617, type, inf_inf_set_rat: set_rat > set_rat > set_rat).
% 34.88/9.15 thf(func_def_618, type, inf_inf_set_real: set_real > set_real > set_real).
% 34.88/9.15 thf(func_def_619, type, semila9081495762789891438tr_nat: (nat > nat > nat) > nat > $o).
% 34.88/9.15 thf(func_def_620, type, semila1623282765462674594er_nat: (nat > nat > nat) > nat > (nat > nat > $o) > (nat > nat > $o) > $o).
% 34.88/9.15 thf(func_def_621, type, sup_sup_int: int > int > int).
% 34.88/9.15 thf(func_def_622, type, sup_sup_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_623, type, sup_sup_rat: rat > rat > rat).
% 34.88/9.15 thf(func_def_624, type, sup_sup_set_complex: set_complex > set_complex > set_complex).
% 34.88/9.15 thf(func_def_625, type, sup_sup_set_int: set_int > set_int > set_int).
% 34.88/9.15 thf(func_def_626, type, sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat).
% 34.88/9.15 thf(func_def_627, type, sup_sup_set_nat: set_nat > set_nat > set_nat).
% 34.88/9.15 thf(func_def_628, type, sup_sup_set_num: set_num > set_num > set_num).
% 34.88/9.15 thf(func_def_629, type, sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_630, type, sup_sup_set_rat: set_rat > set_rat > set_rat).
% 34.88/9.15 thf(func_def_631, type, sup_sup_set_real: set_real > set_real > set_real).
% 34.88/9.15 thf(func_def_632, type, sup_sup_set_set_nat: set_set_nat > set_set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_633, type, lattic8265883725875713057ax_nat: set_nat > nat).
% 34.88/9.15 thf(func_def_634, type, lattic5364784637807008409ex_nat: (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_635, type, lattic1922116423962787043ex_num: (complex > num) > set_complex > complex).
% 34.88/9.15 thf(func_def_636, type, lattic4729654577720512673ex_rat: (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_637, type, lattic5003618458639192673nt_num: (int > num) > set_int > int).
% 34.88/9.15 thf(func_def_638, type, lattic7811156612396918303nt_rat: (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_639, type, lattic7446932960582359483at_nat: (nat > nat) > set_nat > nat).
% 34.88/9.15 thf(func_def_640, type, lattic4004264746738138117at_num: (nat > num) > set_nat > nat).
% 34.88/9.15 thf(func_def_641, type, lattic6811802900495863747at_rat: (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_642, type, lattic1613168225601753569al_num: (real > num) > set_real > real).
% 34.88/9.15 thf(func_def_643, type, lattic4420706379359479199al_rat: (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_644, type, lattic7826324295020591184_F_nat: (nat > nat > nat) > nat > set_nat > nat).
% 34.88/9.15 thf(func_def_645, type, bfun_nat_real: (nat > real) > filter_nat > $o).
% 34.88/9.15 thf(func_def_646, type, append_nat: list_nat > list_nat > list_nat).
% 34.88/9.15 thf(func_def_647, type, concat_o: list_list_o > list_o).
% 34.88/9.15 thf(func_def_648, type, concat_int: list_list_int > list_int).
% 34.88/9.15 thf(func_def_649, type, concat_nat: list_list_nat > list_nat).
% 34.88/9.15 thf(func_def_650, type, concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_651, type, count_list_o: list_o > $o > nat).
% 34.88/9.15 thf(func_def_652, type, count_list_complex: list_complex > complex > nat).
% 34.88/9.15 thf(func_def_653, type, count_list_int: list_int > int > nat).
% 34.88/9.15 thf(func_def_654, type, count_list_nat: list_nat > nat > nat).
% 34.88/9.15 thf(func_def_655, type, count_list_real: list_real > real > nat).
% 34.88/9.15 thf(func_def_656, type, count_list_set_nat: list_set_nat > set_nat > nat).
% 34.88/9.15 thf(func_def_657, type, count_list_VEBT_VEBT: list_VEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_658, type, distinct_o: list_o > $o).
% 34.88/9.15 thf(func_def_659, type, distinct_complex: list_complex > $o).
% 34.88/9.15 thf(func_def_660, type, distinct_int: list_int > $o).
% 34.88/9.15 thf(func_def_661, type, distinct_list_nat: list_list_nat > $o).
% 34.88/9.15 thf(func_def_662, type, distinct_nat: list_nat > $o).
% 34.88/9.15 thf(func_def_663, type, distin6923225563576452346at_nat: list_P6011104703257516679at_nat > $o).
% 34.88/9.15 thf(func_def_664, type, distinct_real: list_real > $o).
% 34.88/9.15 thf(func_def_665, type, distinct_set_nat: list_set_nat > $o).
% 34.88/9.15 thf(func_def_666, type, distinct_VEBT_VEBT: list_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_667, type, enumerate_o: nat > list_o > list_P7333126701944960589_nat_o).
% 34.88/9.15 thf(func_def_668, type, enumerate_int: nat > list_int > list_P3521021558325789923at_int).
% 34.88/9.15 thf(func_def_669, type, enumerate_nat: nat > list_nat > list_P6011104703257516679at_nat).
% 34.88/9.15 thf(func_def_670, type, enumerate_VEBT_VEBT: nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 34.88/9.15 thf(func_def_671, type, find_o: ($o > $o) > list_o > option_o).
% 34.88/9.15 thf(func_def_672, type, find_int: (int > $o) > list_int > option_int).
% 34.88/9.15 thf(func_def_673, type, find_nat: (nat > $o) > list_nat > option_nat).
% 34.88/9.15 thf(func_def_674, type, find_num: (num > $o) > list_num > option_num).
% 34.88/9.15 thf(func_def_675, type, find_P8199882355184865565at_nat: (product_prod_nat_nat > $o) > list_P6011104703257516679at_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_676, type, find_VEBT_VEBT: (vEBT_VEBT > $o) > list_VEBT_VEBT > option_VEBT_VEBT).
% 34.88/9.15 thf(func_def_677, type, fold_nat_nat: (nat > nat > nat) > list_nat > nat > nat).
% 34.88/9.15 thf(func_def_678, type, lenlex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o).
% 34.88/9.15 thf(func_def_679, type, lenlex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger).
% 34.88/9.15 thf(func_def_680, type, lenlex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int).
% 34.88/9.15 thf(func_def_681, type, lenlex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat).
% 34.88/9.15 thf(func_def_682, type, lenlex325483962726685836at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat).
% 34.88/9.15 thf(func_def_683, type, lenlex1357538814655152620at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat).
% 34.88/9.15 thf(func_def_684, type, lenlex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT).
% 34.88/9.15 thf(func_def_685, type, lex_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o).
% 34.88/9.15 thf(func_def_686, type, lex_Code_integer: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger).
% 34.88/9.15 thf(func_def_687, type, lex_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int).
% 34.88/9.15 thf(func_def_688, type, lex_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat).
% 34.88/9.15 thf(func_def_689, type, lex_Pr8571645452597969515at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat).
% 34.88/9.15 thf(func_def_690, type, lex_se2245640040323279819at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat).
% 34.88/9.15 thf(func_def_691, type, lex_VEBT_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT).
% 34.88/9.15 thf(func_def_692, type, linord2614967742042102400et_nat: set_nat > list_nat).
% 34.88/9.15 thf(func_def_693, type, cons_C1897838848541180310er_nat: (code_integer > nat) > list_C4705013386053401436er_nat > list_C4705013386053401436er_nat).
% 34.88/9.15 thf(func_def_694, type, cons_int_nat: (int > nat) > list_int_nat > list_int_nat).
% 34.88/9.15 thf(func_def_695, type, cons_nat_nat: (nat > nat) > list_nat_nat > list_nat_nat).
% 34.88/9.15 thf(func_def_696, type, cons_P4861729644591583992at_nat: (product_prod_nat_nat > nat) > list_P9162950289778280392at_nat > list_P9162950289778280392at_nat).
% 34.88/9.15 thf(func_def_697, type, cons_s2538900923071588440at_nat: (set_Pr1261947904930325089at_nat > nat) > list_s9130966667114977576at_nat > list_s9130966667114977576at_nat).
% 34.88/9.15 thf(func_def_698, type, cons_o: $o > list_o > list_o).
% 34.88/9.15 thf(func_def_699, type, cons_Code_integer: code_integer > list_Code_integer > list_Code_integer).
% 34.88/9.15 thf(func_def_700, type, cons_complex: complex > list_complex > list_complex).
% 34.88/9.15 thf(func_def_701, type, cons_int: int > list_int > list_int).
% 34.88/9.15 thf(func_def_702, type, cons_nat: nat > list_nat > list_nat).
% 34.88/9.15 thf(func_def_703, type, cons_num: num > list_num > list_num).
% 34.88/9.15 thf(func_def_704, type, cons_P9044669534377732177nteger: produc8923325533196201883nteger > list_P5578671422887162913nteger > list_P5578671422887162913nteger).
% 34.88/9.15 thf(func_def_705, type, cons_P3334398858971670639nt_int: product_prod_int_int > list_P5707943133018811711nt_int > list_P5707943133018811711nt_int).
% 34.88/9.15 thf(func_def_706, type, cons_P6512896166579812791at_nat: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat).
% 34.88/9.15 thf(func_def_707, type, cons_P8732206157123786781at_nat: produc859450856879609959at_nat > list_P8469869581646625389at_nat > list_P8469869581646625389at_nat).
% 34.88/9.15 thf(func_def_708, type, cons_P3940603068885512221at_nat: produc3843707927480180839at_nat > list_P5464809261938338413at_nat > list_P5464809261938338413at_nat).
% 34.88/9.15 thf(func_def_709, type, cons_real: real > list_real > list_real).
% 34.88/9.15 thf(func_def_710, type, cons_set_nat: set_nat > list_set_nat > list_set_nat).
% 34.88/9.15 thf(func_def_711, type, cons_s6881495754146722583at_nat: set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat).
% 34.88/9.15 thf(func_def_712, type, cons_VEBT_VEBT: vEBT_VEBT > list_VEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_713, type, nil_nat: list_nat).
% 34.88/9.15 thf(func_def_714, type, map_nat_nat: (nat > nat) > list_nat > list_nat).
% 34.88/9.15 thf(func_def_715, type, map_VE8901447254227204932T_VEBT: (vEBT_VEBT > vEBT_VEBT) > list_VEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_716, type, set_o2: list_o > set_o).
% 34.88/9.15 thf(func_def_717, type, set_Code_integer2: list_Code_integer > set_Code_integer).
% 34.88/9.15 thf(func_def_718, type, set_complex2: list_complex > set_complex).
% 34.88/9.15 thf(func_def_719, type, set_int2: list_int > set_int).
% 34.88/9.15 thf(func_def_720, type, set_list_o2: list_list_o > set_list_o).
% 34.88/9.15 thf(func_def_721, type, set_list_int2: list_list_int > set_list_int).
% 34.88/9.15 thf(func_def_722, type, set_list_nat2: list_list_nat > set_list_nat).
% 34.88/9.15 thf(func_def_723, type, set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_724, type, set_nat2: list_nat > set_nat).
% 34.88/9.15 thf(func_def_725, type, set_Pr1389080609085208608omplex: list_P3924974545808530565omplex > set_Pr5421754520313593387omplex).
% 34.88/9.15 thf(func_def_726, type, set_Pr2600826154070092190o_real: list_P5232166724548748803o_real > set_Pr6573716822653411497o_real).
% 34.88/9.15 thf(func_def_727, type, set_Pr655345902815428824T_VEBT: list_P7495141550334521929T_VEBT > set_Pr7543698050874017315T_VEBT).
% 34.88/9.15 thf(func_def_728, type, set_Pr920681315882439344nteger: list_P5578671422887162913nteger > set_Pr4811707699266497531nteger).
% 34.88/9.15 thf(func_def_729, type, set_Pr6829704231520703882plex_o: list_P7942624414058669295plex_o > set_Pr216032351708956309plex_o).
% 34.88/9.15 thf(func_def_730, type, set_Pr8199049879907524818omplex: list_P7664491975274850627omplex > set_Pr5085853215250843933omplex).
% 34.88/9.15 thf(func_def_731, type, set_Pr4995810437751016784ex_int: list_P2206113689347244737ex_int > set_Pr2254670189886740123ex_int).
% 34.88/9.15 thf(func_def_732, type, set_Pr9173661457260213492ex_nat: list_P4696196834278971493ex_nat > set_Pr4744753334818466879ex_nat).
% 34.88/9.15 thf(func_def_733, type, set_Pr1225976482156248400x_real: list_P7647014805210017729x_real > set_Pr1133549439701694107x_real).
% 34.88/9.15 thf(func_def_734, type, set_Pr5158653123227461798T_VEBT: list_P7977503562704621835T_VEBT > set_Pr4085867452638698417T_VEBT).
% 34.88/9.15 thf(func_def_735, type, set_Pr3989287306472219216omplex: list_P1797514011394873281omplex > set_Pr1846070511934368667omplex).
% 34.88/9.15 thf(func_def_736, type, set_Pr2470121279949933262nt_int: list_P5707943133018811711nt_int > set_Pr958786334691620121nt_int).
% 34.88/9.15 thf(func_def_737, type, set_Pr112895574167722958t_real: list_P6863124054624500543t_real > set_Pr3538720872664544793t_real).
% 34.88/9.15 thf(func_def_738, type, set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_739, type, set_Pr5518436109238095868at_nat: list_P8469869581646625389at_nat > set_Pr8693737435421807431at_nat).
% 34.88/9.15 thf(func_def_740, type, set_Pr5196769464307566348real_o: list_P3595434254542482545real_o > set_Pr4936984352647145239real_o).
% 34.88/9.15 thf(func_def_741, type, set_Pr8536649499196266448omplex: list_P3881527313128557121omplex > set_Pr6591433984475009307omplex).
% 34.88/9.15 thf(func_def_742, type, set_Pr8219819362198175822al_int: list_P4344331454722006975al_int > set_Pr1019928272762051225al_int).
% 34.88/9.15 thf(func_def_743, type, set_Pr3174298344852596722al_nat: list_P6834414599653733731al_nat > set_Pr3510011417693777981al_nat).
% 34.88/9.15 thf(func_def_744, type, set_Pr5999470521830281550l_real: list_P8689742595348180415l_real > set_Pr6218003697084177305l_real).
% 34.88/9.15 thf(func_def_745, type, set_Pr8897343066327330088T_VEBT: list_P877281246627933069T_VEBT > set_Pr6019664923565264691T_VEBT).
% 34.88/9.15 thf(func_def_746, type, set_Pr9040384385603167362et_nat: list_P6254988961118846195et_nat > set_Pr5488025237498180813et_nat).
% 34.88/9.15 thf(func_def_747, type, set_Pr3765526544606949372at_nat: list_P5464809261938338413at_nat > set_Pr4329608150637261639at_nat).
% 34.88/9.15 thf(func_def_748, type, set_Pr7708085864119495200VEBT_o: list_P3126845725202233233VEBT_o > set_Pr3175402225741728619VEBT_o).
% 34.88/9.15 thf(func_def_749, type, set_Pr6387300694196750780omplex: list_P4108580160459392801omplex > set_Pr216944050393469383omplex).
% 34.88/9.15 thf(func_def_750, type, set_Pr2853735649769556538BT_int: list_P4547456442757143711BT_int > set_Pr5066593544530342725BT_int).
% 34.88/9.15 thf(func_def_751, type, set_Pr7031586669278753246BT_nat: list_P7037539587688870467BT_nat > set_Pr7556676689462069481BT_nat).
% 34.88/9.15 thf(func_def_752, type, set_Pr1087130671499945274T_real: list_P2623026923184700063T_real > set_Pr7765410600122031685T_real).
% 34.88/9.15 thf(func_def_753, type, set_Pr9182192707038809660T_VEBT: list_P7413028617227757229T_VEBT > set_Pr6192946355708809607T_VEBT).
% 34.88/9.15 thf(func_def_754, type, set_real2: list_real > set_real).
% 34.88/9.15 thf(func_def_755, type, set_set_nat2: list_set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_756, type, set_se5049602875457034614at_nat: list_s1210847774152347623at_nat > set_se7855581050983116737at_nat).
% 34.88/9.15 thf(func_def_757, type, set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT).
% 34.88/9.15 thf(func_def_758, type, size_list_typerep: (typerep > nat) > list_typerep > nat).
% 34.88/9.15 thf(func_def_759, type, size_list_VEBT_VEBT: (vEBT_VEBT > nat) > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_760, type, tl_nat: list_nat > list_nat).
% 34.88/9.15 thf(func_def_761, type, list_update_o: list_o > nat > $o > list_o).
% 34.88/9.15 thf(func_def_762, type, list_u5447711078246177391nteger: list_Code_integer > nat > code_integer > list_Code_integer).
% 34.88/9.15 thf(func_def_763, type, list_update_complex: list_complex > nat > complex > list_complex).
% 34.88/9.15 thf(func_def_764, type, list_update_int: list_int > nat > int > list_int).
% 34.88/9.15 thf(func_def_765, type, list_update_nat: list_nat > nat > nat > list_nat).
% 34.88/9.15 thf(func_def_766, type, list_u2254550707601501961nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger > list_P5578671422887162913nteger).
% 34.88/9.15 thf(func_def_767, type, list_u3002344382305578791nt_int: list_P5707943133018811711nt_int > nat > product_prod_int_int > list_P5707943133018811711nt_int).
% 34.88/9.15 thf(func_def_768, type, list_u6180841689913720943at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat > list_P6011104703257516679at_nat).
% 34.88/9.15 thf(func_def_769, type, list_u5003261594476800725at_nat: list_P8469869581646625389at_nat > nat > produc859450856879609959at_nat > list_P8469869581646625389at_nat).
% 34.88/9.15 thf(func_def_770, type, list_u4696772448584712917at_nat: list_P5464809261938338413at_nat > nat > produc3843707927480180839at_nat > list_P5464809261938338413at_nat).
% 34.88/9.15 thf(func_def_771, type, list_u6961636818849549845T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT > list_P7413028617227757229T_VEBT).
% 34.88/9.15 thf(func_def_772, type, list_update_real: list_real > nat > real > list_real).
% 34.88/9.15 thf(func_def_773, type, list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat).
% 34.88/9.15 thf(func_def_774, type, list_u8444657558853818831at_nat: list_s1210847774152347623at_nat > nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat).
% 34.88/9.15 thf(func_def_775, type, list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_776, type, listrel_o_o: set_Product_prod_o_o > set_Pr6227168374412355847list_o).
% 34.88/9.15 thf(func_def_777, type, listrel_o_int: set_Pr8834758594704517033_o_int > set_Pr5001190662893202239st_int).
% 34.88/9.15 thf(func_def_778, type, listrel_o_nat: set_Pr2101469702781467981_o_nat > set_Pr591367044826345187st_nat).
% 34.88/9.15 thf(func_def_779, type, listrel_o_VEBT_VEBT: set_Pr7543698050874017315T_VEBT > set_Pr5170412164475753123T_VEBT).
% 34.88/9.15 thf(func_def_780, type, listre5734910445319291053nteger: set_Pr4811707699266497531nteger > set_Pr7565137564259432987nteger).
% 34.88/9.15 thf(func_def_781, type, listrel_int_int: set_Pr958786334691620121nt_int > set_Pr765067013931698361st_int).
% 34.88/9.15 thf(func_def_782, type, listrel_nat_o: set_Pr3149072824959771635_nat_o > set_Pr1150278048023938153list_o).
% 34.88/9.15 thf(func_def_783, type, listrel_nat_nat: set_Pr1261947904930325089at_nat > set_Pr3451248702717554689st_nat).
% 34.88/9.15 thf(func_def_784, type, listre5761932458788874033T_VEBT: set_Pr6167073792073659919T_VEBT > set_Pr1262583345697558789T_VEBT).
% 34.88/9.15 thf(func_def_785, type, listre818007680106770737at_nat: set_Pr8693737435421807431at_nat > set_Pr1542805901266377927at_nat).
% 34.88/9.15 thf(func_def_786, type, listre2047417242196832561at_nat: set_Pr4329608150637261639at_nat > set_Pr4333006031979791559at_nat).
% 34.88/9.15 thf(func_def_787, type, listrel_VEBT_VEBT_o: set_Pr3175402225741728619VEBT_o > set_Pr7508168486584781291list_o).
% 34.88/9.15 thf(func_def_788, type, listre5898179758603845167BT_int: set_Pr5066593544530342725BT_int > set_Pr4080907618048478043st_int).
% 34.88/9.15 thf(func_def_789, type, listre5900670229112895443BT_nat: set_Pr7556676689462069481BT_nat > set_Pr8894456036836396799st_nat).
% 34.88/9.15 thf(func_def_790, type, listre1230615542750757617T_VEBT: set_Pr6192946355708809607T_VEBT > set_Pr1916528119006554503T_VEBT).
% 34.88/9.15 thf(func_def_791, type, measur8870801148506250077nteger: list_C4705013386053401436er_nat > set_Pr4811707699266497531nteger).
% 34.88/9.15 thf(func_def_792, type, measures_int: list_int_nat > set_Pr958786334691620121nt_int).
% 34.88/9.15 thf(func_def_793, type, measures_nat: list_nat_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_794, type, measur2679027848233739777at_nat: list_P9162950289778280392at_nat > set_Pr8693737435421807431at_nat).
% 34.88/9.15 thf(func_def_795, type, measur2694323259624372065at_nat: list_s9130966667114977576at_nat > set_Pr4329608150637261639at_nat).
% 34.88/9.15 thf(func_def_796, type, nth_o: list_o > nat > $o).
% 34.88/9.15 thf(func_def_797, type, nth_Code_integer: list_Code_integer > nat > code_integer).
% 34.88/9.15 thf(func_def_798, type, nth_complex: list_complex > nat > complex).
% 34.88/9.15 thf(func_def_799, type, nth_int: list_int > nat > int).
% 34.88/9.15 thf(func_def_800, type, nth_nat: list_nat > nat > nat).
% 34.88/9.15 thf(func_def_801, type, nth_num: list_num > nat > num).
% 34.88/9.15 thf(func_def_802, type, nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o).
% 34.88/9.15 thf(func_def_803, type, nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int).
% 34.88/9.15 thf(func_def_804, type, nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat).
% 34.88/9.15 thf(func_def_805, type, nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT).
% 34.88/9.15 thf(func_def_806, type, nth_Pr2304437835452373666nteger: list_P5578671422887162913nteger > nat > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_807, type, nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o).
% 34.88/9.15 thf(func_def_808, type, nth_Pr3440142176431000676at_int: list_P3521021558325789923at_int > nat > product_prod_nat_int).
% 34.88/9.15 thf(func_def_809, type, nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_810, type, nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT).
% 34.88/9.15 thf(func_def_811, type, nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o).
% 34.88/9.15 thf(func_def_812, type, nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int).
% 34.88/9.15 thf(func_def_813, type, nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat).
% 34.88/9.15 thf(func_def_814, type, nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT).
% 34.88/9.15 thf(func_def_815, type, nth_real: list_real > nat > real).
% 34.88/9.15 thf(func_def_816, type, nth_set_nat: list_set_nat > nat > set_nat).
% 34.88/9.15 thf(func_def_817, type, nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_818, type, product_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 34.88/9.15 thf(func_def_819, type, product_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 34.88/9.15 thf(func_def_820, type, product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 34.88/9.15 thf(func_def_821, type, product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 34.88/9.15 thf(func_def_822, type, produc8792966785426426881nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger).
% 34.88/9.15 thf(func_def_823, type, product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o).
% 34.88/9.15 thf(func_def_824, type, produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 34.88/9.15 thf(func_def_825, type, product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 34.88/9.15 thf(func_def_826, type, produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 34.88/9.15 thf(func_def_827, type, produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 34.88/9.15 thf(func_def_828, type, produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 34.88/9.15 thf(func_def_829, type, product_lists_o: list_list_o > list_list_o).
% 34.88/9.15 thf(func_def_830, type, product_lists_int: list_list_int > list_list_int).
% 34.88/9.15 thf(func_def_831, type, product_lists_nat: list_list_nat > list_list_nat).
% 34.88/9.15 thf(func_def_832, type, produc3021084454716106787T_VEBT: list_list_VEBT_VEBT > list_list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_833, type, replicate_o: nat > $o > list_o).
% 34.88/9.15 thf(func_def_834, type, replicate_complex: nat > complex > list_complex).
% 34.88/9.15 thf(func_def_835, type, replicate_int: nat > int > list_int).
% 34.88/9.15 thf(func_def_836, type, replicate_nat: nat > nat > list_nat).
% 34.88/9.15 thf(func_def_837, type, replicate_real: nat > real > list_real).
% 34.88/9.15 thf(func_def_838, type, replicate_set_nat: nat > set_nat > list_set_nat).
% 34.88/9.15 thf(func_def_839, type, replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_840, type, rotate1_o: list_o > list_o).
% 34.88/9.15 thf(func_def_841, type, rotate1_int: list_int > list_int).
% 34.88/9.15 thf(func_def_842, type, rotate1_nat: list_nat > list_nat).
% 34.88/9.15 thf(func_def_843, type, rotate1_VEBT_VEBT: list_VEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_844, type, sorted_wrt_nat: (nat > nat > $o) > list_nat > $o).
% 34.88/9.15 thf(func_def_845, type, take_nat: nat > list_nat > list_nat).
% 34.88/9.15 thf(func_def_846, type, take_VEBT_VEBT: nat > list_VEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_847, type, upt: nat > nat > list_nat).
% 34.88/9.15 thf(func_def_848, type, upto: int > int > list_int).
% 34.88/9.15 thf(func_def_849, type, zip_o_o: list_o > list_o > list_P4002435161011370285od_o_o).
% 34.88/9.15 thf(func_def_850, type, zip_o_complex: list_o > list_complex > list_P3924974545808530565omplex).
% 34.88/9.15 thf(func_def_851, type, zip_o_int: list_o > list_int > list_P3795440434834930179_o_int).
% 34.88/9.15 thf(func_def_852, type, zip_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat).
% 34.88/9.15 thf(func_def_853, type, zip_o_real: list_o > list_real > list_P5232166724548748803o_real).
% 34.88/9.15 thf(func_def_854, type, zip_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT).
% 34.88/9.15 thf(func_def_855, type, zip_Co3543743374963494515nteger: list_Code_integer > list_Code_integer > list_P5578671422887162913nteger).
% 34.88/9.15 thf(func_def_856, type, zip_complex_o: list_complex > list_o > list_P7942624414058669295plex_o).
% 34.88/9.15 thf(func_def_857, type, zip_complex_complex: list_complex > list_complex > list_P7664491975274850627omplex).
% 34.88/9.15 thf(func_def_858, type, zip_complex_int: list_complex > list_int > list_P2206113689347244737ex_int).
% 34.88/9.15 thf(func_def_859, type, zip_complex_nat: list_complex > list_nat > list_P4696196834278971493ex_nat).
% 34.88/9.15 thf(func_def_860, type, zip_complex_real: list_complex > list_real > list_P7647014805210017729x_real).
% 34.88/9.15 thf(func_def_861, type, zip_co9157518722488180109T_VEBT: list_complex > list_VEBT_VEBT > list_P7977503562704621835T_VEBT).
% 34.88/9.15 thf(func_def_862, type, zip_int_complex: list_int > list_complex > list_P1797514011394873281omplex).
% 34.88/9.15 thf(func_def_863, type, zip_int_int: list_int > list_int > list_P5707943133018811711nt_int).
% 34.88/9.15 thf(func_def_864, type, zip_int_real: list_int > list_real > list_P6863124054624500543t_real).
% 34.88/9.15 thf(func_def_865, type, zip_nat_nat: list_nat > list_nat > list_P6011104703257516679at_nat).
% 34.88/9.15 thf(func_def_866, type, zip_nat_VEBT_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT).
% 34.88/9.15 thf(func_def_867, type, zip_Pr4664179122662387191at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > list_P8469869581646625389at_nat).
% 34.88/9.15 thf(func_def_868, type, zip_real_o: list_real > list_o > list_P3595434254542482545real_o).
% 34.88/9.15 thf(func_def_869, type, zip_real_complex: list_real > list_complex > list_P3881527313128557121omplex).
% 34.88/9.15 thf(func_def_870, type, zip_real_int: list_real > list_int > list_P4344331454722006975al_int).
% 34.88/9.15 thf(func_def_871, type, zip_real_nat: list_real > list_nat > list_P6834414599653733731al_nat).
% 34.88/9.15 thf(func_def_872, type, zip_real_real: list_real > list_real > list_P8689742595348180415l_real).
% 34.88/9.15 thf(func_def_873, type, zip_real_VEBT_VEBT: list_real > list_VEBT_VEBT > list_P877281246627933069T_VEBT).
% 34.88/9.15 thf(func_def_874, type, zip_set_nat_set_nat: list_set_nat > list_set_nat > list_P6254988961118846195et_nat).
% 34.88/9.15 thf(func_def_875, type, zip_se5600341670672612855at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > list_P5464809261938338413at_nat).
% 34.88/9.15 thf(func_def_876, type, zip_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o).
% 34.88/9.15 thf(func_def_877, type, zip_VE2794733401258833515omplex: list_VEBT_VEBT > list_complex > list_P4108580160459392801omplex).
% 34.88/9.15 thf(func_def_878, type, zip_VEBT_VEBT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int).
% 34.88/9.15 thf(func_def_879, type, zip_VEBT_VEBT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat).
% 34.88/9.15 thf(func_def_880, type, zip_VEBT_VEBT_real: list_VEBT_VEBT > list_real > list_P2623026923184700063T_real).
% 34.88/9.15 thf(func_def_881, type, zip_VE537291747668921783T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT).
% 34.88/9.15 thf(func_def_882, type, suc: nat > nat).
% 34.88/9.15 thf(func_def_883, type, compow_nat_nat: nat > (nat > nat) > nat > nat).
% 34.88/9.15 thf(func_def_884, type, case_nat_o: $o > (nat > $o) > nat > $o).
% 34.88/9.15 thf(func_def_885, type, case_nat_nat: nat > (nat > nat) > nat > nat).
% 34.88/9.15 thf(func_def_886, type, pred: nat > nat).
% 34.88/9.15 thf(func_def_887, type, semiri4939895301339042750nteger: nat > code_integer).
% 34.88/9.15 thf(func_def_888, type, semiri3763490453095760265atural: nat > code_natural).
% 34.88/9.15 thf(func_def_889, type, semiri8010041392384452111omplex: nat > complex).
% 34.88/9.15 thf(func_def_890, type, semiri4216267220026989637d_enat: nat > extended_enat).
% 34.88/9.15 thf(func_def_891, type, semiri1314217659103216013at_int: nat > int).
% 34.88/9.15 thf(func_def_892, type, semiri1316708129612266289at_nat: nat > nat).
% 34.88/9.15 thf(func_def_893, type, semiri681578069525770553at_rat: nat > rat).
% 34.88/9.15 thf(func_def_894, type, semiri5074537144036343181t_real: nat > real).
% 34.88/9.15 thf(func_def_895, type, semiri4055485073559036834nteger: (code_integer > code_integer) > nat > code_integer > code_integer).
% 34.88/9.15 thf(func_def_896, type, semiri2816024913162550771omplex: (complex > complex) > nat > complex > complex).
% 34.88/9.15 thf(func_def_897, type, semiri8420488043553186161ux_int: (int > int) > nat > int > int).
% 34.88/9.15 thf(func_def_898, type, semiri8422978514062236437ux_nat: (nat > nat) > nat > nat > nat).
% 34.88/9.15 thf(func_def_899, type, semiri7787848453975740701ux_rat: (rat > rat) > nat > rat > rat).
% 34.88/9.15 thf(func_def_900, type, semiri7260567687927622513x_real: (real > real) > nat > real > real).
% 34.88/9.15 thf(func_def_901, type, size_size_list_o: list_o > nat).
% 34.88/9.15 thf(func_def_902, type, size_s3445333598471063425nteger: list_Code_integer > nat).
% 34.88/9.15 thf(func_def_903, type, size_s3451745648224563538omplex: list_complex > nat).
% 34.88/9.15 thf(func_def_904, type, size_size_list_int: list_int > nat).
% 34.88/9.15 thf(func_def_905, type, size_s2710708370519433104list_o: list_list_o > nat).
% 34.88/9.15 thf(func_def_906, type, size_s533118279054570080st_int: list_list_int > nat).
% 34.88/9.15 thf(func_def_907, type, size_s3023201423986296836st_nat: list_list_nat > nat).
% 34.88/9.15 thf(func_def_908, type, size_s8217280938318005548T_VEBT: list_list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_909, type, size_size_list_nat: list_nat > nat).
% 34.88/9.15 thf(func_def_910, type, size_size_list_num: list_num > nat).
% 34.88/9.15 thf(func_def_911, type, size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat).
% 34.88/9.15 thf(func_def_912, type, size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat).
% 34.88/9.15 thf(func_def_913, type, size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat).
% 34.88/9.15 thf(func_def_914, type, size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat).
% 34.88/9.15 thf(func_def_915, type, size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat).
% 34.88/9.15 thf(func_def_916, type, size_s2970893825323803983at_int: list_P3521021558325789923at_int > nat).
% 34.88/9.15 thf(func_def_917, type, size_s5460976970255530739at_nat: list_P6011104703257516679at_nat > nat).
% 34.88/9.15 thf(func_def_918, type, size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat).
% 34.88/9.15 thf(func_def_919, type, size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat).
% 34.88/9.15 thf(func_def_920, type, size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat).
% 34.88/9.15 thf(func_def_921, type, size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat).
% 34.88/9.15 thf(func_def_922, type, size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat).
% 34.88/9.15 thf(func_def_923, type, size_size_list_real: list_real > nat).
% 34.88/9.15 thf(func_def_924, type, size_s3254054031482475050et_nat: list_set_nat > nat).
% 34.88/9.15 thf(func_def_925, type, size_s8736152011456118867at_nat: list_s1210847774152347623at_nat > nat).
% 34.88/9.15 thf(func_def_926, type, size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_927, type, size_size_num: num > nat).
% 34.88/9.15 thf(func_def_928, type, size_size_option_nat: option_nat > nat).
% 34.88/9.15 thf(func_def_929, type, size_size_option_num: option_num > nat).
% 34.88/9.15 thf(func_def_930, type, size_s170228958280169651at_nat: option4927543243414619207at_nat > nat).
% 34.88/9.15 thf(func_def_931, type, size_size_char: char > nat).
% 34.88/9.15 thf(func_def_932, type, size_size_typerep: typerep > nat).
% 34.88/9.15 thf(func_def_933, type, size_size_VEBT_VEBT: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_934, type, nat_int_decode: nat > int).
% 34.88/9.15 thf(func_def_935, type, nat_int_encode: int > nat).
% 34.88/9.15 thf(func_def_936, type, nat_list_decode: nat > list_nat).
% 34.88/9.15 thf(func_def_937, type, nat_list_decode_rel: nat > nat > $o).
% 34.88/9.15 thf(func_def_938, type, nat_list_encode: list_nat > nat).
% 34.88/9.15 thf(func_def_939, type, nat_list_encode_rel: list_nat > list_nat > $o).
% 34.88/9.15 thf(func_def_940, type, nat_prod_decode: nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_941, type, nat_prod_decode_aux: nat > nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_942, type, nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_943, type, nat_prod_encode: product_prod_nat_nat > nat).
% 34.88/9.15 thf(func_def_944, type, nat_set_decode: nat > set_nat).
% 34.88/9.15 thf(func_def_945, type, nat_set_encode: set_nat > nat).
% 34.88/9.15 thf(func_def_946, type, nat_sum_decode: nat > sum_sum_nat_nat).
% 34.88/9.15 thf(func_def_947, type, nat_sum_encode: sum_sum_nat_nat > nat).
% 34.88/9.15 thf(func_def_948, type, nat_triangle: nat > nat).
% 34.88/9.15 thf(func_def_949, type, root: nat > real > real).
% 34.88/9.15 thf(func_def_950, type, sqrt: real > real).
% 34.88/9.15 thf(func_def_951, type, bitM: num > num).
% 34.88/9.15 thf(func_def_952, type, inc: num > num).
% 34.88/9.15 thf(func_def_953, type, nat_of_num: num > nat).
% 34.88/9.15 thf(func_def_954, type, neg_nu8804712462038260780nteger: code_integer > code_integer).
% 34.88/9.15 thf(func_def_955, type, neg_nu7009210354673126013omplex: complex > complex).
% 34.88/9.15 thf(func_def_956, type, neg_numeral_dbl_int: int > int).
% 34.88/9.15 thf(func_def_957, type, neg_numeral_dbl_rat: rat > rat).
% 34.88/9.15 thf(func_def_958, type, neg_numeral_dbl_real: real > real).
% 34.88/9.15 thf(func_def_959, type, neg_nu7757733837767384882nteger: code_integer > code_integer).
% 34.88/9.15 thf(func_def_960, type, neg_nu6511756317524482435omplex: complex > complex).
% 34.88/9.15 thf(func_def_961, type, neg_nu3811975205180677377ec_int: int > int).
% 34.88/9.15 thf(func_def_962, type, neg_nu3179335615603231917ec_rat: rat > rat).
% 34.88/9.15 thf(func_def_963, type, neg_nu6075765906172075777c_real: real > real).
% 34.88/9.15 thf(func_def_964, type, neg_nu5831290666863070958nteger: code_integer > code_integer).
% 34.88/9.15 thf(func_def_965, type, neg_nu8557863876264182079omplex: complex > complex).
% 34.88/9.15 thf(func_def_966, type, neg_nu5851722552734809277nc_int: int > int).
% 34.88/9.15 thf(func_def_967, type, neg_nu5219082963157363817nc_rat: rat > rat).
% 34.88/9.15 thf(func_def_968, type, neg_nu8295874005876285629c_real: real > real).
% 34.88/9.15 thf(func_def_969, type, neg_numeral_sub_int: num > num > int).
% 34.88/9.15 thf(func_def_970, type, bit0: num > num).
% 34.88/9.15 thf(func_def_971, type, bit1: num > num).
% 34.88/9.15 thf(func_def_972, type, one: num).
% 34.88/9.15 thf(func_def_973, type, size_num: num > nat).
% 34.88/9.15 thf(func_def_974, type, num_of_nat: nat > num).
% 34.88/9.15 thf(func_def_975, type, numera6620942414471956472nteger: num > code_integer).
% 34.88/9.15 thf(func_def_976, type, numera5444537566228673987atural: num > code_natural).
% 34.88/9.15 thf(func_def_977, type, numera6690914467698888265omplex: num > complex).
% 34.88/9.15 thf(func_def_978, type, numera1916890842035813515d_enat: num > extended_enat).
% 34.88/9.15 thf(func_def_979, type, numeral_numeral_int: num > int).
% 34.88/9.15 thf(func_def_980, type, numeral_numeral_nat: num > nat).
% 34.88/9.15 thf(func_def_981, type, numeral_numeral_rat: num > rat).
% 34.88/9.15 thf(func_def_982, type, numeral_numeral_real: num > real).
% 34.88/9.15 thf(func_def_983, type, pow: num > num > num).
% 34.88/9.15 thf(func_def_984, type, pred_numeral: num > nat).
% 34.88/9.15 thf(func_def_985, type, sqr: num > num).
% 34.88/9.15 thf(func_def_986, type, none_nat: option_nat).
% 34.88/9.15 thf(func_def_987, type, none_num: option_num).
% 34.88/9.15 thf(func_def_988, type, none_P5556105721700978146at_nat: option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_989, type, some_o: $o > option_o).
% 34.88/9.15 thf(func_def_990, type, some_int: int > option_int).
% 34.88/9.15 thf(func_def_991, type, some_nat: nat > option_nat).
% 34.88/9.15 thf(func_def_992, type, some_num: num > option_num).
% 34.88/9.15 thf(func_def_993, type, some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_994, type, some_VEBT_VEBT: vEBT_VEBT > option_VEBT_VEBT).
% 34.88/9.15 thf(func_def_995, type, case_o184042715313410164at_nat: $o > (product_prod_nat_nat > $o) > option4927543243414619207at_nat > $o).
% 34.88/9.15 thf(func_def_996, type, case_option_num_num: num > (num > num) > option_num > num).
% 34.88/9.15 thf(func_def_997, type, case_o6005452278849405969um_num: option_num > (num > option_num) > option_num > option_num).
% 34.88/9.15 thf(func_def_998, type, size_option_nat: (nat > nat) > option_nat > nat).
% 34.88/9.15 thf(func_def_999, type, size_option_num: (num > nat) > option_num > nat).
% 34.88/9.15 thf(func_def_1000, type, size_o8335143837870341156at_nat: (product_prod_nat_nat > nat) > option4927543243414619207at_nat > nat).
% 34.88/9.15 thf(func_def_1001, type, the_nat: option_nat > nat).
% 34.88/9.15 thf(func_def_1002, type, the_num: option_num > num).
% 34.88/9.15 thf(func_def_1003, type, the_Pr8591224930841456533at_nat: option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_1004, type, order_4473980167227706203on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1005, type, order_5251275573222108571on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1006, type, order_4861654808422542329on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1007, type, order_underS_nat: set_Pr1261947904930325089at_nat > nat > set_nat).
% 34.88/9.15 thf(func_def_1008, type, order_2888998067076097458on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1009, type, bot_bot_nat: nat).
% 34.88/9.15 thf(func_def_1010, type, bot_bot_set_o: set_o).
% 34.88/9.15 thf(func_def_1011, type, bot_bot_set_complex: set_complex).
% 34.88/9.15 thf(func_def_1012, type, bot_bot_set_int: set_int).
% 34.88/9.15 thf(func_def_1013, type, bot_bot_set_list_nat: set_list_nat).
% 34.88/9.15 thf(func_def_1014, type, bot_bot_set_nat: set_nat).
% 34.88/9.15 thf(func_def_1015, type, bot_bot_set_num: set_num).
% 34.88/9.15 thf(func_def_1016, type, bot_bo2099793752762293965at_nat: set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1017, type, bot_bot_set_rat: set_rat).
% 34.88/9.15 thf(func_def_1018, type, bot_bot_set_real: set_real).
% 34.88/9.15 thf(func_def_1019, type, bot_bot_set_set_nat: set_set_nat).
% 34.88/9.15 thf(func_def_1020, type, bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1021, type, ord_Least_nat: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_1022, type, ord_le6747313008572928689nteger: code_integer > code_integer > $o).
% 34.88/9.15 thf(func_def_1023, type, ord_le72135733267957522d_enat: extended_enat > extended_enat > $o).
% 34.88/9.15 thf(func_def_1024, type, ord_less_int: int > int > $o).
% 34.88/9.15 thf(func_def_1025, type, ord_less_nat: nat > nat > $o).
% 34.88/9.15 thf(func_def_1026, type, ord_less_num: num > num > $o).
% 34.88/9.15 thf(func_def_1027, type, ord_less_rat: rat > rat > $o).
% 34.88/9.15 thf(func_def_1028, type, ord_less_real: real > real > $o).
% 34.88/9.15 thf(func_def_1029, type, ord_less_set_complex: set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1030, type, ord_less_set_int: set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1031, type, ord_less_set_nat: set_nat > set_nat > $o).
% 34.88/9.15 thf(func_def_1032, type, ord_less_set_num: set_num > set_num > $o).
% 34.88/9.15 thf(func_def_1033, type, ord_less_set_rat: set_rat > set_rat > $o).
% 34.88/9.15 thf(func_def_1034, type, ord_less_set_real: set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1035, type, ord_less_set_set_nat: set_set_nat > set_set_nat > $o).
% 34.88/9.15 thf(func_def_1036, type, ord_le3102999989581377725nteger: code_integer > code_integer > $o).
% 34.88/9.15 thf(func_def_1037, type, ord_le1926595141338095240atural: code_natural > code_natural > $o).
% 34.88/9.15 thf(func_def_1038, type, ord_le2932123472753598470d_enat: extended_enat > extended_enat > $o).
% 34.88/9.15 thf(func_def_1039, type, ord_le2510731241096832064er_nat: filter_nat > filter_nat > $o).
% 34.88/9.15 thf(func_def_1040, type, ord_less_eq_int: int > int > $o).
% 34.88/9.15 thf(func_def_1041, type, ord_less_eq_nat: nat > nat > $o).
% 34.88/9.15 thf(func_def_1042, type, ord_less_eq_num: num > num > $o).
% 34.88/9.15 thf(func_def_1043, type, ord_less_eq_rat: rat > rat > $o).
% 34.88/9.15 thf(func_def_1044, type, ord_less_eq_real: real > real > $o).
% 34.88/9.15 thf(func_def_1045, type, ord_less_eq_set_o: set_o > set_o > $o).
% 34.88/9.15 thf(func_def_1046, type, ord_le211207098394363844omplex: set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1047, type, ord_less_eq_set_int: set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1048, type, ord_le6045566169113846134st_nat: set_list_nat > set_list_nat > $o).
% 34.88/9.15 thf(func_def_1049, type, ord_less_eq_set_nat: set_nat > set_nat > $o).
% 34.88/9.15 thf(func_def_1050, type, ord_less_eq_set_num: set_num > set_num > $o).
% 34.88/9.15 thf(func_def_1051, type, ord_le3146513528884898305at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1052, type, ord_less_eq_set_rat: set_rat > set_rat > $o).
% 34.88/9.15 thf(func_def_1053, type, ord_less_eq_set_real: set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1054, type, ord_le6893508408891458716et_nat: set_set_nat > set_set_nat > $o).
% 34.88/9.15 thf(func_def_1055, type, ord_le4337996190870823476T_VEBT: set_VEBT_VEBT > set_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1056, type, ord_max_Code_integer: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_1057, type, ord_ma741700101516333627d_enat: extended_enat > extended_enat > extended_enat).
% 34.88/9.15 thf(func_def_1058, type, ord_max_int: int > int > int).
% 34.88/9.15 thf(func_def_1059, type, ord_max_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_1060, type, ord_max_num: num > num > num).
% 34.88/9.15 thf(func_def_1061, type, ord_max_rat: rat > rat > rat).
% 34.88/9.15 thf(func_def_1062, type, ord_max_real: real > real > real).
% 34.88/9.15 thf(func_def_1063, type, ord_max_set_int: set_int > set_int > set_int).
% 34.88/9.15 thf(func_def_1064, type, ord_max_set_nat: set_nat > set_nat > set_nat).
% 34.88/9.15 thf(func_def_1065, type, ord_max_set_real: set_real > set_real > set_real).
% 34.88/9.15 thf(func_def_1066, type, ord_min_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_1067, type, order_Greatest_nat: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_1068, type, order_mono_nat_nat: (nat > nat) > $o).
% 34.88/9.15 thf(func_def_1069, type, order_5726023648592871131at_nat: (nat > nat) > $o).
% 34.88/9.15 thf(func_def_1070, type, ordering_top_nat: (nat > nat > $o) > (nat > nat > $o) > nat > $o).
% 34.88/9.15 thf(func_def_1071, type, top_top_set_int: set_int).
% 34.88/9.15 thf(func_def_1072, type, top_top_set_list_nat: set_list_nat).
% 34.88/9.15 thf(func_def_1073, type, top_top_set_nat: set_nat).
% 34.88/9.15 thf(func_def_1074, type, top_to4669805908274784177at_nat: set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1075, type, top_top_set_real: set_real).
% 34.88/9.15 thf(func_def_1076, type, top_top_set_char: set_char).
% 34.88/9.15 thf(func_def_1077, type, top_to6661820994512907621at_nat: set_Sum_sum_nat_nat).
% 34.88/9.15 thf(func_def_1078, type, power_8256067586552552935nteger: code_integer > nat > code_integer).
% 34.88/9.15 thf(func_def_1079, type, power_7079662738309270450atural: code_natural > nat > code_natural).
% 34.88/9.15 thf(func_def_1080, type, power_power_complex: complex > nat > complex).
% 34.88/9.15 thf(func_def_1081, type, power_8040749407984259932d_enat: extended_enat > nat > extended_enat).
% 34.88/9.15 thf(func_def_1082, type, power_power_int: int > nat > int).
% 34.88/9.15 thf(func_def_1083, type, power_power_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_1084, type, power_power_rat: rat > nat > rat).
% 34.88/9.15 thf(func_def_1085, type, power_power_real: real > nat > real).
% 34.88/9.15 thf(func_def_1086, type, produc4035269172776083154on_nat: (nat > nat > $o) > produc4953844613479565601on_nat > produc2233624965454879586on_nat).
% 34.88/9.15 thf(func_def_1087, type, produc3209952032786966637at_nat: (nat > nat > nat) > produc7248412053542808358at_nat > produc4471711990508489141at_nat).
% 34.88/9.15 thf(func_def_1088, type, produc8929957630744042906on_nat: (nat > nat > nat) > produc4953844613479565601on_nat > produc8306885398267862888on_nat).
% 34.88/9.15 thf(func_def_1089, type, produc3576312749637752826on_num: (num > num > $o) > produc3447558737645232053on_num > produc7036089656553540234on_num).
% 34.88/9.15 thf(func_def_1090, type, produc5778274026573060048on_num: (num > num > num) > produc3447558737645232053on_num > produc1193250871479095198on_num).
% 34.88/9.15 thf(func_def_1091, type, produc3994169339658061776at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > produc6121120109295599847at_nat > produc5491161045314408544at_nat).
% 34.88/9.15 thf(func_def_1092, type, produc2899441246263362727at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > produc6121120109295599847at_nat > produc5542196010084753463at_nat).
% 34.88/9.15 thf(func_def_1093, type, product_Pair_o_o: $o > $o > product_prod_o_o).
% 34.88/9.15 thf(func_def_1094, type, produc414345526774272751omplex: $o > complex > produc648051720047351925omplex).
% 34.88/9.15 thf(func_def_1095, type, product_Pair_o_int: $o > int > product_prod_o_int).
% 34.88/9.15 thf(func_def_1096, type, product_Pair_o_nat: $o > nat > product_prod_o_nat).
% 34.88/9.15 thf(func_def_1097, type, product_Pair_o_real: $o > real > product_prod_o_real).
% 34.88/9.15 thf(func_def_1098, type, produc2982872950893828659T_VEBT: $o > vEBT_VEBT > produc2504756804600209347T_VEBT).
% 34.88/9.15 thf(func_def_1099, type, produc1086072967326762835nteger: code_integer > code_integer > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_1100, type, produc3574140220909816553atural: code_natural > code_natural > produc7822875418678951345atural).
% 34.88/9.15 thf(func_def_1101, type, produc6639722614265839536atural: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 34.88/9.15 thf(func_def_1102, type, produc2908979694703026321plex_o: complex > $o > produc6088675342482847199plex_o).
% 34.88/9.15 thf(func_def_1103, type, produc101793102246108661omplex: complex > complex > produc4411394909380815293omplex).
% 34.88/9.15 thf(func_def_1104, type, produc1367138851071493491ex_int: complex > int > produc6845221339535797307ex_int).
% 34.88/9.15 thf(func_def_1105, type, produc1369629321580543767ex_nat: complex > nat > produc1799700322190218207ex_nat).
% 34.88/9.15 thf(func_def_1106, type, produc1746590499379883635x_real: complex > real > produc8892588492097263291x_real).
% 34.88/9.15 thf(func_def_1107, type, produc2757191886755552429T_VEBT: complex > vEBT_VEBT > produc7151440242714718331T_VEBT).
% 34.88/9.15 thf(func_def_1108, type, produc7948753499206759283omplex: int > complex > produc5838698208256999739omplex).
% 34.88/9.15 thf(func_def_1109, type, product_Pair_int_int: int > int > product_prod_int_int).
% 34.88/9.15 thf(func_def_1110, type, produc801115645435158769t_real: int > real > produc679980390762269497t_real).
% 34.88/9.15 thf(func_def_1111, type, produc8435520187683070743list_o: list_o > list_o > produc7102631898165422375list_o).
% 34.88/9.15 thf(func_def_1112, type, produc2951025481305455875st_int: list_o > list_int > produc1713839591385758857st_int).
% 34.88/9.15 thf(func_def_1113, type, produc7128876500814652583st_nat: list_o > list_nat > produc4203922736317485613st_nat).
% 34.88/9.15 thf(func_def_1114, type, produc6043759678074843571T_VEBT: list_o > list_VEBT_VEBT > produc1922972420619397443T_VEBT).
% 34.88/9.15 thf(func_def_1115, type, produc750622340256944499nteger: list_Code_integer > list_Code_integer > produc862207588354017979nteger).
% 34.88/9.15 thf(func_def_1116, type, produc364263696895485585st_int: list_int > list_int > produc1186641810826059865st_int).
% 34.88/9.15 thf(func_def_1117, type, produc699922362453767013list_o: list_nat > list_o > produc149729814636038835list_o).
% 34.88/9.15 thf(func_def_1118, type, produc2694037385005941721st_nat: list_nat > list_nat > produc1828647624359046049st_nat).
% 34.88/9.15 thf(func_def_1119, type, produc8335345208264861441T_VEBT: list_nat > list_VEBT_VEBT > produc872621073311890639T_VEBT).
% 34.88/9.15 thf(func_def_1120, type, produc5943733680697469783at_nat: list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > produc6392793444374437607at_nat).
% 34.88/9.15 thf(func_def_1121, type, produc7536900900485677911at_nat: list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > produc424102278133772007at_nat).
% 34.88/9.15 thf(func_def_1122, type, produc2717590391345394939list_o: list_VEBT_VEBT > list_o > produc3962069817607390347list_o).
% 34.88/9.15 thf(func_def_1123, type, produc1392282695434103839st_int: list_VEBT_VEBT > list_int > produc7831203938951381541st_int).
% 34.88/9.15 thf(func_def_1124, type, produc5570133714943300547st_nat: list_VEBT_VEBT > list_nat > produc1097915047028332489st_nat).
% 34.88/9.15 thf(func_def_1125, type, produc3897820843166775703T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > produc9211091688327510695T_VEBT).
% 34.88/9.15 thf(func_def_1126, type, product_Pair_nat_o: nat > $o > product_prod_nat_o).
% 34.88/9.15 thf(func_def_1127, type, product_Pair_nat_int: nat > int > product_prod_nat_int).
% 34.88/9.15 thf(func_def_1128, type, product_Pair_nat_nat: nat > nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_1129, type, produc487386426758144856at_nat: nat > product_prod_nat_nat > produc7248412053542808358at_nat).
% 34.88/9.15 thf(func_def_1130, type, produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT).
% 34.88/9.15 thf(func_def_1131, type, produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat).
% 34.88/9.15 thf(func_def_1132, type, produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num).
% 34.88/9.15 thf(func_def_1133, type, produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat).
% 34.88/9.15 thf(func_def_1134, type, produc6161850002892822231at_nat: product_prod_nat_nat > product_prod_nat_nat > produc859450856879609959at_nat).
% 34.88/9.15 thf(func_def_1135, type, product_Pair_real_o: real > $o > product_prod_real_o).
% 34.88/9.15 thf(func_def_1136, type, produc1693001998875562995omplex: real > complex > produc6979889472282505531omplex).
% 34.88/9.15 thf(func_def_1137, type, produc3179012173361985393al_int: real > int > produc8786904178792722361al_int).
% 34.88/9.15 thf(func_def_1138, type, produc3181502643871035669al_nat: real > nat > produc3741383161447143261al_nat).
% 34.88/9.15 thf(func_def_1139, type, produc4511245868158468465l_real: real > real > produc2422161461964618553l_real).
% 34.88/9.15 thf(func_def_1140, type, produc6931449550656315951T_VEBT: real > vEBT_VEBT > produc3757001726724277373T_VEBT).
% 34.88/9.15 thf(func_def_1141, type, produc4532415448927165861et_nat: set_nat > set_nat > produc7819656566062154093et_nat).
% 34.88/9.15 thf(func_def_1142, type, produc2922128104949294807at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > produc3843707927480180839at_nat).
% 34.88/9.15 thf(func_def_1143, type, produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o).
% 34.88/9.15 thf(func_def_1144, type, produc5617778602380981643omplex: vEBT_VEBT > complex > produc8380087813684007313omplex).
% 34.88/9.15 thf(func_def_1145, type, produc581526299967858633d_enat: vEBT_VEBT > extended_enat > produc7272778201969148633d_enat).
% 34.88/9.15 thf(func_def_1146, type, produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int).
% 34.88/9.15 thf(func_def_1147, type, produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat).
% 34.88/9.15 thf(func_def_1148, type, produc8117437818029410057T_real: vEBT_VEBT > real > produc5170161368751668367T_real).
% 34.88/9.15 thf(func_def_1149, type, produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT).
% 34.88/9.15 thf(func_def_1150, type, produc457027306803732586at_nat: set_nat > (nat > set_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1151, type, produc6499014454317279255nteger: (code_integer > code_integer) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_1152, type, produc1553301316500091796er_int: (code_integer > code_integer > int) > produc8923325533196201883nteger > int).
% 34.88/9.15 thf(func_def_1153, type, produc1555791787009142072er_nat: (code_integer > code_integer > nat) > produc8923325533196201883nteger > nat).
% 34.88/9.15 thf(func_def_1154, type, produc6916734918728496179nteger: (code_integer > code_integer > produc8923325533196201883nteger) > produc8923325533196201883nteger > produc8923325533196201883nteger).
% 34.88/9.15 thf(func_def_1155, type, produc4947309494688390418_int_o: (int > int > $o) > product_prod_int_int > $o).
% 34.88/9.15 thf(func_def_1156, type, produc8211389475949308722nt_int: (int > int > int) > product_prod_int_int > int).
% 34.88/9.15 thf(func_def_1157, type, produc4245557441103728435nt_int: (int > int > product_prod_int_int) > product_prod_int_int > product_prod_int_int).
% 34.88/9.15 thf(func_def_1158, type, produc8739625826339149834_nat_o: (nat > nat > product_prod_nat_nat > $o) > product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_1159, type, produc27273713700761075at_nat: (nat > nat > product_prod_nat_nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_1160, type, produc6081775807080527818_nat_o: (nat > nat > $o) > product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_1161, type, produc2761476792215241774st_nat: (nat > nat > list_nat) > product_prod_nat_nat > list_nat).
% 34.88/9.15 thf(func_def_1162, type, produc6842872674320459806at_nat: (nat > nat > nat) > product_prod_nat_nat > nat).
% 34.88/9.15 thf(func_def_1163, type, produc2626176000494625587at_nat: (nat > nat > product_prod_nat_nat) > product_prod_nat_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_1164, type, produc6207742614233964070at_rat: (nat > nat > rat) > product_prod_nat_nat > rat).
% 34.88/9.15 thf(func_def_1165, type, product_fst_int_int: product_prod_int_int > int).
% 34.88/9.15 thf(func_def_1166, type, product_fst_nat_nat: product_prod_nat_nat > nat).
% 34.88/9.15 thf(func_def_1167, type, product_snd_int_int: product_prod_int_int > int).
% 34.88/9.15 thf(func_def_1168, type, product_snd_nat_nat: product_prod_nat_nat > nat).
% 34.88/9.15 thf(func_def_1169, type, produc5538323210962509403atural: (produc7822875418678951345atural > produc5835291356934675326atural) > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > produc7822875418678951345atural > produc5835291356934675326atural).
% 34.88/9.15 thf(func_def_1170, type, iterat8892046348760725948atural: code_natural > (code_natural > produc7822875418678951345atural > produc5835291356934675326atural) > code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 34.88/9.15 thf(func_def_1171, type, log: code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_1172, type, minus_shift: code_natural > code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_1173, type, next: produc7822875418678951345atural > produc5835291356934675326atural).
% 34.88/9.15 thf(func_def_1174, type, range: code_natural > produc7822875418678951345atural > produc5835291356934675326atural).
% 34.88/9.15 thf(func_def_1175, type, abs_Rat: product_prod_int_int > rat).
% 34.88/9.15 thf(func_def_1176, type, fract: int > int > rat).
% 34.88/9.15 thf(func_def_1177, type, rep_Rat: rat > product_prod_int_int).
% 34.88/9.15 thf(func_def_1178, type, field_5140801741446780682s_real: set_real).
% 34.88/9.15 thf(func_def_1179, type, normalize: product_prod_int_int > product_prod_int_int).
% 34.88/9.15 thf(func_def_1180, type, pcr_rat: product_prod_int_int > rat > $o).
% 34.88/9.15 thf(func_def_1181, type, positive: rat > $o).
% 34.88/9.15 thf(func_def_1182, type, quotient_of: rat > product_prod_int_int).
% 34.88/9.15 thf(func_def_1183, type, ratrel: product_prod_int_int > product_prod_int_int > $o).
% 34.88/9.15 thf(func_def_1184, type, ratreal: rat > real).
% 34.88/9.15 thf(func_def_1185, type, real2: (nat > rat) > real).
% 34.88/9.15 thf(func_def_1186, type, cauchy: (nat > rat) > $o).
% 34.88/9.15 thf(func_def_1187, type, pcr_real: (nat > rat) > real > $o).
% 34.88/9.15 thf(func_def_1188, type, positive2: real > $o).
% 34.88/9.15 thf(func_def_1189, type, realrel: (nat > rat) > (nat > rat) > $o).
% 34.88/9.15 thf(func_def_1190, type, rep_real: real > nat > rat).
% 34.88/9.15 thf(func_def_1191, type, vanishes: (nat > rat) > $o).
% 34.88/9.15 thf(func_def_1192, type, real_V2521375963428798218omplex: set_complex).
% 34.88/9.15 thf(func_def_1193, type, real_V5970128139526366754l_real: (real > real) > $o).
% 34.88/9.15 thf(func_def_1194, type, real_V4572627801940501177l_real: (real > real) > $o).
% 34.88/9.15 thf(func_def_1195, type, real_V1022390504157884413omplex: complex > real).
% 34.88/9.15 thf(func_def_1196, type, real_V7735802525324610683m_real: real > real).
% 34.88/9.15 thf(func_def_1197, type, real_V4546457046886955230omplex: real > complex).
% 34.88/9.15 thf(func_def_1198, type, real_V2046097035970521341omplex: real > complex > complex).
% 34.88/9.15 thf(func_def_1199, type, real_V1485227260804924795R_real: real > real > real).
% 34.88/9.15 thf(func_def_1200, type, field_nat: set_Pr1261947904930325089at_nat > set_nat).
% 34.88/9.15 thf(func_def_1201, type, id_nat2: set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1202, type, antisym_nat: set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1203, type, refl_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1204, type, total_on_nat: set_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1205, type, trans_nat: set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1206, type, algebr932160517623751201me_int: int > int > $o).
% 34.88/9.15 thf(func_def_1207, type, algebr934650988132801477me_nat: nat > nat > $o).
% 34.88/9.15 thf(func_def_1208, type, divide6298287555418463151nteger: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_1209, type, divide5121882707175180666atural: code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_1210, type, divide1717551699836669952omplex: complex > complex > complex).
% 34.88/9.15 thf(func_def_1211, type, divide_divide_int: int > int > int).
% 34.88/9.15 thf(func_def_1212, type, divide_divide_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_1213, type, divide_divide_rat: rat > rat > rat).
% 34.88/9.15 thf(func_def_1214, type, divide_divide_real: real > real > real).
% 34.88/9.15 thf(func_def_1215, type, dvd_dvd_Code_integer: code_integer > code_integer > $o).
% 34.88/9.15 thf(func_def_1216, type, dvd_dvd_Code_natural: code_natural > code_natural > $o).
% 34.88/9.15 thf(func_def_1217, type, dvd_dvd_complex: complex > complex > $o).
% 34.88/9.15 thf(func_def_1218, type, dvd_dvd_int: int > int > $o).
% 34.88/9.15 thf(func_def_1219, type, dvd_dvd_nat: nat > nat > $o).
% 34.88/9.15 thf(func_def_1220, type, dvd_dvd_rat: rat > rat > $o).
% 34.88/9.15 thf(func_def_1221, type, dvd_dvd_real: real > real > $o).
% 34.88/9.15 thf(func_def_1222, type, modulo364778990260209775nteger: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_1223, type, modulo8411746178871703098atural: code_natural > code_natural > code_natural).
% 34.88/9.15 thf(func_def_1224, type, modulo_modulo_int: int > int > int).
% 34.88/9.15 thf(func_def_1225, type, modulo_modulo_nat: nat > nat > nat).
% 34.88/9.15 thf(func_def_1226, type, unit_f2748546683901255202or_nat: nat > nat).
% 34.88/9.15 thf(func_def_1227, type, zero_n356916108424825756nteger: $o > code_integer).
% 34.88/9.15 thf(func_def_1228, type, zero_n8403883297036319079atural: $o > code_natural).
% 34.88/9.15 thf(func_def_1229, type, zero_n1201886186963655149omplex: $o > complex).
% 34.88/9.15 thf(func_def_1230, type, zero_n2684676970156552555ol_int: $o > int).
% 34.88/9.15 thf(func_def_1231, type, zero_n2687167440665602831ol_nat: $o > nat).
% 34.88/9.15 thf(func_def_1232, type, zero_n2052037380579107095ol_rat: $o > rat).
% 34.88/9.15 thf(func_def_1233, type, zero_n3304061248610475627l_real: $o > real).
% 34.88/9.15 thf(func_def_1234, type, suminf_real: (nat > real) > real).
% 34.88/9.15 thf(func_def_1235, type, summable_real: (nat > real) > $o).
% 34.88/9.15 thf(func_def_1236, type, sums_complex: (nat > complex) > complex > $o).
% 34.88/9.15 thf(func_def_1237, type, sums_int: (nat > int) > int > $o).
% 34.88/9.15 thf(func_def_1238, type, sums_nat: (nat > nat) > nat > $o).
% 34.88/9.15 thf(func_def_1239, type, sums_real: (nat > real) > real > $o).
% 34.88/9.15 thf(func_def_1240, type, collect_complex: (complex > $o) > set_complex).
% 34.88/9.15 thf(func_def_1241, type, collect_int: (int > $o) > set_int).
% 34.88/9.15 thf(func_def_1242, type, collect_list_o: (list_o > $o) > set_list_o).
% 34.88/9.15 thf(func_def_1243, type, collect_list_complex: (list_complex > $o) > set_list_complex).
% 34.88/9.15 thf(func_def_1244, type, collect_list_int: (list_int > $o) > set_list_int).
% 34.88/9.15 thf(func_def_1245, type, collec5989764272469232197st_nat: (list_list_nat > $o) > set_list_list_nat).
% 34.88/9.15 thf(func_def_1246, type, collect_list_nat: (list_nat > $o) > set_list_nat).
% 34.88/9.15 thf(func_def_1247, type, collect_list_set_nat: (list_set_nat > $o) > set_list_set_nat).
% 34.88/9.15 thf(func_def_1248, type, collec5608196760682091941T_VEBT: (list_VEBT_VEBT > $o) > set_list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1249, type, collect_nat: (nat > $o) > set_nat).
% 34.88/9.15 thf(func_def_1250, type, collect_num: (num > $o) > set_num).
% 34.88/9.15 thf(func_def_1251, type, collec3392354462482085612at_nat: (product_prod_nat_nat > $o) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1252, type, collect_rat: (rat > $o) > set_rat).
% 34.88/9.15 thf(func_def_1253, type, collect_real: (real > $o) > set_real).
% 34.88/9.15 thf(func_def_1254, type, collect_set_nat: (set_nat > $o) > set_set_nat).
% 34.88/9.15 thf(func_def_1255, type, pow_nat: set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_1256, type, image_int_int: (int > int) > set_int > set_int).
% 34.88/9.15 thf(func_def_1257, type, image_int_nat: (int > nat) > set_int > set_nat).
% 34.88/9.15 thf(func_def_1258, type, image_list_nat_nat: (list_nat > nat) > set_list_nat > set_nat).
% 34.88/9.15 thf(func_def_1259, type, image_nat_int: (nat > int) > set_nat > set_int).
% 34.88/9.15 thf(func_def_1260, type, image_nat_list_nat: (nat > list_nat) > set_nat > set_list_nat).
% 34.88/9.15 thf(func_def_1261, type, image_nat_nat: (nat > nat) > set_nat > set_nat).
% 34.88/9.15 thf(func_def_1262, type, image_5846123807819985514at_nat: (nat > product_prod_nat_nat) > set_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1263, type, image_nat_set_nat: (nat > set_nat) > set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_1264, type, image_nat_char: (nat > char) > set_nat > set_char).
% 34.88/9.15 thf(func_def_1265, type, image_678696785212003926at_nat: (nat > sum_sum_nat_nat) > set_nat > set_Sum_sum_nat_nat).
% 34.88/9.15 thf(func_def_1266, type, image_2486076414777270412at_nat: (product_prod_nat_nat > nat) > set_Pr1261947904930325089at_nat > set_nat).
% 34.88/9.15 thf(func_def_1267, type, image_real_real: (real > real) > set_real > set_real).
% 34.88/9.15 thf(func_def_1268, type, image_char_nat: (char > nat) > set_char > set_nat).
% 34.88/9.15 thf(func_def_1269, type, image_1320371278474632150at_nat: (sum_sum_nat_nat > nat) > set_Sum_sum_nat_nat > set_nat).
% 34.88/9.15 thf(func_def_1270, type, insert_o: $o > set_o > set_o).
% 34.88/9.15 thf(func_def_1271, type, insert_complex: complex > set_complex > set_complex).
% 34.88/9.15 thf(func_def_1272, type, insert_int: int > set_int > set_int).
% 34.88/9.15 thf(func_def_1273, type, insert_list_nat: list_nat > set_list_nat > set_list_nat).
% 34.88/9.15 thf(func_def_1274, type, insert_nat: nat > set_nat > set_nat).
% 34.88/9.15 thf(func_def_1275, type, insert_num: num > set_num > set_num).
% 34.88/9.15 thf(func_def_1276, type, insert8211810215607154385at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1277, type, insert_rat: rat > set_rat > set_rat).
% 34.88/9.15 thf(func_def_1278, type, insert_real: real > set_real > set_real).
% 34.88/9.15 thf(func_def_1279, type, insert_set_nat: set_nat > set_set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_1280, type, insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1281, type, vimage_nat_nat: (nat > nat) > set_nat > set_nat).
% 34.88/9.15 thf(func_def_1282, type, set_fo1084959871951514735nteger: (nat > code_integer > code_integer) > nat > nat > code_integer > code_integer).
% 34.88/9.15 thf(func_def_1283, type, set_fo1517530859248394432omplex: (nat > complex > complex) > nat > nat > complex > complex).
% 34.88/9.15 thf(func_def_1284, type, set_fo2581907887559384638at_int: (nat > int > int) > nat > nat > int > int).
% 34.88/9.15 thf(func_def_1285, type, set_fo2584398358068434914at_nat: (nat > nat > nat) > nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_1286, type, set_fo1949268297981939178at_rat: (nat > rat > rat) > nat > nat > rat > rat).
% 34.88/9.15 thf(func_def_1287, type, set_fo3111899725591712190t_real: (nat > real > real) > nat > nat > real > real).
% 34.88/9.15 thf(func_def_1288, type, set_or1266510415728281911st_int: int > int > set_int).
% 34.88/9.15 thf(func_def_1289, type, set_or1269000886237332187st_nat: nat > nat > set_nat).
% 34.88/9.15 thf(func_def_1290, type, set_or7049704709247886629st_num: num > num > set_num).
% 34.88/9.15 thf(func_def_1291, type, set_or633870826150836451st_rat: rat > rat > set_rat).
% 34.88/9.15 thf(func_def_1292, type, set_or1222579329274155063t_real: real > real > set_real).
% 34.88/9.15 thf(func_def_1293, type, set_or4548717258645045905et_nat: set_nat > set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_1294, type, set_or4662586982721622107an_int: int > int > set_int).
% 34.88/9.15 thf(func_def_1295, type, set_or4665077453230672383an_nat: nat > nat > set_nat).
% 34.88/9.15 thf(func_def_1296, type, set_ord_atLeast_nat: nat > set_nat).
% 34.88/9.15 thf(func_def_1297, type, set_ord_atMost_int: int > set_int).
% 34.88/9.15 thf(func_def_1298, type, set_ord_atMost_nat: nat > set_nat).
% 34.88/9.15 thf(func_def_1299, type, set_ord_atMost_num: num > set_num).
% 34.88/9.15 thf(func_def_1300, type, set_ord_atMost_rat: rat > set_rat).
% 34.88/9.15 thf(func_def_1301, type, set_ord_atMost_real: real > set_real).
% 34.88/9.15 thf(func_def_1302, type, set_or4236626031148496127et_nat: set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_1303, type, set_or6656581121297822940st_int: int > int > set_int).
% 34.88/9.15 thf(func_def_1304, type, set_or6659071591806873216st_nat: nat > nat > set_nat).
% 34.88/9.15 thf(func_def_1305, type, set_or5832277885323065728an_int: int > int > set_int).
% 34.88/9.15 thf(func_def_1306, type, set_or5834768355832116004an_nat: nat > nat > set_nat).
% 34.88/9.15 thf(func_def_1307, type, set_or1633881224788618240n_real: real > real > set_real).
% 34.88/9.15 thf(func_def_1308, type, set_or1210151606488870762an_nat: nat > set_nat).
% 34.88/9.15 thf(func_def_1309, type, set_or5849166863359141190n_real: real > set_real).
% 34.88/9.15 thf(func_def_1310, type, set_ord_lessThan_int: int > set_int).
% 34.88/9.15 thf(func_def_1311, type, set_ord_lessThan_nat: nat > set_nat).
% 34.88/9.15 thf(func_def_1312, type, set_ord_lessThan_num: num > set_num).
% 34.88/9.15 thf(func_def_1313, type, set_ord_lessThan_rat: rat > set_rat).
% 34.88/9.15 thf(func_def_1314, type, set_or5984915006950818249n_real: real > set_real).
% 34.88/9.15 thf(func_def_1315, type, set_or890127255671739683et_nat: set_nat > set_set_nat).
% 34.88/9.15 thf(func_def_1316, type, char2: $o > $o > $o > $o > $o > $o > $o > $o > char).
% 34.88/9.15 thf(func_def_1317, type, size_char: char > nat).
% 34.88/9.15 thf(func_def_1318, type, comm_s629917340098488124ar_nat: char > nat).
% 34.88/9.15 thf(func_def_1319, type, integer_of_char: char > code_integer).
% 34.88/9.15 thf(func_def_1320, type, unique3096191561947761185of_nat: nat > char).
% 34.88/9.15 thf(func_def_1321, type, sum_Inl_nat_nat: nat > sum_sum_nat_nat).
% 34.88/9.15 thf(func_def_1322, type, sum_Inr_nat_nat: nat > sum_sum_nat_nat).
% 34.88/9.15 thf(func_def_1323, type, sum_ca7763040182479039464nt_nat: (nat > int) > (nat > int) > sum_sum_nat_nat > int).
% 34.88/9.15 thf(func_def_1324, type, sum_ca6763686470577984908at_nat: (nat > nat) > (nat > nat) > sum_sum_nat_nat > nat).
% 34.88/9.15 thf(func_def_1325, type, topolo4422821103128117721l_real: filter_real > (real > real) > $o).
% 34.88/9.15 thf(func_def_1326, type, topolo5044208981011980120l_real: set_real > (real > real) > $o).
% 34.88/9.15 thf(func_def_1327, type, topolo6980174941875973593q_real: (nat > real) > $o).
% 34.88/9.15 thf(func_def_1328, type, topolo2177554685111907308n_real: real > set_real > filter_real).
% 34.88/9.15 thf(func_def_1329, type, topolo7531315842566124627t_real: (nat > real) > $o).
% 34.88/9.15 thf(func_def_1330, type, topolo2815343760600316023s_real: real > filter_real).
% 34.88/9.15 thf(func_def_1331, type, topolo4055970368930404560y_real: (nat > real) > $o).
% 34.88/9.15 thf(func_def_1332, type, arccos: real > real).
% 34.88/9.15 thf(func_def_1333, type, arcosh_real: real > real).
% 34.88/9.15 thf(func_def_1334, type, arctan: real > real).
% 34.88/9.15 thf(func_def_1335, type, arsinh_real: real > real).
% 34.88/9.15 thf(func_def_1336, type, artanh_real: real > real).
% 34.88/9.15 thf(func_def_1337, type, cos_complex: complex > complex).
% 34.88/9.15 thf(func_def_1338, type, cos_real: real > real).
% 34.88/9.15 thf(func_def_1339, type, cos_coeff: nat > real).
% 34.88/9.15 thf(func_def_1340, type, cot_real: real > real).
% 34.88/9.15 thf(func_def_1341, type, exp_complex: complex > complex).
% 34.88/9.15 thf(func_def_1342, type, exp_real: real > real).
% 34.88/9.15 thf(func_def_1343, type, ln_ln_real: real > real).
% 34.88/9.15 thf(func_def_1344, type, log2: real > real > real).
% 34.88/9.15 thf(func_def_1345, type, pi: real).
% 34.88/9.15 thf(func_def_1346, type, powr_real: real > real > real).
% 34.88/9.15 thf(func_def_1347, type, sin_complex: complex > complex).
% 34.88/9.15 thf(func_def_1348, type, sin_real: real > real).
% 34.88/9.15 thf(func_def_1349, type, sin_coeff: nat > real).
% 34.88/9.15 thf(func_def_1350, type, tan_real: real > real).
% 34.88/9.15 thf(func_def_1351, type, tanh_real: real > real).
% 34.88/9.15 thf(func_def_1352, type, transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1353, type, transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1354, type, transi2163837189807498211lp_nat: (nat > nat > $o) > nat > nat > $o).
% 34.88/9.15 thf(func_def_1355, type, typerep2: literal > list_typerep > typerep).
% 34.88/9.15 thf(func_def_1356, type, size_typerep: typerep > nat).
% 34.88/9.15 thf(func_def_1357, type, vEBT_Leaf: $o > $o > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1358, type, vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1359, type, vEBT_size_VEBT: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_1360, type, vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1361, type, vEBT_VEBT_elim_dead: vEBT_VEBT > extended_enat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1362, type, vEBT_V312737461966249ad_rel: produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o).
% 34.88/9.15 thf(func_def_1363, type, vEBT_VEBT_high: nat > nat > nat).
% 34.88/9.15 thf(func_def_1364, type, vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1365, type, vEBT_VEBT_low: nat > nat > nat).
% 34.88/9.15 thf(func_def_1366, type, vEBT_VEBT_membermima: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1367, type, vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1368, type, vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1369, type, vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1370, type, vEBT_VEBT_valid: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1371, type, vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1372, type, vEBT_invar_vebt: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1373, type, vEBT_set_vebt: vEBT_VEBT > set_nat).
% 34.88/9.15 thf(func_def_1374, type, vEBT_vebt_buildup: nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1375, type, vEBT_v4011308405150292612up_rel: nat > nat > $o).
% 34.88/9.15 thf(func_def_1376, type, vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1377, type, vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1378, type, vEBT_VEBT_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1379, type, vEBT_VEBT_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1380, type, vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1381, type, vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1382, type, vEBT_VEBT_bit_concat: nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_1383, type, vEBT_VEBT_minNull: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1384, type, vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1385, type, vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat).
% 34.88/9.15 thf(func_def_1386, type, vEBT_vebt_member: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1387, type, vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1388, type, vEBT_VEBT_add: option_nat > option_nat > option_nat).
% 34.88/9.15 thf(func_def_1389, type, vEBT_VEBT_greater: option_nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1390, type, vEBT_VEBT_less: option_nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1391, type, vEBT_VEBT_lesseq: option_nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1392, type, vEBT_VEBT_max_in_set: set_nat > nat > $o).
% 34.88/9.15 thf(func_def_1393, type, vEBT_VEBT_min_in_set: set_nat > nat > $o).
% 34.88/9.15 thf(func_def_1394, type, vEBT_VEBT_mul: option_nat > option_nat > option_nat).
% 34.88/9.15 thf(func_def_1395, type, vEBT_V2881884560877996034ft_nat: (nat > nat > $o) > option_nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1396, type, vEBT_V4262088993061758097ft_nat: (nat > nat > nat) > option_nat > option_nat > option_nat).
% 34.88/9.15 thf(func_def_1397, type, vEBT_V819420779217536731ft_num: (num > num > num) > option_num > option_num > option_num).
% 34.88/9.15 thf(func_def_1398, type, vEBT_V1502963449132264192at_nat: (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_1399, type, vEBT_VEBT_power: option_nat > option_nat > option_nat).
% 34.88/9.15 thf(func_def_1400, type, vEBT_vebt_maxt: vEBT_VEBT > option_nat).
% 34.88/9.15 thf(func_def_1401, type, vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1402, type, vEBT_vebt_mint: vEBT_VEBT > option_nat).
% 34.88/9.15 thf(func_def_1403, type, vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1404, type, vEBT_is_pred_in_set: set_nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1405, type, vEBT_vebt_pred: vEBT_VEBT > nat > option_nat).
% 34.88/9.15 thf(func_def_1406, type, vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1407, type, vEBT_is_succ_in_set: set_nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1408, type, vEBT_vebt_succ: vEBT_VEBT > nat > option_nat).
% 34.88/9.15 thf(func_def_1409, type, vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1410, type, accp_list_nat: (list_nat > list_nat > $o) > list_nat > $o).
% 34.88/9.15 thf(func_def_1411, type, accp_nat: (nat > nat > $o) > nat > $o).
% 34.88/9.15 thf(func_def_1412, type, accp_P1096762738010456898nt_int: (product_prod_int_int > product_prod_int_int > $o) > product_prod_int_int > $o).
% 34.88/9.15 thf(func_def_1413, type, accp_P4275260045618599050at_nat: (product_prod_nat_nat > product_prod_nat_nat > $o) > product_prod_nat_nat > $o).
% 34.88/9.15 thf(func_def_1414, type, accp_P6183159247885693666d_enat: (produc7272778201969148633d_enat > produc7272778201969148633d_enat > $o) > produc7272778201969148633d_enat > $o).
% 34.88/9.15 thf(func_def_1415, type, accp_P2887432264394892906BT_nat: (produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o) > produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1416, type, accp_VEBT_VEBT: (vEBT_VEBT > vEBT_VEBT > $o) > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1417, type, less_than: set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1418, type, pred_nat: set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1419, type, member_o: $o > set_o > $o).
% 34.88/9.15 thf(func_def_1420, type, member_Code_integer: code_integer > set_Code_integer > $o).
% 34.88/9.15 thf(func_def_1421, type, member_complex: complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1422, type, member_int: int > set_int > $o).
% 34.88/9.15 thf(func_def_1423, type, member_list_o: list_o > set_list_o > $o).
% 34.88/9.15 thf(func_def_1424, type, member_list_int: list_int > set_list_int > $o).
% 34.88/9.15 thf(func_def_1425, type, member_list_nat: list_nat > set_list_nat > $o).
% 34.88/9.15 thf(func_def_1426, type, member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1427, type, member_nat: nat > set_nat > $o).
% 34.88/9.15 thf(func_def_1428, type, member_num: num > set_num > $o).
% 34.88/9.15 thf(func_def_1429, type, member7466972457876170832od_o_o: product_prod_o_o > set_Product_prod_o_o > $o).
% 34.88/9.15 thf(func_def_1430, type, member1046615901120239500omplex: produc648051720047351925omplex > set_Pr5421754520313593387omplex > $o).
% 34.88/9.15 thf(func_def_1431, type, member7847949116333733898_o_int: product_prod_o_int > set_Pr8834758594704517033_o_int > $o).
% 34.88/9.15 thf(func_def_1432, type, member2802428098988154798_o_nat: product_prod_o_nat > set_Pr2101469702781467981_o_nat > $o).
% 34.88/9.15 thf(func_def_1433, type, member7400031367953476362o_real: product_prod_o_real > set_Pr6573716822653411497o_real > $o).
% 34.88/9.15 thf(func_def_1434, type, member5477980866518848620T_VEBT: produc2504756804600209347T_VEBT > set_Pr7543698050874017315T_VEBT > $o).
% 34.88/9.15 thf(func_def_1435, type, member157494554546826820nteger: produc8923325533196201883nteger > set_Pr4811707699266497531nteger > $o).
% 34.88/9.15 thf(func_def_1436, type, member6487239523555734774plex_o: produc6088675342482847199plex_o > set_Pr216032351708956309plex_o > $o).
% 34.88/9.15 thf(func_def_1437, type, member5793383173714906214omplex: produc4411394909380815293omplex > set_Pr5085853215250843933omplex > $o).
% 34.88/9.15 thf(func_def_1438, type, member595073364599660772ex_int: produc6845221339535797307ex_int > set_Pr2254670189886740123ex_int > $o).
% 34.88/9.15 thf(func_def_1439, type, member4772924384108857480ex_nat: produc1799700322190218207ex_nat > set_Pr4744753334818466879ex_nat > $o).
% 34.88/9.15 thf(func_def_1440, type, member47443559803733732x_real: produc8892588492097263291x_real > set_Pr1133549439701694107x_real > $o).
% 34.88/9.15 thf(func_def_1441, type, member1978952105866562066T_VEBT: produc7151440242714718331T_VEBT > set_Pr4085867452638698417T_VEBT > $o).
% 34.88/9.15 thf(func_def_1442, type, member8811922270175639012omplex: produc5838698208256999739omplex > set_Pr1846070511934368667omplex > $o).
% 34.88/9.15 thf(func_def_1443, type, member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o).
% 34.88/9.15 thf(func_def_1444, type, member2744130022092475746t_real: produc679980390762269497t_real > set_Pr3538720872664544793t_real > $o).
% 34.88/9.15 thf(func_def_1445, type, member4159035015898711888list_o: produc7102631898165422375list_o > set_Pr6227168374412355847list_o > $o).
% 34.88/9.15 thf(func_def_1446, type, member8253032945758599840st_int: produc1713839591385758857st_int > set_Pr5001190662893202239st_int > $o).
% 34.88/9.15 thf(func_def_1447, type, member1519744053835550788st_nat: produc4203922736317485613st_nat > set_Pr591367044826345187st_nat > $o).
% 34.88/9.15 thf(func_def_1448, type, member1087064965665443052T_VEBT: produc1922972420619397443T_VEBT > set_Pr5170412164475753123T_VEBT > $o).
% 34.88/9.15 thf(func_def_1449, type, member749217712838834276nteger: produc862207588354017979nteger > set_Pr7565137564259432987nteger > $o).
% 34.88/9.15 thf(func_def_1450, type, member6698963635872716290st_int: produc1186641810826059865st_int > set_Pr765067013931698361st_int > $o).
% 34.88/9.15 thf(func_def_1451, type, member6688923169008879818list_o: produc149729814636038835list_o > set_Pr1150278048023938153list_o > $o).
% 34.88/9.15 thf(func_def_1452, type, member7340969449405702474st_nat: produc1828647624359046049st_nat > set_Pr3451248702717554689st_nat > $o).
% 34.88/9.15 thf(func_def_1453, type, member5968030670617646438T_VEBT: produc872621073311890639T_VEBT > set_Pr1262583345697558789T_VEBT > $o).
% 34.88/9.15 thf(func_def_1454, type, member6693912407220327184at_nat: produc6392793444374437607at_nat > set_Pr1542805901266377927at_nat > $o).
% 34.88/9.15 thf(func_def_1455, type, member4080735728053443344at_nat: produc424102278133772007at_nat > set_Pr4333006031979791559at_nat > $o).
% 34.88/9.15 thf(func_def_1456, type, member3126162362653435956list_o: produc3962069817607390347list_o > set_Pr7508168486584781291list_o > $o).
% 34.88/9.15 thf(func_def_1457, type, member3703241499402361532st_int: produc7831203938951381541st_int > set_Pr4080907618048478043st_int > $o).
% 34.88/9.15 thf(func_def_1458, type, member6193324644334088288st_nat: produc1097915047028332489st_nat > set_Pr8894456036836396799st_nat > $o).
% 34.88/9.15 thf(func_def_1459, type, member4439316823752958928T_VEBT: produc9211091688327510695T_VEBT > set_Pr1916528119006554503T_VEBT > $o).
% 34.88/9.15 thf(func_def_1460, type, member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o).
% 34.88/9.15 thf(func_def_1461, type, member8549952807677709168T_VEBT: produc8025551001238799321T_VEBT > set_Pr6167073792073659919T_VEBT > $o).
% 34.88/9.15 thf(func_def_1462, type, member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o).
% 34.88/9.15 thf(func_def_1463, type, member772602641336174712real_o: product_prod_real_o > set_Pr4936984352647145239real_o > $o).
% 34.88/9.15 thf(func_def_1464, type, member7358116576843751780omplex: produc6979889472282505531omplex > set_Pr6591433984475009307omplex > $o).
% 34.88/9.15 thf(func_def_1465, type, member1627681773268152802al_int: produc8786904178792722361al_int > set_Pr1019928272762051225al_int > $o).
% 34.88/9.15 thf(func_def_1466, type, member5805532792777349510al_nat: produc3741383161447143261al_nat > set_Pr3510011417693777981al_nat > $o).
% 34.88/9.15 thf(func_def_1467, type, member7849222048561428706l_real: produc2422161461964618553l_real > set_Pr6218003697084177305l_real > $o).
% 34.88/9.15 thf(func_def_1468, type, member7262085504369356948T_VEBT: produc3757001726724277373T_VEBT > set_Pr6019664923565264691T_VEBT > $o).
% 34.88/9.15 thf(func_def_1469, type, member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o).
% 34.88/9.15 thf(func_def_1470, type, member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o).
% 34.88/9.15 thf(func_def_1471, type, member3307348790968139188VEBT_o: produc334124729049499915VEBT_o > set_Pr3175402225741728619VEBT_o > $o).
% 34.88/9.15 thf(func_def_1472, type, member3207599676835851048omplex: produc8380087813684007313omplex > set_Pr216944050393469383omplex > $o).
% 34.88/9.15 thf(func_def_1473, type, member5419026705395827622BT_int: produc4894624898956917775BT_int > set_Pr5066593544530342725BT_int > $o).
% 34.88/9.15 thf(func_def_1474, type, member373505688050248522BT_nat: produc9072475918466114483BT_nat > set_Pr7556676689462069481BT_nat > $o).
% 34.88/9.15 thf(func_def_1475, type, member8675245146396747942T_real: produc5170161368751668367T_real > set_Pr7765410600122031685T_real > $o).
% 34.88/9.15 thf(func_def_1476, type, member568628332442017744T_VEBT: produc8243902056947475879T_VEBT > set_Pr6192946355708809607T_VEBT > $o).
% 34.88/9.15 thf(func_def_1477, type, member_rat: rat > set_rat > $o).
% 34.88/9.15 thf(func_def_1478, type, member_real: real > set_real > $o).
% 34.88/9.15 thf(func_def_1479, type, member_set_nat: set_nat > set_set_nat > $o).
% 34.88/9.15 thf(func_def_1480, type, member2643936169264416010at_nat: set_Pr1261947904930325089at_nat > set_se7855581050983116737at_nat > $o).
% 34.88/9.15 thf(func_def_1481, type, member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1484, type, deg: nat).
% 34.88/9.15 thf(func_def_1485, type, info: option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_1486, type, m: nat).
% 34.88/9.15 thf(func_def_1487, type, ma: nat).
% 34.88/9.15 thf(func_def_1488, type, mi: nat).
% 34.88/9.15 thf(func_def_1489, type, na: nat).
% 34.88/9.15 thf(func_def_1490, type, sa: vEBT_VEBT).
% 34.88/9.15 thf(func_def_1491, type, summary: vEBT_VEBT).
% 34.88/9.15 thf(func_def_1492, type, summary2: vEBT_VEBT).
% 34.88/9.15 thf(func_def_1493, type, treeList: list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1494, type, treeList2: list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1513, type, sP0: (nat > $o) > $o).
% 34.88/9.15 thf(func_def_1514, type, sP1: real > real > real > $o).
% 34.88/9.15 thf(func_def_1515, type, sP2: real > real > real > $o).
% 34.88/9.15 thf(func_def_1516, type, sP3: real > num > real > $o).
% 34.88/9.15 thf(func_def_1517, type, sP4: (int > $o) > $o).
% 34.88/9.15 thf(func_def_1518, type, sP5: list_VEBT_VEBT > nat > nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1519, type, sP6: nat > vEBT_VEBT > list_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1520, type, sP7: set_int > set_int > (int > int) > set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1521, type, sP8: set_int > (int > complex) > $o).
% 34.88/9.15 thf(func_def_1522, type, sP9: set_int > set_int > (int > int) > (int > int) > $o).
% 34.88/9.15 thf(func_def_1523, type, sP10: set_int > (int > complex) > $o).
% 34.88/9.15 thf(func_def_1524, type, sP11: real > real > real > $o).
% 34.88/9.15 thf(func_def_1525, type, sP12: (option4927543243414619207at_nat > option_num > $o) > option4927543243414619207at_nat > option_num > $o).
% 34.88/9.15 thf(func_def_1526, type, sP13: set_nat > set_nat > (nat > nat > $o) > $o).
% 34.88/9.15 thf(func_def_1527, type, sP14: rat > num > rat > $o).
% 34.88/9.15 thf(func_def_1528, type, sP15: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1529, type, sP16: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1530, type, sP17: nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1531, type, sP18: nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1532, type, sP19: nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1533, type, sP20: real > (real > real) > (real > real) > real > $o).
% 34.88/9.15 thf(func_def_1534, type, sP21: num > num > num > $o).
% 34.88/9.15 thf(func_def_1535, type, sP22: num > num > num > $o).
% 34.88/9.15 thf(func_def_1536, type, sP23: num > num > num > $o).
% 34.88/9.15 thf(func_def_1537, type, sP24: real > num > real > $o).
% 34.88/9.15 thf(func_def_1538, type, sP25: $o > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1539, type, sP26: vEBT_VEBT > $o > $o).
% 34.88/9.15 thf(func_def_1540, type, sP27: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 34.88/9.15 thf(func_def_1541, type, sP28: nat > nat > list_VEBT_VEBT > nat > nat > $o > $o).
% 34.88/9.15 thf(func_def_1542, type, sP29: $o > $o > nat > $o).
% 34.88/9.15 thf(func_def_1543, type, sP30: $o > $o > nat > $o > $o).
% 34.88/9.15 thf(func_def_1544, type, sP31: $o > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1545, type, sP32: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1546, type, sP33: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1547, type, sP34: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1548, type, sP35: (complex > complex) > (complex > complex) > set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1549, type, sP36: (complex > complex) > (complex > complex) > (complex > complex) > set_complex > $o).
% 34.88/9.15 thf(func_def_1550, type, sP37: set_complex > (complex > complex) > $o).
% 34.88/9.15 thf(func_def_1551, type, sP38: (complex > complex) > set_complex > $o).
% 34.88/9.15 thf(func_def_1552, type, sP39: rat > num > rat > $o).
% 34.88/9.15 thf(func_def_1553, type, sP40: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1554, type, sP41: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1555, type, sP42: real > nat > real > $o).
% 34.88/9.15 thf(func_def_1556, type, sP43: real > num > real > $o).
% 34.88/9.15 thf(func_def_1557, type, sP44: $o > $o > nat > $o).
% 34.88/9.15 thf(func_def_1558, type, sP45: nat > (nat > nat) > $o).
% 34.88/9.15 thf(func_def_1559, type, sP46: $o > $o > nat > $o).
% 34.88/9.15 thf(func_def_1560, type, sP47: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1561, type, sP48: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_1562, type, sP49: (nat > int > $o) > set_nat > set_int > $o).
% 34.88/9.15 thf(func_def_1563, type, sP50: num > real > real > $o).
% 34.88/9.15 thf(func_def_1564, type, sP51: option_nat > option_nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1565, type, sP52: real > num > real > $o).
% 34.88/9.15 thf(func_def_1566, type, sP53: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > $o).
% 34.88/9.15 thf(func_def_1567, type, sP54: set_real > set_complex > (complex > real > $o) > $o).
% 34.88/9.15 thf(func_def_1568, type, sP55: vEBT_VEBT > $o > $o).
% 34.88/9.15 thf(func_def_1569, type, sP56: vEBT_VEBT > $o > $o).
% 34.88/9.15 thf(func_def_1570, type, sP57: $o > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1571, type, sP58: $o > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1572, type, sP59: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1573, type, sP60: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1574, type, sP61: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1575, type, sP62: (real > complex) > (complex > real) > set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1576, type, sP63: set_real > (real > complex) > $o).
% 34.88/9.15 thf(func_def_1577, type, sP64: (complex > complex) > set_complex > $o).
% 34.88/9.15 thf(func_def_1578, type, sP65: set_real > set_real > (real > complex) > set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1579, type, sP66: (int > $o) > int > set_int > (int > $o) > $o).
% 34.88/9.15 thf(func_def_1580, type, sP67: set_real > (int > real > $o) > set_int > $o).
% 34.88/9.15 thf(func_def_1581, type, sP68: rat > num > rat > $o).
% 34.88/9.15 thf(func_def_1582, type, sP69: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1583, type, sP70: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1584, type, sP71: (real > real) > set_real > set_real > set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1585, type, sP72: (real > real) > set_real > $o).
% 34.88/9.15 thf(func_def_1586, type, sP73: set_real > set_real > (real > real) > set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1587, type, sP74: set_real > (real > real) > (real > real) > (real > real) > $o).
% 34.88/9.15 thf(func_def_1588, type, sP75: (option_nat > option_num > $o) > option_num > option_nat > $o).
% 34.88/9.15 thf(func_def_1589, type, sP76: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1590, type, sP77: real > real > real > $o).
% 34.88/9.15 thf(func_def_1591, type, sP78: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1592, type, sP79: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1593, type, sP80: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1594, type, sP81: option_num > option_num > option_num > $o).
% 34.88/9.15 thf(func_def_1595, type, sP82: vEBT_VEBT > nat > $o > $o).
% 34.88/9.15 thf(func_def_1596, type, sP83: list_nat > nat > $o).
% 34.88/9.15 thf(func_def_1597, type, sP84: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1598, type, sP85: vEBT_VEBT > nat > $o > $o).
% 34.88/9.15 thf(func_def_1599, type, sP86: $o > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1600, type, sP87: nat > $o > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1601, type, sP88: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1602, type, sP89: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1603, type, sP90: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1604, type, sP91: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1605, type, sP92: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1606, type, sP93: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1607, type, sP94: set_real > (nat > real > $o) > set_nat > $o).
% 34.88/9.15 thf(func_def_1608, type, sP95: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1609, type, sP96: $o > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1610, type, sP97: nat > $o > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1611, type, sP98: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1612, type, sP99: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1613, type, sP100: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1614, type, sP101: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1615, type, sP102: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1616, type, sP103: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1617, type, sP104: int > (int > $o) > int > $o).
% 34.88/9.15 thf(func_def_1618, type, sP105: int > (int > $o) > int > $o).
% 34.88/9.15 thf(func_def_1619, type, sP106: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1620, type, sP107: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1621, type, sP108: rat > num > rat > $o).
% 34.88/9.15 thf(func_def_1622, type, sP109: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1623, type, sP110: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1624, type, sP111: (real > real > $o) > set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1625, type, sP112: rat > num > rat > $o).
% 34.88/9.15 thf(func_def_1626, type, sP113: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1627, type, sP114: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1628, type, sP115: vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1629, type, sP116: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1630, type, sP117: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1631, type, sP118: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1632, type, sP119: (option_num > option_num > $o) > option_num > option_num > $o).
% 34.88/9.15 thf(func_def_1633, type, sP120: product_prod_int_int > int > int > $o).
% 34.88/9.15 thf(func_def_1634, type, sP121: int > int > int > $o).
% 34.88/9.15 thf(func_def_1635, type, sP122: int > int > int > $o).
% 34.88/9.15 thf(func_def_1636, type, sP123: int > int > int > $o).
% 34.88/9.15 thf(func_def_1637, type, sP124: real > num > real > $o).
% 34.88/9.15 thf(func_def_1638, type, sP125: set_nat > set_real > (real > nat > $o) > $o).
% 34.88/9.15 thf(func_def_1639, type, sP126: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_1640, type, sP127: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_1641, type, sP128: list_nat > nat > $o).
% 34.88/9.15 thf(func_def_1642, type, sP129: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1643, type, sP130: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.15 thf(func_def_1644, type, sP131: vEBT_VEBT > nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1645, type, sP132: option_nat > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1646, type, sP133: real > (real > real) > real > $o).
% 34.88/9.15 thf(func_def_1647, type, sP134: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1648, type, sP135: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1649, type, sP136: rat > num > rat > $o).
% 34.88/9.15 thf(func_def_1650, type, sP137: (real > complex) > set_real > $o).
% 34.88/9.15 thf(func_def_1651, type, sP138: set_real > set_real > (real > real) > set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1652, type, sP139: set_real > (real > complex) > (real > complex) > (real > real) > $o).
% 34.88/9.15 thf(func_def_1653, type, sP140: (real > real) > (real > real) > set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1654, type, sP141: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1655, type, sP142: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1656, type, sP143: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1657, type, sP144: vEBT_VEBT > nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1658, type, sP145: (real > int) > set_int > set_int > set_real > set_real > $o).
% 34.88/9.15 thf(func_def_1659, type, sP146: set_real > (real > complex) > (int > complex) > (real > int) > $o).
% 34.88/9.15 thf(func_def_1660, type, sP147: (int > complex) > set_int > $o).
% 34.88/9.15 thf(func_def_1661, type, sP148: set_int > set_int > (real > int) > (int > real) > $o).
% 34.88/9.15 thf(func_def_1662, type, sP149: (option_nat > option_nat > $o) > option_nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1663, type, sP150: int > int > (int > $o) > $o).
% 34.88/9.15 thf(func_def_1664, type, sP151: (int > $o) > int > int > $o).
% 34.88/9.15 thf(func_def_1665, type, sP152: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1666, type, sP153: $o > nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1667, type, sP154: $o > $o > nat > $o).
% 34.88/9.15 thf(func_def_1668, type, sP155: $o > $o > nat > $o > $o).
% 34.88/9.15 thf(func_def_1669, type, sP156: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1670, type, sP157: vEBT_VEBT > nat > $o > $o).
% 34.88/9.15 thf(func_def_1671, type, sP158: real > num > real > $o).
% 34.88/9.15 thf(func_def_1672, type, sP159: (option_num > option4927543243414619207at_nat > $o) > option_num > option4927543243414619207at_nat > $o).
% 34.88/9.15 thf(func_def_1673, type, sP160: real > real > (real > real) > $o).
% 34.88/9.15 thf(func_def_1674, type, sP161: (real > real) > (real > real) > real > real > $o).
% 34.88/9.15 thf(func_def_1675, type, sP162: real > (real > real) > (real > real) > real > $o).
% 34.88/9.15 thf(func_def_1676, type, sP163: real > real > (real > real) > $o).
% 34.88/9.15 thf(func_def_1677, type, sP164: real > real > real > $o).
% 34.88/9.15 thf(func_def_1678, type, sP165: nat > real > (nat > real > real) > real > $o).
% 34.88/9.15 thf(func_def_1679, type, sP166: (real > real) > (nat > real > real) > real > real > nat > $o).
% 34.88/9.15 thf(func_def_1680, type, sP167: $o > nat > vEBT_VEBT > option4927543243414619207at_nat > nat > list_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1681, type, sP168: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1682, type, sP169: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1683, type, sP170: nat > real > (nat > real > real) > $o).
% 34.88/9.15 thf(func_def_1684, type, sP171: num > real > real > $o).
% 34.88/9.15 thf(func_def_1685, type, sP172: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1686, type, sP173: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1687, type, sP174: vEBT_VEBT > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1688, type, sP175: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1689, type, sP176: (nat > real > real) > real > nat > $o).
% 34.88/9.15 thf(func_def_1690, type, sP177: int > int > int > $o).
% 34.88/9.15 thf(func_def_1691, type, sP178: real > nat > (nat > real > real) > real > $o).
% 34.88/9.15 thf(func_def_1692, type, sP179: set_complex > set_complex > (complex > int) > set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1693, type, sP180: (complex > int) > (int > complex) > set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1694, type, sP181: set_complex > (complex > complex) > $o).
% 34.88/9.15 thf(func_def_1695, type, sP182: set_int > set_int > (int > complex) > set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1696, type, sP183: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1697, type, sP184: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1698, type, sP185: real > real > real > $o).
% 34.88/9.15 thf(func_def_1699, type, sP186: set_int > set_real > (real > int > $o) > $o).
% 34.88/9.15 thf(func_def_1700, type, sP187: set_complex > (complex > complex) > (int > complex) > (complex > int) > $o).
% 34.88/9.15 thf(func_def_1701, type, sP188: (complex > int) > set_int > set_int > set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1702, type, sP189: (complex > int) > (int > complex) > set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1703, type, sP190: (int > complex) > set_int > $o).
% 34.88/9.15 thf(func_def_1704, type, sP191: (complex > nat > $o) > set_nat > set_complex > $o).
% 34.88/9.15 thf(func_def_1705, type, sP192: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1706, type, sP193: set_real > set_real > (int > real) > (real > int) > $o).
% 34.88/9.15 thf(func_def_1707, type, sP194: (int > complex) > (real > complex) > (int > real) > set_int > $o).
% 34.88/9.15 thf(func_def_1708, type, sP195: (int > real) > set_real > set_real > set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1709, type, sP196: set_real > set_real > (real > int) > set_int > set_int > $o).
% 34.88/9.15 thf(func_def_1710, type, sP197: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1711, type, sP198: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1712, type, sP199: nat > nat > list_VEBT_VEBT > nat > nat > $o).
% 34.88/9.15 thf(func_def_1713, type, sP200: list_VEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1714, type, sP201: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1715, type, sP202: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1716, type, sP203: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1717, type, sP204: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1718, type, sP205: real > real > real > $o).
% 34.88/9.15 thf(func_def_1719, type, sP206: (real > real) > (real > real) > real > real > $o).
% 34.88/9.15 thf(func_def_1720, type, sP207: real > real > (real > real) > $o).
% 34.88/9.15 thf(func_def_1721, type, sP208: real > (real > real) > real > $o).
% 34.88/9.15 thf(func_def_1722, type, sP209: real > (real > real) > real > $o).
% 34.88/9.15 thf(func_def_1723, type, sP210: real > real > real > $o).
% 34.88/9.15 thf(func_def_1724, type, sP211: (option_num > option_nat > $o) > option_nat > option_num > $o).
% 34.88/9.15 thf(func_def_1725, type, sP212: option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat > $o).
% 34.88/9.15 thf(func_def_1726, type, sP213: vEBT_VEBT > extended_enat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1727, type, sP214: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1728, type, sP215: (int > $o) > int > (int > $o) > set_int > $o).
% 34.88/9.15 thf(func_def_1729, type, sP216: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1730, type, sP217: set_nat > (int > nat > $o) > set_int > $o).
% 34.88/9.15 thf(func_def_1731, type, sP218: (option_nat > option4927543243414619207at_nat > $o) > option_nat > option4927543243414619207at_nat > $o).
% 34.88/9.15 thf(func_def_1732, type, sP219: num > rat > rat > $o).
% 34.88/9.15 thf(func_def_1733, type, sP220: $o > $o > nat > $o).
% 34.88/9.15 thf(func_def_1734, type, sP221: $o > $o > nat > $o > $o).
% 34.88/9.15 thf(func_def_1735, type, sP222: $o > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1736, type, sP223: rat > rat > rat > $o).
% 34.88/9.15 thf(func_def_1737, type, sP224: extended_enat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1738, type, sP225: vEBT_VEBT > vEBT_VEBT > extended_enat > $o).
% 34.88/9.15 thf(func_def_1739, type, sP226: rat > num > rat > $o).
% 34.88/9.15 thf(func_def_1740, type, sP227: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1741, type, sP228: nat > list_VEBT_VEBT > nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_1742, type, sP229: nat > nat > list_VEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1743, type, sP230: (option4927543243414619207at_nat > option_nat > $o) > option4927543243414619207at_nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1744, type, sP231: (nat > $o) > nat > nat > $o).
% 34.88/9.15 thf(func_def_1745, type, sP232: set_real > set_real > (complex > real) > (real > complex) > $o).
% 34.88/9.15 thf(func_def_1746, type, sP233: (complex > complex) > set_complex > $o).
% 34.88/9.15 thf(func_def_1747, type, sP234: set_real > (real > complex) > $o).
% 34.88/9.15 thf(func_def_1748, type, sP235: set_real > set_real > (real > complex) > set_complex > set_complex > $o).
% 34.88/9.15 thf(func_def_1749, type, sP236: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_1750, type, sP237: option_nat > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1751, type, sP238: option_nat > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1752, type, sP239: vEBT_VEBT > nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1753, type, sP240: vEBT_VEBT > nat > option_nat > $o).
% 34.88/9.15 thf(func_def_1754, type, sP241: option_nat > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1755, type, sP242: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.15 thf(func_def_1756, type, sP243: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1757, type, sP244: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1758, type, sP245: nat > vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_1759, type, sP246: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.15 thf(func_def_1760, type, sP247: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.15 thf(func_def_1761, type, sP248: (nat > $o) > nat > nat > $o).
% 34.88/9.15 thf(func_def_1762, type, sP249: $o > $o > nat > $o).
% 34.88/9.15 thf(func_def_1763, type, sP250: $o > $o > $o > nat > $o).
% 34.88/9.15 thf(func_def_1764, type, sP251: $o > nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1765, type, sP252: vEBT_VEBT > $o > nat > $o).
% 34.88/9.15 thf(func_def_1766, type, sP253: vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1767, type, sP254: (nat > real > real) > real > nat > $o).
% 34.88/9.15 thf(func_def_1768, type, sP255: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_1769, type, sP256: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_1770, type, sP257: (nat > int) > int > nat > nat > $o).
% 34.88/9.15 thf(func_def_1771, type, sK258: set_set_nat > nat > set_set_nat).
% 34.88/9.15 thf(func_def_1772, type, sK259: nat > list_o).
% 34.88/9.15 thf(func_def_1773, type, sK260: nat > set_nat > nat).
% 34.88/9.15 thf(func_def_1774, type, sK261: int > int).
% 34.88/9.15 thf(func_def_1775, type, sK262: list_int > (int > $o) > int).
% 34.88/9.15 thf(func_def_1776, type, sK263: (nat > rat) > set_nat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_1777, type, sK264: option_nat > nat).
% 34.88/9.15 thf(func_def_1778, type, sK265: product_prod_int_int > int).
% 34.88/9.15 thf(func_def_1779, type, sK266: product_prod_int_int > int).
% 34.88/9.15 thf(func_def_1780, type, sK267: int > set_int > int).
% 34.88/9.15 thf(func_def_1781, type, sK268: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_1782, type, sK269: nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_1783, type, sK270: nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_1784, type, sK271: (int > rat) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_1785, type, sK272: (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_1786, type, sK273: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_1787, type, sK274: set_nat > nat).
% 34.88/9.15 thf(func_def_1788, type, sK275: set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_1789, type, sK276: set_complex > (complex > rat) > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_1790, type, sK277: list_real > list_VEBT_VEBT > real > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1791, type, sK278: (nat > $o) > nat > nat).
% 34.88/9.15 thf(func_def_1792, type, sK279: (nat > $o) > nat > nat).
% 34.88/9.15 thf(func_def_1793, type, sK280: (num > rat) > num).
% 34.88/9.15 thf(func_def_1794, type, sK281: (num > rat) > num).
% 34.88/9.15 thf(func_def_1795, type, sK282: (nat > rat) > (nat > rat) > rat).
% 34.88/9.15 thf(func_def_1796, type, sK283: nat > (nat > rat) > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_1797, type, sK284: rat > (nat > rat) > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_1798, type, sK285: (real > nat) > (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_1799, type, sK286: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1800, type, sK287: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1801, type, sK288: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1802, type, sK289: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1803, type, sK290: set_int > nat > set_int).
% 34.88/9.15 thf(func_def_1804, type, sK291: set_int > nat > int).
% 34.88/9.15 thf(func_def_1805, type, sK292: set_nat > (nat > complex) > set_nat > nat).
% 34.88/9.15 thf(func_def_1806, type, sK293: (nat > code_integer) > set_nat > nat).
% 34.88/9.15 thf(func_def_1807, type, sK294: (set_nat > $o) > list_set_nat > nat).
% 34.88/9.15 thf(func_def_1808, type, sK295: set_real > (real > rat) > real).
% 34.88/9.15 thf(func_def_1809, type, sK296: (int > nat) > (int > nat) > set_int > int).
% 34.88/9.15 thf(func_def_1810, type, sK297: set_real > (real > code_integer) > code_integer > real).
% 34.88/9.15 thf(func_def_1811, type, sK298: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1812, type, sK299: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1813, type, sK300: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1814, type, sK301: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1815, type, sK302: (nat > rat) > (rat > rat > $o) > (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_1816, type, sK303: (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_1817, type, sK304: (int > rat) > (int > nat) > set_int > set_nat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_1818, type, sK305: set_real > set_real > nat > (real > real > $o) > real).
% 34.88/9.15 thf(func_def_1819, type, sK306: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1820, type, sK307: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1821, type, sK308: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1822, type, sK309: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1823, type, sK310: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1824, type, sK311: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1825, type, sK312: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1826, type, sK313: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1827, type, sK314: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1828, type, sK315: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1829, type, sK316: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1830, type, sK317: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1831, type, sK318: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1832, type, sK319: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1833, type, sK320: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1834, type, sK321: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1835, type, sK322: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1836, type, sK323: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1837, type, sK324: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_1838, type, sK325: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1839, type, sK326: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_1840, type, sK327: (real > real) > (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_1841, type, sK328: set_complex > (complex > int) > set_complex > complex).
% 34.88/9.15 thf(func_def_1842, type, sK329: (int > $o) > int).
% 34.88/9.15 thf(func_def_1843, type, sK330: (int > $o) > int).
% 34.88/9.15 thf(func_def_1844, type, sK331: nat > nat).
% 34.88/9.15 thf(func_def_1845, type, sK332: set_set_nat > (set_nat > complex) > real > set_nat).
% 34.88/9.15 thf(func_def_1846, type, sK333: nat > list_list_int > list_int).
% 34.88/9.15 thf(func_def_1847, type, sK334: (int > rat) > set_int > set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_1848, type, sK335: (int > rat) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_1849, type, sK336: set_int > set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_1850, type, sK337: nat > vEBT_VEBT > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_1851, type, sK338: nat > vEBT_VEBT > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_1852, type, sK339: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_1853, type, sK340: list_VEBT_VEBT > nat > nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_1854, type, sK341: list_VEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1855, type, sK342: list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1856, type, sK343: list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_1857, type, sK344: set_complex > (complex > complex) > (complex > complex) > complex).
% 34.88/9.15 thf(func_def_1858, type, sK345: set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_1859, type, sK346: int > nat).
% 34.88/9.15 thf(func_def_1860, type, sK347: int > nat).
% 34.88/9.15 thf(func_def_1861, type, sK348: int > int).
% 34.88/9.15 thf(func_def_1862, type, sK349: nat > nat).
% 34.88/9.15 thf(func_def_1863, type, sK350: set_int > (int > complex) > int).
% 34.88/9.15 thf(func_def_1864, type, sK351: set_int > set_int > (int > int) > (int > int) > int).
% 34.88/9.15 thf(func_def_1865, type, sK352: set_int > (int > complex) > int).
% 34.88/9.15 thf(func_def_1866, type, sK353: set_int > set_int > (int > int) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_1867, type, sK354: set_int > set_int > set_int > (int > int) > set_int > int).
% 34.88/9.15 thf(func_def_1868, type, sK355: (int > complex) > (int > complex) > set_int > (int > int) > int).
% 34.88/9.15 thf(func_def_1869, type, sK356: (int > int) > set_int > set_int > (int > int) > int).
% 34.88/9.15 thf(func_def_1870, type, sK357: (real > rat) > real).
% 34.88/9.15 thf(func_def_1871, type, sK358: (real > rat) > real).
% 34.88/9.15 thf(func_def_1872, type, sK359: set_complex > (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_1873, type, sK360: set_real > (real > int) > (real > int) > real).
% 34.88/9.15 thf(func_def_1874, type, sK361: num > num).
% 34.88/9.15 thf(func_def_1875, type, sK362: num > num).
% 34.88/9.15 thf(func_def_1876, type, sK363: int > int).
% 34.88/9.15 thf(func_def_1877, type, sK364: set_complex > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_1878, type, sK365: (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_1879, type, sK366: set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_1880, type, sK367: set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_1881, type, sK368: complex > real).
% 34.88/9.15 thf(func_def_1882, type, sK369: (nat > complex) > nat > complex).
% 34.88/9.15 thf(func_def_1883, type, sK370: set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_1884, type, sK371: set_real > (real > nat) > real).
% 34.88/9.15 thf(func_def_1885, type, sK372: (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_1886, type, sK373: set_complex > (complex > code_integer) > code_integer > complex).
% 34.88/9.15 thf(func_def_1887, type, sK374: (num > int) > num).
% 34.88/9.15 thf(func_def_1888, type, sK375: (num > int) > num).
% 34.88/9.15 thf(func_def_1889, type, sK376: product_prod_int_int > int).
% 34.88/9.15 thf(func_def_1890, type, sK377: product_prod_int_int > int).
% 34.88/9.15 thf(func_def_1891, type, sK378: (real > real) > real > real).
% 34.88/9.15 thf(func_def_1892, type, sK379: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_1893, type, sK380: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_1894, type, sK381: (set_nat > nat) > set_set_nat > (set_nat > nat) > set_nat).
% 34.88/9.15 thf(func_def_1895, type, sK382: nat > real > nat).
% 34.88/9.15 thf(func_def_1896, type, sK383: list_o > list_o > set_Product_prod_o_o > nat).
% 34.88/9.15 thf(func_def_1897, type, sK384: (nat > nat) > nat).
% 34.88/9.15 thf(func_def_1898, type, sK385: (nat > nat) > nat).
% 34.88/9.15 thf(func_def_1899, type, sK386: set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_1900, type, sK387: set_nat > (nat > rat) > rat > nat).
% 34.88/9.15 thf(func_def_1901, type, sK388: (real > nat) > real).
% 34.88/9.15 thf(func_def_1902, type, sK389: (real > nat) > real).
% 34.88/9.15 thf(func_def_1903, type, sK390: (complex > int) > (complex > int) > set_complex > complex).
% 34.88/9.15 thf(func_def_1904, type, sK391: (nat > $o) > nat > nat).
% 34.88/9.15 thf(func_def_1905, type, sK392: (nat > $o) > nat > nat).
% 34.88/9.15 thf(func_def_1906, type, sK393: nat > nat > nat).
% 34.88/9.15 thf(func_def_1907, type, sK394: nat > nat > nat).
% 34.88/9.15 thf(func_def_1908, type, sK395: nat > nat > nat).
% 34.88/9.15 thf(func_def_1909, type, sK396: (int > rat) > int).
% 34.88/9.15 thf(func_def_1910, type, sK397: (int > rat) > int).
% 34.88/9.15 thf(func_def_1911, type, sK398: nat > nat > nat).
% 34.88/9.15 thf(func_def_1912, type, sK399: (int > rat) > (int > rat) > (rat > rat > $o) > set_int > int).
% 34.88/9.15 thf(func_def_1913, type, sK400: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1914, type, sK401: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1915, type, sK402: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1916, type, sK403: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_1917, type, sK404: int > int > int).
% 34.88/9.15 thf(func_def_1918, type, sK405: int > int > int).
% 34.88/9.15 thf(func_def_1919, type, sK406: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_1920, type, sK407: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_1921, type, sK408: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_1922, type, sK409: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_1923, type, sK410: (nat > nat > $o) > set_complex > (complex > nat) > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_1924, type, sK411: (option4927543243414619207at_nat > option_num > $o) > option4927543243414619207at_nat > option_num > num).
% 34.88/9.15 thf(func_def_1925, type, sK412: (option4927543243414619207at_nat > option_num > $o) > option4927543243414619207at_nat > option_num > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_1926, type, sK413: set_complex > (complex > code_integer) > complex).
% 34.88/9.15 thf(func_def_1927, type, sK414: code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_1928, type, sK415: rat > rat > rat).
% 34.88/9.15 thf(func_def_1929, type, sK416: set_nat > set_nat > (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_1930, type, sK417: set_nat > set_nat > (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_1931, type, sK418: set_nat > set_nat > (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_1932, type, sK419: set_nat > (nat > nat > $o) > set_nat > nat).
% 34.88/9.15 thf(func_def_1933, type, sK420: set_int > int).
% 34.88/9.15 thf(func_def_1934, type, sK421: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_1935, type, sK422: set_int > (int > real) > (int > real) > int).
% 34.88/9.15 thf(func_def_1936, type, sK423: set_int > set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_1937, type, sK424: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1938, type, sK425: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1939, type, sK426: (num > nat) > num).
% 34.88/9.15 thf(func_def_1940, type, sK427: (num > nat) > num).
% 34.88/9.15 thf(func_def_1941, type, sK428: set_real > (real > complex) > set_real > real).
% 34.88/9.15 thf(func_def_1942, type, sK429: set_real > (real > complex) > (real > complex) > real).
% 34.88/9.15 thf(func_def_1943, type, sK430: set_real > (real > rat) > real).
% 34.88/9.15 thf(func_def_1944, type, sK431: (nat > int) > nat).
% 34.88/9.15 thf(func_def_1945, type, sK432: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1946, type, sK433: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1947, type, sK434: set_rat > rat).
% 34.88/9.15 thf(func_def_1948, type, sK435: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_1949, type, sK436: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_1950, type, sK437: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_1951, type, sK438: vEBT_VEBT > nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_1952, type, sK439: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1953, type, sK440: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_1954, type, sK441: list_o > list_VEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_1955, type, sK442: (real > nat) > real).
% 34.88/9.15 thf(func_def_1956, type, sK443: (real > nat) > real).
% 34.88/9.15 thf(func_def_1957, type, sK444: set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_1958, type, sK445: (int > num) > int).
% 34.88/9.15 thf(func_def_1959, type, sK446: (int > num) > int).
% 34.88/9.15 thf(func_def_1960, type, sK447: (real > real) > set_real > real > real).
% 34.88/9.15 thf(func_def_1961, type, sK448: (real > real) > set_real > real > real).
% 34.88/9.15 thf(func_def_1962, type, sK449: num > num).
% 34.88/9.15 thf(func_def_1963, type, sK450: nat > list_VEBT_VEBT > (vEBT_VEBT > $o) > nat).
% 34.88/9.15 thf(func_def_1964, type, sK451: vEBT_VEBT > list_VEBT_VEBT > (vEBT_VEBT > $o) > nat).
% 34.88/9.15 thf(func_def_1965, type, sK452: (int > int > int) > int).
% 34.88/9.15 thf(func_def_1966, type, sK453: (int > int > int) > int).
% 34.88/9.15 thf(func_def_1967, type, sK454: (int > int > int) > int).
% 34.88/9.15 thf(func_def_1968, type, sK455: (int > int > int) > int).
% 34.88/9.15 thf(func_def_1969, type, sK456: (int > int > int) > int).
% 34.88/9.15 thf(func_def_1970, type, sK457: (int > int > int) > int).
% 34.88/9.15 thf(func_def_1971, type, sK458: (int > int > int) > int).
% 34.88/9.15 thf(func_def_1972, type, sK459: set_int > (int > rat) > int > int).
% 34.88/9.15 thf(func_def_1973, type, sK460: set_complex > complex).
% 34.88/9.15 thf(func_def_1974, type, sK461: set_complex > complex).
% 34.88/9.15 thf(func_def_1975, type, sK462: (int > nat) > set_int > int).
% 34.88/9.15 thf(func_def_1976, type, sK463: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_1977, type, sK464: set_list_o > nat).
% 34.88/9.15 thf(func_def_1978, type, sK465: set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_1979, type, sK466: set_real > (real > real) > real).
% 34.88/9.15 thf(func_def_1980, type, sK467: rat > rat).
% 34.88/9.15 thf(func_def_1981, type, sK468: (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_1982, type, sK469: (nat > rat) > set_nat > (int > rat) > set_int > (nat > int) > int).
% 34.88/9.15 thf(func_def_1983, type, sK470: real > real > real).
% 34.88/9.15 thf(func_def_1984, type, sK471: (real > code_integer) > set_real > real).
% 34.88/9.15 thf(func_def_1985, type, sK472: code_integer > (real > code_integer) > code_integer > set_real > real).
% 34.88/9.15 thf(func_def_1986, type, sK473: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1987, type, sK474: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat).
% 34.88/9.15 thf(func_def_1988, type, sK475: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat).
% 34.88/9.15 thf(func_def_1989, type, sK476: list_P5464809261938338413at_nat > list_s1210847774152347623at_nat > produc3843707927480180839at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_1990, type, sK477: rat > rat).
% 34.88/9.15 thf(func_def_1991, type, sK478: (complex > rat) > set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_1992, type, sK479: set_nat > set_nat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_1993, type, sK480: nat > real > (nat > real) > nat > real).
% 34.88/9.15 thf(func_def_1994, type, sK481: set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_1995, type, sK482: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_1996, type, sK483: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_1997, type, sK484: nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_1998, type, sK485: (produc859450856879609959at_nat > $o) > nat).
% 34.88/9.15 thf(func_def_1999, type, sK486: (produc859450856879609959at_nat > $o) > nat).
% 34.88/9.15 thf(func_def_2000, type, sK487: (produc859450856879609959at_nat > $o) > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2001, type, sK488: complex > nat > nat).
% 34.88/9.15 thf(func_def_2002, type, sK489: set_complex > (complex > real) > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2003, type, sK490: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_2004, type, sK491: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_2005, type, sK492: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_2006, type, sK493: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_2007, type, sK494: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2008, type, sK495: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2009, type, sK496: set_nat > nat).
% 34.88/9.15 thf(func_def_2010, type, sK497: (nat > $o) > list_nat > nat).
% 34.88/9.15 thf(func_def_2011, type, sK498: set_complex > (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2012, type, sK499: nat > list_nat).
% 34.88/9.15 thf(func_def_2013, type, sK500: int > int).
% 34.88/9.15 thf(func_def_2014, type, sK501: (set_complex > $o) > (complex > rat) > set_complex).
% 34.88/9.15 thf(func_def_2015, type, sK502: (set_complex > $o) > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_2016, type, sK503: real > (real > real) > (real > real) > real > real).
% 34.88/9.15 thf(func_def_2017, type, sK504: real > real > (real > real) > (real > real) > real).
% 34.88/9.15 thf(func_def_2018, type, sK505: list_VEBT_VEBT > nat > list_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2019, type, sK506: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2020, type, sK507: (int > rat) > (set_int > $o) > set_int).
% 34.88/9.15 thf(func_def_2021, type, sK508: (int > rat) > (set_int > $o) > int).
% 34.88/9.15 thf(func_def_2022, type, sK509: nat > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2023, type, sK510: (real > real) > real).
% 34.88/9.15 thf(func_def_2024, type, sK511: nat > nat).
% 34.88/9.15 thf(func_def_2025, type, sK512: int > int).
% 34.88/9.15 thf(func_def_2026, type, sK513: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2027, type, sK514: set_complex > set_complex > (complex > complex) > complex).
% 34.88/9.15 thf(func_def_2028, type, sK515: set_complex > set_complex > (complex > complex) > complex).
% 34.88/9.15 thf(func_def_2029, type, sK516: nat > set_nat > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2030, type, sK517: set_nat > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2031, type, sK518: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2032, type, sK519: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2033, type, sK520: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2034, type, sK521: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2035, type, sK522: set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_2036, type, sK523: real > real > nat).
% 34.88/9.15 thf(func_def_2037, type, sK524: set_nat > nat > nat).
% 34.88/9.15 thf(func_def_2038, type, sK525: nat > nat > nat).
% 34.88/9.15 thf(func_def_2039, type, sK526: nat > (nat > nat) > nat > nat).
% 34.88/9.15 thf(func_def_2040, type, sK527: real > (real > real) > nat > (nat > real) > real).
% 34.88/9.15 thf(func_def_2041, type, sK528: (real > rat) > rat > set_real > real).
% 34.88/9.15 thf(func_def_2042, type, sK529: real > set_int > (int > complex) > int).
% 34.88/9.15 thf(func_def_2043, type, sK530: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2044, type, sK531: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2045, type, sK532: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2046, type, sK533: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2047, type, sK534: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2048, type, sK535: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2049, type, sK536: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2050, type, sK537: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2051, type, sK538: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2052, type, sK539: set_int > (int > real) > int > int).
% 34.88/9.15 thf(func_def_2053, type, sK540: (complex > complex) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2054, type, sK541: complex > (nat > complex) > nat > nat > complex).
% 34.88/9.15 thf(func_def_2055, type, sK542: list_nat > list_nat > nat).
% 34.88/9.15 thf(func_def_2056, type, sK543: (nat > real > real) > nat).
% 34.88/9.15 thf(func_def_2057, type, sK544: (nat > real > real) > real).
% 34.88/9.15 thf(func_def_2058, type, sK545: real > (nat > real > real) > nat > (real > real) > real).
% 34.88/9.15 thf(func_def_2059, type, sK546: list_o > nat > list_o).
% 34.88/9.15 thf(func_def_2060, type, sK547: list_o > nat > $o).
% 34.88/9.15 thf(func_def_2061, type, sK548: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2062, type, sK549: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2063, type, sK550: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2064, type, sK551: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2065, type, sK552: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2066, type, sK553: vEBT_VEBT > $o > nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2067, type, sK554: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2068, type, sK555: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2069, type, sK556: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2070, type, sK557: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2071, type, sK558: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2072, type, sK559: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2073, type, sK560: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2074, type, sK561: $o > nat > vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2075, type, sK562: $o > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_2076, type, sK563: $o > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_2077, type, sK564: (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_2078, type, sK565: set_complex > (complex > complex) > complex).
% 34.88/9.15 thf(func_def_2079, type, sK566: (complex > complex) > (complex > complex) > (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_2080, type, sK567: (complex > complex) > (complex > complex) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2081, type, sK568: set_complex > set_complex > set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_2082, type, sK569: (complex > complex) > set_complex > set_complex > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2083, type, sK570: (complex > complex) > set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_2084, type, sK571: list_o > list_complex > complex > $o).
% 34.88/9.15 thf(func_def_2085, type, sK572: list_nat > nat > nat).
% 34.88/9.15 thf(func_def_2086, type, sK573: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2087, type, sK574: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2088, type, sK575: nat > real > real).
% 34.88/9.15 thf(func_def_2089, type, sK576: (complex > int) > set_complex > (complex > int) > complex).
% 34.88/9.15 thf(func_def_2090, type, sK577: nat > nat).
% 34.88/9.15 thf(func_def_2091, type, sK578: set_int > set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_2092, type, sK579: (real > real) > (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2093, type, sK580: nat > nat > nat).
% 34.88/9.15 thf(func_def_2094, type, sK581: set_real > set_real > (real > nat) > real).
% 34.88/9.15 thf(func_def_2095, type, sK582: set_real > set_real > (real > nat) > real).
% 34.88/9.15 thf(func_def_2096, type, sK583: nat > nat).
% 34.88/9.15 thf(func_def_2097, type, sK584: nat > nat).
% 34.88/9.15 thf(func_def_2098, type, sK585: nat > nat).
% 34.88/9.15 thf(func_def_2099, type, sK586: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2100, type, sK587: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2101, type, sK588: real > nat).
% 34.88/9.15 thf(func_def_2102, type, sK589: set_list_nat > nat > list_nat).
% 34.88/9.15 thf(func_def_2103, type, sK590: set_list_nat > nat > set_list_nat).
% 34.88/9.15 thf(func_def_2104, type, sK591: set_num > num > num).
% 34.88/9.15 thf(func_def_2105, type, sK592: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > set_Pr8693737435421807431at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2106, type, sK593: product_prod_nat_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat > set_Pr8693737435421807431at_nat > list_P6011104703257516679at_nat).
% 34.88/9.15 thf(func_def_2107, type, sK594: nat > real > real).
% 34.88/9.15 thf(func_def_2108, type, sK595: int > int).
% 34.88/9.15 thf(func_def_2109, type, sK596: (complex > nat) > (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2110, type, sK597: real > real > real).
% 34.88/9.15 thf(func_def_2111, type, sK598: filter_nat > nat).
% 34.88/9.15 thf(func_def_2112, type, sK599: nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_2113, type, sK600: complex > (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2114, type, sK601: (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2115, type, sK602: real > set_real > real).
% 34.88/9.15 thf(func_def_2116, type, sK603: nat > list_nat > nat).
% 34.88/9.15 thf(func_def_2117, type, sK604: nat > list_nat > list_nat).
% 34.88/9.15 thf(func_def_2118, type, sK605: (nat > int) > nat).
% 34.88/9.15 thf(func_def_2119, type, sK606: set_real > (real > rat) > real > real).
% 34.88/9.15 thf(func_def_2120, type, sK607: set_real > (real > rat) > (real > rat) > real).
% 34.88/9.15 thf(func_def_2121, type, sK608: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2122, type, sK609: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2123, type, sK610: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2124, type, sK611: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2125, type, sK612: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2126, type, sK613: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2127, type, sK614: (complex > nat) > set_complex > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_2128, type, sK615: real > nat).
% 34.88/9.15 thf(func_def_2129, type, sK616: real > nat).
% 34.88/9.15 thf(func_def_2130, type, sK617: set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2131, type, sK618: set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2132, type, sK619: (code_integer > $o) > $o).
% 34.88/9.15 thf(func_def_2133, type, sK620: (code_integer > $o) > code_integer).
% 34.88/9.15 thf(func_def_2134, type, sK621: (code_integer > $o) > code_integer).
% 34.88/9.15 thf(func_def_2135, type, sK622: nat > (nat > real > real) > real > nat).
% 34.88/9.15 thf(func_def_2136, type, sK623: nat > (nat > real > real) > real > real).
% 34.88/9.15 thf(func_def_2137, type, sK624: (real > real) > real).
% 34.88/9.15 thf(func_def_2138, type, sK625: (real > real) > real).
% 34.88/9.15 thf(func_def_2139, type, sK626: set_int > (int > nat) > nat > int).
% 34.88/9.15 thf(func_def_2140, type, sK627: (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2141, type, sK628: set_nat > (rat > rat > $o) > (nat > rat) > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2142, type, sK629: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2143, type, sK630: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2144, type, sK631: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2145, type, sK632: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2146, type, sK633: set_complex > complex).
% 34.88/9.15 thf(func_def_2147, type, sK634: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2148, type, sK635: set_Pr1261947904930325089at_nat > nat).
% 34.88/9.15 thf(func_def_2149, type, sK636: set_list_nat > nat > set_list_nat).
% 34.88/9.15 thf(func_def_2150, type, sK637: set_list_nat > nat > list_nat).
% 34.88/9.15 thf(func_def_2151, type, sK638: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2152, type, sK639: list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2153, type, sK640: list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2154, type, sK641: nat > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2155, type, sK642: (real > rat) > set_real > (real > rat) > real).
% 34.88/9.15 thf(func_def_2156, type, sK643: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2157, type, sK644: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2158, type, sK645: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2159, type, sK646: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2160, type, sK647: (nat > complex) > (complex > complex > $o) > set_nat > (nat > complex) > nat).
% 34.88/9.15 thf(func_def_2161, type, sK648: (int > rat) > int).
% 34.88/9.15 thf(func_def_2162, type, sK649: (int > rat) > int).
% 34.88/9.15 thf(func_def_2163, type, sK650: set_int > (int > nat) > int).
% 34.88/9.15 thf(func_def_2164, type, sK651: set_nat > (nat > rat) > rat > nat).
% 34.88/9.15 thf(func_def_2165, type, sK652: product_prod_nat_nat > nat).
% 34.88/9.15 thf(func_def_2166, type, sK653: product_prod_nat_nat > nat).
% 34.88/9.15 thf(func_def_2167, type, sK654: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2168, type, sK655: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2169, type, sK656: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2170, type, sK657: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2171, type, sK658: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2172, type, sK659: (nat > complex) > nat > nat).
% 34.88/9.15 thf(func_def_2173, type, sK660: set_nat > nat > nat).
% 34.88/9.15 thf(func_def_2174, type, sK661: set_nat > nat > set_nat).
% 34.88/9.15 thf(func_def_2175, type, sK662: nat > set_complex > set_complex).
% 34.88/9.15 thf(func_def_2176, type, sK663: (complex > real) > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2177, type, sK664: (complex > real) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2178, type, sK665: list_VEBT_VEBT > (vEBT_VEBT > $o) > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2179, type, sK666: (complex > real) > set_complex > complex).
% 34.88/9.15 thf(func_def_2180, type, sK667: (int > int > $o) > int).
% 34.88/9.15 thf(func_def_2181, type, sK668: (int > int > $o) > int).
% 34.88/9.15 thf(func_def_2182, type, sK669: (int > int > $o) > int).
% 34.88/9.15 thf(func_def_2183, type, sK670: (int > int > $o) > int).
% 34.88/9.15 thf(func_def_2184, type, sK671: (int > int > $o) > int).
% 34.88/9.15 thf(func_def_2185, type, sK672: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2186, type, sK673: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2187, type, sK674: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2188, type, sK675: extended_enat > nat > extended_enat > nat).
% 34.88/9.15 thf(func_def_2189, type, sK676: extended_enat > nat > extended_enat > nat).
% 34.88/9.15 thf(func_def_2190, type, sK677: (nat > $o) > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2191, type, sK678: nat > nat > nat).
% 34.88/9.15 thf(func_def_2192, type, sK679: nat > nat > nat).
% 34.88/9.15 thf(func_def_2193, type, sK680: nat > nat > nat).
% 34.88/9.15 thf(func_def_2194, type, sK681: nat > real > real).
% 34.88/9.15 thf(func_def_2195, type, sK682: nat > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2196, type, sK683: nat > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2197, type, sK684: (nat > nat) > nat > nat).
% 34.88/9.15 thf(func_def_2198, type, sK685: (nat > nat) > nat > nat).
% 34.88/9.15 thf(func_def_2199, type, sK686: option_num > num).
% 34.88/9.15 thf(func_def_2200, type, sK687: nat > (nat > real) > (nat > real) > nat).
% 34.88/9.15 thf(func_def_2201, type, sK688: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2202, type, sK689: (nat > real) > (nat > real) > real).
% 34.88/9.15 thf(func_def_2203, type, sK690: (nat > real) > (nat > real) > nat).
% 34.88/9.15 thf(func_def_2204, type, sK691: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2205, type, sK692: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2206, type, sK693: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2207, type, sK694: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2208, type, sK695: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2209, type, sK696: set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2210, type, sK697: set_real > (real > complex) > set_real > real).
% 34.88/9.15 thf(func_def_2211, type, sK698: set_real > (real > complex) > (real > complex) > real).
% 34.88/9.15 thf(func_def_2212, type, sK699: nat > nat > nat).
% 34.88/9.15 thf(func_def_2213, type, sK700: (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_2214, type, sK701: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2215, type, sK702: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2216, type, sK703: (real > int) > real).
% 34.88/9.15 thf(func_def_2217, type, sK704: (real > int) > real).
% 34.88/9.15 thf(func_def_2218, type, sK705: set_int > (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_2219, type, sK706: set_int > (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_2220, type, sK707: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_2221, type, sK708: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_2222, type, sK709: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2223, type, sK710: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2224, type, sK711: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2225, type, sK712: vEBT_VEBT > option_nat > nat).
% 34.88/9.15 thf(func_def_2226, type, sK713: vEBT_VEBT > option_nat > nat).
% 34.88/9.15 thf(func_def_2227, type, sK714: vEBT_VEBT > option_nat > nat).
% 34.88/9.15 thf(func_def_2228, type, sK715: vEBT_VEBT > option_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2229, type, sK716: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2230, type, sK717: vEBT_VEBT > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2231, type, sK718: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2232, type, sK719: set_complex > real > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2233, type, sK720: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2234, type, sK721: nat > nat > nat).
% 34.88/9.15 thf(func_def_2235, type, sK722: nat > nat > nat).
% 34.88/9.15 thf(func_def_2236, type, sK723: nat > nat > nat).
% 34.88/9.15 thf(func_def_2237, type, sK724: real > nat).
% 34.88/9.15 thf(func_def_2238, type, sK725: real > nat).
% 34.88/9.15 thf(func_def_2239, type, sK726: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2240, type, sK727: real > (nat > real) > real).
% 34.88/9.15 thf(func_def_2241, type, sK728: real > (nat > real) > nat).
% 34.88/9.15 thf(func_def_2242, type, sK729: set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_2243, type, sK730: (rat > num) > rat).
% 34.88/9.15 thf(func_def_2244, type, sK731: (rat > num) > rat).
% 34.88/9.15 thf(func_def_2245, type, sK732: real > real > real > real).
% 34.88/9.15 thf(func_def_2246, type, sK733: set_set_nat > set_nat).
% 34.88/9.15 thf(func_def_2247, type, sK734: nat > real > real).
% 34.88/9.15 thf(func_def_2248, type, sK735: set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2249, type, sK736: set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2250, type, sK737: list_nat > list_nat > set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2251, type, sK738: nat > list_list_o > list_o).
% 34.88/9.15 thf(func_def_2252, type, sK739: list_s1210847774152347623at_nat > set_Pr4329608150637261639at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2253, type, sK740: list_s1210847774152347623at_nat > set_Pr4329608150637261639at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat).
% 34.88/9.15 thf(func_def_2254, type, sK741: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2255, type, sK742: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2256, type, sK743: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2257, type, sK744: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2258, type, sK745: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2259, type, sK746: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2260, type, sK747: (set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat) > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2261, type, sK748: (rat > int) > rat).
% 34.88/9.15 thf(func_def_2262, type, sK749: (rat > int) > rat).
% 34.88/9.15 thf(func_def_2263, type, sK750: set_nat > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2264, type, sK751: list_real > list_o > real > $o).
% 34.88/9.15 thf(func_def_2265, type, sK752: (nat > real) > set_nat > set_nat > nat).
% 34.88/9.15 thf(func_def_2266, type, sK753: (nat > int > $o) > set_nat > set_int > int).
% 34.88/9.15 thf(func_def_2267, type, sK754: (nat > int > $o) > set_nat > set_int > nat).
% 34.88/9.15 thf(func_def_2268, type, sK755: (nat > int > $o) > set_nat > set_int > nat).
% 34.88/9.15 thf(func_def_2269, type, sK756: set_int > set_nat > (nat > int > $o) > nat).
% 34.88/9.15 thf(func_def_2270, type, sK757: (int > complex) > set_int > int).
% 34.88/9.15 thf(func_def_2271, type, sK758: (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2272, type, sK759: (complex > $o) > complex > complex).
% 34.88/9.15 thf(func_def_2273, type, sK760: (complex > $o) > complex > complex).
% 34.88/9.15 thf(func_def_2274, type, sK761: int > nat).
% 34.88/9.15 thf(func_def_2275, type, sK762: int > nat).
% 34.88/9.15 thf(func_def_2276, type, sK763: (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_2277, type, sK764: (complex > real) > real > set_complex > complex).
% 34.88/9.15 thf(func_def_2278, type, sK765: complex > list_complex > nat).
% 34.88/9.15 thf(func_def_2279, type, sK766: nat > list_VEBT_VEBT > (vEBT_VEBT > $o) > nat).
% 34.88/9.15 thf(func_def_2280, type, sK767: vEBT_VEBT > list_VEBT_VEBT > (vEBT_VEBT > $o) > nat).
% 34.88/9.15 thf(func_def_2281, type, sK768: set_rat > rat).
% 34.88/9.15 thf(func_def_2282, type, sK769: set_real > real > (real > nat) > real).
% 34.88/9.15 thf(func_def_2283, type, sK770: (list_nat > real) > real > set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2284, type, sK771: code_integer > code_integer).
% 34.88/9.15 thf(func_def_2285, type, sK772: (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2286, type, sK773: (real > rat) > (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_2287, type, sK774: (real > rat) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_2288, type, sK775: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2289, type, sK776: (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_2290, type, sK777: (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_2291, type, sK778: rat > rat > rat).
% 34.88/9.15 thf(func_def_2292, type, sK779: (int > complex) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_2293, type, sK780: set_real > set_real > (real > real) > real).
% 34.88/9.15 thf(func_def_2294, type, sK781: (real > real) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_2295, type, sK782: (int > rat) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_2296, type, sK783: (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_2297, type, sK784: (int > rat) > (int > int) > set_int > (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_2298, type, sK785: set_complex > (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2299, type, sK786: set_complex > (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2300, type, sK787: set_complex > (complex > rat) > (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2301, type, sK788: (int > rat) > (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_2302, type, sK789: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2303, type, sK790: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2304, type, sK791: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2305, type, sK792: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2306, type, sK793: (real > real > $o) > set_complex > (complex > real) > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2307, type, sK794: (real > nat) > real).
% 34.88/9.15 thf(func_def_2308, type, sK795: (real > nat) > real).
% 34.88/9.15 thf(func_def_2309, type, sK796: option_nat > nat).
% 34.88/9.15 thf(func_def_2310, type, sK797: option_nat > (nat > nat > nat) > option_nat > option_nat > nat).
% 34.88/9.15 thf(func_def_2311, type, sK798: option_nat > (nat > nat > nat) > option_nat > option_nat > nat).
% 34.88/9.15 thf(func_def_2312, type, sK799: set_nat > (nat > int) > nat).
% 34.88/9.15 thf(func_def_2313, type, sK800: (nat > code_integer) > set_nat > code_integer > nat).
% 34.88/9.15 thf(func_def_2314, type, sK801: list_o > $o > ($o > $o) > nat).
% 34.88/9.15 thf(func_def_2315, type, sK802: nat > list_o > ($o > $o) > nat).
% 34.88/9.15 thf(func_def_2316, type, sK803: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.15 thf(func_def_2317, type, sK804: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat > list_s1210847774152347623at_nat).
% 34.88/9.15 thf(func_def_2318, type, sK805: (num > real) > num).
% 34.88/9.15 thf(func_def_2319, type, sK806: (num > real) > num).
% 34.88/9.15 thf(func_def_2320, type, sK807: real > nat > real).
% 34.88/9.15 thf(func_def_2321, type, sK808: set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_2322, type, sK809: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2323, type, sK810: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2324, type, sK811: set_int > (int > code_integer) > int).
% 34.88/9.15 thf(func_def_2325, type, sK812: nat > int > (nat > int) > nat > int).
% 34.88/9.15 thf(func_def_2326, type, sK813: real > real > real).
% 34.88/9.15 thf(func_def_2327, type, sK814: set_complex > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_2328, type, sK815: (set_nat > $o) > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2329, type, sK816: (set_nat > $o) > (nat > rat) > set_nat).
% 34.88/9.15 thf(func_def_2330, type, sK817: set_int > (int > nat) > (int > nat) > int).
% 34.88/9.15 thf(func_def_2331, type, sK818: int > set_nat > (nat > int) > nat).
% 34.88/9.15 thf(func_def_2332, type, sK819: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2333, type, sK820: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2334, type, sK821: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2335, type, sK822: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2336, type, sK823: set_list_nat > nat > set_list_nat).
% 34.88/9.15 thf(func_def_2337, type, sK824: real > (nat > real > real) > nat > nat).
% 34.88/9.15 thf(func_def_2338, type, sK825: real > (nat > real > real) > nat > real).
% 34.88/9.15 thf(func_def_2339, type, sK826: real > (real > real) > (nat > real > real) > nat > real).
% 34.88/9.15 thf(func_def_2340, type, sK827: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_2341, type, sK828: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_2342, type, sK829: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_2343, type, sK830: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > code_integer).
% 34.88/9.15 thf(func_def_2344, type, sK831: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > list_Code_integer).
% 34.88/9.15 thf(func_def_2345, type, sK832: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > list_Code_integer).
% 34.88/9.15 thf(func_def_2346, type, sK833: list_P5578671422887162913nteger > produc8923325533196201883nteger > list_Code_integer > list_Code_integer > code_integer).
% 34.88/9.15 thf(func_def_2347, type, sK834: set_nat > (nat > code_integer) > (code_integer > code_integer > $o) > (nat > code_integer) > nat).
% 34.88/9.15 thf(func_def_2348, type, sK835: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.15 thf(func_def_2349, type, sK836: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.15 thf(func_def_2350, type, sK837: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.15 thf(func_def_2351, type, sK838: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.15 thf(func_def_2352, type, sK839: (rat > int) > rat).
% 34.88/9.15 thf(func_def_2353, type, sK840: (rat > int) > rat).
% 34.88/9.15 thf(func_def_2354, type, sK841: real > int).
% 34.88/9.15 thf(func_def_2355, type, sK842: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2356, type, sK843: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2357, type, sK844: int > nat).
% 34.88/9.15 thf(func_def_2358, type, sK845: int > int).
% 34.88/9.15 thf(func_def_2359, type, sK846: set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_2360, type, sK847: (complex > nat) > complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2361, type, sK848: produc2233624965454879586on_nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_2362, type, sK849: produc2233624965454879586on_nat > nat).
% 34.88/9.15 thf(func_def_2363, type, sK850: produc2233624965454879586on_nat > option_nat).
% 34.88/9.15 thf(func_def_2364, type, sK851: produc2233624965454879586on_nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_2365, type, sK852: produc2233624965454879586on_nat > nat > nat > $o).
% 34.88/9.15 thf(func_def_2366, type, sK853: produc2233624965454879586on_nat > nat).
% 34.88/9.15 thf(func_def_2367, type, sK854: produc2233624965454879586on_nat > nat).
% 34.88/9.15 thf(func_def_2368, type, sK855: set_complex > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_2369, type, sK856: set_nat > (nat > code_integer) > nat).
% 34.88/9.15 thf(func_def_2370, type, sK857: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2371, type, sK858: set_complex > (complex > real) > set_complex > complex).
% 34.88/9.15 thf(func_def_2372, type, sK859: (nat > complex) > nat > nat).
% 34.88/9.15 thf(func_def_2373, type, sK860: nat > (nat > complex) > nat).
% 34.88/9.15 thf(func_def_2374, type, sK861: nat > set_Pr1261947904930325089at_nat > list_nat > list_nat > list_nat).
% 34.88/9.15 thf(func_def_2375, type, sK862: nat > set_Pr1261947904930325089at_nat > list_nat > list_nat > nat).
% 34.88/9.15 thf(func_def_2376, type, sK863: list_complex > list_int > complex > int).
% 34.88/9.15 thf(func_def_2377, type, sK864: set_complex > set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_2378, type, sK865: set_nat > (nat > complex) > set_nat > nat).
% 34.88/9.15 thf(func_def_2379, type, sK866: rat > rat).
% 34.88/9.15 thf(func_def_2380, type, sK867: set_list_nat > nat).
% 34.88/9.15 thf(func_def_2381, type, sK868: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2382, type, sK869: produc5542196010084753463at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2383, type, sK870: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2384, type, sK871: produc5542196010084753463at_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2385, type, sK872: produc5542196010084753463at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2386, type, sK873: produc5542196010084753463at_nat > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2387, type, sK874: produc5542196010084753463at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2388, type, sK875: set_nat > set_nat > (nat > complex) > nat).
% 34.88/9.15 thf(func_def_2389, type, sK876: set_num > num).
% 34.88/9.15 thf(func_def_2390, type, sK877: real > set_nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_2391, type, sK878: (nat > $o) > nat > nat > nat).
% 34.88/9.15 thf(func_def_2392, type, sK879: (real > real) > real).
% 34.88/9.15 thf(func_def_2393, type, sK880: (real > real) > real).
% 34.88/9.15 thf(func_def_2394, type, sK881: set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2395, type, sK882: set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2396, type, sK883: (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_2397, type, sK884: (set_complex > $o) > (complex > num) > complex).
% 34.88/9.15 thf(func_def_2398, type, sK885: (set_complex > $o) > (complex > num) > set_complex).
% 34.88/9.15 thf(func_def_2399, type, sK886: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2400, type, sK887: (option4927543243414619207at_nat > option4927543243414619207at_nat > $o) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2401, type, sK888: (complex > rat) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2402, type, sK889: (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2403, type, sK890: set_set_nat > set_nat > set_nat).
% 34.88/9.15 thf(func_def_2404, type, sK891: int > int > int > int).
% 34.88/9.15 thf(func_def_2405, type, sK892: int > int > int > int).
% 34.88/9.15 thf(func_def_2406, type, sK893: (nat > int) > (nat > int) > set_nat > nat).
% 34.88/9.15 thf(func_def_2407, type, sK894: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2408, type, sK895: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2409, type, sK896: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2410, type, sK897: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2411, type, sK898: set_nat > (nat > complex) > (complex > complex > $o) > (nat > complex) > nat).
% 34.88/9.15 thf(func_def_2412, type, sK899: (real > nat) > (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_2413, type, sK900: list_Code_integer > list_Code_integer > code_integer > code_integer).
% 34.88/9.15 thf(func_def_2414, type, sK901: rat > rat > rat > rat).
% 34.88/9.15 thf(func_def_2415, type, sK902: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2416, type, sK903: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2417, type, sK904: nat > nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2418, type, sK905: nat > nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2419, type, sK906: rat > set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_2420, type, sK907: (nat > $o) > nat > nat > nat).
% 34.88/9.15 thf(func_def_2421, type, sK908: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2422, type, sK909: set_complex > (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2423, type, sK910: set_complex > complex).
% 34.88/9.15 thf(func_def_2424, type, sK911: set_complex > complex).
% 34.88/9.15 thf(func_def_2425, type, sK912: complex > complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2426, type, sK913: list_int > nat > list_int).
% 34.88/9.15 thf(func_def_2427, type, sK914: list_int > nat > int).
% 34.88/9.15 thf(func_def_2428, type, sK915: (nat > real) > (nat > real) > nat).
% 34.88/9.15 thf(func_def_2429, type, sK916: (num > rat) > num).
% 34.88/9.15 thf(func_def_2430, type, sK917: (num > rat) > num).
% 34.88/9.15 thf(func_def_2431, type, sK918: (int > rat) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_2432, type, sK919: set_real > set_complex > (complex > real > $o) > complex).
% 34.88/9.15 thf(func_def_2433, type, sK920: set_real > set_complex > (complex > real > $o) > real).
% 34.88/9.15 thf(func_def_2434, type, sK921: set_real > set_complex > (complex > real > $o) > complex).
% 34.88/9.15 thf(func_def_2435, type, sK922: (complex > real > $o) > set_complex > set_real > complex).
% 34.88/9.15 thf(func_def_2436, type, sK923: list_nat > nat > nat).
% 34.88/9.15 thf(func_def_2437, type, sK924: real > set_real > (real > real) > real > real).
% 34.88/9.15 thf(func_def_2438, type, sK925: set_real > (real > real) > real).
% 34.88/9.15 thf(func_def_2439, type, sK926: (real > int) > set_real > (real > int) > real).
% 34.88/9.15 thf(func_def_2440, type, sK927: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2441, type, sK928: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2442, type, sK929: set_complex > set_complex > (complex > real) > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2443, type, sK930: (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_2444, type, sK931: (num > nat) > num).
% 34.88/9.15 thf(func_def_2445, type, sK932: (num > nat) > num).
% 34.88/9.15 thf(func_def_2446, type, sK933: (rat > num) > rat).
% 34.88/9.15 thf(func_def_2447, type, sK934: (rat > num) > rat).
% 34.88/9.15 thf(func_def_2448, type, sK935: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2449, type, sK936: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2450, type, sK937: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2451, type, sK938: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2452, type, sK939: (rat > rat > $o) > rat).
% 34.88/9.15 thf(func_def_2453, type, sK940: (num > real) > num).
% 34.88/9.15 thf(func_def_2454, type, sK941: (num > real) > num).
% 34.88/9.15 thf(func_def_2455, type, sK942: (int > complex) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_2456, type, sK943: (rat > num) > rat).
% 34.88/9.15 thf(func_def_2457, type, sK944: (rat > num) > rat).
% 34.88/9.15 thf(func_def_2458, type, sK945: real > real > real).
% 34.88/9.15 thf(func_def_2459, type, sK946: nat > extended_enat > nat).
% 34.88/9.15 thf(func_def_2460, type, sK947: set_Pr4811707699266497531nteger > list_Code_integer > list_Code_integer > nat).
% 34.88/9.15 thf(func_def_2461, type, sK948: real > int).
% 34.88/9.15 thf(func_def_2462, type, sK949: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2463, type, sK950: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2464, type, sK951: $o > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2465, type, sK952: $o > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2466, type, sK953: $o > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2467, type, sK954: vEBT_VEBT > $o > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2468, type, sK955: vEBT_VEBT > $o > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2469, type, sK956: vEBT_VEBT > $o > nat).
% 34.88/9.15 thf(func_def_2470, type, sK957: vEBT_VEBT > $o > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2471, type, sK958: vEBT_VEBT > $o > $o).
% 34.88/9.15 thf(func_def_2472, type, sK959: vEBT_VEBT > $o > $o).
% 34.88/9.15 thf(func_def_2473, type, sK960: set_real > set_real > (real > complex) > set_complex > set_complex > real).
% 34.88/9.15 thf(func_def_2474, type, sK961: (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_2475, type, sK962: set_real > (real > complex) > real).
% 34.88/9.15 thf(func_def_2476, type, sK963: (real > complex) > (complex > real) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2477, type, sK964: set_complex > (complex > complex) > (real > complex) > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2478, type, sK965: set_real > (real > complex) > set_real > (complex > real) > real).
% 34.88/9.15 thf(func_def_2479, type, sK966: set_complex > set_complex > set_real > set_real > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2480, type, sK967: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2481, type, sK968: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2482, type, sK969: set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_2483, type, sK970: (real > rat) > real).
% 34.88/9.15 thf(func_def_2484, type, sK971: (real > rat) > real).
% 34.88/9.15 thf(func_def_2485, type, sK972: (rat > int) > rat).
% 34.88/9.15 thf(func_def_2486, type, sK973: (rat > int) > rat).
% 34.88/9.15 thf(func_def_2487, type, sK974: (nat > complex) > nat).
% 34.88/9.15 thf(func_def_2488, type, sK975: set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2489, type, sK976: (list_nat > $o) > list_nat).
% 34.88/9.15 thf(func_def_2490, type, sK977: num > num).
% 34.88/9.15 thf(func_def_2491, type, sK978: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2492, type, sK979: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2493, type, sK980: (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2494, type, sK981: (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2495, type, sK982: set_real > (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_2496, type, sK983: set_real > set_real > (real > nat) > real).
% 34.88/9.15 thf(func_def_2497, type, sK984: set_real > (real > nat) > set_real > (real > nat) > real).
% 34.88/9.15 thf(func_def_2498, type, sK985: set_nat > nat).
% 34.88/9.15 thf(func_def_2499, type, sK986: nat > set_nat > nat).
% 34.88/9.15 thf(func_def_2500, type, sK987: set_Pr2101469702781467981_o_nat > list_o > list_nat > nat).
% 34.88/9.15 thf(func_def_2501, type, sK988: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_2502, type, sK989: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_2503, type, sK990: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2504, type, sK991: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2505, type, sK992: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2506, type, sK993: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2507, type, sK994: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2508, type, sK995: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2509, type, sK996: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2510, type, sK997: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2511, type, sK998: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2512, type, sK999: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2513, type, sK1000: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2514, type, sK1001: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2515, type, sK1002: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2516, type, sK1003: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2517, type, sK1004: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2518, type, sK1005: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2519, type, sK1006: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2520, type, sK1007: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2521, type, sK1008: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2522, type, sK1009: nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_2523, type, sK1010: nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_2524, type, sK1011: int > set_int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2525, type, sK1012: int > set_int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2526, type, sK1013: (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2527, type, sK1014: (int > $o) > int).
% 34.88/9.15 thf(func_def_2528, type, sK1015: int > (int > $o) > (int > $o) > int).
% 34.88/9.15 thf(func_def_2529, type, sK1016: set_int > int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2530, type, sK1017: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2531, type, sK1018: int > (int > $o) > int).
% 34.88/9.15 thf(func_def_2532, type, sK1019: (int > nat) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_2533, type, sK1020: set_complex > rat > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_2534, type, sK1021: set_real > (int > real > $o) > set_int > int).
% 34.88/9.15 thf(func_def_2535, type, sK1022: set_real > (int > real > $o) > set_int > real).
% 34.88/9.15 thf(func_def_2536, type, sK1023: set_real > (int > real > $o) > set_int > int).
% 34.88/9.15 thf(func_def_2537, type, sK1024: set_real > set_int > (int > real > $o) > int).
% 34.88/9.15 thf(func_def_2538, type, sK1025: set_nat > nat).
% 34.88/9.15 thf(func_def_2539, type, sK1026: set_nat > nat).
% 34.88/9.15 thf(func_def_2540, type, sK1027: set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2541, type, sK1028: set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_2542, type, sK1029: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2543, type, sK1030: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2544, type, sK1031: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2545, type, sK1032: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2546, type, sK1033: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2547, type, sK1034: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2548, type, sK1035: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2549, type, sK1036: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2550, type, sK1037: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2551, type, sK1038: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2552, type, sK1039: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2553, type, sK1040: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2554, type, sK1041: set_complex > (complex > rat) > complex > complex).
% 34.88/9.15 thf(func_def_2555, type, sK1042: (int > real) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_2556, type, sK1043: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2557, type, sK1044: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2558, type, sK1045: (nat > real) > real).
% 34.88/9.15 thf(func_def_2559, type, sK1046: real > real).
% 34.88/9.15 thf(func_def_2560, type, sK1047: real > set_real > real).
% 34.88/9.15 thf(func_def_2561, type, sK1048: set_real > (real > real) > (real > real) > (real > real) > real).
% 34.88/9.15 thf(func_def_2562, type, sK1049: set_real > set_real > (real > real) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_2563, type, sK1050: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2564, type, sK1051: (real > real) > set_real > set_real > set_real > set_real > real).
% 34.88/9.15 thf(func_def_2565, type, sK1052: set_real > (real > real) > (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2566, type, sK1053: (real > real) > (real > real) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_2567, type, sK1054: set_real > (real > real) > real).
% 34.88/9.15 thf(func_def_2568, type, sK1055: int > list_int > nat).
% 34.88/9.15 thf(func_def_2569, type, sK1056: (option_nat > option_num > $o) > option_num > option_nat > nat).
% 34.88/9.15 thf(func_def_2570, type, sK1057: (option_nat > option_num > $o) > option_num > option_nat > num).
% 34.88/9.15 thf(func_def_2571, type, sK1058: code_integer > code_integer > set_int > (int > code_integer) > int).
% 34.88/9.15 thf(func_def_2572, type, sK1059: set_int > (int > code_integer) > int).
% 34.88/9.15 thf(func_def_2573, type, sK1060: option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2574, type, sK1061: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2575, type, sK1062: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2576, type, sK1063: (nat > real) > (nat > real) > set_nat > nat).
% 34.88/9.15 thf(func_def_2577, type, sK1064: real > (nat > real) > nat > int).
% 34.88/9.15 thf(func_def_2578, type, sK1065: list_int > list_int > nat).
% 34.88/9.15 thf(func_def_2579, type, sK1066: nat > rat > nat).
% 34.88/9.15 thf(func_def_2580, type, sK1067: nat > nat > nat).
% 34.88/9.15 thf(func_def_2581, type, sK1068: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2582, type, sK1069: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2583, type, sK1070: (nat > nat) > set_nat > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2584, type, sK1071: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2585, type, sK1072: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2586, type, sK1073: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2587, type, sK1074: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2588, type, sK1075: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2589, type, sK1076: set_int > (int > nat) > set_int > int).
% 34.88/9.15 thf(func_def_2590, type, sK1077: set_Pr6167073792073659919T_VEBT > list_nat > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2591, type, sK1078: nat > (product_prod_nat_nat > $o) > list_P6011104703257516679at_nat > nat).
% 34.88/9.15 thf(func_def_2592, type, sK1079: product_prod_nat_nat > (product_prod_nat_nat > $o) > list_P6011104703257516679at_nat > nat).
% 34.88/9.15 thf(func_def_2593, type, sK1080: (complex > real) > set_complex > complex).
% 34.88/9.15 thf(func_def_2594, type, sK1081: $o > list_o > $o).
% 34.88/9.15 thf(func_def_2595, type, sK1082: int > int > int > int).
% 34.88/9.15 thf(func_def_2596, type, sK1083: set_nat > list_set_nat > set_nat).
% 34.88/9.15 thf(func_def_2597, type, sK1084: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2598, type, sK1085: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_2599, type, sK1086: real > nat > real).
% 34.88/9.15 thf(func_def_2600, type, sK1087: set_int > (int > nat) > int).
% 34.88/9.15 thf(func_def_2601, type, sK1088: int > set_int > (int > nat) > int).
% 34.88/9.15 thf(func_def_2602, type, sK1089: nat > nat).
% 34.88/9.15 thf(func_def_2603, type, sK1090: (num > int) > num).
% 34.88/9.15 thf(func_def_2604, type, sK1091: (num > int) > num).
% 34.88/9.15 thf(func_def_2605, type, sK1092: rat > set_rat > rat).
% 34.88/9.15 thf(func_def_2606, type, sK1093: real > (real > $o) > real).
% 34.88/9.15 thf(func_def_2607, type, sK1094: real > (real > $o) > real).
% 34.88/9.15 thf(func_def_2608, type, sK1095: real > (real > $o) > real).
% 34.88/9.15 thf(func_def_2609, type, sK1096: real > (real > $o) > real).
% 34.88/9.15 thf(func_def_2610, type, sK1097: (real > num) > real).
% 34.88/9.15 thf(func_def_2611, type, sK1098: (real > num) > real).
% 34.88/9.15 thf(func_def_2612, type, sK1099: (nat > nat) > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2613, type, sK1100: nat > (num > $o) > list_num > nat).
% 34.88/9.15 thf(func_def_2614, type, sK1101: num > (num > $o) > list_num > nat).
% 34.88/9.15 thf(func_def_2615, type, sK1102: (nat > rat) > set_nat > rat > nat).
% 34.88/9.15 thf(func_def_2616, type, sK1103: set_complex > (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2617, type, sK1104: set_complex > (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2618, type, sK1105: nat > (nat > int) > nat).
% 34.88/9.15 thf(func_def_2619, type, sK1106: nat > (nat > int) > int > nat).
% 34.88/9.15 thf(func_def_2620, type, sK1107: int > nat).
% 34.88/9.15 thf(func_def_2621, type, sK1108: int > nat).
% 34.88/9.15 thf(func_def_2622, type, sK1109: real > real).
% 34.88/9.15 thf(func_def_2623, type, sK1110: set_real > real).
% 34.88/9.15 thf(func_def_2624, type, sK1111: (int > rat) > (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_2625, type, sK1112: (product_prod_int_int > $o) > int).
% 34.88/9.15 thf(func_def_2626, type, sK1113: (product_prod_int_int > $o) > int).
% 34.88/9.15 thf(func_def_2627, type, sK1114: set_complex > complex).
% 34.88/9.15 thf(func_def_2628, type, sK1115: set_complex > complex).
% 34.88/9.15 thf(func_def_2629, type, sK1116: set_complex > complex).
% 34.88/9.15 thf(func_def_2630, type, sK1117: real > real > real).
% 34.88/9.15 thf(func_def_2631, type, sK1118: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2632, type, sK1119: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2633, type, sK1120: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2634, type, sK1121: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2635, type, sK1122: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2636, type, sK1123: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2637, type, sK1124: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2638, type, sK1125: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2639, type, sK1126: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2640, type, sK1127: (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_2641, type, sK1128: set_real > (real > nat) > nat > real).
% 34.88/9.15 thf(func_def_2642, type, sK1129: real > real > real > real).
% 34.88/9.15 thf(func_def_2643, type, sK1130: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2644, type, sK1131: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2645, type, sK1132: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2646, type, sK1133: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2647, type, sK1134: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2648, type, sK1135: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2649, type, sK1136: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2650, type, sK1137: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2651, type, sK1138: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2652, type, sK1139: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2653, type, sK1140: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2654, type, sK1141: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2655, type, sK1142: (nat > complex) > set_nat > nat).
% 34.88/9.15 thf(func_def_2656, type, sK1143: list_nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2657, type, sK1144: list_nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2658, type, sK1145: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2659, type, sK1146: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_2660, type, sK1147: set_int > int).
% 34.88/9.15 thf(func_def_2661, type, sK1148: set_int > int).
% 34.88/9.15 thf(func_def_2662, type, sK1149: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2663, type, sK1150: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2664, type, sK1151: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2665, type, sK1152: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_2666, type, sK1153: (complex > complex) > (complex > complex) > (complex > complex > $o) > set_complex > complex).
% 34.88/9.15 thf(func_def_2667, type, sK1154: (real > nat) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_2668, type, sK1155: (real > nat) > (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_2669, type, sK1156: set_nat > list_set_nat > nat).
% 34.88/9.15 thf(func_def_2670, type, sK1157: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2671, type, sK1158: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2672, type, sK1159: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2673, type, sK1160: nat > vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2674, type, sK1161: nat > vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2675, type, sK1162: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2676, type, sK1163: set_complex > set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_2677, type, sK1164: set_complex > set_complex > (complex > int) > complex).
% 34.88/9.15 thf(func_def_2678, type, sK1165: (real > real) > real).
% 34.88/9.15 thf(func_def_2679, type, sK1166: (real > real) > real).
% 34.88/9.15 thf(func_def_2680, type, sK1167: rat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2681, type, sK1168: set_num > num > num).
% 34.88/9.15 thf(func_def_2682, type, sK1169: set_real > (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2683, type, sK1170: (real > real) > (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2684, type, sK1171: list_VEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2685, type, sK1172: real > nat).
% 34.88/9.15 thf(func_def_2686, type, sK1173: (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2687, type, sK1174: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2688, type, sK1175: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2689, type, sK1176: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2690, type, sK1177: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2691, type, sK1178: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2692, type, sK1179: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2693, type, sK1180: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2694, type, sK1181: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2695, type, sK1182: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2696, type, sK1183: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2697, type, sK1184: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2698, type, sK1185: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2699, type, sK1186: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2700, type, sK1187: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2701, type, sK1188: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2702, type, sK1189: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2703, type, sK1190: (nat > nat) > set_nat > nat).
% 34.88/9.15 thf(func_def_2704, type, sK1191: (int > real) > set_int > real > int).
% 34.88/9.15 thf(func_def_2705, type, sK1192: nat > list_P6011104703257516679at_nat > (product_prod_nat_nat > $o) > nat).
% 34.88/9.15 thf(func_def_2706, type, sK1193: product_prod_nat_nat > list_P6011104703257516679at_nat > (product_prod_nat_nat > $o) > nat).
% 34.88/9.15 thf(func_def_2707, type, sK1194: int > int > set_int > int).
% 34.88/9.15 thf(func_def_2708, type, sK1195: set_int > int).
% 34.88/9.15 thf(func_def_2709, type, sK1196: set_int > int).
% 34.88/9.15 thf(func_def_2710, type, sK1197: (int > nat) > int > set_int > int).
% 34.88/9.15 thf(func_def_2711, type, sK1198: real > real > real).
% 34.88/9.15 thf(func_def_2712, type, sK1199: set_Pr5066593544530342725BT_int > list_int > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2713, type, sK1200: option_num > num).
% 34.88/9.15 thf(func_def_2714, type, sK1201: (num > num > num) > option_num > option_num > option_num > num).
% 34.88/9.15 thf(func_def_2715, type, sK1202: (num > num > num) > option_num > option_num > option_num > num).
% 34.88/9.15 thf(func_def_2716, type, sK1203: set_nat > nat > nat).
% 34.88/9.15 thf(func_def_2717, type, sK1204: (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_2718, type, sK1205: int > (nat > int) > nat > nat).
% 34.88/9.15 thf(func_def_2719, type, sK1206: (int > nat) > set_int > nat > int).
% 34.88/9.15 thf(func_def_2720, type, sK1207: rat > rat > rat).
% 34.88/9.15 thf(func_def_2721, type, sK1208: set_nat > nat).
% 34.88/9.15 thf(func_def_2722, type, sK1209: nat > real > real).
% 34.88/9.15 thf(func_def_2723, type, sK1210: (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2724, type, sK1211: option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2725, type, sK1212: (real > rat) > real).
% 34.88/9.15 thf(func_def_2726, type, sK1213: (real > rat) > real).
% 34.88/9.15 thf(func_def_2727, type, sK1214: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2728, type, sK1215: vEBT_VEBT > nat > $o > nat).
% 34.88/9.15 thf(func_def_2729, type, sK1216: vEBT_VEBT > nat > $o > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2730, type, sK1217: vEBT_VEBT > nat > $o > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2731, type, sK1218: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2732, type, sK1219: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2733, type, sK1220: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2734, type, sK1221: (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_2735, type, sK1222: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2736, type, sK1223: (real > nat > $o) > set_real > set_nat > nat > nat).
% 34.88/9.15 thf(func_def_2737, type, sK1224: set_complex > (int > rat) > (complex > int) > set_int > (complex > rat) > int).
% 34.88/9.15 thf(func_def_2738, type, sK1225: set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_2739, type, sK1226: set_set_nat > set_nat).
% 34.88/9.15 thf(func_def_2740, type, sK1227: (int > int > $o) > set_int > set_int > nat > int).
% 34.88/9.15 thf(func_def_2741, type, sK1228: nat > list_num > (num > $o) > nat).
% 34.88/9.15 thf(func_def_2742, type, sK1229: list_num > (num > $o) > num > nat).
% 34.88/9.15 thf(func_def_2743, type, sK1230: (num > real) > num).
% 34.88/9.15 thf(func_def_2744, type, sK1231: (num > real) > num).
% 34.88/9.15 thf(func_def_2745, type, sK1232: (nat > set_nat) > nat).
% 34.88/9.15 thf(func_def_2746, type, sK1233: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2747, type, sK1234: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2748, type, sK1235: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2749, type, sK1236: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_2750, type, sK1237: (nat > real) > set_nat > (nat > real) > (real > real > $o) > nat).
% 34.88/9.15 thf(func_def_2751, type, sK1238: (int > code_integer) > set_int > code_integer > int).
% 34.88/9.15 thf(func_def_2752, type, sK1239: set_complex > set_complex > (complex > complex) > complex).
% 34.88/9.15 thf(func_def_2753, type, sK1240: (int > real) > int).
% 34.88/9.15 thf(func_def_2754, type, sK1241: (int > real) > int).
% 34.88/9.15 thf(func_def_2755, type, sK1242: set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.15 thf(func_def_2756, type, sK1243: nat > (nat > real) > real > nat).
% 34.88/9.15 thf(func_def_2757, type, sK1244: (real > code_integer) > set_real > real).
% 34.88/9.15 thf(func_def_2758, type, sK1245: nat > nat).
% 34.88/9.15 thf(func_def_2759, type, sK1246: set_list_nat > nat > set_list_nat).
% 34.88/9.15 thf(func_def_2760, type, sK1247: set_list_nat > nat > list_nat).
% 34.88/9.15 thf(func_def_2761, type, sK1248: (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2762, type, sK1249: set_real > real).
% 34.88/9.15 thf(func_def_2763, type, sK1250: set_real > real).
% 34.88/9.15 thf(func_def_2764, type, sK1251: (real > $o) > list_real > nat).
% 34.88/9.15 thf(func_def_2765, type, sK1252: (product_prod_nat_nat > $o) > nat).
% 34.88/9.15 thf(func_def_2766, type, sK1253: nat > (product_prod_nat_nat > $o) > nat).
% 34.88/9.15 thf(func_def_2767, type, sK1254: nat > (product_prod_nat_nat > $o) > nat).
% 34.88/9.15 thf(func_def_2768, type, sK1255: set_int > (int > rat) > (int > rat) > int).
% 34.88/9.15 thf(func_def_2769, type, sK1256: set_complex > complex).
% 34.88/9.15 thf(func_def_2770, type, sK1257: set_complex > complex).
% 34.88/9.15 thf(func_def_2771, type, sK1258: nat > list_nat > nat).
% 34.88/9.15 thf(func_def_2772, type, sK1259: (int > real) > int).
% 34.88/9.15 thf(func_def_2773, type, sK1260: (int > real) > int).
% 34.88/9.15 thf(func_def_2774, type, sK1261: (nat > nat) > set_nat > nat).
% 34.88/9.15 thf(func_def_2775, type, sK1262: real > nat).
% 34.88/9.15 thf(func_def_2776, type, sK1263: real > int).
% 34.88/9.15 thf(func_def_2777, type, sK1264: (int > real) > set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_2778, type, sK1265: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2779, type, sK1266: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2780, type, sK1267: (produc859450856879609959at_nat > $o) > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2781, type, sK1268: (produc859450856879609959at_nat > $o) > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2782, type, sK1269: set_int > (int > int) > int).
% 34.88/9.15 thf(func_def_2783, type, sK1270: (nat > real) > nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_2784, type, sK1271: (nat > real) > nat > (nat > real) > real).
% 34.88/9.15 thf(func_def_2785, type, sK1272: set_complex > (complex > complex) > complex).
% 34.88/9.15 thf(func_def_2786, type, sK1273: int > int).
% 34.88/9.15 thf(func_def_2787, type, sK1274: set_int > set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_2788, type, sK1275: int > int > int).
% 34.88/9.15 thf(func_def_2789, type, sK1276: nat > nat).
% 34.88/9.15 thf(func_def_2790, type, sK1277: set_nat > nat > set_nat).
% 34.88/9.15 thf(func_def_2791, type, sK1278: set_nat > nat > nat).
% 34.88/9.15 thf(func_def_2792, type, sK1279: real > set_list_nat > (list_nat > complex) > list_nat).
% 34.88/9.15 thf(func_def_2793, type, sK1280: nat > $o > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2794, type, sK1281: nat > $o > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2795, type, sK1282: $o > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2796, type, sK1283: $o > vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2797, type, sK1284: $o > vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2798, type, sK1285: $o > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2799, type, sK1286: vEBT_VEBT > nat > $o > nat).
% 34.88/9.15 thf(func_def_2800, type, sK1287: vEBT_VEBT > nat > $o > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2801, type, sK1288: vEBT_VEBT > nat > $o > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2802, type, sK1289: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2803, type, sK1290: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2804, type, sK1291: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2805, type, sK1292: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2806, type, sK1293: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2807, type, sK1294: nat > $o > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2808, type, sK1295: nat > $o > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2809, type, sK1296: vEBT_VEBT > nat > (vEBT_VEBT > $o) > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2810, type, sK1297: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2811, type, sK1298: list_nat > nat > nat).
% 34.88/9.15 thf(func_def_2812, type, sK1299: list_nat > nat > list_nat).
% 34.88/9.15 thf(func_def_2813, type, sK1300: set_int > real > (int > real) > int).
% 34.88/9.15 thf(func_def_2814, type, sK1301: (int > num) > (set_int > $o) > set_int).
% 34.88/9.15 thf(func_def_2815, type, sK1302: (int > num) > (set_int > $o) > int).
% 34.88/9.15 thf(func_def_2816, type, sK1303: int > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2817, type, sK1304: (real > complex) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_2818, type, sK1305: set_real > set_real > (real > complex) > real).
% 34.88/9.15 thf(func_def_2819, type, sK1306: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2820, type, sK1307: (nat > real) > nat).
% 34.88/9.15 thf(func_def_2821, type, sK1308: set_int > (int > rat) > rat > int).
% 34.88/9.15 thf(func_def_2822, type, sK1309: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2823, type, sK1310: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2824, type, sK1311: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2825, type, sK1312: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2826, type, sK1313: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2827, type, sK1314: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2828, type, sK1315: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2829, type, sK1316: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2830, type, sK1317: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2831, type, sK1318: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2832, type, sK1319: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2833, type, sK1320: nat > vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2834, type, sK1321: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_2835, type, sK1322: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_2836, type, sK1323: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2837, type, sK1324: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2838, type, sK1325: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2839, type, sK1326: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2840, type, sK1327: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2841, type, sK1328: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2842, type, sK1329: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2843, type, sK1330: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2844, type, sK1331: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2845, type, sK1332: set_real > (nat > real > $o) > set_nat > nat).
% 34.88/9.15 thf(func_def_2846, type, sK1333: set_real > (nat > real > $o) > set_nat > nat).
% 34.88/9.15 thf(func_def_2847, type, sK1334: set_real > (nat > real > $o) > set_nat > real).
% 34.88/9.15 thf(func_def_2848, type, sK1335: set_nat > set_real > (nat > real > $o) > nat).
% 34.88/9.15 thf(func_def_2849, type, sK1336: (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_2850, type, sK1337: (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_2851, type, sK1338: real > (int > real) > real > set_int > int).
% 34.88/9.15 thf(func_def_2852, type, sK1339: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2853, type, sK1340: set_set_nat > nat > set_nat).
% 34.88/9.15 thf(func_def_2854, type, sK1341: set_set_nat > nat > set_set_nat).
% 34.88/9.15 thf(func_def_2855, type, sK1342: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2856, type, sK1343: (rat > real) > rat).
% 34.88/9.15 thf(func_def_2857, type, sK1344: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2858, type, sK1345: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2859, type, sK1346: (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2860, type, sK1347: set_nat > set_nat > (nat > complex) > nat).
% 34.88/9.15 thf(func_def_2861, type, sK1348: nat > $o > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2862, type, sK1349: nat > $o > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2863, type, sK1350: nat > $o > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2864, type, sK1351: nat > $o > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2865, type, sK1352: $o > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2866, type, sK1353: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2867, type, sK1354: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2868, type, sK1355: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2869, type, sK1356: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2870, type, sK1357: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2871, type, sK1358: vEBT_VEBT > $o > nat > nat).
% 34.88/9.15 thf(func_def_2872, type, sK1359: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2873, type, sK1360: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2874, type, sK1361: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2875, type, sK1362: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2876, type, sK1363: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2877, type, sK1364: (int > nat) > set_int > (int > nat) > int).
% 34.88/9.15 thf(func_def_2878, type, sK1365: set_complex > (complex > nat) > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_2879, type, sK1366: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2880, type, sK1367: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2881, type, sK1368: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2882, type, sK1369: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2883, type, sK1370: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2884, type, sK1371: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2885, type, sK1372: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2886, type, sK1373: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2887, type, sK1374: vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2888, type, sK1375: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2889, type, sK1376: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2890, type, sK1377: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2891, type, sK1378: nat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2892, type, sK1379: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_2893, type, sK1380: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_2894, type, sK1381: nat > nat).
% 34.88/9.15 thf(func_def_2895, type, sK1382: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2896, type, sK1383: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2897, type, sK1384: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2898, type, sK1385: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2899, type, sK1386: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2900, type, sK1387: vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2901, type, sK1388: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2902, type, sK1389: vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2903, type, sK1390: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2904, type, sK1391: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2905, type, sK1392: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2906, type, sK1393: vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2907, type, sK1394: vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2908, type, sK1395: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2909, type, sK1396: vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2910, type, sK1397: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2911, type, sK1398: (list_VEBT_VEBT > $o) > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2912, type, sK1399: list_list_nat > nat > list_nat).
% 34.88/9.15 thf(func_def_2913, type, sK1400: (set_nat > $o) > (set_nat > $o) > set_nat).
% 34.88/9.15 thf(func_def_2914, type, sK1401: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2915, type, sK1402: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2916, type, sK1403: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_2917, type, sK1404: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2918, type, sK1405: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2919, type, sK1406: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2920, type, sK1407: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_2921, type, sK1408: real > (nat > real) > real).
% 34.88/9.15 thf(func_def_2922, type, sK1409: (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_2923, type, sK1410: (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_2924, type, sK1411: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2925, type, sK1412: set_complex > (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2926, type, sK1413: (complex > rat) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_2927, type, sK1414: int > (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2928, type, sK1415: int > (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2929, type, sK1416: int > (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2930, type, sK1417: int > (int > $o) > int > int).
% 34.88/9.15 thf(func_def_2931, type, sK1418: (nat > num) > nat).
% 34.88/9.15 thf(func_def_2932, type, sK1419: (nat > num) > nat).
% 34.88/9.15 thf(func_def_2933, type, sK1420: (real > nat) > nat > set_real > real).
% 34.88/9.15 thf(func_def_2934, type, sK1421: (int > rat) > int).
% 34.88/9.15 thf(func_def_2935, type, sK1422: (int > rat) > int).
% 34.88/9.15 thf(func_def_2936, type, sK1423: (nat > nat) > set_nat > nat).
% 34.88/9.15 thf(func_def_2937, type, sK1424: produc859450856879609959at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2938, type, sK1425: produc859450856879609959at_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_2939, type, sK1426: nat > (nat > int) > nat).
% 34.88/9.15 thf(func_def_2940, type, sK1427: nat > int > (nat > int) > nat).
% 34.88/9.15 thf(func_def_2941, type, sK1428: set_real > (real > real) > real > real).
% 34.88/9.15 thf(func_def_2942, type, sK1429: (nat > num) > nat).
% 34.88/9.15 thf(func_def_2943, type, sK1430: (nat > num) > nat).
% 34.88/9.15 thf(func_def_2944, type, sK1431: set_int > (int > real) > (int > real) > int).
% 34.88/9.15 thf(func_def_2945, type, sK1432: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_2946, type, sK1433: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2947, type, sK1434: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_2948, type, sK1435: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_2949, type, sK1436: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2950, type, sK1437: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_2951, type, sK1438: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_2952, type, sK1439: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2953, type, sK1440: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_2954, type, sK1441: rat > nat).
% 34.88/9.15 thf(func_def_2955, type, sK1442: (nat > real) > set_nat > nat).
% 34.88/9.15 thf(func_def_2956, type, sK1443: (nat > $o) > nat > list_nat > nat).
% 34.88/9.15 thf(func_def_2957, type, sK1444: nat > (nat > $o) > list_nat > nat).
% 34.88/9.15 thf(func_def_2958, type, sK1445: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2959, type, sK1446: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_2960, type, sK1447: (nat > complex) > nat > nat).
% 34.88/9.15 thf(func_def_2961, type, sK1448: (nat > complex) > nat > complex > complex).
% 34.88/9.15 thf(func_def_2962, type, sK1449: set_nat > nat).
% 34.88/9.15 thf(func_def_2963, type, sK1450: set_nat > nat).
% 34.88/9.15 thf(func_def_2964, type, sK1451: set_nat > nat).
% 34.88/9.15 thf(func_def_2965, type, sK1452: set_complex > (complex > nat) > set_complex > complex).
% 34.88/9.15 thf(func_def_2966, type, sK1453: (real > rat) > set_real > (real > rat) > real).
% 34.88/9.15 thf(func_def_2967, type, sK1454: (nat > nat) > (nat > nat) > nat).
% 34.88/9.15 thf(func_def_2968, type, sK1455: nat > list_int).
% 34.88/9.15 thf(func_def_2969, type, sK1456: list_VEBT_VEBT > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_2970, type, sK1457: nat > nat).
% 34.88/9.15 thf(func_def_2971, type, sK1458: real > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2972, type, sK1459: (nat > complex) > nat > (nat > complex) > nat).
% 34.88/9.15 thf(func_def_2973, type, sK1460: (nat > complex) > nat > (nat > complex) > complex).
% 34.88/9.15 thf(func_def_2974, type, sK1461: produc8923325533196201883nteger > code_integer).
% 34.88/9.15 thf(func_def_2975, type, sK1462: produc8923325533196201883nteger > code_integer).
% 34.88/9.15 thf(func_def_2976, type, sK1463: (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_2977, type, sK1464: set_real > real).
% 34.88/9.15 thf(func_def_2978, type, sK1465: produc4471711990508489141at_nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_2979, type, sK1466: produc4471711990508489141at_nat > nat).
% 34.88/9.15 thf(func_def_2980, type, sK1467: produc4471711990508489141at_nat > nat).
% 34.88/9.15 thf(func_def_2981, type, sK1468: produc4471711990508489141at_nat > nat).
% 34.88/9.15 thf(func_def_2982, type, sK1469: nat > (nat > $o) > nat > nat).
% 34.88/9.15 thf(func_def_2983, type, sK1470: (nat > real) > (nat > real) > set_nat > nat).
% 34.88/9.15 thf(func_def_2984, type, sK1471: int > int > int).
% 34.88/9.15 thf(func_def_2985, type, sK1472: (real > complex) > set_real > real > real).
% 34.88/9.15 thf(func_def_2986, type, sK1473: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_2987, type, sK1474: int > int).
% 34.88/9.15 thf(func_def_2988, type, sK1475: real > real > nat).
% 34.88/9.15 thf(func_def_2989, type, sK1476: (real > nat) > set_real > real).
% 34.88/9.15 thf(func_def_2990, type, sK1477: rat > rat).
% 34.88/9.15 thf(func_def_2991, type, sK1478: set_nat > (nat > complex) > set_nat > nat).
% 34.88/9.15 thf(func_def_2992, type, sK1479: list_o > list_complex > complex > $o).
% 34.88/9.15 thf(func_def_2993, type, sK1480: set_int > (int > complex) > set_int > int).
% 34.88/9.15 thf(func_def_2994, type, sK1481: nat > vEBT_VEBT > (vEBT_VEBT > $o) > vEBT_VEBT).
% 34.88/9.15 thf(func_def_2995, type, sK1482: (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_2996, type, sK1483: (nat > num) > nat).
% 34.88/9.15 thf(func_def_2997, type, sK1484: (nat > num) > nat).
% 34.88/9.15 thf(func_def_2998, type, sK1485: (int > $o) > int > int > int).
% 34.88/9.15 thf(func_def_2999, type, sK1486: int > (int > $o) > int > int).
% 34.88/9.15 thf(func_def_3000, type, sK1487: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3001, type, sK1488: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3002, type, sK1489: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3003, type, sK1490: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3004, type, sK1491: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3005, type, sK1492: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_3006, type, sK1493: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3007, type, sK1494: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3008, type, sK1495: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3009, type, sK1496: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_3010, type, sK1497: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3011, type, sK1498: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3012, type, sK1499: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3013, type, sK1500: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3014, type, sK1501: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3015, type, sK1502: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3016, type, sK1503: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3017, type, sK1504: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3018, type, sK1505: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3019, type, sK1506: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3020, type, sK1507: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3021, type, sK1508: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3022, type, sK1509: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3023, type, sK1510: set_int > set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_3024, type, sK1511: (int > rat) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_3025, type, sK1512: set_int > (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_3026, type, sK1513: set_int > (int > real) > (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_3027, type, sK1514: set_int > (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_3028, type, sK1515: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_3029, type, sK1516: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_3030, type, sK1517: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_3031, type, sK1518: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_3032, type, sK1519: (nat > nat > $o) > nat).
% 34.88/9.15 thf(func_def_3033, type, sK1520: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_3034, type, sK1521: (nat > $o) > $o).
% 34.88/9.15 thf(func_def_3035, type, sK1522: (nat > $o) > nat).
% 34.88/9.15 thf(func_def_3036, type, sK1523: (nat > rat) > rat).
% 34.88/9.15 thf(func_def_3037, type, sK1524: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_3038, type, sK1525: set_int > (int > real) > (int > real) > int).
% 34.88/9.15 thf(func_def_3039, type, sK1526: set_nat > (nat > code_integer) > set_nat > nat).
% 34.88/9.15 thf(func_def_3040, type, sK1527: produc7036089656553540234on_num > num).
% 34.88/9.15 thf(func_def_3041, type, sK1528: produc7036089656553540234on_num > num).
% 34.88/9.15 thf(func_def_3042, type, sK1529: produc7036089656553540234on_num > num > num > $o).
% 34.88/9.15 thf(func_def_3043, type, sK1530: produc7036089656553540234on_num > num > num > $o).
% 34.88/9.15 thf(func_def_3044, type, sK1531: produc7036089656553540234on_num > num).
% 34.88/9.15 thf(func_def_3045, type, sK1532: produc7036089656553540234on_num > num > num > $o).
% 34.88/9.15 thf(func_def_3046, type, sK1533: produc7036089656553540234on_num > option_num).
% 34.88/9.15 thf(func_def_3047, type, sK1534: set_Pr4811707699266497531nteger > code_integer).
% 34.88/9.15 thf(func_def_3048, type, sK1535: (int > nat) > set_int > int).
% 34.88/9.15 thf(func_def_3049, type, sK1536: rat > rat > rat).
% 34.88/9.15 thf(func_def_3050, type, sK1537: (int > nat) > set_int > int).
% 34.88/9.15 thf(func_def_3051, type, sK1538: real > nat).
% 34.88/9.15 thf(func_def_3052, type, sK1539: real > nat).
% 34.88/9.15 thf(func_def_3053, type, sK1540: set_set_nat > set_nat).
% 34.88/9.15 thf(func_def_3054, type, sK1541: set_set_nat > set_nat).
% 34.88/9.15 thf(func_def_3055, type, sK1542: set_nat > set_nat > set_set_nat > set_nat).
% 34.88/9.15 thf(func_def_3056, type, sK1543: (nat > int) > (nat > int) > nat).
% 34.88/9.15 thf(func_def_3057, type, sK1544: num > num).
% 34.88/9.15 thf(func_def_3058, type, sK1545: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_3059, type, sK1546: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3060, type, sK1547: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3061, type, sK1548: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3062, type, sK1549: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3063, type, sK1550: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3064, type, sK1551: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3065, type, sK1552: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3066, type, sK1553: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3067, type, sK1554: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3068, type, sK1555: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_3069, type, sK1556: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3070, type, sK1557: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3071, type, sK1558: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3072, type, sK1559: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3073, type, sK1560: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3074, type, sK1561: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_3075, type, sK1562: (real > real > $o) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3076, type, sK1563: (real > real > $o) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3077, type, sK1564: (real > real > $o) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3078, type, sK1565: set_real > set_real > (real > real > $o) > real).
% 34.88/9.15 thf(func_def_3079, type, sK1566: (rat > real) > rat).
% 34.88/9.15 thf(func_def_3080, type, sK1567: (rat > real) > rat).
% 34.88/9.15 thf(func_def_3081, type, sK1568: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3082, type, sK1569: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3083, type, sK1570: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3084, type, sK1571: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3085, type, sK1572: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3086, type, sK1573: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3087, type, sK1574: vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3088, type, sK1575: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3089, type, sK1576: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3090, type, sK1577: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3091, type, sK1578: nat > list_VEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3092, type, sK1579: nat > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3093, type, sK1580: real > nat).
% 34.88/9.15 thf(func_def_3094, type, sK1581: complex > list_complex > nat).
% 34.88/9.15 thf(func_def_3095, type, sK1582: (nat > real) > set_nat > real > nat).
% 34.88/9.15 thf(func_def_3096, type, sK1583: (nat > $o) > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_3097, type, sK1584: real > real > (real > $o) > real).
% 34.88/9.15 thf(func_def_3098, type, sK1585: real > real > (real > $o) > real).
% 34.88/9.15 thf(func_def_3099, type, sK1586: real > int).
% 34.88/9.15 thf(func_def_3100, type, sK1587: (nat > int) > nat).
% 34.88/9.15 thf(func_def_3101, type, sK1588: set_nat > (nat > code_integer) > nat).
% 34.88/9.15 thf(func_def_3102, type, sK1589: (rat > num) > rat).
% 34.88/9.15 thf(func_def_3103, type, sK1590: (rat > num) > rat).
% 34.88/9.15 thf(func_def_3104, type, sK1591: (real > $o) > list_real > real).
% 34.88/9.15 thf(func_def_3105, type, sK1592: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3106, type, sK1593: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3107, type, sK1594: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3108, type, sK1595: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3109, type, sK1596: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3110, type, sK1597: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3111, type, sK1598: nat > vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3112, type, sK1599: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3113, type, sK1600: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3114, type, sK1601: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3115, type, sK1602: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_3116, type, sK1603: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.15 thf(func_def_3117, type, sK1604: vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3118, type, sK1605: vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3119, type, sK1606: vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3120, type, sK1607: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3121, type, sK1608: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3122, type, sK1609: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3123, type, sK1610: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3124, type, sK1611: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3125, type, sK1612: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3126, type, sK1613: vEBT_VEBT > vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3127, type, sK1614: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3128, type, sK1615: list_nat > nat > list_nat > set_Pr1261947904930325089at_nat > list_nat).
% 34.88/9.15 thf(func_def_3129, type, sK1616: list_nat > nat > list_nat > set_Pr1261947904930325089at_nat > nat).
% 34.88/9.15 thf(func_def_3130, type, sK1617: nat > nat > nat).
% 34.88/9.15 thf(func_def_3131, type, sK1618: vEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3132, type, sK1619: (nat > real) > nat).
% 34.88/9.15 thf(func_def_3133, type, sK1620: (nat > real) > nat).
% 34.88/9.15 thf(func_def_3134, type, sK1621: list_o > set_Pr8834758594704517033_o_int > list_int > nat).
% 34.88/9.15 thf(func_def_3135, type, sK1622: int > nat).
% 34.88/9.15 thf(func_def_3136, type, sK1623: (nat > real) > nat > int).
% 34.88/9.15 thf(func_def_3137, type, sK1624: set_real > (real > real) > set_real > real).
% 34.88/9.15 thf(func_def_3138, type, sK1625: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3139, type, sK1626: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3140, type, sK1627: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3141, type, sK1628: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3142, type, sK1629: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3143, type, sK1630: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3144, type, sK1631: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3145, type, sK1632: (nat > rat) > set_nat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_3146, type, sK1633: list_VEBT_VEBT > (vEBT_VEBT > $o) > nat).
% 34.88/9.15 thf(func_def_3147, type, sK1634: list_VEBT_VEBT > (vEBT_VEBT > $o) > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3148, type, sK1635: (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_3149, type, sK1636: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_3150, type, sK1637: (rat > nat) > rat).
% 34.88/9.15 thf(func_def_3151, type, sK1638: nat > list_nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_3152, type, sK1639: nat > list_nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_3153, type, sK1640: (complex > real) > set_complex > complex).
% 34.88/9.15 thf(func_def_3154, type, sK1641: nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_3155, type, sK1642: (real > $o) > (real > $o) > real).
% 34.88/9.15 thf(func_def_3156, type, sK1643: (nat > int) > set_nat > nat).
% 34.88/9.15 thf(func_def_3157, type, sK1644: (rat > int) > rat).
% 34.88/9.15 thf(func_def_3158, type, sK1645: (rat > int) > rat).
% 34.88/9.15 thf(func_def_3159, type, sK1646: (rat > int) > rat).
% 34.88/9.15 thf(func_def_3160, type, sK1647: (rat > int) > rat).
% 34.88/9.15 thf(func_def_3161, type, sK1648: set_int > set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_3162, type, sK1649: set_int > (int > rat) > set_int > int).
% 34.88/9.15 thf(func_def_3163, type, sK1650: (nat > $o) > list_nat > nat).
% 34.88/9.15 thf(func_def_3164, type, sK1651: (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_3165, type, sK1652: nat > (nat > int > $o) > int).
% 34.88/9.15 thf(func_def_3166, type, sK1653: list_int > nat > (nat > int > $o) > nat).
% 34.88/9.15 thf(func_def_3167, type, sK1654: nat > (nat > int > $o) > list_int).
% 34.88/9.15 thf(func_def_3168, type, sK1655: nat > (nat > int > $o) > nat).
% 34.88/9.15 thf(func_def_3169, type, sK1656: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3170, type, sK1657: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3171, type, sK1658: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3172, type, sK1659: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3173, type, sK1660: (complex > complex) > set_complex > (complex > complex) > (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3174, type, sK1661: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3175, type, sK1662: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3176, type, sK1663: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3177, type, sK1664: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3178, type, sK1665: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3179, type, sK1666: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3180, type, sK1667: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3181, type, sK1668: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3182, type, sK1669: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3183, type, sK1670: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3184, type, sK1671: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3185, type, sK1672: vEBT_VEBT > nat > nat).
% 34.88/9.15 thf(func_def_3186, type, sK1673: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3187, type, sK1674: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3188, type, sK1675: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3189, type, sK1676: vEBT_VEBT > $o).
% 34.88/9.15 thf(func_def_3190, type, sK1677: nat > set_list_nat > set_list_nat).
% 34.88/9.15 thf(func_def_3191, type, sK1678: nat > set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_3192, type, sK1679: set_nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_3193, type, sK1680: (real > nat) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3194, type, sK1681: (real > nat) > set_real > (real > nat) > real).
% 34.88/9.15 thf(func_def_3195, type, sK1682: (int > $o) > nat).
% 34.88/9.15 thf(func_def_3196, type, sK1683: (int > $o) > nat).
% 34.88/9.15 thf(func_def_3197, type, sK1684: set_int > (int > real) > int).
% 34.88/9.15 thf(func_def_3198, type, sK1685: nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_3199, type, sK1686: nat > nat > nat > nat).
% 34.88/9.15 thf(func_def_3200, type, sK1687: set_list_nat > list_nat).
% 34.88/9.15 thf(func_def_3201, type, sK1688: (real > num) > (set_real > $o) > real).
% 34.88/9.15 thf(func_def_3202, type, sK1689: (real > num) > (set_real > $o) > set_real).
% 34.88/9.15 thf(func_def_3203, type, sK1690: set_real > (real > nat) > real).
% 34.88/9.15 thf(func_def_3204, type, sK1691: (real > rat) > real).
% 34.88/9.15 thf(func_def_3205, type, sK1692: (real > rat) > real).
% 34.88/9.15 thf(func_def_3206, type, sK1693: (real > code_integer) > set_real > real).
% 34.88/9.15 thf(func_def_3207, type, sK1694: list_real > list_VEBT_VEBT > real > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3208, type, sK1695: (nat > num) > (set_nat > $o) > nat).
% 34.88/9.15 thf(func_def_3209, type, sK1696: (nat > num) > (set_nat > $o) > set_nat).
% 34.88/9.15 thf(func_def_3210, type, sK1697: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_3211, type, sK1698: (rat > rat) > rat).
% 34.88/9.15 thf(func_def_3212, type, sK1699: set_complex > (complex > code_integer) > complex).
% 34.88/9.15 thf(func_def_3213, type, sK1700: num > num).
% 34.88/9.15 thf(func_def_3214, type, sK1701: real > nat).
% 34.88/9.15 thf(func_def_3215, type, sK1702: set_nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_3216, type, sK1703: (complex > rat) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_3217, type, sK1704: real > real).
% 34.88/9.15 thf(func_def_3218, type, sK1705: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3219, type, sK1706: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3220, type, sK1707: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3221, type, sK1708: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3222, type, sK1709: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3223, type, sK1710: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3224, type, sK1711: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3225, type, sK1712: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3226, type, sK1713: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3227, type, sK1714: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3228, type, sK1715: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3229, type, sK1716: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3230, type, sK1717: nat > set_nat > nat).
% 34.88/9.15 thf(func_def_3231, type, sK1718: (nat > real) > real).
% 34.88/9.15 thf(func_def_3232, type, sK1719: nat > (nat > real) > nat).
% 34.88/9.15 thf(func_def_3233, type, sK1720: (nat > $o) > nat > nat > nat).
% 34.88/9.15 thf(func_def_3234, type, sK1721: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3235, type, sK1722: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3236, type, sK1723: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3237, type, sK1724: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3238, type, sK1725: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3239, type, sK1726: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3240, type, sK1727: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3241, type, sK1728: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3242, type, sK1729: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3243, type, sK1730: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3244, type, sK1731: nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3245, type, sK1732: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3246, type, sK1733: (option_num > option_num > $o) > option_num > option_num > num).
% 34.88/9.15 thf(func_def_3247, type, sK1734: (option_num > option_num > $o) > option_num > option_num > num).
% 34.88/9.15 thf(func_def_3248, type, sK1735: nat > nat > nat).
% 34.88/9.15 thf(func_def_3249, type, sK1736: (complex > real) > set_complex > set_complex > complex).
% 34.88/9.15 thf(func_def_3250, type, sK1737: set_real > nat > (real > int > $o) > set_int > int).
% 34.88/9.15 thf(func_def_3251, type, sK1738: list_nat > set_Pr7556676689462069481BT_nat > list_VEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3252, type, sK1739: (int > rat) > int).
% 34.88/9.15 thf(func_def_3253, type, sK1740: (int > rat) > int).
% 34.88/9.15 thf(func_def_3254, type, sK1741: product_prod_int_int > int > int > int).
% 34.88/9.15 thf(func_def_3255, type, sK1742: product_prod_int_int > int > int > int).
% 34.88/9.15 thf(func_def_3256, type, sK1743: int > int > product_prod_int_int > int).
% 34.88/9.15 thf(func_def_3257, type, sK1744: complex > real).
% 34.88/9.15 thf(func_def_3258, type, sK1745: complex > real).
% 34.88/9.15 thf(func_def_3259, type, sK1746: (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_3260, type, sK1747: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3261, type, sK1748: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3262, type, sK1749: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3263, type, sK1750: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3264, type, sK1751: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3265, type, sK1752: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3266, type, sK1753: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3267, type, sK1754: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3268, type, sK1755: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3269, type, sK1756: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3270, type, sK1757: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3271, type, sK1758: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3272, type, sK1759: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3273, type, sK1760: produc9072475918466114483BT_nat > option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3274, type, sK1761: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3275, type, sK1762: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3276, type, sK1763: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3277, type, sK1764: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3278, type, sK1765: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3279, type, sK1766: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3280, type, sK1767: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3281, type, sK1768: nat > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3282, type, sK1769: nat > list_VEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3283, type, sK1770: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3284, type, sK1771: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3285, type, sK1772: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3286, type, sK1773: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_3287, type, sK1774: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3288, type, sK1775: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3289, type, sK1776: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3290, type, sK1777: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3291, type, sK1778: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3292, type, sK1779: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3293, type, sK1780: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3294, type, sK1781: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3295, type, sK1782: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3296, type, sK1783: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3297, type, sK1784: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3298, type, sK1785: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3299, type, sK1786: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3300, type, sK1787: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3301, type, sK1788: produc9072475918466114483BT_nat > product_prod_nat_nat).
% 34.88/9.15 thf(func_def_3302, type, sK1789: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3303, type, sK1790: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3304, type, sK1791: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3305, type, sK1792: produc9072475918466114483BT_nat > nat).
% 34.88/9.15 thf(func_def_3306, type, sK1793: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3307, type, sK1794: produc9072475918466114483BT_nat > $o).
% 34.88/9.15 thf(func_def_3308, type, sK1795: set_nat > nat > nat).
% 34.88/9.15 thf(func_def_3309, type, sK1796: set_int > real > (int > real) > int).
% 34.88/9.15 thf(func_def_3310, type, sK1797: (nat > rat) > rat).
% 34.88/9.15 thf(func_def_3311, type, sK1798: nat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_3312, type, sK1799: rat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_3313, type, sK1800: (nat > rat) > nat).
% 34.88/9.15 thf(func_def_3314, type, sK1801: list_o > ($o > $o) > $o).
% 34.88/9.15 thf(func_def_3315, type, sK1802: (real > rat) > set_real > rat > rat > real).
% 34.88/9.15 thf(func_def_3316, type, sK1803: (real > rat) > set_real > real).
% 34.88/9.15 thf(func_def_3317, type, sK1804: nat > ($o > $o) > list_o > nat).
% 34.88/9.15 thf(func_def_3318, type, sK1805: ($o > $o) > list_o > $o > nat).
% 34.88/9.15 thf(func_def_3319, type, sK1806: nat > real > (real > $o) > real).
% 34.88/9.15 thf(func_def_3320, type, sK1807: list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3321, type, sK1808: set_int > (int > rat) > (int > rat) > int).
% 34.88/9.15 thf(func_def_3322, type, sK1809: rat > set_int > (int > rat) > int).
% 34.88/9.15 thf(func_def_3323, type, sK1810: (rat > int) > rat).
% 34.88/9.15 thf(func_def_3324, type, sK1811: (rat > int) > rat).
% 34.88/9.15 thf(func_def_3325, type, sK1812: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3326, type, sK1813: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3327, type, sK1814: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3328, type, sK1815: (complex > complex > $o) > complex).
% 34.88/9.15 thf(func_def_3329, type, sK1816: (complex > complex > $o) > (int > complex) > (int > complex) > set_int > int).
% 34.88/9.15 thf(func_def_3330, type, sK1817: (int > nat) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_3331, type, sK1818: real > nat).
% 34.88/9.15 thf(func_def_3332, type, sK1819: (int > real) > (real > real > $o) > (int > real) > set_int > int).
% 34.88/9.15 thf(func_def_3333, type, sK1820: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_3334, type, sK1821: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_3335, type, sK1822: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_3336, type, sK1823: (real > real > $o) > real).
% 34.88/9.15 thf(func_def_3337, type, sK1824: nat > nat).
% 34.88/9.15 thf(func_def_3338, type, sK1825: nat > (nat > $o) > nat).
% 34.88/9.15 thf(func_def_3339, type, sK1826: set_real > nat > (complex > real > $o) > set_complex > real).
% 34.88/9.15 thf(func_def_3340, type, sK1827: $o > list_o > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3341, type, sK1828: list_int > list_VEBT_VEBT > int > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3342, type, sK1829: vEBT_VEBT > nat > nat > nat).
% 34.88/9.15 thf(func_def_3343, type, sK1830: (int > complex) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_3344, type, sK1831: (int > complex) > (int > complex) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_3345, type, sK1832: (int > complex) > set_int > set_int > int).
% 34.88/9.15 thf(func_def_3346, type, sK1833: nat > real > real).
% 34.88/9.15 thf(func_def_3347, type, sK1834: (real > complex > $o) > set_complex > set_real > nat > complex).
% 34.88/9.15 thf(func_def_3348, type, sK1835: (real > rat) > set_real > rat > real).
% 34.88/9.15 thf(func_def_3349, type, sK1836: (real > real) > real).
% 34.88/9.15 thf(func_def_3350, type, sK1837: (real > real) > real).
% 34.88/9.15 thf(func_def_3351, type, sK1838: set_nat > set_real > (real > nat > $o) > nat).
% 34.88/9.15 thf(func_def_3352, type, sK1839: set_nat > set_real > (real > nat > $o) > real).
% 34.88/9.15 thf(func_def_3353, type, sK1840: set_nat > set_real > (real > nat > $o) > real).
% 34.88/9.15 thf(func_def_3354, type, sK1841: set_real > set_nat > (real > nat > $o) > real).
% 34.88/9.15 thf(func_def_3355, type, sK1842: (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_3356, type, sK1843: set_nat > (nat > rat) > (nat > nat) > (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_3357, type, sK1844: rat > rat > rat).
% 34.88/9.15 thf(func_def_3358, type, sK1845: ($o > $o) > list_o > nat).
% 34.88/9.15 thf(func_def_3359, type, sK1846: ($o > $o) > list_o > $o).
% 34.88/9.15 thf(func_def_3360, type, sK1847: set_nat > (nat > rat) > nat).
% 34.88/9.15 thf(func_def_3361, type, sK1848: set_complex > (complex > real) > complex).
% 34.88/9.15 thf(func_def_3362, type, sK1849: list_o > ($o > $o) > nat).
% 34.88/9.15 thf(func_def_3363, type, sK1850: (complex > rat) > set_complex > complex).
% 34.88/9.15 thf(func_def_3364, type, sK1851: (nat > vEBT_VEBT > $o) > nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3365, type, sK1852: (nat > vEBT_VEBT > $o) > nat > nat).
% 34.88/9.15 thf(func_def_3366, type, sK1853: nat > (nat > vEBT_VEBT > $o) > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3367, type, sK1854: list_VEBT_VEBT > (nat > vEBT_VEBT > $o) > nat > nat).
% 34.88/9.15 thf(func_def_3368, type, sK1855: vEBT_VEBT > option_nat > nat).
% 34.88/9.15 thf(func_def_3369, type, sK1856: vEBT_VEBT > option_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3370, type, sK1857: vEBT_VEBT > option_nat > nat).
% 34.88/9.15 thf(func_def_3371, type, sK1858: vEBT_VEBT > option_nat > nat).
% 34.88/9.15 thf(func_def_3372, type, sK1859: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3373, type, sK1860: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_3374, type, sK1861: vEBT_VEBT > option_nat > $o).
% 34.88/9.15 thf(func_def_3375, type, sK1862: vEBT_VEBT > option_nat > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3376, type, sK1863: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3377, type, sK1864: vEBT_VEBT > option_nat > nat).
% 34.88/9.15 thf(func_def_3378, type, sK1865: (int > $o) > list_int > int).
% 34.88/9.15 thf(func_def_3379, type, sK1866: set_complex > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_3380, type, sK1867: nat > rat > (nat > rat) > nat > rat).
% 34.88/9.15 thf(func_def_3381, type, sK1868: (num > rat) > num).
% 34.88/9.15 thf(func_def_3382, type, sK1869: (num > rat) > num).
% 34.88/9.15 thf(func_def_3383, type, sK1870: set_complex > (complex > real) > complex > complex).
% 34.88/9.15 thf(func_def_3384, type, sK1871: (real > real) > (real > real) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3385, type, sK1872: (real > real) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3386, type, sK1873: (real > real) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3387, type, sK1874: (set_real > $o) > (real > rat) > real).
% 34.88/9.15 thf(func_def_3388, type, sK1875: (set_real > $o) > (real > rat) > set_real).
% 34.88/9.15 thf(func_def_3389, type, sK1876: nat > set_real > real).
% 34.88/9.15 thf(func_def_3390, type, sK1877: nat > set_real > set_real).
% 34.88/9.15 thf(func_def_3391, type, sK1878: list_o > $o > nat).
% 34.88/9.15 thf(func_def_3392, type, sK1879: list_nat > nat > nat).
% 34.88/9.15 thf(func_def_3393, type, sK1880: list_nat > nat > list_nat).
% 34.88/9.15 thf(func_def_3394, type, sK1881: (nat > real) > (nat > real) > set_nat > nat).
% 34.88/9.15 thf(func_def_3395, type, sK1882: (complex > rat) > set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_3396, type, sK1883: set_complex > set_complex > (complex > rat) > complex).
% 34.88/9.15 thf(func_def_3397, type, sK1884: (complex > nat) > set_complex > (complex > nat) > complex).
% 34.88/9.15 thf(func_def_3398, type, sK1885: set_real > set_real > (real > complex) > real).
% 34.88/9.15 thf(func_def_3399, type, sK1886: (real > complex) > set_real > set_real > real).
% 34.88/9.15 thf(func_def_3400, type, sK1887: produc1193250871479095198on_num > num > num > num).
% 34.88/9.15 thf(func_def_3401, type, sK1888: produc1193250871479095198on_num > num).
% 34.88/9.15 thf(func_def_3402, type, sK1889: produc1193250871479095198on_num > num).
% 34.88/9.15 thf(func_def_3403, type, sK1890: produc1193250871479095198on_num > num > num > num).
% 34.88/9.15 thf(func_def_3404, type, sK1891: produc1193250871479095198on_num > num).
% 34.88/9.15 thf(func_def_3405, type, sK1892: produc1193250871479095198on_num > option_num).
% 34.88/9.15 thf(func_def_3406, type, sK1893: produc1193250871479095198on_num > num > num > num).
% 34.88/9.15 thf(func_def_3407, type, sK1894: set_nat > nat).
% 34.88/9.15 thf(func_def_3408, type, sK1895: set_nat > nat).
% 34.88/9.15 thf(func_def_3409, type, sK1896: (nat > rat) > set_nat > nat).
% 34.88/9.15 thf(func_def_3410, type, sK1897: rat > rat).
% 34.88/9.15 thf(func_def_3411, type, sK1898: option4927543243414619207at_nat).
% 34.88/9.15 thf(func_def_3412, type, sK1899: vEBT_VEBT).
% 34.88/9.15 thf(func_def_3413, type, sK1900: list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3414, type, sK1901: (nat > int) > nat > nat).
% 34.88/9.15 thf(func_def_3415, type, sK1902: (nat > int) > nat > nat).
% 34.88/9.15 thf(func_def_3416, type, sK1903: option_nat > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3417, type, sK1904: option_nat > nat > vEBT_VEBT > nat).
% 34.88/9.15 thf(func_def_3418, type, sK1905: option_nat > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.15 thf(func_def_3419, type, sK1906: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.15 thf(func_def_3420, type, sK1907: option_nat > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3421, type, sK1908: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3422, type, sK1909: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3423, type, sK1910: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.16 thf(func_def_3424, type, sK1911: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.16 thf(func_def_3425, type, sK1912: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3426, type, sK1913: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3427, type, sK1914: nat > nat).
% 34.88/9.16 thf(func_def_3428, type, sK1915: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3429, type, sK1916: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3430, type, sK1917: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3431, type, sK1918: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3432, type, sK1919: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3433, type, sK1920: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3434, type, sK1921: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3435, type, sK1922: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3436, type, sK1923: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3437, type, sK1924: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_3438, type, sK1925: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_3439, type, sK1926: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_3440, type, sK1927: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_3441, type, sK1928: set_real > (real > code_integer) > real).
% 34.88/9.16 thf(func_def_3442, type, sK1929: set_Pr6192946355708809607T_VEBT > list_VEBT_VEBT > list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3443, type, sK1930: real > (real > $o) > real).
% 34.88/9.16 thf(func_def_3444, type, sK1931: real > (real > $o) > real).
% 34.88/9.16 thf(func_def_3445, type, sK1932: (real > $o) > real > real).
% 34.88/9.16 thf(func_def_3446, type, sK1933: (real > $o) > real > real).
% 34.88/9.16 thf(func_def_3447, type, sK1934: (nat > complex) > set_nat > real > nat).
% 34.88/9.16 thf(func_def_3448, type, sK1935: real > list_real > list_nat > nat).
% 34.88/9.16 thf(func_def_3449, type, sK1936: set_int > set_int > (int > complex) > int).
% 34.88/9.16 thf(func_def_3450, type, sK1937: set_int > (int > complex) > (int > complex) > int).
% 34.88/9.16 thf(func_def_3451, type, sK1938: ($o > $o) > list_o > $o).
% 34.88/9.16 thf(func_def_3452, type, sK1939: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3453, type, sK1940: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3454, type, sK1941: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3455, type, sK1942: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3456, type, sK1943: (complex > code_integer) > (code_integer > code_integer > $o) > (complex > code_integer) > set_complex > complex).
% 34.88/9.16 thf(func_def_3457, type, sK1944: set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_3458, type, sK1945: rat > rat).
% 34.88/9.16 thf(func_def_3459, type, sK1946: real > (real > real) > real > real).
% 34.88/9.16 thf(func_def_3460, type, sK1947: real > (real > real) > real > real).
% 34.88/9.16 thf(func_def_3461, type, sK1948: real > real > (real > real) > real).
% 34.88/9.16 thf(func_def_3462, type, sK1949: set_int > set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_3463, type, sK1950: set_real > (real > int) > set_real > real).
% 34.88/9.16 thf(func_def_3464, type, sK1951: nat > set_int > int).
% 34.88/9.16 thf(func_def_3465, type, sK1952: nat > set_int > set_int).
% 34.88/9.16 thf(func_def_3466, type, sK1953: nat > nat > nat).
% 34.88/9.16 thf(func_def_3467, type, sK1954: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3468, type, sK1955: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3469, type, sK1956: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3470, type, sK1957: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3471, type, sK1958: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3472, type, sK1959: set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_3473, type, sK1960: set_complex > real > (complex > real) > real > complex).
% 34.88/9.16 thf(func_def_3474, type, sK1961: list_int > nat > list_int).
% 34.88/9.16 thf(func_def_3475, type, sK1962: list_int > nat > int).
% 34.88/9.16 thf(func_def_3476, type, sK1963: (rat > num) > rat).
% 34.88/9.16 thf(func_def_3477, type, sK1964: (rat > num) > rat).
% 34.88/9.16 thf(func_def_3478, type, sK1965: produc7272778201969148633d_enat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3479, type, sK1966: produc7272778201969148633d_enat > nat).
% 34.88/9.16 thf(func_def_3480, type, sK1967: produc7272778201969148633d_enat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3481, type, sK1968: produc7272778201969148633d_enat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3482, type, sK1969: produc7272778201969148633d_enat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3483, type, sK1970: produc7272778201969148633d_enat > nat).
% 34.88/9.16 thf(func_def_3484, type, sK1971: produc7272778201969148633d_enat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3485, type, sK1972: produc7272778201969148633d_enat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3486, type, sK1973: produc7272778201969148633d_enat > nat).
% 34.88/9.16 thf(func_def_3487, type, sK1974: produc7272778201969148633d_enat > extended_enat).
% 34.88/9.16 thf(func_def_3488, type, sK1975: produc7272778201969148633d_enat > $o).
% 34.88/9.16 thf(func_def_3489, type, sK1976: produc7272778201969148633d_enat > $o).
% 34.88/9.16 thf(func_def_3490, type, sK1977: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3491, type, sK1978: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3492, type, sK1979: (num > nat) > num).
% 34.88/9.16 thf(func_def_3493, type, sK1980: (num > nat) > num).
% 34.88/9.16 thf(func_def_3494, type, sK1981: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3495, type, sK1982: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3496, type, sK1983: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3497, type, sK1984: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3498, type, sK1985: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3499, type, sK1986: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3500, type, sK1987: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3501, type, sK1988: produc859450856879609959at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3502, type, sK1989: produc859450856879609959at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3503, type, sK1990: rat > rat > nat).
% 34.88/9.16 thf(func_def_3504, type, sK1991: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3505, type, sK1992: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3506, type, sK1993: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3507, type, sK1994: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3508, type, sK1995: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3509, type, sK1996: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3510, type, sK1997: set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_3511, type, sK1998: real > int).
% 34.88/9.16 thf(func_def_3512, type, sK1999: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3513, type, sK2000: nat > nat > nat).
% 34.88/9.16 thf(func_def_3514, type, sK2001: set_real > (real > real) > set_real > real).
% 34.88/9.16 thf(func_def_3515, type, sK2002: set_real > (real > real) > real).
% 34.88/9.16 thf(func_def_3516, type, sK2003: (int > $o) > int > int).
% 34.88/9.16 thf(func_def_3517, type, sK2004: (nat > int) > nat).
% 34.88/9.16 thf(func_def_3518, type, sK2005: (num > rat) > num).
% 34.88/9.16 thf(func_def_3519, type, sK2006: (num > rat) > num).
% 34.88/9.16 thf(func_def_3520, type, sK2007: (nat > real) > nat > nat).
% 34.88/9.16 thf(func_def_3521, type, sK2008: (nat > real) > nat > nat).
% 34.88/9.16 thf(func_def_3522, type, sK2009: (real > int) > real).
% 34.88/9.16 thf(func_def_3523, type, sK2010: (real > int) > real).
% 34.88/9.16 thf(func_def_3524, type, sK2011: nat > set_complex > complex).
% 34.88/9.16 thf(func_def_3525, type, sK2012: nat > set_complex > set_complex).
% 34.88/9.16 thf(func_def_3526, type, sK2013: (real > real) > (real > real) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_3527, type, sK2014: set_real > (real > complex) > (real > complex) > (real > real) > real).
% 34.88/9.16 thf(func_def_3528, type, sK2015: set_real > set_real > (real > real) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_3529, type, sK2016: (real > complex) > set_real > real).
% 34.88/9.16 thf(func_def_3530, type, sK2017: (real > real) > (real > real) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_3531, type, sK2018: (real > real) > set_real > set_real > set_real > set_real > real).
% 34.88/9.16 thf(func_def_3532, type, sK2019: (real > complex) > set_real > real).
% 34.88/9.16 thf(func_def_3533, type, sK2020: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3534, type, sK2021: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3535, type, sK2022: (int > $o) > int > int).
% 34.88/9.16 thf(func_def_3536, type, sK2023: (int > $o) > int > int).
% 34.88/9.16 thf(func_def_3537, type, sK2024: (int > $o) > int > int).
% 34.88/9.16 thf(func_def_3538, type, sK2025: (int > $o) > int).
% 34.88/9.16 thf(func_def_3539, type, sK2026: (real > nat) > set_real > real).
% 34.88/9.16 thf(func_def_3540, type, sK2027: (int > complex) > (int > complex) > set_int > int).
% 34.88/9.16 thf(func_def_3541, type, sK2028: (int > complex) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_3542, type, sK2029: set_real > (real > complex) > (real > complex) > set_real > real).
% 34.88/9.16 thf(func_def_3543, type, sK2030: set_real > (real > complex) > set_real > real).
% 34.88/9.16 thf(func_def_3544, type, sK2031: set_real > (real > complex) > set_real > real).
% 34.88/9.16 thf(func_def_3545, type, sK2032: (real > real) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_3546, type, sK2033: (real > real) > (real > real) > set_real > real).
% 34.88/9.16 thf(func_def_3547, type, sK2034: (complex > real) > set_complex > complex).
% 34.88/9.16 thf(func_def_3548, type, sK2035: (nat > rat) > rat > nat).
% 34.88/9.16 thf(func_def_3549, type, sK2036: set_nat > (nat > nat) > nat).
% 34.88/9.16 thf(func_def_3550, type, sK2037: set_int > (int > complex) > set_int > int).
% 34.88/9.16 thf(func_def_3551, type, sK2038: (int > complex) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_3552, type, sK2039: nat > (nat > rat) > set_nat > nat).
% 34.88/9.16 thf(func_def_3553, type, sK2040: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3554, type, sK2041: nat > (nat > real) > real).
% 34.88/9.16 thf(func_def_3555, type, sK2042: nat > (nat > real) > nat).
% 34.88/9.16 thf(func_def_3556, type, sK2043: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3557, type, sK2044: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3558, type, sK2045: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3559, type, sK2046: rat > set_rat > rat).
% 34.88/9.16 thf(func_def_3560, type, sK2047: set_real > (real > real) > real).
% 34.88/9.16 thf(func_def_3561, type, sK2048: (rat > int) > rat).
% 34.88/9.16 thf(func_def_3562, type, sK2049: (rat > int) > rat).
% 34.88/9.16 thf(func_def_3563, type, sK2050: nat > nat).
% 34.88/9.16 thf(func_def_3564, type, sK2051: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3565, type, sK2052: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3566, type, sK2053: nat > option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3567, type, sK2054: nat > option_nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3568, type, sK2055: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3569, type, sK2056: nat > option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3570, type, sK2057: nat > option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3571, type, sK2058: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3572, type, sK2059: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3573, type, sK2060: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3574, type, sK2061: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3575, type, sK2062: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3576, type, sK2063: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3577, type, sK2064: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3578, type, sK2065: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3579, type, sK2066: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3580, type, sK2067: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3581, type, sK2068: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3582, type, sK2069: set_int > set_int > (real > int) > (int > real) > int).
% 34.88/9.16 thf(func_def_3583, type, sK2070: (int > complex) > set_int > int).
% 34.88/9.16 thf(func_def_3584, type, sK2071: set_real > (real > complex) > (int > complex) > (real > int) > real).
% 34.88/9.16 thf(func_def_3585, type, sK2072: (real > int) > set_int > set_int > set_real > set_real > real).
% 34.88/9.16 thf(func_def_3586, type, sK2073: set_real > (real > complex) > real).
% 34.88/9.16 thf(func_def_3587, type, sK2074: set_int > set_real > set_real > set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_3588, type, sK2075: (real > int) > set_real > set_real > (int > real) > real).
% 34.88/9.16 thf(func_def_3589, type, sK2076: set_Pr8693737435421807431at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3590, type, sK2077: list_nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3591, type, sK2078: product_prod_nat_nat > nat).
% 34.88/9.16 thf(func_def_3592, type, sK2079: product_prod_nat_nat > nat).
% 34.88/9.16 thf(func_def_3593, type, sK2080: set_int > int).
% 34.88/9.16 thf(func_def_3594, type, sK2081: produc8923325533196201883nteger > code_integer).
% 34.88/9.16 thf(func_def_3595, type, sK2082: produc8923325533196201883nteger > code_integer).
% 34.88/9.16 thf(func_def_3596, type, sK2083: set_complex > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_3597, type, sK2084: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3598, type, sK2085: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3599, type, sK2086: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3600, type, sK2087: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3601, type, sK2088: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3602, type, sK2089: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3603, type, sK2090: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3604, type, sK2091: set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_3605, type, sK2092: real > real).
% 34.88/9.16 thf(func_def_3606, type, sK2093: (int > int > $o) > int).
% 34.88/9.16 thf(func_def_3607, type, sK2094: set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_3608, type, sK2095: set_nat > (nat > complex) > nat).
% 34.88/9.16 thf(func_def_3609, type, sK2096: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3610, type, sK2097: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3611, type, sK2098: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3612, type, sK2099: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_3613, type, sK2100: (code_integer > code_integer > $o) > (int > code_integer) > set_int > (int > code_integer) > int).
% 34.88/9.16 thf(func_def_3614, type, sK2101: (option_nat > option_nat > $o) > option_nat > option_nat > nat).
% 34.88/9.16 thf(func_def_3615, type, sK2102: (option_nat > option_nat > $o) > option_nat > option_nat > nat).
% 34.88/9.16 thf(func_def_3616, type, sK2103: (int > real) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_3617, type, sK2104: (int > real) > set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_3618, type, sK2105: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3619, type, sK2106: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3620, type, sK2107: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_3621, type, sK2108: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_3622, type, sK2109: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_3623, type, sK2110: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_3624, type, sK2111: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_3625, type, sK2112: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_3626, type, sK2113: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_3627, type, sK2114: (int > $o) > int > int > int).
% 34.88/9.16 thf(func_def_3628, type, sK2115: (int > $o) > int > int > int).
% 34.88/9.16 thf(func_def_3629, type, sK2116: int > int > (int > $o) > int).
% 34.88/9.16 thf(func_def_3630, type, sK2117: int > int > (int > $o) > int).
% 34.88/9.16 thf(func_def_3631, type, sK2118: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3632, type, sK2119: list_real > list_int > real > int).
% 34.88/9.16 thf(func_def_3633, type, sK2120: (real > rat) > set_real > real).
% 34.88/9.16 thf(func_def_3634, type, sK2121: (nat > $o) > nat > nat).
% 34.88/9.16 thf(func_def_3635, type, sK2122: vEBT_VEBT > nat > $o > $o).
% 34.88/9.16 thf(func_def_3636, type, sK2123: vEBT_VEBT > nat > $o > $o).
% 34.88/9.16 thf(func_def_3637, type, sK2124: vEBT_VEBT > $o > nat > nat).
% 34.88/9.16 thf(func_def_3638, type, sK2125: vEBT_VEBT > $o > nat > nat).
% 34.88/9.16 thf(func_def_3639, type, sK2126: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3640, type, sK2127: vEBT_VEBT > $o > nat > nat).
% 34.88/9.16 thf(func_def_3641, type, sK2128: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3642, type, sK2129: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3643, type, sK2130: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3644, type, sK2131: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3645, type, sK2132: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3646, type, sK2133: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3647, type, sK2134: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3648, type, sK2135: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3649, type, sK2136: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3650, type, sK2137: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3651, type, sK2138: nat > list_o > $o).
% 34.88/9.16 thf(func_def_3652, type, sK2139: nat > list_o > list_o).
% 34.88/9.16 thf(func_def_3653, type, sK2140: rat > rat > rat > rat).
% 34.88/9.16 thf(func_def_3654, type, sK2141: set_list_nat > list_nat).
% 34.88/9.16 thf(func_def_3655, type, sK2142: set_list_nat > list_nat).
% 34.88/9.16 thf(func_def_3656, type, sK2143: set_list_nat > list_nat).
% 34.88/9.16 thf(func_def_3657, type, sK2144: (int > rat) > (int > rat) > set_int > int).
% 34.88/9.16 thf(func_def_3658, type, sK2145: (int > rat) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_3659, type, sK2146: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > list_P6011104703257516679at_nat).
% 34.88/9.16 thf(func_def_3660, type, sK2147: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3661, type, sK2148: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > list_P6011104703257516679at_nat).
% 34.88/9.16 thf(func_def_3662, type, sK2149: list_P6011104703257516679at_nat > list_P8469869581646625389at_nat > list_P6011104703257516679at_nat > produc859450856879609959at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3663, type, sK2150: int > nat).
% 34.88/9.16 thf(func_def_3664, type, sK2151: set_real > (real > rat) > rat > real).
% 34.88/9.16 thf(func_def_3665, type, sK2152: real > list_real > nat).
% 34.88/9.16 thf(func_def_3666, type, sK2153: rat > (rat > $o) > rat).
% 34.88/9.16 thf(func_def_3667, type, sK2154: rat > (rat > $o) > rat).
% 34.88/9.16 thf(func_def_3668, type, sK2155: rat > (rat > $o) > rat).
% 34.88/9.16 thf(func_def_3669, type, sK2156: rat > (rat > $o) > rat).
% 34.88/9.16 thf(func_def_3670, type, sK2157: set_nat > nat > set_nat).
% 34.88/9.16 thf(func_def_3671, type, sK2158: set_nat > nat > nat).
% 34.88/9.16 thf(func_def_3672, type, sK2159: (option_num > option4927543243414619207at_nat > $o) > option_num > option4927543243414619207at_nat > num).
% 34.88/9.16 thf(func_def_3673, type, sK2160: (option_num > option4927543243414619207at_nat > $o) > option_num > option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3674, type, sK2161: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3675, type, sK2162: (int > nat) > set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_3676, type, sK2163: set_nat > (nat > nat) > nat).
% 34.88/9.16 thf(func_def_3677, type, sK2164: nat > set_nat > (nat > nat) > nat).
% 34.88/9.16 thf(func_def_3678, type, sK2165: (num > nat) > num).
% 34.88/9.16 thf(func_def_3679, type, sK2166: (num > nat) > num).
% 34.88/9.16 thf(func_def_3680, type, sK2167: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3681, type, sK2168: (nat > $o) > nat > nat).
% 34.88/9.16 thf(func_def_3682, type, sK2169: (nat > $o > $o) > nat > list_o).
% 34.88/9.16 thf(func_def_3683, type, sK2170: (nat > $o > $o) > nat > nat).
% 34.88/9.16 thf(func_def_3684, type, sK2171: nat > (nat > $o > $o) > $o).
% 34.88/9.16 thf(func_def_3685, type, sK2172: list_o > (nat > $o > $o) > nat > nat).
% 34.88/9.16 thf(func_def_3686, type, sK2173: set_nat > nat > nat).
% 34.88/9.16 thf(func_def_3687, type, sK2174: (produc8923325533196201883nteger > $o) > code_integer).
% 34.88/9.16 thf(func_def_3688, type, sK2175: (produc8923325533196201883nteger > $o) > code_integer).
% 34.88/9.16 thf(func_def_3689, type, sK2176: nat > set_set_nat > set_set_nat).
% 34.88/9.16 thf(func_def_3690, type, sK2177: nat > set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_3691, type, sK2178: set_real > (real > nat) > set_real > real).
% 34.88/9.16 thf(func_def_3692, type, sK2179: list_int > int > nat).
% 34.88/9.16 thf(func_def_3693, type, sK2180: nat > set_complex > complex).
% 34.88/9.16 thf(func_def_3694, type, sK2181: nat > set_complex > set_complex).
% 34.88/9.16 thf(func_def_3695, type, sK2182: (num > $o) > num).
% 34.88/9.16 thf(func_def_3696, type, sK2183: set_real > (real > real) > real).
% 34.88/9.16 thf(func_def_3697, type, sK2184: (real > rat) > real).
% 34.88/9.16 thf(func_def_3698, type, sK2185: (real > rat) > real).
% 34.88/9.16 thf(func_def_3699, type, sK2186: (nat > int) > nat).
% 34.88/9.16 thf(func_def_3700, type, sK2187: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > nat).
% 34.88/9.16 thf(func_def_3701, type, sK2188: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > list_nat).
% 34.88/9.16 thf(func_def_3702, type, sK2189: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > list_nat).
% 34.88/9.16 thf(func_def_3703, type, sK2190: list_nat > product_prod_nat_nat > list_P6011104703257516679at_nat > list_nat > nat).
% 34.88/9.16 thf(func_def_3704, type, sK2191: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3705, type, sK2192: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3706, type, sK2193: set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_3707, type, sK2194: (int > int > $o) > int > int > int).
% 34.88/9.16 thf(func_def_3708, type, sK2195: (int > int > $o) > int > int > int).
% 34.88/9.16 thf(func_def_3709, type, sK2196: (nat > $o) > nat > nat).
% 34.88/9.16 thf(func_def_3710, type, sK2197: (nat > $o) > nat > nat).
% 34.88/9.16 thf(func_def_3711, type, sK2198: real > nat).
% 34.88/9.16 thf(func_def_3712, type, sK2199: real > nat).
% 34.88/9.16 thf(func_def_3713, type, sK2200: nat > nat > nat).
% 34.88/9.16 thf(func_def_3714, type, sK2201: (nat > real > real) > real).
% 34.88/9.16 thf(func_def_3715, type, sK2202: (nat > real > real) > nat).
% 34.88/9.16 thf(func_def_3716, type, sK2203: real > nat > (nat > real > real) > (real > real) > real).
% 34.88/9.16 thf(func_def_3717, type, sK2204: set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_3718, type, sK2205: (complex > real) > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_3719, type, sK2206: list_nat > list_nat).
% 34.88/9.16 thf(func_def_3720, type, sK2207: list_nat > nat).
% 34.88/9.16 thf(func_def_3721, type, sK2208: real > real > (real > real) > real).
% 34.88/9.16 thf(func_def_3722, type, sK2209: real > (real > real) > (real > real) > real > real).
% 34.88/9.16 thf(func_def_3723, type, sK2210: (real > real) > (real > real) > real > real > real).
% 34.88/9.16 thf(func_def_3724, type, sK2211: real > real > (real > real) > real).
% 34.88/9.16 thf(func_def_3725, type, sK2212: (real > real) > real > (real > real) > real > (real > real) > (real > real) > real).
% 34.88/9.16 thf(func_def_3726, type, sK2213: list_complex > complex > complex).
% 34.88/9.16 thf(func_def_3727, type, sK2214: list_o > list_o > nat).
% 34.88/9.16 thf(func_def_3728, type, sK2215: rat > set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_3729, type, sK2216: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3730, type, sK2217: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3731, type, sK2218: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3732, type, sK2219: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3733, type, sK2220: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3734, type, sK2221: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3735, type, sK2222: (nat > nat > nat) > nat).
% 34.88/9.16 thf(func_def_3736, type, sK2223: (product_prod_nat_nat > complex) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3737, type, sK2224: set_complex > (complex > rat) > rat > complex).
% 34.88/9.16 thf(func_def_3738, type, sK2225: int > (int > $o) > int).
% 34.88/9.16 thf(func_def_3739, type, sK2226: int > (int > $o) > int).
% 34.88/9.16 thf(func_def_3740, type, sK2227: (int > $o) > int).
% 34.88/9.16 thf(func_def_3741, type, sK2228: int > (int > $o) > (int > $o) > int).
% 34.88/9.16 thf(func_def_3742, type, sK2229: (complex > real) > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_3743, type, sK2230: nat > real > (nat > real > real) > real > nat).
% 34.88/9.16 thf(func_def_3744, type, sK2231: nat > real > (nat > real > real) > real > real).
% 34.88/9.16 thf(func_def_3745, type, sK2232: real > (real > real) > (nat > real > real) > nat > real > real).
% 34.88/9.16 thf(func_def_3746, type, sK2233: set_real > set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_3747, type, sK2234: set_real > set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_3748, type, sK2235: (complex > nat) > (set_complex > $o) > complex).
% 34.88/9.16 thf(func_def_3749, type, sK2236: (complex > nat) > (set_complex > $o) > set_complex).
% 34.88/9.16 thf(func_def_3750, type, sK2237: nat > list_nat > nat).
% 34.88/9.16 thf(func_def_3751, type, sK2238: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3752, type, sK2239: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3753, type, sK2240: set_int > nat > set_int).
% 34.88/9.16 thf(func_def_3754, type, sK2241: (nat > nat) > nat).
% 34.88/9.16 thf(func_def_3755, type, sK2242: set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_3756, type, sK2243: set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_3757, type, sK2244: (int > int > $o) > int > int > int).
% 34.88/9.16 thf(func_def_3758, type, sK2245: (int > int > $o) > int > int > int).
% 34.88/9.16 thf(func_def_3759, type, sK2246: set_nat > nat > nat).
% 34.88/9.16 thf(func_def_3760, type, sK2247: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3761, type, sK2248: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3762, type, sK2249: list_int > (int > $o) > nat).
% 34.88/9.16 thf(func_def_3763, type, sK2250: list_int > (int > $o) > int).
% 34.88/9.16 thf(func_def_3764, type, sK2251: nat > list_int > list_int).
% 34.88/9.16 thf(func_def_3765, type, sK2252: nat > list_int > int).
% 34.88/9.16 thf(func_def_3766, type, sK2253: (int > nat) > (nat > nat > $o) > (int > nat) > set_int > int).
% 34.88/9.16 thf(func_def_3767, type, sK2254: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3768, type, sK2255: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3769, type, sK2256: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3770, type, sK2257: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3771, type, sK2258: set_int > set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_3772, type, sK2259: set_int > set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_3773, type, sK2260: (real > real) > (nat > real > real) > real > real > nat > real).
% 34.88/9.16 thf(func_def_3774, type, sK2261: nat > (nat > real > real) > real > real > nat).
% 34.88/9.16 thf(func_def_3775, type, sK2262: nat > (nat > real > real) > real > real > real).
% 34.88/9.16 thf(func_def_3776, type, sK2263: nat > nat > nat).
% 34.88/9.16 thf(func_def_3777, type, sK2264: real > (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_3778, type, sK2265: (nat > rat) > rat).
% 34.88/9.16 thf(func_def_3779, type, sK2266: nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_3780, type, sK2267: nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_3781, type, sK2268: (produc3843707927480180839at_nat > $o) > set_Pr1261947904930325089at_nat).
% 34.88/9.16 thf(func_def_3782, type, sK2269: (produc3843707927480180839at_nat > $o) > set_Pr1261947904930325089at_nat).
% 34.88/9.16 thf(func_def_3783, type, sK2270: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_3784, type, sK2271: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_3785, type, sK2272: rat > (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_3786, type, sK2273: (rat > num) > rat).
% 34.88/9.16 thf(func_def_3787, type, sK2274: (rat > num) > rat).
% 34.88/9.16 thf(func_def_3788, type, sK2275: vEBT_VEBT > $o > nat > $o).
% 34.88/9.16 thf(func_def_3789, type, sK2276: vEBT_VEBT > $o > nat > $o).
% 34.88/9.16 thf(func_def_3790, type, sK2277: nat > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3791, type, sK2278: nat > $o > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3792, type, sK2279: nat > $o > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3793, type, sK2280: nat > $o > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3794, type, sK2281: nat > $o > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3795, type, sK2282: rat > set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_3796, type, sK2283: option_num > num).
% 34.88/9.16 thf(func_def_3797, type, sK2284: (rat > real) > rat).
% 34.88/9.16 thf(func_def_3798, type, sK2285: (rat > real) > rat).
% 34.88/9.16 thf(func_def_3799, type, sK2286: set_list_nat > nat > set_list_nat).
% 34.88/9.16 thf(func_def_3800, type, sK2287: nat > nat).
% 34.88/9.16 thf(func_def_3801, type, sK2288: nat > set_nat > (complex > nat > $o) > set_complex > nat).
% 34.88/9.16 thf(func_def_3802, type, sK2289: nat > nat > nat).
% 34.88/9.16 thf(func_def_3803, type, sK2290: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3804, type, sK2291: (nat > num) > nat).
% 34.88/9.16 thf(func_def_3805, type, sK2292: nat > list_nat > list_nat).
% 34.88/9.16 thf(func_def_3806, type, sK2293: nat > list_nat > nat).
% 34.88/9.16 thf(func_def_3807, type, sK2294: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3808, type, sK2295: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3809, type, sK2296: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3810, type, sK2297: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3811, type, sK2298: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3812, type, sK2299: nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3813, type, sK2300: nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3814, type, sK2301: set_set_nat > nat > set_set_nat).
% 34.88/9.16 thf(func_def_3815, type, sK2302: set_set_nat > nat > set_nat).
% 34.88/9.16 thf(func_def_3816, type, sK2303: (vEBT_VEBT > $o) > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3817, type, sK2304: nat > real > (nat > real) > real).
% 34.88/9.16 thf(func_def_3818, type, sK2305: (real > real) > set_real > real).
% 34.88/9.16 thf(func_def_3819, type, sK2306: (real > real) > set_real > real).
% 34.88/9.16 thf(func_def_3820, type, sK2307: complex > (nat > complex) > nat > nat > complex).
% 34.88/9.16 thf(func_def_3821, type, sK2308: set_complex > (complex > int) > (complex > int) > complex).
% 34.88/9.16 thf(func_def_3822, type, sK2309: (rat > $o) > rat > rat).
% 34.88/9.16 thf(func_def_3823, type, sK2310: (rat > $o) > rat > rat).
% 34.88/9.16 thf(func_def_3824, type, sK2311: (rat > $o) > rat > rat).
% 34.88/9.16 thf(func_def_3825, type, sK2312: (rat > $o) > rat > rat).
% 34.88/9.16 thf(func_def_3826, type, sK2313: list_set_nat > (set_nat > $o) > set_nat).
% 34.88/9.16 thf(func_def_3827, type, sK2314: set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_3828, type, sK2315: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3829, type, sK2316: (nat > $o) > nat > nat).
% 34.88/9.16 thf(func_def_3830, type, sK2317: (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_3831, type, sK2318: set_int > (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_3832, type, sK2319: set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_3833, type, sK2320: (nat > rat) > set_nat > rat > rat > nat).
% 34.88/9.16 thf(func_def_3834, type, sK2321: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_3835, type, sK2322: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_3836, type, sK2323: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_3837, type, sK2324: (real > rat) > set_real > real).
% 34.88/9.16 thf(func_def_3838, type, sK2325: (complex > real) > (int > real) > set_int > (complex > int) > set_complex > int).
% 34.88/9.16 thf(func_def_3839, type, sK2326: (complex > real) > set_complex > complex).
% 34.88/9.16 thf(func_def_3840, type, sK2327: nat > extended_enat > nat).
% 34.88/9.16 thf(func_def_3841, type, sK2328: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_3842, type, sK2329: produc5491161045314408544at_nat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3843, type, sK2330: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.16 thf(func_def_3844, type, sK2331: produc5491161045314408544at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3845, type, sK2332: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.16 thf(func_def_3846, type, sK2333: produc5491161045314408544at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3847, type, sK2334: produc5491161045314408544at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_3848, type, sK2335: produc5491161045314408544at_nat > product_prod_nat_nat > product_prod_nat_nat > $o).
% 34.88/9.16 thf(func_def_3849, type, sK2336: list_nat > nat > list_nat).
% 34.88/9.16 thf(func_def_3850, type, sK2337: list_nat > nat > nat).
% 34.88/9.16 thf(func_def_3851, type, sK2338: set_complex > (complex > code_integer) > code_integer > code_integer > complex).
% 34.88/9.16 thf(func_def_3852, type, sK2339: (complex > code_integer) > set_complex > complex).
% 34.88/9.16 thf(func_def_3853, type, sK2340: real > real).
% 34.88/9.16 thf(func_def_3854, type, sK2341: rat > nat).
% 34.88/9.16 thf(func_def_3855, type, sK2342: set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_3856, type, sK2343: set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_3857, type, sK2344: set_complex > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_3858, type, sK2345: set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_3859, type, sK2346: (num > rat) > num).
% 34.88/9.16 thf(func_def_3860, type, sK2347: (num > rat) > num).
% 34.88/9.16 thf(func_def_3861, type, sK2348: set_int > set_complex > (int > complex > $o) > nat > complex).
% 34.88/9.16 thf(func_def_3862, type, sK2349: set_int > set_int > (int > complex) > int).
% 34.88/9.16 thf(func_def_3863, type, sK2350: nat > real > (nat > real > real) > real).
% 34.88/9.16 thf(func_def_3864, type, sK2351: nat > real > (nat > real > real) > nat).
% 34.88/9.16 thf(func_def_3865, type, sK2352: (nat > real > real) > nat > (real > real) > real > real).
% 34.88/9.16 thf(func_def_3866, type, sK2353: set_int > (int > rat) > set_int > int).
% 34.88/9.16 thf(func_def_3867, type, sK2354: set_list_int > nat).
% 34.88/9.16 thf(func_def_3868, type, sK2355: nat > (nat > real) > real > nat > real).
% 34.88/9.16 thf(func_def_3869, type, sK2356: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_3870, type, sK2357: nat > nat > nat).
% 34.88/9.16 thf(func_def_3871, type, sK2358: (real > rat) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_3872, type, sK2359: (real > rat) > (real > rat) > set_real > real).
% 34.88/9.16 thf(func_def_3873, type, sK2360: (complex > real) > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_3874, type, sK2361: set_complex > (complex > real) > set_complex > complex).
% 34.88/9.16 thf(func_def_3875, type, sK2362: set_int > int > int).
% 34.88/9.16 thf(func_def_3876, type, sK2363: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > list_int).
% 34.88/9.16 thf(func_def_3877, type, sK2364: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > int).
% 34.88/9.16 thf(func_def_3878, type, sK2365: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > int).
% 34.88/9.16 thf(func_def_3879, type, sK2366: list_int > list_P5707943133018811711nt_int > product_prod_int_int > list_int > list_int).
% 34.88/9.16 thf(func_def_3880, type, sK2367: (list_int > $o) > list_int).
% 34.88/9.16 thf(func_def_3881, type, sK2368: (nat > num) > nat).
% 34.88/9.16 thf(func_def_3882, type, sK2369: (nat > num) > nat).
% 34.88/9.16 thf(func_def_3883, type, sK2370: list_set_nat > set_nat > nat).
% 34.88/9.16 thf(func_def_3884, type, sK2371: set_nat > (nat > int) > (nat > int) > nat).
% 34.88/9.16 thf(func_def_3885, type, sK2372: set_nat > nat > set_nat).
% 34.88/9.16 thf(func_def_3886, type, sK2373: vEBT_VEBT > vEBT_VEBT > nat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3887, type, sK2374: vEBT_VEBT > vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3888, type, sK2375: vEBT_VEBT > vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3889, type, sK2376: vEBT_VEBT > nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_3890, type, sK2377: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3891, type, sK2378: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3892, type, sK2379: vEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3893, type, sK2380: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3894, type, sK2381: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3895, type, sK2382: vEBT_VEBT > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3896, type, sK2383: vEBT_VEBT > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3897, type, sK2384: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_3898, type, sK2385: vEBT_VEBT > vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_3899, type, sK2386: nat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3900, type, sK2387: nat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3901, type, sK2388: nat > vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3902, type, sK2389: nat > (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3903, type, sK2390: list_nat > nat > (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3904, type, sK2391: nat > (nat > nat > $o) > list_nat).
% 34.88/9.16 thf(func_def_3905, type, sK2392: nat > (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3906, type, sK2393: (nat > real > real) > real > nat > real).
% 34.88/9.16 thf(func_def_3907, type, sK2394: (nat > real > real) > real > nat > nat).
% 34.88/9.16 thf(func_def_3908, type, sK2395: (nat > real > real) > real > nat > (real > real) > real).
% 34.88/9.16 thf(func_def_3909, type, sK2396: set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_3910, type, sK2397: (nat > nat) > set_nat > nat).
% 34.88/9.16 thf(func_def_3911, type, sK2398: nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_3912, type, sK2399: nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_3913, type, sK2400: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3914, type, sK2401: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3915, type, sK2402: (complex > nat) > set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_3916, type, sK2403: (num > num) > num).
% 34.88/9.16 thf(func_def_3917, type, sK2404: (num > num) > num).
% 34.88/9.16 thf(func_def_3918, type, sK2405: (num > rat) > num).
% 34.88/9.16 thf(func_def_3919, type, sK2406: (num > rat) > num).
% 34.88/9.16 thf(func_def_3920, type, sK2407: (rat > nat) > rat).
% 34.88/9.16 thf(func_def_3921, type, sK2408: (rat > nat) > rat).
% 34.88/9.16 thf(func_def_3922, type, sK2409: rat > rat > rat).
% 34.88/9.16 thf(func_def_3923, type, sK2410: real > nat > (nat > real > real) > real > nat).
% 34.88/9.16 thf(func_def_3924, type, sK2411: real > nat > (nat > real > real) > real > real).
% 34.88/9.16 thf(func_def_3925, type, sK2412: (real > real) > nat > (nat > real > real) > real > real > real).
% 34.88/9.16 thf(func_def_3926, type, sK2413: set_nat > nat > set_nat).
% 34.88/9.16 thf(func_def_3927, type, sK2414: set_nat > nat > nat).
% 34.88/9.16 thf(func_def_3928, type, sK2415: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3929, type, sK2416: (nat > real) > nat).
% 34.88/9.16 thf(func_def_3930, type, sK2417: (complex > nat) > set_complex > complex).
% 34.88/9.16 thf(func_def_3931, type, sK2418: list_VEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3932, type, sK2419: (complex > rat) > (complex > rat) > set_complex > (rat > rat > $o) > complex).
% 34.88/9.16 thf(func_def_3933, type, sK2420: (rat > rat > $o) > rat).
% 34.88/9.16 thf(func_def_3934, type, sK2421: (rat > rat > $o) > rat).
% 34.88/9.16 thf(func_def_3935, type, sK2422: (rat > rat > $o) > rat).
% 34.88/9.16 thf(func_def_3936, type, sK2423: (rat > rat > $o) > rat).
% 34.88/9.16 thf(func_def_3937, type, sK2424: (real > real) > real > set_real > real).
% 34.88/9.16 thf(func_def_3938, type, sK2425: nat > set_nat > set_int > (int > nat > $o) > nat).
% 34.88/9.16 thf(func_def_3939, type, sK2426: (nat > nat) > (nat > nat) > set_nat > nat).
% 34.88/9.16 thf(func_def_3940, type, sK2427: set_real > set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_3941, type, sK2428: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3942, type, sK2429: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3943, type, sK2430: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3944, type, sK2431: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3945, type, sK2432: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3946, type, sK2433: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3947, type, sK2434: (set_nat > set_nat > set_nat) > set_nat).
% 34.88/9.16 thf(func_def_3948, type, sK2435: code_integer > code_integer > code_integer).
% 34.88/9.16 thf(func_def_3949, type, sK2436: nat > nat > nat).
% 34.88/9.16 thf(func_def_3950, type, sK2437: set_complex > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_3951, type, sK2438: nat > set_real > real).
% 34.88/9.16 thf(func_def_3952, type, sK2439: nat > set_real > set_real).
% 34.88/9.16 thf(func_def_3953, type, sK2440: (nat > set_nat) > nat).
% 34.88/9.16 thf(func_def_3954, type, sK2441: set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_3955, type, sK2442: (complex > complex) > (complex > real) > set_complex > set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_3956, type, sK2443: (nat > rat) > set_nat > nat).
% 34.88/9.16 thf(func_def_3957, type, sK2444: nat > nat > nat).
% 34.88/9.16 thf(func_def_3958, type, sK2445: (nat > num) > nat).
% 34.88/9.16 thf(func_def_3959, type, sK2446: (real > real) > real).
% 34.88/9.16 thf(func_def_3960, type, sK2447: (real > real) > real).
% 34.88/9.16 thf(func_def_3961, type, sK2448: set_real > real).
% 34.88/9.16 thf(func_def_3962, type, sK2449: set_real > real).
% 34.88/9.16 thf(func_def_3963, type, sK2450: set_real > real).
% 34.88/9.16 thf(func_def_3964, type, sK2451: real > nat > real).
% 34.88/9.16 thf(func_def_3965, type, sK2452: nat > (nat > rat) > rat > nat).
% 34.88/9.16 thf(func_def_3966, type, sK2453: nat > set_real > set_real).
% 34.88/9.16 thf(func_def_3967, type, sK2454: nat > set_real > real).
% 34.88/9.16 thf(func_def_3968, type, sK2455: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_3969, type, sK2456: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_3970, type, sK2457: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_3971, type, sK2458: (num > real) > num).
% 34.88/9.16 thf(func_def_3972, type, sK2459: (num > real) > num).
% 34.88/9.16 thf(func_def_3973, type, sK2460: set_int > set_int > (int > complex) > set_complex > set_complex > int).
% 34.88/9.16 thf(func_def_3974, type, sK2461: set_complex > (complex > complex) > complex).
% 34.88/9.16 thf(func_def_3975, type, sK2462: (complex > int) > (int > complex) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_3976, type, sK2463: set_complex > set_complex > (complex > int) > set_int > set_int > complex).
% 34.88/9.16 thf(func_def_3977, type, sK2464: set_int > (int > complex) > int).
% 34.88/9.16 thf(func_def_3978, type, sK2465: (int > complex) > set_int > (int > complex) > (complex > complex) > int).
% 34.88/9.16 thf(func_def_3979, type, sK2466: (int > complex) > set_complex > set_complex > (complex > int) > complex).
% 34.88/9.16 thf(func_def_3980, type, sK2467: (nat > complex) > nat > nat).
% 34.88/9.16 thf(func_def_3981, type, sK2468: set_int > (int > real) > real > int).
% 34.88/9.16 thf(func_def_3982, type, sK2469: (real > nat) > set_real > (real > nat) > real).
% 34.88/9.16 thf(func_def_3983, type, sK2470: list_Code_integer > code_integer > list_Code_integer > code_integer).
% 34.88/9.16 thf(func_def_3984, type, sK2471: rat > rat > set_complex > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_3985, type, sK2472: (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_3986, type, sK2473: (real > int) > real).
% 34.88/9.16 thf(func_def_3987, type, sK2474: (real > int) > real).
% 34.88/9.16 thf(func_def_3988, type, sK2475: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3989, type, sK2476: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_3990, type, sK2477: real > real > real).
% 34.88/9.16 thf(func_def_3991, type, sK2478: real > nat > real).
% 34.88/9.16 thf(func_def_3992, type, sK2479: set_complex > (complex > complex) > set_complex > (complex > complex) > complex).
% 34.88/9.16 thf(func_def_3993, type, sK2480: set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.16 thf(func_def_3994, type, sK2481: set_complex > set_complex > (complex > complex) > complex).
% 34.88/9.16 thf(func_def_3995, type, sK2482: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3996, type, sK2483: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_3997, type, sK2484: set_nat > (nat > code_integer) > nat).
% 34.88/9.16 thf(func_def_3998, type, sK2485: set_nat > code_integer > code_integer > (nat > code_integer) > nat).
% 34.88/9.16 thf(func_def_3999, type, sK2486: (complex > nat) > nat > set_complex > complex).
% 34.88/9.16 thf(func_def_4000, type, sK2487: (num > rat) > num).
% 34.88/9.16 thf(func_def_4001, type, sK2488: (num > rat) > num).
% 34.88/9.16 thf(func_def_4002, type, sK2489: (real > $o) > real).
% 34.88/9.16 thf(func_def_4003, type, sK2490: (real > $o) > real).
% 34.88/9.16 thf(func_def_4004, type, sK2491: (real > $o) > nat).
% 34.88/9.16 thf(func_def_4005, type, sK2492: (nat > real) > nat).
% 34.88/9.16 thf(func_def_4006, type, sK2493: (nat > real) > nat).
% 34.88/9.16 thf(func_def_4007, type, sK2494: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_4008, type, sK2495: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_4009, type, sK2496: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4010, type, sK2497: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4011, type, sK2498: (num > num) > num).
% 34.88/9.16 thf(func_def_4012, type, sK2499: (num > num) > num).
% 34.88/9.16 thf(func_def_4013, type, sK2500: set_real > nat > set_real).
% 34.88/9.16 thf(func_def_4014, type, sK2501: set_real > nat > real).
% 34.88/9.16 thf(func_def_4015, type, sK2502: (num > int) > num).
% 34.88/9.16 thf(func_def_4016, type, sK2503: (num > int) > num).
% 34.88/9.16 thf(func_def_4017, type, sK2504: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_4018, type, sK2505: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_4019, type, sK2506: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_4020, type, sK2507: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_4021, type, sK2508: (num > num > $o) > num).
% 34.88/9.16 thf(func_def_4022, type, sK2509: list_real > real > real).
% 34.88/9.16 thf(func_def_4023, type, sK2510: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4024, type, sK2511: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4025, type, sK2512: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4026, type, sK2513: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4027, type, sK2514: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4028, type, sK2515: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4029, type, sK2516: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4030, type, sK2517: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4031, type, sK2518: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4032, type, sK2519: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4033, type, sK2520: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4034, type, sK2521: nat > vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4035, type, sK2522: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4036, type, sK2523: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4037, type, sK2524: nat > vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4038, type, sK2525: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4039, type, sK2526: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4040, type, sK2527: set_complex > real > (complex > real) > complex).
% 34.88/9.16 thf(func_def_4041, type, sK2528: (nat > nat) > (set_nat > $o) > nat).
% 34.88/9.16 thf(func_def_4042, type, sK2529: (nat > nat) > (set_nat > $o) > set_nat).
% 34.88/9.16 thf(func_def_4043, type, sK2530: (real > num) > real).
% 34.88/9.16 thf(func_def_4044, type, sK2531: (real > num) > real).
% 34.88/9.16 thf(func_def_4045, type, sK2532: nat > nat > nat).
% 34.88/9.16 thf(func_def_4046, type, sK2533: nat > nat > nat).
% 34.88/9.16 thf(func_def_4047, type, sK2534: produc859450856879609959at_nat > nat).
% 34.88/9.16 thf(func_def_4048, type, sK2535: produc859450856879609959at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4049, type, sK2536: produc859450856879609959at_nat > nat).
% 34.88/9.16 thf(func_def_4050, type, sK2537: (real > $o) > real).
% 34.88/9.16 thf(func_def_4051, type, sK2538: (real > $o) > real).
% 34.88/9.16 thf(func_def_4052, type, sK2539: (real > $o) > nat).
% 34.88/9.16 thf(func_def_4053, type, sK2540: nat > nat).
% 34.88/9.16 thf(func_def_4054, type, sK2541: (num > num) > num).
% 34.88/9.16 thf(func_def_4055, type, sK2542: (num > num) > num).
% 34.88/9.16 thf(func_def_4056, type, sK2543: set_int > set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_4057, type, sK2544: real > real > real).
% 34.88/9.16 thf(func_def_4058, type, sK2545: (complex > code_integer) > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_4059, type, sK2546: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.16 thf(func_def_4060, type, sK2547: produc3843707927480180839at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.16 thf(func_def_4061, type, sK2548: option_num > num).
% 34.88/9.16 thf(func_def_4062, type, sK2549: set_complex > (complex > nat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4063, type, sK2550: (list_nat > $o) > (list_nat > $o) > list_nat).
% 34.88/9.16 thf(func_def_4064, type, sK2551: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_4065, type, sK2552: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_4066, type, sK2553: (real > real) > real).
% 34.88/9.16 thf(func_def_4067, type, sK2554: (real > real) > real).
% 34.88/9.16 thf(func_def_4068, type, sK2555: list_real > real > list_o > $o).
% 34.88/9.16 thf(func_def_4069, type, sK2556: (real > rat) > set_real > real).
% 34.88/9.16 thf(func_def_4070, type, sK2557: option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4071, type, sK2558: set_Pr7543698050874017315T_VEBT > list_VEBT_VEBT > list_o > nat).
% 34.88/9.16 thf(func_def_4072, type, sK2559: set_set_nat > set_nat > set_nat).
% 34.88/9.16 thf(func_def_4073, type, sK2560: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4074, type, sK2561: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4075, type, sK2562: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4076, type, sK2563: vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4077, type, sK2564: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4078, type, sK2565: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4079, type, sK2566: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4080, type, sK2567: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4081, type, sK2568: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4082, type, sK2569: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4083, type, sK2570: (real > int) > int > set_real > real).
% 34.88/9.16 thf(func_def_4084, type, sK2571: nat > nat > set_nat > nat).
% 34.88/9.16 thf(func_def_4085, type, sK2572: set_nat > nat).
% 34.88/9.16 thf(func_def_4086, type, sK2573: set_nat > nat).
% 34.88/9.16 thf(func_def_4087, type, sK2574: set_real > (real > complex) > real).
% 34.88/9.16 thf(func_def_4088, type, sK2575: (nat > nat) > nat).
% 34.88/9.16 thf(func_def_4089, type, sK2576: (nat > nat) > nat).
% 34.88/9.16 thf(func_def_4090, type, sK2577: nat > (nat > complex) > real > real).
% 34.88/9.16 thf(func_def_4091, type, sK2578: set_nat > set_nat > (nat > real) > nat).
% 34.88/9.16 thf(func_def_4092, type, sK2579: set_Pr4329608150637261639at_nat > set_Pr1261947904930325089at_nat).
% 34.88/9.16 thf(func_def_4093, type, sK2580: set_int > set_real > (real > int > $o) > real).
% 34.88/9.16 thf(func_def_4094, type, sK2581: set_int > set_real > (real > int > $o) > real).
% 34.88/9.16 thf(func_def_4095, type, sK2582: set_int > set_real > (real > int > $o) > int).
% 34.88/9.16 thf(func_def_4096, type, sK2583: set_int > set_real > (real > int > $o) > real).
% 34.88/9.16 thf(func_def_4097, type, sK2584: set_int > (int > nat) > set_int > int).
% 34.88/9.16 thf(func_def_4098, type, sK2585: set_complex > (complex > int) > set_complex > complex).
% 34.88/9.16 thf(func_def_4099, type, sK2586: (num > num) > num).
% 34.88/9.16 thf(func_def_4100, type, sK2587: (num > num) > num).
% 34.88/9.16 thf(func_def_4101, type, sK2588: (int > nat) > set_int > int).
% 34.88/9.16 thf(func_def_4102, type, sK2589: (num > num) > num).
% 34.88/9.16 thf(func_def_4103, type, sK2590: (num > num) > num).
% 34.88/9.16 thf(func_def_4104, type, sK2591: set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_4105, type, sK2592: (int > nat) > set_int > int).
% 34.88/9.16 thf(func_def_4106, type, sK2593: (int > nat) > set_int > int).
% 34.88/9.16 thf(func_def_4107, type, sK2594: option_nat > nat).
% 34.88/9.16 thf(func_def_4108, type, sK2595: (int > complex) > set_int > int).
% 34.88/9.16 thf(func_def_4109, type, sK2596: (complex > int) > (int > complex) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4110, type, sK2597: (complex > int) > set_int > set_int > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_4111, type, sK2598: set_complex > (complex > complex) > (int > complex) > (complex > int) > complex).
% 34.88/9.16 thf(func_def_4112, type, sK2599: set_complex > (complex > complex) > complex).
% 34.88/9.16 thf(func_def_4113, type, sK2600: set_complex > (complex > int) > (int > complex) > set_complex > complex).
% 34.88/9.16 thf(func_def_4114, type, sK2601: set_complex > (int > complex) > set_complex > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4115, type, sK2602: rat > set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4116, type, sK2603: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4117, type, sK2604: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4118, type, sK2605: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4119, type, sK2606: vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4120, type, sK2607: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4121, type, sK2608: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4122, type, sK2609: rat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4123, type, sK2610: int > int > int).
% 34.88/9.16 thf(func_def_4124, type, sK2611: (complex > nat) > set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_4125, type, sK2612: real > real > real).
% 34.88/9.16 thf(func_def_4126, type, sK2613: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4127, type, sK2614: (real > rat) > set_real > real).
% 34.88/9.16 thf(func_def_4128, type, sK2615: list_o > $o > nat).
% 34.88/9.16 thf(func_def_4129, type, sK2616: rat > (int > rat) > set_int > int).
% 34.88/9.16 thf(func_def_4130, type, sK2617: set_int > set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_4131, type, sK2618: (complex > nat > $o) > set_nat > set_complex > nat).
% 34.88/9.16 thf(func_def_4132, type, sK2619: (complex > nat > $o) > set_nat > set_complex > complex).
% 34.88/9.16 thf(func_def_4133, type, sK2620: (complex > nat > $o) > set_nat > set_complex > complex).
% 34.88/9.16 thf(func_def_4134, type, sK2621: (complex > nat > $o) > set_complex > set_nat > complex).
% 34.88/9.16 thf(func_def_4135, type, sK2622: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4136, type, sK2623: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4137, type, sK2624: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4138, type, sK2625: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4139, type, sK2626: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4140, type, sK2627: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4141, type, sK2628: set_int > (int > code_integer) > int).
% 34.88/9.16 thf(func_def_4142, type, sK2629: (nat > rat) > nat > rat > nat > rat).
% 34.88/9.16 thf(func_def_4143, type, sK2630: set_complex > (complex > complex) > complex).
% 34.88/9.16 thf(func_def_4144, type, sK2631: set_complex > (complex > rat) > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_4145, type, sK2632: complex > set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_4146, type, sK2633: set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_4147, type, sK2634: set_real > real).
% 34.88/9.16 thf(func_def_4148, type, sK2635: set_real > set_real > (real > int) > set_int > set_int > real).
% 34.88/9.16 thf(func_def_4149, type, sK2636: (int > real) > set_real > set_real > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4150, type, sK2637: (int > complex) > (real > complex) > (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_4151, type, sK2638: set_real > set_real > (int > real) > (real > int) > real).
% 34.88/9.16 thf(func_def_4152, type, sK2639: set_real > (real > complex) > real).
% 34.88/9.16 thf(func_def_4153, type, sK2640: (int > real) > set_int > (real > int) > set_int > int).
% 34.88/9.16 thf(func_def_4154, type, sK2641: (int > complex) > set_int > int).
% 34.88/9.16 thf(func_def_4155, type, sK2642: (rat > int) > rat).
% 34.88/9.16 thf(func_def_4156, type, sK2643: (rat > int) > rat).
% 34.88/9.16 thf(func_def_4157, type, sK2644: list_int > (int > $o) > nat).
% 34.88/9.16 thf(func_def_4158, type, sK2645: set_int > nat > set_int).
% 34.88/9.16 thf(func_def_4159, type, sK2646: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_4160, type, sK2647: (complex > nat) > set_complex > nat > complex).
% 34.88/9.16 thf(func_def_4161, type, sK2648: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4162, type, sK2649: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4163, type, sK2650: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4164, type, sK2651: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4165, type, sK2652: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4166, type, sK2653: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4167, type, sK2654: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4168, type, sK2655: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4169, type, sK2656: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4170, type, sK2657: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4171, type, sK2658: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4172, type, sK2659: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4173, type, sK2660: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4174, type, sK2661: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4175, type, sK2662: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4176, type, sK2663: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4177, type, sK2664: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4178, type, sK2665: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4179, type, sK2666: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4180, type, sK2667: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4181, type, sK2668: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4182, type, sK2669: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4183, type, sK2670: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4184, type, sK2671: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4185, type, sK2672: nat > list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4186, type, sK2673: nat > list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4187, type, sK2674: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4188, type, sK2675: vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4189, type, sK2676: list_list_VEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4190, type, sK2677: (complex > $o) > list_complex > complex).
% 34.88/9.16 thf(func_def_4191, type, sK2678: (nat > rat) > set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4192, type, sK2679: set_real > (real > real) > real > real).
% 34.88/9.16 thf(func_def_4193, type, sK2680: (product_prod_nat_nat > $o) > nat).
% 34.88/9.16 thf(func_def_4194, type, sK2681: (product_prod_nat_nat > $o) > nat).
% 34.88/9.16 thf(func_def_4195, type, sK2682: (num > int) > num).
% 34.88/9.16 thf(func_def_4196, type, sK2683: (num > int) > num).
% 34.88/9.16 thf(func_def_4197, type, sK2684: (complex > complex) > set_complex > real > complex).
% 34.88/9.16 thf(func_def_4198, type, sK2685: (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4199, type, sK2686: (nat > rat) > set_nat > nat).
% 34.88/9.16 thf(func_def_4200, type, sK2687: (nat > rat) > set_nat > nat).
% 34.88/9.16 thf(func_def_4201, type, sK2688: real > (real > real) > real > real).
% 34.88/9.16 thf(func_def_4202, type, sK2689: real > (real > real) > real > real).
% 34.88/9.16 thf(func_def_4203, type, sK2690: real > real > (real > real) > real).
% 34.88/9.16 thf(func_def_4204, type, sK2691: (real > real) > (real > real) > real > real > real).
% 34.88/9.16 thf(func_def_4205, type, sK2692: (real > real) > (real > real) > real > real > real).
% 34.88/9.16 thf(func_def_4206, type, sK2693: (real > real) > (real > real) > real > real > real).
% 34.88/9.16 thf(func_def_4207, type, sK2694: real > (real > real) > real > real).
% 34.88/9.16 thf(func_def_4208, type, sK2695: (int > code_integer) > set_int > int).
% 34.88/9.16 thf(func_def_4209, type, sK2696: set_int > (int > code_integer) > set_int > int).
% 34.88/9.16 thf(func_def_4210, type, sK2697: nat > nat).
% 34.88/9.16 thf(func_def_4211, type, sK2698: int > nat).
% 34.88/9.16 thf(func_def_4212, type, sK2699: int > nat).
% 34.88/9.16 thf(func_def_4213, type, sK2700: (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_4214, type, sK2701: (int > real) > (int > int) > (int > real) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4215, type, sK2702: int > nat).
% 34.88/9.16 thf(func_def_4216, type, sK2703: set_nat > (nat > real) > nat).
% 34.88/9.16 thf(func_def_4217, type, sK2704: int > list_int > int).
% 34.88/9.16 thf(func_def_4218, type, sK2705: (nat > nat) > nat).
% 34.88/9.16 thf(func_def_4219, type, sK2706: (complex > rat) > (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4220, type, sK2707: (int > real) > set_int > (real > real > $o) > (int > real) > int).
% 34.88/9.16 thf(func_def_4221, type, sK2708: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4222, type, sK2709: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4223, type, sK2710: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4224, type, sK2711: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4225, type, sK2712: list_VEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4226, type, sK2713: (option_num > option_nat > $o) > option_nat > option_num > nat).
% 34.88/9.16 thf(func_def_4227, type, sK2714: (option_num > option_nat > $o) > option_nat > option_num > num).
% 34.88/9.16 thf(func_def_4228, type, sK2715: set_nat > (nat > rat) > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4229, type, sK2716: nat > set_nat > nat).
% 34.88/9.16 thf(func_def_4230, type, sK2717: complex > complex).
% 34.88/9.16 thf(func_def_4231, type, sK2718: complex > real).
% 34.88/9.16 thf(func_def_4232, type, sK2719: option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4233, type, sK2720: option4927543243414619207at_nat > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4234, type, sK2721: option4927543243414619207at_nat > (product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat) > option4927543243414619207at_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4235, type, sK2722: (num > real) > num).
% 34.88/9.16 thf(func_def_4236, type, sK2723: (num > real) > num).
% 34.88/9.16 thf(func_def_4237, type, sK2724: set_list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4238, type, sK2725: (real > rat) > (real > rat) > set_real > real).
% 34.88/9.16 thf(func_def_4239, type, sK2726: (num > rat) > num).
% 34.88/9.16 thf(func_def_4240, type, sK2727: (num > rat) > num).
% 34.88/9.16 thf(func_def_4241, type, sK2728: list_VEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4242, type, sK2729: set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4243, type, sK2730: set_int > (int > code_integer) > int).
% 34.88/9.16 thf(func_def_4244, type, sK2731: set_real > (real > real) > real > real).
% 34.88/9.16 thf(func_def_4245, type, sK2732: vEBT_VEBT > extended_enat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4246, type, sK2733: vEBT_VEBT > extended_enat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4247, type, sK2734: vEBT_VEBT > extended_enat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4248, type, sK2735: vEBT_VEBT > extended_enat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4249, type, sK2736: vEBT_VEBT > extended_enat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4250, type, sK2737: vEBT_VEBT > vEBT_VEBT > extended_enat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4251, type, sK2738: vEBT_VEBT > vEBT_VEBT > extended_enat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4252, type, sK2739: vEBT_VEBT > vEBT_VEBT > extended_enat > nat).
% 34.88/9.16 thf(func_def_4253, type, sK2740: vEBT_VEBT > vEBT_VEBT > extended_enat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4254, type, sK2741: vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4255, type, sK2742: vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4256, type, sK2743: (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_4257, type, sK2744: (list_o > $o) > list_o).
% 34.88/9.16 thf(func_def_4258, type, sK2745: (int > int > $o) > int).
% 34.88/9.16 thf(func_def_4259, type, sK2746: (int > int > $o) > int).
% 34.88/9.16 thf(func_def_4260, type, sK2747: (int > int > $o) > int).
% 34.88/9.16 thf(func_def_4261, type, sK2748: (int > int > $o) > int).
% 34.88/9.16 thf(func_def_4262, type, sK2749: set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_4263, type, sK2750: int > set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_4264, type, sK2751: (rat > num) > rat).
% 34.88/9.16 thf(func_def_4265, type, sK2752: (rat > num) > rat).
% 34.88/9.16 thf(func_def_4266, type, sK2753: int > (int > $o) > int).
% 34.88/9.16 thf(func_def_4267, type, sK2754: int > (int > $o) > int).
% 34.88/9.16 thf(func_def_4268, type, sK2755: int > (int > $o) > (int > $o) > int).
% 34.88/9.16 thf(func_def_4269, type, sK2756: (int > $o) > int).
% 34.88/9.16 thf(func_def_4270, type, sK2757: (real > rat) > (real > rat) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_4271, type, sK2758: (real > rat) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_4272, type, sK2759: (real > rat) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_4273, type, sK2760: (nat > real) > nat > nat).
% 34.88/9.16 thf(func_def_4274, type, sK2761: (int > $o) > int > int).
% 34.88/9.16 thf(func_def_4275, type, sK2762: (int > $o) > int > int).
% 34.88/9.16 thf(func_def_4276, type, sK2763: set_real > (real > int) > real).
% 34.88/9.16 thf(func_def_4277, type, sK2764: (set_nat > real) > real > set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_4278, type, sK2765: (int > real) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4279, type, sK2766: set_real > set_real > (real > nat) > real).
% 34.88/9.16 thf(func_def_4280, type, sK2767: (real > nat) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_4281, type, sK2768: (complex > $o) > (complex > $o) > complex).
% 34.88/9.16 thf(func_def_4282, type, sK2769: set_complex > (complex > complex) > set_complex > complex).
% 34.88/9.16 thf(func_def_4283, type, sK2770: set_complex > (complex > complex) > (complex > complex) > complex).
% 34.88/9.16 thf(func_def_4284, type, sK2771: (int > $o) > int).
% 34.88/9.16 thf(func_def_4285, type, sK2772: int > (int > $o) > set_int > int).
% 34.88/9.16 thf(func_def_4286, type, sK2773: int > (int > $o) > set_int > int).
% 34.88/9.16 thf(func_def_4287, type, sK2774: (int > $o) > int > int).
% 34.88/9.16 thf(func_def_4288, type, sK2775: int > (int > $o) > int).
% 34.88/9.16 thf(func_def_4289, type, sK2776: int > (int > $o) > int).
% 34.88/9.16 thf(func_def_4290, type, sK2777: int > (int > $o) > (int > $o) > int).
% 34.88/9.16 thf(func_def_4291, type, sK2778: int > set_int > (int > $o) > int).
% 34.88/9.16 thf(func_def_4292, type, sK2779: (complex > int) > set_complex > int > complex).
% 34.88/9.16 thf(func_def_4293, type, sK2780: nat > nat).
% 34.88/9.16 thf(func_def_4294, type, sK2781: (nat > nat) > nat).
% 34.88/9.16 thf(func_def_4295, type, sK2782: (rat > nat) > rat).
% 34.88/9.16 thf(func_def_4296, type, sK2783: (rat > nat) > rat).
% 34.88/9.16 thf(func_def_4297, type, sK2784: (complex > real) > (complex > real) > set_complex > (real > real > $o) > complex).
% 34.88/9.16 thf(func_def_4298, type, sK2785: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4299, type, sK2786: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4300, type, sK2787: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4301, type, sK2788: (real > real > $o) > real).
% 34.88/9.16 thf(func_def_4302, type, sK2789: (rat > real) > rat).
% 34.88/9.16 thf(func_def_4303, type, sK2790: (rat > real) > rat).
% 34.88/9.16 thf(func_def_4304, type, sK2791: set_real > (real > real) > real).
% 34.88/9.16 thf(func_def_4305, type, sK2792: (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_4306, type, sK2793: (complex > complex) > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_4307, type, sK2794: set_complex > set_complex > (complex > complex) > complex).
% 34.88/9.16 thf(func_def_4308, type, sK2795: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4309, type, sK2796: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4310, type, sK2797: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > list_Code_integer).
% 34.88/9.16 thf(func_def_4311, type, sK2798: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > code_integer).
% 34.88/9.16 thf(func_def_4312, type, sK2799: (nat > num) > nat).
% 34.88/9.16 thf(func_def_4313, type, sK2800: set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_4314, type, sK2801: (rat > num) > rat).
% 34.88/9.16 thf(func_def_4315, type, sK2802: (rat > num) > rat).
% 34.88/9.16 thf(func_def_4316, type, sK2803: (int > $o) > int > list_int > nat).
% 34.88/9.16 thf(func_def_4317, type, sK2804: nat > (int > $o) > list_int > nat).
% 34.88/9.16 thf(func_def_4318, type, sK2805: set_real > (real > real) > real).
% 34.88/9.16 thf(func_def_4319, type, sK2806: nat > set_complex > set_complex).
% 34.88/9.16 thf(func_def_4320, type, sK2807: option_nat > nat).
% 34.88/9.16 thf(func_def_4321, type, sK2808: int > (int > $o) > list_int > nat).
% 34.88/9.16 thf(func_def_4322, type, sK2809: nat > (int > $o) > list_int > nat).
% 34.88/9.16 thf(func_def_4323, type, sK2810: vEBT_VEBT > nat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4324, type, sK2811: vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4325, type, sK2812: vEBT_VEBT > nat > nat).
% 34.88/9.16 thf(func_def_4326, type, sK2813: vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4327, type, sK2814: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4328, type, sK2815: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4329, type, sK2816: set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_4330, type, sK2817: (rat > nat) > rat).
% 34.88/9.16 thf(func_def_4331, type, sK2818: (rat > nat) > rat).
% 34.88/9.16 thf(func_def_4332, type, sK2819: list_o > nat > $o).
% 34.88/9.16 thf(func_def_4333, type, sK2820: list_o > nat > list_o).
% 34.88/9.16 thf(func_def_4334, type, sK2821: real > real).
% 34.88/9.16 thf(func_def_4335, type, sK2822: set_nat > (int > nat > $o) > set_int > nat).
% 34.88/9.16 thf(func_def_4336, type, sK2823: set_nat > (int > nat > $o) > set_int > int).
% 34.88/9.16 thf(func_def_4337, type, sK2824: set_nat > (int > nat > $o) > set_int > int).
% 34.88/9.16 thf(func_def_4338, type, sK2825: set_nat > (int > nat > $o) > set_int > int).
% 34.88/9.16 thf(func_def_4339, type, sK2826: nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4340, type, sK2827: nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4341, type, sK2828: (nat > rat) > rat).
% 34.88/9.16 thf(func_def_4342, type, sK2829: nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4343, type, sK2830: nat > nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4344, type, sK2831: (nat > int) > set_nat > nat).
% 34.88/9.16 thf(func_def_4345, type, sK2832: (nat > real > real) > nat).
% 34.88/9.16 thf(func_def_4346, type, sK2833: (nat > real > real) > real).
% 34.88/9.16 thf(func_def_4347, type, sK2834: real > (nat > real > real) > nat > (real > real) > real).
% 34.88/9.16 thf(func_def_4348, type, sK2835: int > int > int).
% 34.88/9.16 thf(func_def_4349, type, sK2836: (code_integer > code_integer > $o) > code_integer).
% 34.88/9.16 thf(func_def_4350, type, sK2837: (complex > real) > set_complex > complex).
% 34.88/9.16 thf(func_def_4351, type, sK2838: (int > complex) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4352, type, sK2839: (nat > real) > real > (real > nat > real) > real > real).
% 34.88/9.16 thf(func_def_4353, type, sK2840: (nat > real) > real > (real > nat > real) > real > nat).
% 34.88/9.16 thf(func_def_4354, type, sK2841: (nat > real) > real > (real > nat > real) > real > real).
% 34.88/9.16 thf(func_def_4355, type, sK2842: real > (real > nat > real) > (real > nat > real) > nat).
% 34.88/9.16 thf(func_def_4356, type, sK2843: real > (real > nat > real) > real > real).
% 34.88/9.16 thf(func_def_4357, type, sK2844: nat > nat > nat).
% 34.88/9.16 thf(func_def_4358, type, sK2845: set_real > (real > int) > real).
% 34.88/9.16 thf(func_def_4359, type, sK2846: set_real > set_real > (real > int) > real).
% 34.88/9.16 thf(func_def_4360, type, sK2847: set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_4361, type, sK2848: (int > real) > int).
% 34.88/9.16 thf(func_def_4362, type, sK2849: (int > real) > int).
% 34.88/9.16 thf(func_def_4363, type, sK2850: (option_nat > option4927543243414619207at_nat > $o) > option_nat > option4927543243414619207at_nat > nat).
% 34.88/9.16 thf(func_def_4364, type, sK2851: (option_nat > option4927543243414619207at_nat > $o) > option_nat > option4927543243414619207at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4365, type, sK2852: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4366, type, sK2853: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4367, type, sK2854: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4368, type, sK2855: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4369, type, sK2856: nat > list_nat > nat).
% 34.88/9.16 thf(func_def_4370, type, sK2857: complex > list_VEBT_VEBT > list_complex > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4371, type, sK2858: $o > list_o > $o).
% 34.88/9.16 thf(func_def_4372, type, sK2859: (complex > nat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4373, type, sK2860: (real > num) > real).
% 34.88/9.16 thf(func_def_4374, type, sK2861: (real > num) > real).
% 34.88/9.16 thf(func_def_4375, type, sK2862: $o > nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4376, type, sK2863: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4377, type, sK2864: $o > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4378, type, sK2865: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4379, type, sK2866: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4380, type, sK2867: vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4381, type, sK2868: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4382, type, sK2869: $o > vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4383, type, sK2870: $o > vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4384, type, sK2871: nat > (nat > complex) > nat).
% 34.88/9.16 thf(func_def_4385, type, sK2872: nat > (nat > complex) > complex).
% 34.88/9.16 thf(func_def_4386, type, sK2873: (nat > num) > nat).
% 34.88/9.16 thf(func_def_4387, type, sK2874: (complex > rat) > (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4388, type, sK2875: set_complex > (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4389, type, sK2876: (int > nat) > set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_4390, type, sK2877: (complex > real) > (complex > real) > set_complex > complex).
% 34.88/9.16 thf(func_def_4391, type, sK2878: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > code_integer).
% 34.88/9.16 thf(func_def_4392, type, sK2879: code_integer > list_Code_integer > list_Code_integer > set_Pr4811707699266497531nteger > list_Code_integer).
% 34.88/9.16 thf(func_def_4393, type, sK2880: nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4394, type, sK2881: (int > complex) > set_int > int).
% 34.88/9.16 thf(func_def_4395, type, sK2882: produc9072475918466114483BT_nat > $o).
% 34.88/9.16 thf(func_def_4396, type, sK2883: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4397, type, sK2884: produc9072475918466114483BT_nat > $o).
% 34.88/9.16 thf(func_def_4398, type, sK2885: produc9072475918466114483BT_nat > $o).
% 34.88/9.16 thf(func_def_4399, type, sK2886: produc9072475918466114483BT_nat > $o).
% 34.88/9.16 thf(func_def_4400, type, sK2887: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4401, type, sK2888: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4402, type, sK2889: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4403, type, sK2890: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4404, type, sK2891: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4405, type, sK2892: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4406, type, sK2893: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4407, type, sK2894: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4408, type, sK2895: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4409, type, sK2896: produc9072475918466114483BT_nat > $o).
% 34.88/9.16 thf(func_def_4410, type, sK2897: produc9072475918466114483BT_nat > $o).
% 34.88/9.16 thf(func_def_4411, type, sK2898: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4412, type, sK2899: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4413, type, sK2900: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4414, type, sK2901: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4415, type, sK2902: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4416, type, sK2903: produc9072475918466114483BT_nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4417, type, sK2904: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4418, type, sK2905: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4419, type, sK2906: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4420, type, sK2907: produc9072475918466114483BT_nat > nat).
% 34.88/9.16 thf(func_def_4421, type, sK2908: produc9072475918466114483BT_nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4422, type, sK2909: rat > (rat > $o) > rat).
% 34.88/9.16 thf(func_def_4423, type, sK2910: rat > (rat > $o) > rat).
% 34.88/9.16 thf(func_def_4424, type, sK2911: (real > real) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_4425, type, sK2912: set_real > (real > real) > set_real > real).
% 34.88/9.16 thf(func_def_4426, type, sK2913: (num > num) > num).
% 34.88/9.16 thf(func_def_4427, type, sK2914: (num > num) > num).
% 34.88/9.16 thf(func_def_4428, type, sK2915: (rat > real) > rat).
% 34.88/9.16 thf(func_def_4429, type, sK2916: (rat > real) > rat).
% 34.88/9.16 thf(func_def_4430, type, sK2917: set_int > set_int > (int > complex) > int).
% 34.88/9.16 thf(func_def_4431, type, sK2918: (int > complex) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4432, type, sK2919: (nat > $o) > nat > nat).
% 34.88/9.16 thf(func_def_4433, type, sK2920: nat > nat > nat).
% 34.88/9.16 thf(func_def_4434, type, sK2921: nat > nat > nat).
% 34.88/9.16 thf(func_def_4435, type, sK2922: set_Pr958786334691620121nt_int > list_int > list_int > int > int).
% 34.88/9.16 thf(func_def_4436, type, sK2923: set_Pr958786334691620121nt_int > list_int > list_int > int > list_int).
% 34.88/9.16 thf(func_def_4437, type, sK2924: set_complex > (complex > code_integer) > complex).
% 34.88/9.16 thf(func_def_4438, type, sK2925: nat > real > real).
% 34.88/9.16 thf(func_def_4439, type, sK2926: set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_4440, type, sK2927: (complex > rat) > set_complex > (complex > nat) > set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4441, type, sK2928: (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4442, type, sK2929: real > real).
% 34.88/9.16 thf(func_def_4443, type, sK2930: (num > int) > num).
% 34.88/9.16 thf(func_def_4444, type, sK2931: (num > int) > num).
% 34.88/9.16 thf(func_def_4445, type, sK2932: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4446, type, sK2933: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4447, type, sK2934: (num > nat) > num).
% 34.88/9.16 thf(func_def_4448, type, sK2935: (num > nat) > num).
% 34.88/9.16 thf(func_def_4449, type, sK2936: nat > set_nat > set_nat).
% 34.88/9.16 thf(func_def_4450, type, sK2937: list_complex > list_VEBT_VEBT > complex > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4451, type, sK2938: nat > set_int > int).
% 34.88/9.16 thf(func_def_4452, type, sK2939: nat > set_int > set_int).
% 34.88/9.16 thf(func_def_4453, type, sK2940: (num > nat) > num).
% 34.88/9.16 thf(func_def_4454, type, sK2941: (num > nat) > num).
% 34.88/9.16 thf(func_def_4455, type, sK2942: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4456, type, sK2943: (int > real) > set_int > int).
% 34.88/9.16 thf(func_def_4457, type, sK2944: (int > real) > (int > complex) > set_int > (complex > real) > set_complex > complex).
% 34.88/9.16 thf(func_def_4458, type, sK2945: set_nat > (nat > rat) > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4459, type, sK2946: (int > $o) > int).
% 34.88/9.16 thf(func_def_4460, type, sK2947: (int > $o) > $o).
% 34.88/9.16 thf(func_def_4461, type, sK2948: (int > $o) > int).
% 34.88/9.16 thf(func_def_4462, type, sK2949: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4463, type, sK2950: (complex > $o) > list_complex > nat).
% 34.88/9.16 thf(func_def_4464, type, sK2951: set_nat > (nat > real) > real > nat).
% 34.88/9.16 thf(func_def_4465, type, sK2952: set_complex > (complex > rat) > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_4466, type, sK2953: int > int > int).
% 34.88/9.16 thf(func_def_4467, type, sK2954: nat > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4468, type, sK2955: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4469, type, sK2956: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4470, type, sK2957: nat > set_int > int).
% 34.88/9.16 thf(func_def_4471, type, sK2958: nat > set_int > set_int).
% 34.88/9.16 thf(func_def_4472, type, sK2959: set_complex > set_complex > (complex > real) > complex).
% 34.88/9.16 thf(func_def_4473, type, sK2960: set_complex > (complex > real) > (complex > real) > complex).
% 34.88/9.16 thf(func_def_4474, type, sK2961: set_Pr958786334691620121nt_int > int).
% 34.88/9.16 thf(func_def_4475, type, sK2962: set_int > (int > int) > int).
% 34.88/9.16 thf(func_def_4476, type, sK2963: set_int > set_real > (int > real > $o) > nat > real).
% 34.88/9.16 thf(func_def_4477, type, sK2964: set_nat > (nat > real) > nat).
% 34.88/9.16 thf(func_def_4478, type, sK2965: (nat > rat) > rat).
% 34.88/9.16 thf(func_def_4479, type, sK2966: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4480, type, sK2967: nat > rat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4481, type, sK2968: (real > nat) > set_real > (real > nat) > real).
% 34.88/9.16 thf(func_def_4482, type, sK2969: list_o > set_Pr3175402225741728619VEBT_o > list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4483, type, sK2970: vEBT_VEBT > vEBT_VEBT > extended_enat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4484, type, sK2971: vEBT_VEBT > vEBT_VEBT > extended_enat > nat).
% 34.88/9.16 thf(func_def_4485, type, sK2972: vEBT_VEBT > vEBT_VEBT > extended_enat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4486, type, sK2973: vEBT_VEBT > vEBT_VEBT > extended_enat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4487, type, sK2974: vEBT_VEBT > vEBT_VEBT > extended_enat > nat).
% 34.88/9.16 thf(func_def_4488, type, sK2975: extended_enat > vEBT_VEBT > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4489, type, sK2976: extended_enat > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4490, type, sK2977: extended_enat > vEBT_VEBT > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4491, type, sK2978: extended_enat > vEBT_VEBT > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4492, type, sK2979: extended_enat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4493, type, sK2980: extended_enat > vEBT_VEBT > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4494, type, sK2981: (nat > rat) > rat).
% 34.88/9.16 thf(func_def_4495, type, sK2982: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4496, type, sK2983: nat > rat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4497, type, sK2984: set_set_nat > nat > set_set_nat).
% 34.88/9.16 thf(func_def_4498, type, sK2985: set_set_nat > nat > set_nat).
% 34.88/9.16 thf(func_def_4499, type, sK2986: nat > (nat > real) > nat).
% 34.88/9.16 thf(func_def_4500, type, sK2987: (nat > complex) > set_nat > nat).
% 34.88/9.16 thf(func_def_4501, type, sK2988: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_4502, type, sK2989: (rat > rat) > rat).
% 34.88/9.16 thf(func_def_4503, type, sK2990: set_real > rat > (real > rat) > real).
% 34.88/9.16 thf(func_def_4504, type, sK2991: set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_4505, type, sK2992: set_complex > (complex > nat) > complex).
% 34.88/9.16 thf(func_def_4506, type, sK2993: real > (complex > real) > set_complex > complex).
% 34.88/9.16 thf(func_def_4507, type, sK2994: nat > nat).
% 34.88/9.16 thf(func_def_4508, type, sK2995: nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4509, type, sK2996: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4510, type, sK2997: list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4511, type, sK2998: list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4512, type, sK2999: list_VEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4513, type, sK3000: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4514, type, sK3001: set_int > (int > nat) > int).
% 34.88/9.16 thf(func_def_4515, type, sK3002: (nat > real) > nat > nat).
% 34.88/9.16 thf(func_def_4516, type, sK3003: (nat > real) > nat > nat).
% 34.88/9.16 thf(func_def_4517, type, sK3004: set_complex > nat > set_complex).
% 34.88/9.16 thf(func_def_4518, type, sK3005: set_complex > nat > complex).
% 34.88/9.16 thf(func_def_4519, type, sK3006: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4520, type, sK3007: nat > (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4521, type, sK3008: list_VEBT_VEBT > (vEBT_VEBT > $o) > nat).
% 34.88/9.16 thf(func_def_4522, type, sK3009: nat > (nat > real) > real > real).
% 34.88/9.16 thf(func_def_4523, type, sK3010: nat > (nat > real) > nat).
% 34.88/9.16 thf(func_def_4524, type, sK3011: list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4525, type, sK3012: list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4526, type, sK3013: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4527, type, sK3014: nat > list_VEBT_VEBT > nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4528, type, sK3015: nat > list_VEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4529, type, sK3016: vEBT_VEBT > nat > list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4530, type, sK3017: vEBT_VEBT > nat > list_VEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4531, type, sK3018: (option4927543243414619207at_nat > option_nat > $o) > option4927543243414619207at_nat > option_nat > nat).
% 34.88/9.16 thf(func_def_4532, type, sK3019: (option4927543243414619207at_nat > option_nat > $o) > option4927543243414619207at_nat > option_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4533, type, sK3020: rat > set_complex > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_4534, type, sK3021: (real > nat) > set_real > real).
% 34.88/9.16 thf(func_def_4535, type, sK3022: (nat > nat) > nat > nat).
% 34.88/9.16 thf(func_def_4536, type, sK3023: (nat > nat) > nat > nat).
% 34.88/9.16 thf(func_def_4537, type, sK3024: (int > rat) > set_int > int).
% 34.88/9.16 thf(func_def_4538, type, sK3025: (real > rat) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_4539, type, sK3026: (real > rat) > set_real > set_real > real).
% 34.88/9.16 thf(func_def_4540, type, sK3027: int > nat).
% 34.88/9.16 thf(func_def_4541, type, sK3028: int > list_int > int).
% 34.88/9.16 thf(func_def_4542, type, sK3029: (int > rat) > set_int > set_int > int).
% 34.88/9.16 thf(func_def_4543, type, sK3030: (num > rat) > num).
% 34.88/9.16 thf(func_def_4544, type, sK3031: (num > rat) > num).
% 34.88/9.16 thf(func_def_4545, type, sK3032: (int > rat) > (int > rat) > set_int > int).
% 34.88/9.16 thf(func_def_4546, type, sK3033: list_VEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4547, type, sK3034: list_VEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4548, type, sK3035: (nat > int) > set_nat > (nat > int) > nat).
% 34.88/9.16 thf(func_def_4549, type, sK3036: (nat > $o) > nat > nat > nat).
% 34.88/9.16 thf(func_def_4550, type, sK3037: (nat > $o) > nat > nat > nat).
% 34.88/9.16 thf(func_def_4551, type, sK3038: (int > rat) > set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_4552, type, sK3039: set_int > (int > rat) > set_int > int).
% 34.88/9.16 thf(func_def_4553, type, sK3040: set_real > set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_4554, type, sK3041: set_real > (real > rat) > real).
% 34.88/9.16 thf(func_def_4555, type, sK3042: real > real > nat).
% 34.88/9.16 thf(func_def_4556, type, sK3043: set_real > set_real > (real > complex) > set_complex > set_complex > real).
% 34.88/9.16 thf(func_def_4557, type, sK3044: set_real > (real > complex) > real).
% 34.88/9.16 thf(func_def_4558, type, sK3045: (complex > complex) > set_complex > complex).
% 34.88/9.16 thf(func_def_4559, type, sK3046: set_real > set_real > (complex > real) > (real > complex) > real).
% 34.88/9.16 thf(func_def_4560, type, sK3047: (real > complex) > (complex > real) > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_4561, type, sK3048: (real > complex) > (real > complex) > (complex > complex) > set_real > real).
% 34.88/9.16 thf(func_def_4562, type, sK3049: set_real > set_real > (complex > real) > set_complex > set_complex > complex).
% 34.88/9.16 thf(func_def_4563, type, sK3050: (nat > $o) > nat > nat > nat).
% 34.88/9.16 thf(func_def_4564, type, sK3051: set_complex > (complex > real) > (complex > real) > complex).
% 34.88/9.16 thf(func_def_4565, type, sK3052: (int > nat) > set_int > int).
% 34.88/9.16 thf(func_def_4566, type, sK3053: vEBT_VEBT > option_nat > $o).
% 34.88/9.16 thf(func_def_4567, type, sK3054: vEBT_VEBT > option_nat > $o).
% 34.88/9.16 thf(func_def_4568, type, sK3055: option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4569, type, sK3056: option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4570, type, sK3057: option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4571, type, sK3058: option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4572, type, sK3059: option_nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4573, type, sK3060: vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4574, type, sK3061: vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4575, type, sK3062: vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4576, type, sK3063: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4577, type, sK3064: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4578, type, sK3065: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4579, type, sK3066: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4580, type, sK3067: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4581, type, sK3068: real > list_real > nat).
% 34.88/9.16 thf(func_def_4582, type, sK3069: list_nat > nat > nat).
% 34.88/9.16 thf(func_def_4583, type, sK3070: (real > rat) > real).
% 34.88/9.16 thf(func_def_4584, type, sK3071: (real > rat) > real).
% 34.88/9.16 thf(func_def_4585, type, sK3072: set_int > (int > rat) > int).
% 34.88/9.16 thf(func_def_4586, type, sK3073: option_nat > vEBT_VEBT > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4587, type, sK3074: option_nat > vEBT_VEBT > nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4588, type, sK3075: option_nat > vEBT_VEBT > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4589, type, sK3076: vEBT_VEBT > nat > option_nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4590, type, sK3077: vEBT_VEBT > nat > option_nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4591, type, sK3078: vEBT_VEBT > nat > option_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4592, type, sK3079: vEBT_VEBT > nat > option_nat > $o).
% 34.88/9.16 thf(func_def_4593, type, sK3080: vEBT_VEBT > nat > option_nat > $o).
% 34.88/9.16 thf(func_def_4594, type, sK3081: vEBT_VEBT > nat > option_nat > nat).
% 34.88/9.16 thf(func_def_4595, type, sK3082: option_nat > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4596, type, sK3083: option_nat > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4597, type, sK3084: option_nat > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4598, type, sK3085: option_nat > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4599, type, sK3086: option_nat > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4600, type, sK3087: option_nat > vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4601, type, sK3088: option_nat > vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4602, type, sK3089: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4603, type, sK3090: vEBT_VEBT > option_nat > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4604, type, sK3091: vEBT_VEBT > option_nat > nat > nat).
% 34.88/9.16 thf(func_def_4605, type, sK3092: set_real > (real > code_integer) > set_real > real).
% 34.88/9.16 thf(func_def_4606, type, sK3093: (real > code_integer) > set_real > real).
% 34.88/9.16 thf(func_def_4607, type, sK3094: vEBT_VEBT > option_nat > nat > nat).
% 34.88/9.16 thf(func_def_4608, type, sK3095: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4609, type, sK3096: vEBT_VEBT > option_nat > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4610, type, sK3097: vEBT_VEBT > option_nat > nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4611, type, sK3098: vEBT_VEBT > option_nat > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4612, type, sK3099: vEBT_VEBT > option_nat > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4613, type, sK3100: nat > vEBT_VEBT > option_nat > $o).
% 34.88/9.16 thf(func_def_4614, type, sK3101: nat > vEBT_VEBT > option_nat > $o).
% 34.88/9.16 thf(func_def_4615, type, sK3102: nat > option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4616, type, sK3103: nat > option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4617, type, sK3104: nat > option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4618, type, sK3105: nat > option_nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4619, type, sK3106: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4620, type, sK3107: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4621, type, sK3108: nat > option_nat > vEBT_VEBT > $o).
% 34.88/9.16 thf(func_def_4622, type, sK3109: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.16 thf(func_def_4623, type, sK3110: vEBT_VEBT > option_nat > nat > $o).
% 34.88/9.16 thf(func_def_4624, type, sK3111: vEBT_VEBT > option_nat > nat > nat).
% 34.88/9.16 thf(func_def_4625, type, sK3112: nat > option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4626, type, sK3113: nat > option_nat > vEBT_VEBT > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4627, type, sK3114: nat > option_nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4628, type, sK3115: (nat > $o) > nat > nat).
% 34.88/9.16 thf(func_def_4629, type, sK3116: (nat > rat) > nat > nat).
% 34.88/9.16 thf(func_def_4630, type, sK3117: (nat > rat) > nat > nat).
% 34.88/9.16 thf(func_def_4631, type, sK3118: int > int > int > int).
% 34.88/9.16 thf(func_def_4632, type, sK3119: int > int > int > int).
% 34.88/9.16 thf(func_def_4633, type, sK3120: list_nat > complex > list_complex > nat).
% 34.88/9.16 thf(func_def_4634, type, sK3121: set_int > set_int > (int > code_integer) > int).
% 34.88/9.16 thf(func_def_4635, type, sK3122: (nat > $o) > nat > nat > nat).
% 34.88/9.16 thf(func_def_4636, type, sK3123: (nat > $o) > nat > nat > nat).
% 34.88/9.16 thf(func_def_4637, type, sK3124: (nat > real) > nat > real).
% 34.88/9.16 thf(func_def_4638, type, sK3125: vEBT_VEBT > $o > nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4639, type, sK3126: vEBT_VEBT > $o > nat > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4640, type, sK3127: vEBT_VEBT > $o > nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4641, type, sK3128: $o > nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4642, type, sK3129: $o > nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4643, type, sK3130: $o > nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4644, type, sK3131: $o > nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4645, type, sK3132: vEBT_VEBT > nat > $o > $o).
% 34.88/9.16 thf(func_def_4646, type, sK3133: vEBT_VEBT > nat > $o > $o).
% 34.88/9.16 thf(func_def_4647, type, sK3134: int > nat).
% 34.88/9.16 thf(func_def_4648, type, sK3135: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_4649, type, sK3136: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_4650, type, sK3137: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_4651, type, sK3138: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_4652, type, sK3139: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_4653, type, sK3140: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_4654, type, sK3141: (rat > rat > rat) > rat).
% 34.88/9.16 thf(func_def_4655, type, sK3142: (int > int > int) > int).
% 34.88/9.16 thf(func_def_4656, type, sK3143: (int > int > int) > int).
% 34.88/9.16 thf(func_def_4657, type, sK3144: (int > int > int) > int).
% 34.88/9.16 thf(func_def_4658, type, sK3145: (int > int > int) > int).
% 34.88/9.16 thf(func_def_4659, type, sK3146: (int > int > int) > int).
% 34.88/9.16 thf(func_def_4660, type, sK3147: (int > int > int) > int).
% 34.88/9.16 thf(func_def_4661, type, sK3148: (int > int > int) > int).
% 34.88/9.16 thf(func_def_4662, type, sK3149: set_nat > (nat > nat) > (nat > nat) > nat).
% 34.88/9.16 thf(func_def_4663, type, sK3150: rat > rat).
% 34.88/9.16 thf(func_def_4664, type, sK3151: (real > nat) > set_real > real).
% 34.88/9.16 thf(func_def_4665, type, sK3152: (nat > real) > set_nat > nat).
% 34.88/9.16 thf(func_def_4666, type, sK3153: list_P6011104703257516679at_nat > product_prod_nat_nat > set_Pr8693737435421807431at_nat > list_P6011104703257516679at_nat > list_P6011104703257516679at_nat).
% 34.88/9.16 thf(func_def_4667, type, sK3154: list_P6011104703257516679at_nat > product_prod_nat_nat > set_Pr8693737435421807431at_nat > list_P6011104703257516679at_nat > product_prod_nat_nat).
% 34.88/9.16 thf(func_def_4668, type, sK3155: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4669, type, sK3156: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4670, type, sK3157: (int > int) > set_int > int).
% 34.88/9.16 thf(func_def_4671, type, sK3158: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4672, type, sK3159: vEBT_VEBT > nat > $o).
% 34.88/9.16 thf(func_def_4673, type, sK3160: nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4674, type, sK3161: nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4675, type, sK3162: nat > vEBT_VEBT > option4927543243414619207at_nat).
% 34.88/9.16 thf(func_def_4676, type, sK3163: nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4677, type, sK3164: list_int > int > set_Pr958786334691620121nt_int > list_int > list_int).
% 34.88/9.16 thf(func_def_4678, type, sK3165: list_int > int > set_Pr958786334691620121nt_int > list_int > int).
% 34.88/9.16 thf(func_def_4679, type, sK3166: rat > rat > rat).
% 34.88/9.16 thf(func_def_4680, type, sK3167: set_nat > nat).
% 34.88/9.16 thf(func_def_4681, type, sK3168: set_nat > nat).
% 34.88/9.16 thf(func_def_4682, type, sK3169: set_nat > (nat > nat) > nat).
% 34.88/9.16 thf(func_def_4683, type, sK3170: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4684, type, sK3171: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4685, type, sK3172: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4686, type, sK3173: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4687, type, sK3174: (nat > nat > $o) > nat).
% 34.88/9.16 thf(func_def_4688, type, sK3175: int > (nat > int) > nat > nat > int).
% 34.88/9.16 thf(func_def_4689, type, sK3176: set_num > num).
% 34.88/9.16 thf(func_def_4690, type, sK3177: nat > set_complex > complex).
% 34.88/9.16 thf(func_def_4691, type, sK3178: nat > set_complex > set_complex).
% 34.88/9.16 thf(func_def_4692, type, sK3179: set_int > int).
% 34.88/9.16 thf(func_def_4693, type, sK3180: set_int > int).
% 34.88/9.16 thf(func_def_4694, type, sK3181: set_int > int).
% 34.88/9.16 thf(func_def_4695, type, sK3182: rat > nat).
% 34.88/9.16 thf(func_def_4696, type, sK3183: real > nat > real).
% 34.88/9.16 thf(func_def_4697, type, sK3184: set_int > set_int > (int > real) > int).
% 34.88/9.16 thf(func_def_4698, type, sK3185: set_set_nat > nat > set_set_nat).
% 34.88/9.16 thf(func_def_4699, type, sK3186: set_nat > (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4700, type, sK3187: (nat > real > real) > real > nat > nat).
% 34.88/9.16 thf(func_def_4701, type, sK3188: (nat > real > real) > real > nat > real).
% 34.88/9.16 thf(func_def_4702, type, sK3189: (nat > real > real) > real > (real > real) > nat > real).
% 34.88/9.16 thf(func_def_4703, type, sK3190: set_complex > (complex > code_integer) > set_complex > complex).
% 34.88/9.16 thf(func_def_4704, type, sK3191: set_complex > (complex > code_integer) > complex).
% 34.88/9.16 thf(func_def_4705, type, sK3192: (complex > complex > $o) > complex).
% 34.88/9.16 thf(func_def_4706, type, sK3193: (complex > complex > $o) > complex).
% 34.88/9.16 thf(func_def_4707, type, sK3194: (complex > complex > $o) > complex).
% 34.88/9.16 thf(func_def_4708, type, sK3195: (complex > complex > $o) > complex).
% 34.88/9.16 thf(func_def_4709, type, sK3196: set_int > (int > complex) > (int > complex) > (complex > complex > $o) > int).
% 34.88/9.16 thf(func_def_4710, type, sK3197: set_int > int).
% 34.88/9.16 thf(func_def_4711, type, sK3198: set_int > int).
% 34.88/9.16 thf(func_def_4712, type, sK3199: product_prod_nat_nat > nat).
% 34.88/9.16 thf(func_def_4713, type, sK3200: product_prod_nat_nat > nat).
% 34.88/9.16 thf(func_def_4714, type, sK3201: set_nat > set_nat > nat).
% 34.88/9.16 thf(func_def_4715, type, sK3202: (nat > rat) > rat).
% 34.88/9.16 thf(func_def_4716, type, sK3203: (nat > rat) > nat).
% 34.88/9.16 thf(func_def_4717, type, sK3204: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_4718, type, sK3205: set_set_nat > set_nat).
% 34.88/9.16 thf(func_def_4719, type, sK3206: (nat > $o) > nat).
% 34.88/9.16 thf(func_def_4720, type, sK3207: produc8306885398267862888on_nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4721, type, sK3208: produc8306885398267862888on_nat > option_nat).
% 34.88/9.16 thf(func_def_4722, type, sK3209: produc8306885398267862888on_nat > nat).
% 34.88/9.16 thf(func_def_4723, type, sK3210: produc8306885398267862888on_nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4724, type, sK3211: produc8306885398267862888on_nat > nat).
% 34.88/9.16 thf(func_def_4725, type, sK3212: produc8306885398267862888on_nat > nat > nat > nat).
% 34.88/9.16 thf(func_def_4726, type, sK3213: produc8306885398267862888on_nat > nat).
% 34.88/9.16 thf(func_def_4727, type, sK3214: vEBT_VEBT > option_nat > nat).
% 34.88/9.16 thf(func_def_4728, type, sK3215: vEBT_VEBT > option_nat > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4729, type, sK3216: vEBT_VEBT > option_nat > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4730, type, sK3217: vEBT_VEBT > option_nat > nat).
% 34.88/9.16 thf(func_def_4731, type, sK3218: vEBT_VEBT > option_nat > nat).
% 34.88/9.16 thf(func_def_4732, type, sK3219: vEBT_VEBT > option_nat > $o).
% 34.88/9.16 thf(func_def_4733, type, sK3220: vEBT_VEBT > option_nat > $o).
% 34.88/9.16 thf(func_def_4734, type, sK3221: option_nat > vEBT_VEBT > vEBT_VEBT).
% 34.88/9.16 thf(func_def_4735, type, sK3222: option_nat > vEBT_VEBT > list_VEBT_VEBT).
% 34.88/9.16 thf(func_def_4736, type, sK3223: option_nat > vEBT_VEBT > nat).
% 34.88/9.16 thf(func_def_4737, type, sK3224: (rat > num) > rat).
% 34.88/9.16 thf(func_def_4738, type, sK3225: (rat > num) > rat).
% 34.88/9.16 thf(func_def_4739, type, sK3226: set_int > int).
% 34.88/9.16 thf(func_def_4740, type, sK3227: (nat > int) > int > nat > nat > nat).
% 34.88/9.16 thf(func_def_4741, type, sK3228: nat > nat > (nat > int) > nat).
% 34.88/9.16 thf(func_def_4742, type, sK3229: (nat > real) > nat).
% 34.88/9.16 thf(func_def_4743, type, sK3230: (nat > real) > nat).
% 34.88/9.16 thf(func_def_4744, type, sK3231: (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4745, type, sK3232: (complex > rat) > set_complex > complex).
% 34.88/9.16 thf(func_def_4746, type, sK3233: (nat > $o) > nat > nat > nat).
% 34.88/9.16 thf(func_def_4747, type, sK3234: real > (real > $o) > real).
% 34.88/9.16 thf(func_def_4748, type, sK3235: real > (real > $o) > real).
% 34.88/9.16 thf(func_def_4749, type, sK3236: real > real > real).
% 34.88/9.16 thf(func_def_4750, type, sK3237: real > real > real).
% 34.88/9.16 thf(func_def_4751, type, sK3238: set_complex > set_complex > (complex > rat) > complex).
% 34.88/9.16 thf(func_def_4753, type, ph3240: !>[X0: $tType]:(X0)).
% 34.88/9.16 thf(f60782,plain,(
% 34.88/9.16 $false),
% 34.88/9.16 inference(subsumption_resolution,[status(thm)],[f60781,f55785])).
% 34.88/9.16 thf(f55785,plain,(
% 34.88/9.16 ( ! [X0 : nat] : (((ord_less_eq_nat @ (suc @ X0) @ X0) != $true)) )),
% 34.88/9.16 inference(cnf_transformation,[status(thm)],[f25931])).
% 34.88/9.16 thf(f25931,plain,(
% 34.88/9.16 ! [X0 : nat] : ((ord_less_eq_nat @ (suc @ X0) @ X0) != $true)),
% 34.88/9.16 inference(flattening,[status(thm)],[f21359])).
% 34.88/9.16 thf(f21359,plain,(
% 34.88/9.16 ! [X0 : nat] : ~((ord_less_eq_nat @ (suc @ X0) @ X0) = $true)),
% 34.88/9.16 inference(fool_elimination,[status(thm)],[f21358])).
% 34.88/9.16 thf(f21358,plain,(
% 34.88/9.16 ! [X0 : nat] : ~(ord_less_eq_nat @ (suc @ X0) @ X0)),
% 34.88/9.16 inference(rectify,[status(thm)],[f104])).
% 34.88/9.16 thf(f104,axiom,(
% 34.88/9.16 ! [X29 : nat] : ~(ord_less_eq_nat @ (suc @ X29) @ X29)),
% 34.88/9.16 file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_103_Suc__n__not__le__n)).
% 34.88/9.16 thf(f60781,plain,(
% 34.88/9.16 ((ord_less_eq_nat @ (suc @ one_one_nat) @ one_one_nat) = $true)),
% 34.88/9.16 inference(forward_demodulation,[status(thm)],[f60780,f60489])).
% 34.88/9.16 thf(f60489,plain,(
% 34.88/9.16 (deg = one_one_nat)),
% 34.88/9.16 inference(backward_demodulation,[status(thm)],[f53864,f41780])).
% 34.88/9.16 thf(f41780,plain,(
% 34.88/9.16 ((suc @ zero_zero_nat) = one_one_nat)),
% 34.88/9.16 inference(cnf_transformation,[status(thm)],[f1159])).
% 34.88/9.16 thf(f1159,axiom,(
% 34.88/9.16 ((suc @ zero_zero_nat) = one_one_nat)),
% 34.88/9.16 file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_1158_One__nat__def)).
% 34.88/9.16 thf(f53864,plain,(
% 34.88/9.16 (deg = (suc @ zero_zero_nat))),
% 34.88/9.16 inference(cnf_transformation,[status(thm)],[f76])).
% 34.88/9.16 thf(f76,axiom,(
% 34.88/9.16 (deg = (suc @ zero_zero_nat))),
% 34.88/9.16 file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_75__C1_C_I2_J)).
% 34.88/9.16 thf(f60780,plain,(
% 34.88/9.16 ((ord_less_eq_nat @ (suc @ one_one_nat) @ deg) = $true)),
% 34.88/9.16 inference(forward_demodulation,[status(thm)],[f40310,f48221])).
% 34.88/9.16 thf(f48221,plain,(
% 34.88/9.16 ((numeral_numeral_nat @ (bit0 @ one)) = (suc @ one_one_nat))),
% 34.88/9.16 inference(cnf_transformation,[status(thm)],[f3213])).
% 34.88/9.16 thf(f3213,axiom,(
% 34.88/9.16 ((numeral_numeral_nat @ (bit0 @ one)) = (suc @ one_one_nat))),
% 34.88/9.16 file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_3212_Suc__1)).
% 34.88/9.16 thf(f40310,plain,(
% 34.88/9.16 ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) = $true)),
% 34.88/9.16 inference(cnf_transformation,[status(thm)],[f16210])).
% 34.88/9.16 thf(f16210,plain,(
% 34.88/9.16 ((ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg) = $true)),
% 34.88/9.16 inference(fool_elimination,[status(thm)],[f16209])).
% 34.88/9.16 thf(f16209,plain,(
% 34.88/9.16 (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)),
% 34.88/9.16 inference(rectify,[status(thm)],[f2987])).
% 34.88/9.16 thf(f2987,axiom,(
% 34.88/9.16 (ord_less_eq_nat @ (numeral_numeral_nat @ (bit0 @ one)) @ deg)),
% 34.88/9.16 file('/export/starexec/sandbox/tmp/tmp.PIdpKzho5U/DTF2THF_14485.p',fact_2986_a0)).
% 34.88/9.16 % SZS output end Proof for DTF2THF_14485
% 34.88/9.16 % (14942)------------------------------
% 34.88/9.16 % (14942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.88/9.16 % (14942)Termination reason: Refutation
% 34.88/9.16
% 34.88/9.16 % (14942)Memory used [KB]: 55521
% 34.88/9.16 % (14942)Time elapsed: 1.697 s
% 34.88/9.16 % (14942)Instructions burned: 5407 (million)
% 34.88/9.16 % (14942)------------------------------
% 34.88/9.16 % (14942)------------------------------
% 34.88/9.16 % (14820)Success in time 4.237 s
%------------------------------------------------------------------------------